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for Q13, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-13-repeated-question-p17", "type": "question", "target": "01-13#printed-question", "description": "Repeated complete question including marks and attribution." }, { "id": "01-13-diagram-original-p17", "type": "diagram", "target": "01-13#printed-question", "description": "Native SVG native-01-13-original.svg; source-specific curve traces, coordinates and asymptotes." }, { "id": "01-13-note-17-0", "type": "teacher-note", "target": "01-13#teacher-notes", "description": "vertical asymptote" }, { "id": "01-13-note-17-1", "type": "teacher-note", "target": "01-13#teacher-notes", "description": "oblique asymptote" }, { "id": "01-13-note-17-2", "type": "teacher-note", "target": "01-13#teacher-notes", "description": "remainder constant" } ], "unresolved": [] }, { "file": "01 Curve sketching and transformation sol.pdf", "page": 18, "visualChecked": true, "status": "audited-native", "items": [ { "id": "01-meta-01 Curve sketching and transformation sol.pdf-18", "type": "header-footer", "target": "topic-01#source-metadata", "description": "Repeated header/title/pagination, printed page 18." }, { "id": "01-13-working-p18", "type": "working", "target": "01-13#printed-working", "description": "Printed working text for Q13, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-13-diagram-iii-p18", "type": "diagram", "target": "01-13#printed-working", "description": "Native SVG native-01-13-iii.svg; source-specific curve traces, coordinates and asymptotes." }, { "id": "01-13-note-18-0", "type": "teacher-note", "target": "01-13#teacher-notes", "description": "negative-root intersection" }, { "id": "01-13-note-18-1", "type": "teacher-note", "target": "01-13#teacher-notes", "description": "negative-x arc" }, { "id": "01-13-note-18-2", "type": "teacher-note", "target": "01-13#teacher-notes", "description": "circle radius distance" } ], "unresolved": [] }, { "file": "01 Curve sketching and transformation sol.pdf", "page": 19, "visualChecked": true, "status": "audited-native", "items": [ { "id": "01-meta-01 Curve sketching and transformation sol.pdf-19", "type": "header-footer", "target": "topic-01#source-metadata", "description": "Repeated header/title/pagination, printed page 19." }, { "id": "01-14-working-p19", "type": "working", "target": "01-14#printed-working", "description": "Printed working text for Q14, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-14-repeated-question-p19", "type": "question", "target": "01-14#printed-question", "description": "Repeated complete question including marks and attribution." }, { "id": "01-14-diagram-sign-p19", "type": "diagram", "target": "01-14#printed-working", "description": "Native SVG native-01-14-sign.svg; source-specific curve traces, coordinates and asymptotes." } ], "unresolved": [] }, { "file": "01 Curve sketching and transformation sol.pdf", "page": 20, "visualChecked": true, "status": "audited-native", "items": [ { "id": "01-meta-01 Curve sketching and transformation sol.pdf-20", "type": "header-footer", "target": "topic-01#source-metadata", "description": "Repeated header/title/pagination, printed page 20." }, { "id": "01-14-working-p20", "type": "working", "target": "01-14#printed-working", "description": "Printed working text for Q14, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-14-diagram-iii-p20", "type": "diagram", "target": "01-14#printed-working", "description": "Native SVG native-01-14-iii.svg; source-specific curve traces, coordinates and asymptotes." }, { "id": "01-14-diagram-iv-p20", "type": "diagram", "target": "01-14#printed-working", "description": "Native SVG native-01-14-iv.svg; source-specific curve traces, coordinates and asymptotes." }, { "id": "01-14-note-20-0", "type": "teacher-note", "target": "01-14#teacher-notes", "description": "reciprocal log domain" }, { "id": "01-14-note-20-1", "type": "teacher-note", "target": "01-14#teacher-notes", "description": "one intersection boundary" } ], "unresolved": [] }, { "file": "01 Curve sketching and transformation sol.pdf", "page": 21, "visualChecked": true, "status": "audited-native", "items": [ { "id": "01-meta-01 Curve sketching and transformation sol.pdf-21", "type": "header-footer", "target": "topic-01#source-metadata", "description": "Repeated header/title/pagination, printed page 21." }, { "id": "01-15-working-p21", "type": "working", "target": "01-15#printed-working", "description": "Printed working text for Q15, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-15-repeated-question-p21", "type": "question", "target": "01-15#printed-question", "description": "Repeated complete question including marks and attribution." }, { "id": "01-15-note-21-0", "type": "teacher-note", "target": "01-15#teacher-notes", "description": "no stationary points" }, { "id": "01-15-note-21-1", "type": "teacher-note", "target": "01-15#teacher-notes", "description": "asymptotes and vertices" } ], "unresolved": [] }, { "file": "01 Curve sketching and transformation sol.pdf", "page": 22, "visualChecked": true, "status": "audited-native", "items": [ { "id": "01-meta-01 Curve sketching and transformation sol.pdf-22", "type": "header-footer", "target": "topic-01#source-metadata", "description": "Repeated header/title/pagination, printed page 22." }, { "id": "01-15-working-p22", "type": "working", "target": "01-15#printed-working", "description": "Printed working text for Q15, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-16-working-p22", "type": "working", "target": "01-16#printed-working", "description": "Printed working text for Q16, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-16-repeated-question-p22", "type": "question", "target": "01-16#printed-question", "description": "Repeated complete question including marks and attribution." }, { "id": "01-15-diagram-iii-p22", "type": "diagram", "target": "01-15#printed-working", "description": "Native SVG native-01-15-iii.svg; source-specific curve traces, coordinates and asymptotes." }, { "id": "01-15-note-22-0", "type": "teacher-note", "target": "01-15#teacher-notes", "description": "positive hyperbola branch" }, { "id": "01-15-note-22-1", "type": "teacher-note", "target": "01-15#teacher-notes", "description": "inequality graph interpretation" } ], "unresolved": [] }, { "file": "01 Curve sketching and transformation sol.pdf", "page": 23, "visualChecked": true, "status": "audited-native", "items": [ { "id": "01-meta-01 Curve sketching and transformation sol.pdf-23", "type": "header-footer", "target": "topic-01#source-metadata", "description": "Repeated header/title/pagination, printed page 23." }, { "id": "01-16-working-p23", "type": "working", "target": "01-16#printed-working", "description": "Printed working text for Q16, all subparts, marks, intermediate equations, source attribution or key variants." }, { "id": "01-16-diagram-bi-p23", "type": "diagram", "target": "01-16#printed-working", "description": "Native SVG native-01-16-bi.svg; source-specific curve traces, coordinates and asymptotes." }, { "id": "01-16-note-23-0", "type": "teacher-note", "target": "01-16#printed-working", "description": "10$, i.e. make one side of the inequality zero by bringing all terms from one side of the inequality to the other." }, { "id": "03-01-note-3-p1", "type": "teacher-note", "target": "03-01#teacher-note-3", "description": "Multiply both sides of the inequality with $(x+3)^2$. Since $(x+3)^2$ is always positive for $x\\ne-3$, the inequality sign remains unchanged after the multiplication." }, { "id": "03-01-note-4-p1", "type": "teacher-note", "target": "03-01#teacher-note-4", "description": "Solution is written as “… or …”, **NOT “and”**: “or” is the union between the ranges, while “and” is the intersection of the ranges." }, { "id": "03-01-diagram-1-p1", "type": "diagram", "target": "03-01#source-diagrams", "description": "Printed cubic sign sketch: roots −3, 0 and 5; the negative branches x<−3 and 00$ for all $x\\in\\mathbb R$, there is no sign change when both sides of inequality (*) are multiplied by $x^2+5$." }, { "id": "03-03-diagram-1-p3", "type": "diagram", "target": "03-03#source-diagrams", "description": "Printed cubic sign sketch with roots 1−√7, 0 and 1+√7; open positive intervals between the first root and zero and to the right of the last root." } ], "unresolved": [] }, { "file": "03 Inequalities sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "03-solution-4-edition", "type": "header-footer", "target": "topic-03#source-metadata", "description": "Compilation header/topic title/printed pagination: 4." }, { "id": "03-04-working-p4", "type": "working", "target": "03-04#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "03-04-solution-statement-p4", "type": "question", "target": "03-04#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "03-04-note-1-p4", "type": "teacher-note", "target": "03-04#teacher-note-1", "description": "As $x$ is a variable, $x$ and $x-1$ can be either negative or positive. As such, **DO NOT cross-multiply**." }, { "id": "03-04-note-2-p4", "type": "teacher-note", "target": "03-04#teacher-note-2", "description": "Express the inequality in the form $f(x)/g(x)>0$. Since numerator $f(x)$ is always positive, denominator $g(x)$ has to be positive for $f(x)/g(x)>0$." }, { "id": "03-04-note-3-p4", "type": "teacher-note", "target": "03-04#teacher-note-3", "description": "$e^x$ is always $>0$, i.e. $e^x>0$ for all $x\\in\\mathbb R$, so there is no real solution for $e^x<0$." }, { "id": "03-04-note-4-p4", "type": "teacher-note", "target": "03-04#teacher-note-4", "description": "**NOTE:** Let $y=p$, $p$ constant. The range of values that $y$ can take is the values of $y$ (i.e. $p$) for which the line $y=p$ intersects the curve: $(1+kx)/(x^2-1)=p$, i.e. $px^2-kx-(p+1)=0$ has r" } ], "unresolved": [] }, { "file": "03 Inequalities sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "03-solution-5-edition", "type": "header-footer", "target": "topic-03#source-metadata", "description": "Compilation header/topic title/printed pagination: 5." }, { "id": "03-04-working-p5", "type": "working", "target": "03-04#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "03-04-diagram-1-p5", "type": "diagram", "target": "03-04#source-diagrams", "description": "Native reconstruction of the printed positive-k rational-curve sketch, showing x=−1, x=1, y=0 and the two stationary ordinate levels. Exceptional k cases are separately qualified." } ], "unresolved": [] }, { "file": "03 Inequalities sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "03-solution-6-edition", "type": "header-footer", "target": "topic-03#source-metadata", "description": "Compilation header/topic title/printed pagination: 6." }, { "id": "03-05-working-p6", "type": "working", "target": "03-05#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "03-05-solution-statement-p6", "type": "question", "target": "03-05#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "03-05-note-1-p6", "type": "teacher-note", "target": "03-05#teacher-note-1", "description": "At A, $x>2$, so $|x-2|=x-2$." }, { "id": "03-05-note-2-p6", "type": "teacher-note", "target": "03-05#teacher-note-2", "description": "At B, $x<2$, so $|x-2|=-(x-2)$." }, { "id": "03-05-note-3-p6", "type": "teacher-note", "target": "03-05#teacher-note-3", "description": "The blue curve is above or intersects the red curve." }, { "id": "03-05-diagram-1-p6", "type": "diagram", "target": "03-05#source-diagrams", "description": "Source-specific plot of y=x|x−2| and y=1; B at x=1 is a tangency and A at x=1+√2 is a crossing, with corner at x=2." } ], "unresolved": [] }, { "file": "03 Inequalities sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "03-solution-7-edition", "type": "header-footer", "target": "topic-03#source-metadata", "description": "Compilation header/topic title/printed pagination: 7." }, { "id": "03-06-working-p7", "type": "working", "target": "03-06#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "03-06-solution-statement-p7", "type": "question", "target": "03-06#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "03-06-note-1-p7", "type": "teacher-note", "target": "03-06#teacher-note-1", "description": "Sketch the graph of $y=\\sin2x$, $00$ for all $x\\in\\mathbb R$." } ], "unresolved": [] }, { "file": "03 Inequalities sol.pdf", "page": 16, "visualChecked": true, "status": "audited-native", "items": [ { "id": "03-solution-16-edition", "type": "header-footer", "target": "topic-03#source-metadata", "description": "Compilation header/topic title/printed pagination: 16." }, { "id": "03-14-working-p16", "type": "working", "target": "03-14#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "03-14-solution-statement-p16", "type": "question", "target": "03-14#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "03-14-diagram-1-p16", "type": "diagram", "target": "03-14#source-diagrams", "description": "Source graph of|3⁻²ˣ−18| with y=18 asymptote, exact x-intercept−ln18/(2ln3) and y-intercept(0,17)." }, { "id": "03-14-diagram-2-p16", "type": "diagram", "target": "03-14#source-diagrams", "description": "Same actual source curve with y=9, intersections A(−3/2,9),B(−1,9) and closed interval[−3/2,−1] highlighted." } ], "unresolved": [] } ], "questions": [ { "id": "03-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." }, { "id": "03-14", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All owned original source pages inspected individually; full printed working/teaching notes/key variants transcribed, original errors labelled separately. Analytic D3 diagrams preserve source domains/labels/endpoints; final rendered visual QA recorded separately." } ], "unresolved": [] }, { "topic": "04", "pages": [ { "file": "04 Functions sol.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-1-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 1." }, { "id": "04-01-working-p1", "type": "working", "target": "04-01#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-01-solution-statement-p1", "type": "question", "target": "04-01#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-01-note-1-p1", "type": "teacher-note", "target": "04-01#teacher-note-1", "description": "To find the range of $f$, sketch the graph of $f$ and, from the graph, find the range of y-values." }, { "id": "04-01-note-2-p1", "type": "teacher-note", "target": "04-01#teacher-note-2", "description": "$y=f(x)\\Leftrightarrow x=f^{-1}(y)$. Make $x$ the subject where $x=f^{-1}(y)$. Then replace $y$ by $x$ to find $f^{-1}(x)$." }, { "id": "04-01-note-3-p1", "type": "teacher-note", "target": "04-01#teacher-note-3", "description": "Note that the range of $g$ is from the y-value of the minimum point $(1,2)$ to the y-value of the endpoint $(4,29)$. **Do not just consider the y-values of the two endpoints** to find the range of $g$" }, { "id": "04-01-diagram-1-p1", "type": "diagram", "target": "04-01#source-diagrams", "description": "Printed square-root f graph with closed start(2,0)." }, { "id": "04-01-diagram-2-p1", "type": "diagram", "target": "04-01#source-diagrams", "description": "Printed quadratic g graph on[0,4], labelled(0,5),(1,2),(4,29)." }, { "id": "04-01-diagram-3-p1", "type": "diagram", "target": "04-01#source-diagrams", "description": "Original range/domain inclusion and mapping flow: Rg=[2,29] inside Df=[2,∞), and[0,4] through g then f." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-2-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 2." }, { "id": "04-01-working-p2", "type": "working", "target": "04-01#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-01-note-4-p2", "type": "teacher-note", "target": "04-01#teacher-note-4", "description": "Treat $R_g$ as the new domain for the graph of $f$ to find $R_{fg}$." }, { "id": "04-01-diagram-4-p2", "type": "diagram", "target": "04-01#source-diagrams", "description": "Method1 square-root graph restricted to2≤x≤29, with upper level√27." }, { "id": "04-01-diagram-5-p2", "type": "diagram", "target": "04-01#source-diagrams", "description": "Method2 composite V graph on[0,4], vertex(1,0), endpoint(4,√27) and range arrow." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-3-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 3." }, { "id": "04-01-working-p3", "type": "working", "target": "04-01#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-4-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 4." }, { "id": "04-02-working-p4", "type": "working", "target": "04-02#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-02-solution-statement-p4", "type": "question", "target": "04-02#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-02-note-1-p4", "type": "teacher-note", "target": "04-02#teacher-note-1", "description": "Make $x$ the subject." }, { "id": "04-02-diagram-1-p4", "type": "diagram", "target": "04-02#source-diagrams", "description": "Full periodic source sketch from−1 to4, four source branches and all six labelled endpoint values including the open points(0,1),(3,1)." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-5-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 5." }, { "id": "04-03-working-p5", "type": "working", "target": "04-03#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-03-solution-statement-p5", "type": "question", "target": "04-03#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-03-note-1-p5", "type": "teacher-note", "target": "04-03#teacher-note-1", "description": "The range of $f$ is the set of y-values that $f$ can take. Sketch the graph of $f$ according to the given domain before determining the range." }, { "id": "04-03-note-2-p5", "type": "teacher-note", "target": "04-03#teacher-note-2", "description": "**Graphical method:** use the graph of $f$ sketched in (i). To show $f$ is not1–1, give a counter-example of **one particular horizontal line** that cuts the graph of $f$ more than once." }, { "id": "04-03-note-3-p5", "type": "teacher-note", "target": "04-03#teacher-note-3", "description": "**Counter-example:** give **two different values of x** that result in the **same image y**." }, { "id": "04-03-diagram-1-p5", "type": "diagram", "target": "04-03#source-diagrams", "description": "Original symmetric function graph, maximum(1/5,2), y=0 asymptote and horizontal-line y=1 counter-example." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-6-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 6." }, { "id": "04-03-working-p6", "type": "working", "target": "04-03#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-03-note-4-p6", "type": "teacher-note", "target": "04-03#teacher-note-4", "description": "Deduce the least $k$ from the graph of $f$. State the domain of $f$. To find $f^{-1}(x)$: (1) let $y=f(x)\\Rightarrow x=f^{-1}(y)$; (2) make $x$ the subject, and if there are two possible expressions, " }, { "id": "04-03-note-5-p6", "type": "teacher-note", "target": "04-03#teacher-note-5", "description": "When sketching $f$ and $f^{-1}$ together, use the **same scale** for x- and y-axes; their graphs must be symmetrical about $y=x$. Always include endpoints. In this case the two curves intersect only o" }, { "id": "04-03-note-6-p6", "type": "teacher-note", "target": "04-03#teacher-note-6", "description": "To solve $f(x)=f^{-1}(x)$, it may be easier to solve $f(x)=x$ or $f^{-1}(x)=x$." }, { "id": "04-03-diagram-2-p6", "type": "diagram", "target": "04-03#source-diagrams", "description": "Restricted graph and inverse reflected in y=x using equal coordinate units, endpoints(1/5,2),(2,1/5) and axis asymptotes." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-7-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 7." }, { "id": "04-03-working-p7", "type": "working", "target": "04-03#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-8-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 8." }, { "id": "04-04-working-p8", "type": "working", "target": "04-04#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-04-solution-statement-p8", "type": "question", "target": "04-04#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-04-note-1-p8", "type": "teacher-note", "target": "04-04#teacher-note-1", "description": "For $f$ to be1–1, the minimum at $x=-\\lambda/2$ must be to the right of $x=2$, i.e. $-\\lambda/2\\ge2$. If it is to the left of $x=2$, as in the second diagram, $f$ is not1–1 because horizontal line $y=" }, { "id": "04-04-diagram-1-p8", "type": "diagram", "target": "04-04#source-diagrams", "description": "Both original restricted-quadratic cases, shaded x≤2 domain, minimum−λ/2 and horizontal y=2 counter-example in the non-injective case." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-9-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 9." }, { "id": "04-04-working-p9", "type": "working", "target": "04-04#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-04-note-2-p9", "type": "teacher-note", "target": "04-04#teacher-note-2", "description": "To find $f^{-1}(x)$: (1) let $y=f(x)$ so $x=f^{-1}(y)$; (2) make $x$ the subject and choose the expression corresponding to the domain of $f$; (3) replace $y$ with $x$; (4) define $f^{-1}$ — **both ru" }, { "id": "04-04-note-3-p9", "type": "teacher-note", "target": "04-04#teacher-note-3", "description": "Given two functions $g,h$, $hg$ is $g$ (first function) followed by $h$ (second function). For $hg$ to exist, range of $g\\subseteq$ domain of $h$." }, { "id": "04-04-note-4-p9", "type": "teacher-note", "target": "04-04#teacher-note-4", "description": "To find $R_{hg}$: (1) find $R_g$ using the graph of $g$; (2) sketch the graph of the second function $h$; (3) range of the first function becomes the restricted domain of $h$; (4) use that new domain " }, { "id": "04-04-diagram-2-p9", "type": "diagram", "target": "04-04#source-diagrams", "description": "Original inverse mapping diagram: Df to Rf by f, return by f⁻¹; Rf⁻¹=Df and Df⁻¹=Rf." }, { "id": "04-04-diagram-3-p9", "type": "diagram", "target": "04-04#source-diagrams", "description": "Source quadratic g with minimum(−1/2,3/4)." }, { "id": "04-04-diagram-4-p9", "type": "diagram", "target": "04-04#source-diagrams", "description": "Source h=x+4/x plot: x=0 andy=x asymptotes, minimum(2,4), restricted domain[3/4,∞) and range[4,∞)." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-10-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 10." }, { "id": "04-05-working-p10", "type": "working", "target": "04-05#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-05-solution-statement-p10", "type": "question", "target": "04-05#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-05-note-1-p10", "type": "teacher-note", "target": "04-05#teacher-note-1", "description": "$gh(x)=g(x^2-2x+2)$. To find $R_{gh}$: (1) find $R_h$ using the graph of the first function $h$; (2) sketch the second function $g$; (3) $R_h$ becomes the restricted domain of $g$; (4) use $R_h$ as th" }, { "id": "04-05-note-2-p10", "type": "teacher-note", "target": "04-05#teacher-note-2", "description": "When sketching $f$ and $f^{-1}$ on the same diagram, the **scale must be the same** for the x- and y-axes; their graphs must be symmetrical about $y=x$. Always include endpoints. $D_{g^{-1}g}=D_g=[1,\\" }, { "id": "04-05-note-3-p10", "type": "teacher-note", "target": "04-05#teacher-note-3", "description": "$D_{gg^{-1}}=D_{g^{-1}}=[0,\\infty)$. To compare the two composites, $x\\in D_{g^{-1}g}\\cap D_{gg^{-1}}\\Rightarrow x\\in D_g\\cap D_{g^{-1}}$." }, { "id": "04-05-diagram-1-p10", "type": "diagram", "target": "04-05#source-diagrams", "description": "Original two range-finding graphs, quadratic h with minimum(1,1)/open(0,2), and restricted logarithm g with closed(1,0), including domain/range rays." }, { "id": "04-05-diagram-2-p10", "type": "diagram", "target": "04-05#source-diagrams", "description": "Source composition diagram with Rh inside Dg, h andg arrows and compositegh." }, { "id": "04-05-diagram-3-p10", "type": "diagram", "target": "04-05#source-diagrams", "description": "Restricted logarithm, exponential inverse and identity composite on equal-scale axes, with all three closed endpoints." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-11-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 11." }, { "id": "04-06-working-p11", "type": "working", "target": "04-06#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-06-solution-statement-p11", "type": "question", "target": "04-06#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-06-note-1-p11", "type": "teacher-note", "target": "04-06#teacher-note-1", "description": "From (iii), $f^3(x)=x\\Rightarrow f^3(g(x))=g(x)$. Example: $f^{10}(g(x))=f\\underbrace{f^3f^3f^3}_{3\\text{ blocks}}(g(x))=f\\underbrace{f^3f^3}_{2\\text{ blocks}}(g(x))=f\\underbrace{f^3}_{1\\text{ block}}" }, { "id": "04-06-diagram-1-p11", "type": "diagram", "target": "04-06#source-diagrams", "description": "Source punctured rational graph y=(x−1)/x with x=0,y=1 asymptotes and open deleted point(1,0)." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 12, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-12-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 12." }, { "id": "04-07-working-p12", "type": "working", "target": "04-07#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-07-solution-statement-p12", "type": "question", "target": "04-07#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-07-note-1-p12", "type": "teacher-note", "target": "04-07#teacher-note-1", "description": "For the **graphical method**, draw horizontal line $y=3$ on the same diagram as the graph of $f$, showing it cuts that graph at two points." }, { "id": "04-07-note-2-p12", "type": "teacher-note", "target": "04-07#teacher-note-2", "description": "**Note:** (1) To show $f$ is **not1–1**, only give an example of **one particular horizontal line** cutting its graph more than once. (2) Either write “graph of f”, “graph of y=f(x)”, or “the curve y=" }, { "id": "04-07-note-3-p12", "type": "teacher-note", "target": "04-07#teacher-note-3", "description": "The source says for $x\\ge1/2$, $1-2x<0$, $2x+1>0$, so $|1-2x|=-(1-2x)$ and $|2x+1|=2x+1$, hence $|(1-2x)/(2x+1)|=|1-2x|/|2x+1|=-(1-2x)/(2x+1)$. At the included endpoint $x=1/2$, the first strict sign " }, { "id": "04-07-diagram-1-p12", "type": "diagram", "target": "04-07#source-diagrams", "description": "Complete source absolute rational graph, both asymptotes, cusp1/2 and y=3 counter-example." }, { "id": "04-07-diagram-2-p12", "type": "diagram", "target": "04-07#source-diagrams", "description": "Source arctangent curve y=arctan(2x), ±π/2 limits, point(1/2,π/4) and domain/range endpoint rays." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 13, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-13-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 13." }, { "id": "04-07-working-p13", "type": "working", "target": "04-07#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-08-working-p13", "type": "working", "target": "04-08#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-08-solution-statement-p13", "type": "question", "target": "04-08#complete-question", "description": "Repeated printed question data/subparts/marks and original attribution at solution start." }, { "id": "04-08-note-1-p13", "type": "teacher-note", "target": "04-08#teacher-note-1", "description": "For $fg$ to exist, the range of the first function $g$ must be a subset of the domain of the second function $f$." }, { "id": "04-08-diagram-1-p13", "type": "diagram", "target": "04-08#source-diagrams", "description": "Source g=−ln(1+x) graph with x=−1 asymptote and closed endpoint(1,−ln2), plus range ray." }, { "id": "04-08-diagram-2-p13", "type": "diagram", "target": "04-08#source-diagrams", "description": "Source g then f composition diagram, with Rg inside Df." } ], "unresolved": [] }, { "file": "04 Functions sol.pdf", "page": 14, "visualChecked": true, "status": "audited-native", "items": [ { "id": "04-solution-14-edition", "type": "header-footer", "target": "topic-04#source-metadata", "description": "Compilation header/topic title/printed pagination: 14." }, { "id": "04-08-working-p14", "type": "working", "target": "04-08#printed-working", "description": "Complete printed equation chains, all source methods and continuation blocks; source slips distinguished from reviewed supplements." }, { "id": "04-08-note-2-p14", "type": "teacher-note", "target": "04-08#teacher-note-2", "description": "Use the standard Maclaurin series: $\\ln(1+x)=x-x^2/2+x^3/3-\\cdots+(-1)^{r+1}x^r/r+\\cdots$ and $\\cos x=1-x^2/2!+x^4/4!-\\cdots+(-1)^rx^{2r}/(2r)!+\\cdots$." }, { "id": "04-08-note-3-p14", "type": "teacher-note", "target": "04-08#teacher-note-3", "description": "To find $h^{-1}(x)$: (1) let $y=h(x)\\Rightarrow x=h^{-1}(y)$; (2) make $x$ the subject; (3) replace $y$ with $x$; (4) define $h^{-1}$ — both rule and domain. For the branch $-10 qualified." }, { "id": "04-16", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Square roots recovered visually; cubic sign domain, restricted injectivity and inverse value checked; key(iii)/(iv) numbering slip recorded." }, { "id": "04-17", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rational extrema and asymptote re-evaluated; nonconstant versus constant composite family qualified; shortkey oblique-labely=x corrected separately." } ], "unresolved": [] }, { "topic": "05", "pages": [ { "file": "05 Differentiation (Gradient function).pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "05-question-p1-metadata", "type": "header-footer", "target": "topic-05#source-metadata", "description": "Repeated printed compilation header and footer page 33; section/Answers labels map to topic metadata" }, { "id": "05-01-question-p1", "type": "question", "target": "05-01#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "05-02-question-p1", "type": "question", "target": "05-02#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "05-03-question-p1", "type": "question", "target": "05-03#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "05-03-question-question-p1", "type": "diagram", "target": "05-03#native-diagrams", "description": "Native SVG native-05-03-question.svg; all printed labels represented, repeated source figure reuses same native figure" } ], "unresolved": [] }, { "file": "05 Differentiation (Gradient function).pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "05-question-p2-metadata", "type": "header-footer", "target": "topic-05#source-metadata", "description": "Repeated printed compilation header and footer page 34; section/Answers labels map to topic metadata" }, { "id": "05-04-question-p2", "type": "question", "target": "05-04#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "05-05-question-p2", "type": "question", "target": "05-05#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "05-04-question-question-p2", "type": "diagram", "target": "05-04#native-diagrams", "description": "Native SVG native-05-04-question.svg; all printed labels represented, repeated source figure reuses same native figure" }, { "id": "05-05-question-question-p2", "type": "diagram", "target": "05-05#native-diagrams", "description": "Native SVG native-05-05-question.svg; all printed labels represented, repeated source figure reuses same native figure" } ], "unresolved": [] }, { "file": "05 Differentiation (Gradient function).pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "05-question-p3-metadata", "type": "header-footer", "target": "topic-05#source-metadata", "description": "Repeated printed compilation header and footer page 35; section/Answers labels map to topic metadata" }, { "id": "05-06-question-p3", "type": "question", "target": "05-06#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "05-07-question-p3", "type": "question", "target": "05-07#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "05-06-question-question-p3", "type": "diagram", "target": "05-06#native-diagrams", "description": "Native SVG native-05-06-question.svg; all printed labels represented, repeated source figure reuses same native figure" }, { "id": "05-07-gradient-question-p3", "type": "diagram", "target": "05-07#native-diagrams", "description": "Native SVG native-05-07-gradient.svg; all printed labels represented, repeated source figure reuses same native figure" }, { "id": "05-07-absolute-question-p3", "type": "diagram", "target": "05-07#native-diagrams", "description": "Native SVG native-05-07-absolute.svg; all printed labels represented, repeated source figure reuses same native figure" } ], "unresolved": [] }, { "file": "05 Differentiation (Gradient function).pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "05-question-p4-metadata", "type": "header-footer", "target": "topic-05#source-metadata", "description": "Repeated printed compilation header and footer page 36; section/Answers labels map to topic metadata" }, { "id": "05-01-key-p4", "type": "answer-key", "target": "05-01#answer-key", "description": "Printed short answer including rounding and qualifications; native figure shared where answer is diagrammatic" }, { "id": "05-02-key-p4", "type": "answer-key", "target": "05-02#answer-key", "description": "Printed short answer including rounding and qualifications; 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all printed labels represented, repeated source figure reuses same native figure" } ], "unresolved": [] }, { "file": "06 App of diff sol.pdf", "page": 22, "visualChecked": true, "status": "audited-native", "items": [ { "id": "06-solution-p22-metadata", "type": "header-footer", "target": "topic-06#source-metadata", "description": "Repeated printed compilation header and footer page 22; section/Answers labels map to topic metadata" }, { "id": "06-14-solution-p22", "type": "working", "target": "06-14#printed-working", "description": "All displayed algebra, intermediate steps, case decisions, final answer and alternative methods in this page segment" }, { "id": "06-14-viewing-solution-p22", "type": "diagram", "target": "06-14#native-diagrams", "description": "Native SVG native-06-14-viewing.svg; all printed labels represented, repeated source figure reuses same native figure" }, { "id": "06-14-repeated-statement-p22", "type": "question", "target": "06-14#printed-question", "description": "Repeated full printed question statement, subparts, marks and attribution on solution page; same native statement" } ], "unresolved": [] }, { "file": "06 App of diff sol.pdf", "page": 23, "visualChecked": true, "status": "audited-native", "items": [ { "id": "06-solution-p23-metadata", "type": "header-footer", "target": "topic-06#source-metadata", "description": "Repeated printed compilation header and footer page 23; section/Answers labels map to topic metadata" }, { "id": "06-14-solution-p23", "type": "working", "target": "06-14#printed-working", "description": "All displayed algebra, intermediate steps, case decisions, final answer and alternative methods in this page segment" }, { "id": "06-15-solution-p23", "type": "working", "target": "06-15#printed-working", "description": "All displayed algebra, intermediate steps, case decisions, final answer and alternative methods in this page segment" }, { "id": "06-14-note-p23-1", "type": "teacher-note", "target": "06-14#teacher-notes", "description": "Arctangent chain rule" }, { "id": "06-14-note-p23-2", "type": "teacher-note", "target": "06-14#teacher-notes", "description": "Sketch angle graph" }, { "id": "06-15-note-p23-1", "type": "teacher-note", "target": "06-15#teacher-notes", "description": "Stationary point means dy/dx=0" }, { "id": "06-14-angle-solution-p23", "type": "diagram", "target": "06-14#native-diagrams", "description": "Native SVG native-06-14-angle.svg; all printed labels represented, repeated source figure reuses same native figure" }, { "id": "06-15-repeated-statement-p23", "type": "question", "target": "06-15#printed-question", "description": "Repeated full printed question statement, subparts, marks and attribution on solution page; same native statement" } ], "unresolved": [] }, { "file": "06 App of diff sol.pdf", "page": 24, "visualChecked": true, "status": "audited-native", "items": [ { "id": "06-solution-p24-metadata", "type": "header-footer", "target": "topic-06#source-metadata", "description": "Repeated printed compilation header and footer page 24; section/Answers labels map to topic metadata" }, { "id": "06-15-solution-p24", "type": "working", "target": "06-15#printed-working", "description": "All displayed algebra, intermediate steps, case decisions, final answer and alternative methods in this page segment" } ], "unresolved": [] }, { "file": "06 App of diff sol.pdf", "page": 25, "visualChecked": true, "status": "audited-native", "items": [ { "id": "06-solution-p25-metadata", "type": "header-footer", "target": "topic-06#source-metadata", "description": "Repeated printed compilation header and footer page 25; 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section/Answers labels map to topic metadata" }, { "id": "06-17-solution-p28", "type": "working", "target": "06-17#printed-working", "description": "All displayed algebra, intermediate steps, case decisions, final answer and alternative methods in this page segment" }, { "id": "06-18-solution-p28", "type": "question", "target": "06-18#printed-question", "description": "Full printed statement and marks/attribution" }, { "id": "06-17-region-solution-p28", "type": "diagram", "target": "06-17#native-diagrams", "description": "Native SVG native-06-17-region.svg; all printed labels represented, repeated source figure reuses same native figure" }, { "id": "06-18-capsule-solution-p28", "type": "diagram", "target": "06-18#native-diagrams", "description": "Native SVG native-06-18-capsule.svg; all printed labels represented, repeated source figure reuses same native figure" } ], "unresolved": [] }, { "file": "06 App of diff sol.pdf", "page": 29, "visualChecked": true, "status": "audited-native", "items": [ { "id": "06-solution-p29-metadata", "type": "header-footer", "target": "topic-06#source-metadata", "description": "Repeated printed compilation header and footer page 29; section/Answers labels map to topic metadata" }, { "id": "06-18-solution-p29", "type": "working", "target": "06-18#printed-working", "description": "All displayed algebra, intermediate steps, case decisions, final answer and alternative methods in this page segment" }, { "id": "06-18-note-p29-1", "type": "teacher-note", "target": "06-18#teacher-notes", "description": "One-variable volume" }, { "id": "06-18-note-p29-2", "type": "teacher-note", "target": "06-18#teacher-notes", "description": "Apply chain rule" }, { "id": "06-18-note-p29-3", "type": "teacher-note", "target": "06-18#teacher-notes", "description": "Decreasing x gives negative time derivative" }, { "id": "06-18-capsule-solution-p29", "type": "diagram", "target": "06-18#native-diagrams", "description": "Native SVG native-06-18-capsule.svg; all printed labels represented, repeated source figure reuses same native figure" } ], "unresolved": [] } ], "questions": [ { "id": "06-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Implicit numerator nonzero at P checked; tangent/normal square geometry checked." }, { "id": "06-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Both normals checked; n=0 degeneracy and incomplete short key qualified." }, { "id": "06-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Both printed normal methods checked; a=0 excluded separately; ellipse roots restored visually." }, { "id": "06-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Implicit/product derivative and source calculator values checked; branches/tangent angle coherent." }, { "id": "06-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every parametric derivative and tangent algebra step checked; mixed x/θ chart label recorded." }, { "id": "06-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All derivatives and two sign tables checked; global-max claim invalid without x≥0 and qualified." }, { "id": "06-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Normal algebra checked including vertical special cases; Q factorisation and midpoint/locus checked." }, { "id": "06-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Angular rate, trigonometric tangent simplification, triangle area, midpoint locus checked." }, { "id": "06-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Collision derivative/normal, rounded source area limits and conversion note checked; initial arc region qualified." }, { "id": "06-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Projectile range, moving target equality, early angle comparison and tangent angle checked." }, { "id": "06-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Material expression, quartic factorisation and positive second derivative checked." }, { "id": "06-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Volume, all three external faces, eliminate w, dimensions and printed simplification checked." }, { "id": "06-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Similarity, radius constraint, two derivatives, maximum volume and area bound checked." }, { "id": "06-14", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All source angle labels, arctan chain rule and calculator display checked." }, { "id": "06-15", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Quadratic in x³, cube roots, nonzero A and second derivative signs checked." }, { "id": "06-16", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Similar triangles and chain-rule rate checked." }, { "id": "06-17", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All alternate solutions evaluated; printed +2 and completed-square slips labelled; s=√2 restored visually." }, { "id": "06-18", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Pythagoras/similarity and alternate angle proof checked; decreasing sign and chain-rule volume rate checked." } ], "unresolved": [], "limits": [ "First source transcription/math review, not independent second expert certification. Qualitative source drawings are schematic, not unsupported exact functions.", "Root must integrate declarative SVG geometry through D3 and run route/browser QA; this audit certifies owned source/native content only." ] }, { "topic": "07", "pages": [ { "file": "07 Integration tech.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-question-1-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 46; title / [Solution] / Answers heading where present" }, { "id": "07-01-question-1", "type": "question", "target": "07-01#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "07-02-question-2", "type": "question", "target": "07-02#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "07-03-question-3", "type": "question", "target": "07-03#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "07-04-question-4", "type": "question", "target": "07-04#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "07-05-question-5", "type": "question", "target": "07-05#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "07-06-question-6", "type": "question", "target": "07-06#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "07-01-table-7", "type": "table", "target": "07-01#printed-question", "description": "Two-column (a)–(j) integral exercise table" } ], "unresolved": [] }, { "file": "07 Integration tech.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-question-2-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; 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printed page 50; title / [Solution] / Answers heading where present" }, { "id": "07-09-answer-key-1", "type": "answer-key", "target": "07-09#printed-answer-key", "description": "Printed short answer entry and diagram where shown" }, { "id": "07-10-answer-key-2", "type": "answer-key", "target": "07-10#printed-answer-key", "description": "Printed short answer entry and diagram where shown" }, { "id": "07-11-answer-key-3", "type": "answer-key", "target": "07-11#printed-answer-key", "description": "Printed short answer entry and diagram where shown" }, { "id": "07-12-answer-key-4", "type": "answer-key", "target": "07-12#printed-answer-key", "description": "Printed short answer entry and diagram where shown" }, { "id": "07-13-answer-key-5", "type": "answer-key", "target": "07-13#printed-answer-key", "description": "Printed short answer entry and diagram where shown" }, { "id": "07-14-answer-key-6", "type": "answer-key", "target": "07-14#printed-answer-key", "description": "Printed short answer entry and diagram where shown" }, { "id": "07-09-diagram-7", "type": "diagram", "target": "07-09#source-diagrams-in-native-form", "description": "Repeated answer-key sketch with all labels" }, { "id": "07-13-diagram-8", "type": "diagram", "target": "07-13#source-diagrams-in-native-form", "description": "Repeated answer-key sketch with all labels" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-1-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 1; title / [Solution] / Answers heading where present" }, { "id": "07-01-question-1", "type": "question", "target": "07-01#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-01-working-2", "type": "working", "target": "07-01#printed-working", "description": "(a)–(d)" }, { "id": "07-01-teacher-note-3", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Power formula with f=ln x, f′=1/x, n=5" }, { "id": "07-01-teacher-note-4", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Exponential formula with f=4−x², f′=−2x" }, { "id": "07-01-teacher-note-5", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Parts formula and two u,dv choices" }, { "id": "07-01-teacher-note-6", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "MF27 cos2A formula, replace A by 2θ" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-2-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 2; title / [Solution] / Answers heading where present" }, { "id": "07-01-working-1", "type": "working", "target": "07-01#printed-working", "description": "(e)–(h), partial fraction substitutions" }, { "id": "07-01-teacher-note-2", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Exponential formula with f=cot x, f′=−cosec²x" }, { "id": "07-01-teacher-note-3", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Not-MF27 arctangent composite formula f=x+1,a=2" }, { "id": "07-01-teacher-note-4", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Long division display quotient1 remainder−x+16" }, { "id": "07-01-teacher-note-5", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Logarithmic derivative box and modulus arrows" }, { "id": "07-01-teacher-note-6", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "MF27 reciprocal difference-of-squares formula a=4, modulus arrows" }, { "id": "07-01-teacher-note-7", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Use partial fractions for the proper fraction" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-3-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 3; title / [Solution] / Answers heading where present" }, { "id": "07-02-question-1", "type": "question", "target": "07-02#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-01-working-2", "type": "working", "target": "07-01#printed-working", "description": "(h) continuation, (i),(j)" }, { "id": "07-02-working-3", "type": "working", "target": "07-02#printed-working", "description": "modulus reduction and split" }, { "id": "07-01-teacher-note-4", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Log derivative and MF27 arctangent box, modulus arrows" }, { "id": "07-01-teacher-note-5", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Power formula for exponential denominator" }, { "id": "07-01-teacher-note-6", "type": "teacher-note", "target": "07-01#teacher-notes", "description": "Power and MF27 inverse-sine formula" }, { "id": "07-02-teacher-note-7", "type": "teacher-note", "target": "07-02#teacher-notes", "description": "Denominator positive and piecewise |x−2| on [−2,2]" }, { "id": "07-02-diagram-8", "type": "diagram", "target": "07-02#source-diagrams-in-native-form", "description": "signed versus modulus integrand with shaded area" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-4-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 4; title / [Solution] / Answers heading where present" }, { "id": "07-03-question-1", "type": "question", "target": "07-03#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-02-working-2", "type": "working", "target": "07-02#printed-working", "description": "logarithmic and arctangent evaluation, p,q" }, { "id": "07-03-working-3", "type": "working", "target": "07-03#printed-working", "description": "(a)" }, { "id": "07-02-teacher-note-4", "type": "teacher-note", "target": "07-02#teacher-notes", "description": "Log formula with positive completed square" }, { "id": "07-02-teacher-note-5", "type": "teacher-note", "target": "07-02#teacher-notes", "description": "MF27 arctangent and composite not-MF27 arctangent formulas" }, { "id": "07-03-teacher-note-6", "type": "teacher-note", "target": "07-03#teacher-notes", "description": "MF27 difference-of-squares integral x→t, a→√3/2" }, { "id": "07-03-teacher-note-7", "type": "teacher-note", "target": "07-03#teacher-notes", "description": "Remember modulus in logarithm" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-5-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 5; title / [Solution] / Answers heading where present" }, { "id": "07-04-question-1", "type": "question", "target": "07-04#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-03-working-2", "type": "working", "target": "07-03#printed-working", "description": "(b)" }, { "id": "07-04-working-3", "type": "working", "target": "07-04#printed-working", "description": "(a),(b)" }, { "id": "07-03-teacher-note-4", "type": "teacher-note", "target": "07-03#teacher-notes", "description": "Substitution formula, express integrand in u, return indefinite answer to x" }, { "id": "07-03-teacher-note-5", "type": "teacher-note", "target": "07-03#teacher-notes", "description": "Derivative factor must stay inside integral; explicit 2u·u counterexample" }, { "id": "07-04-teacher-note-6", "type": "teacher-note", "target": "07-04#teacher-notes", "description": "Parts formula and u=x²,dv/dx=2x sec²(x²)" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-6-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 6; title / [Solution] / Answers heading where present" }, { "id": "07-05-question-1", "type": "question", "target": "07-05#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-05-working-2", "type": "working", "target": "07-05#printed-working", "description": "(a),(b), definite integral" }, { "id": "07-05-teacher-note-3", "type": "teacher-note", "target": "07-05#teacher-notes", "description": "Cosine composition integral" }, { "id": "07-05-teacher-note-4", "type": "teacher-note", "target": "07-05#teacher-notes", "description": "Parts formula" }, { "id": "07-05-teacher-note-5", "type": "teacher-note", "target": "07-05#teacher-notes", "description": "Sine composition integral" }, { "id": "07-05-teacher-note-6", "type": "teacher-note", "target": "07-05#teacher-notes", "description": "MF27 double angle and multiple-angle re-expression warning" }, { "id": "07-05-teacher-note-7", "type": "teacher-note", "target": "07-05#teacher-notes", "description": "Starred parts integral u=x,dv/dx=cos2x" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-7-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 7; title / [Solution] / Answers heading where present" }, { "id": "07-06-question-1", "type": "question", "target": "07-06#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-06-working-2", "type": "working", "target": "07-06#printed-working", "description": "(i),(ii)" }, { "id": "07-06-teacher-note-3", "type": "teacher-note", "target": "07-06#teacher-notes", "description": "Substitution formula and final answer in x" }, { "id": "07-06-teacher-note-4", "type": "teacher-note", "target": "07-06#teacher-notes", "description": "Power formula n=−1/2 and MF27 inverse-sine a=1" }, { "id": "07-06-teacher-note-5", "type": "teacher-note", "target": "07-06#teacher-notes", "description": "Boxed parts choices u,du,dv,v" }, { "id": "07-06-teacher-note-6", "type": "teacher-note", "target": "07-06#teacher-notes", "description": "Parts formula" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-8-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 8; title / [Solution] / Answers heading where present" }, { "id": "07-07-question-1", "type": "question", "target": "07-07#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-08-question-2", "type": "question", "target": "07-08#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-07-working-3", "type": "working", "target": "07-07#printed-working", "description": "two parts integrations and recurring-integral algebra" }, { "id": "07-08-working-4", "type": "working", "target": "07-08#printed-working", "description": "(a) coefficient comparison" }, { "id": "07-07-teacher-note-5", "type": "teacher-note", "target": "07-07#teacher-notes", "description": "Parts formula; first u=cos3x, second u=sin3x" }, { "id": "07-07-teacher-note-6", "type": "teacher-note", "target": "07-07#teacher-notes", "description": "Indefinite LHS requires +c on RHS; c1=4c/13" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-9-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 9; title / [Solution] / Answers heading where present" }, { "id": "07-08-working-1", "type": "working", "target": "07-08#printed-working", "description": "(a) integral, (b)(i),(ii)" }, { "id": "07-08-teacher-note-2", "type": "teacher-note", "target": "07-08#teacher-notes", "description": "Log derivative formula" }, { "id": "07-08-teacher-note-3", "type": "teacher-note", "target": "07-08#teacher-notes", "description": "Substitution x=g(t) and change definite limits 1→1,5→3" }, { "id": "07-08-teacher-note-4", "type": "teacher-note", "target": "07-08#teacher-notes", "description": "Log and power formulas f=t+1,n=−2" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-10-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 10; title / [Solution] / Answers heading where present" }, { "id": "07-09-question-1", "type": "question", "target": "07-09#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-09-working-2", "type": "working", "target": "07-09#printed-working", "description": "(a),(b)" }, { "id": "07-09-teacher-note-3", "type": "teacher-note", "target": "07-09#teacher-notes", "description": "Substitution and definite bound changes x0→u3,xln2→u4" }, { "id": "07-09-teacher-note-4", "type": "teacher-note", "target": "07-09#teacher-notes", "description": "Log derivative and modulus sign for ln|ln x|" }, { "id": "07-09-diagram-5", "type": "diagram", "target": "07-09#source-diagrams-in-native-form", "description": "exponential graph with endpoints and ln2" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-11-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 11; title / [Solution] / Answers heading where present" }, { "id": "07-10-question-1", "type": "question", "target": "07-10#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-10-working-2", "type": "working", "target": "07-10#printed-working", "description": "(a)" }, { "id": "07-10-teacher-note-3", "type": "teacher-note", "target": "07-10#teacher-notes", "description": "Substitution formula, changed θ limits, integrand in θ" }, { "id": "07-10-teacher-note-4", "type": "teacher-note", "target": "07-10#teacher-notes", "description": "Derivative factor must remain inside θ integral" }, { "id": "07-10-teacher-note-5", "type": "teacher-note", "target": "07-10#teacher-notes", "description": "MF27 cosecant integral and modulus, replace x by θ" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 12, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-12-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 12; title / [Solution] / Answers heading where present" }, { "id": "07-11-question-1", "type": "question", "target": "07-11#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-10-working-2", "type": "working", "target": "07-10#printed-working", "description": "(b)(i),(ii)" }, { "id": "07-10-teacher-note-3", "type": "teacher-note", "target": "07-10#teacher-notes", "description": "Power formula" }, { "id": "07-10-teacher-note-4", "type": "teacher-note", "target": "07-10#teacher-notes", "description": "Parts formula u=arcsin√x,dv/dx=√x" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 13, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-13-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 13; title / [Solution] / Answers heading where present" }, { "id": "07-11-working-1", "type": "working", "target": "07-11#printed-working", "description": "(a)(i)–(iii), (b)(i)" }, { "id": "07-11-teacher-note-2", "type": "teacher-note", "target": "07-11#teacher-notes", "description": "Power formula" }, { "id": "07-11-teacher-note-3", "type": "teacher-note", "target": "07-11#teacher-notes", "description": "MF27 inverse-sine and composite formula f=x−2,a=√3" }, { "id": "07-11-teacher-note-4", "type": "teacher-note", "target": "07-11#teacher-notes", "description": "Substitution two derivative derivations, return answer to x" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 14, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-14-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 14; title / [Solution] / Answers heading where present" }, { "id": "07-12-question-1", "type": "question", "target": "07-12#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-11-working-2", "type": "working", "target": "07-11#printed-working", "description": "(b)(ii)" }, { "id": "07-12-working-3", "type": "working", "target": "07-12#printed-working", "description": "(a), alternative cosecant method, (b)(i)" }, { "id": "07-11-teacher-note-4", "type": "teacher-note", "target": "07-11#teacher-notes", "description": "Parts formula u=ln(1+√x),dv/dx=1" }, { "id": "07-12-teacher-note-5", "type": "teacher-note", "target": "07-12#teacher-notes", "description": "Substitution x=g(t), derivative, return answer to x" }, { "id": "07-12-teacher-note-6", "type": "teacher-note", "target": "07-12#teacher-notes", "description": "Power formula f=sin t,n=−2" }, { "id": "07-12-diagram-7", "type": "diagram", "target": "07-12#source-diagrams-in-native-form", "description": "right triangle x,1,√(1+x²)" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 15, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-15-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 15; title / [Solution] / Answers heading where present" }, { "id": "07-13-question-1", "type": "question", "target": "07-13#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-12-working-2", "type": "working", "target": "07-12#printed-working", "description": "(b)(ii)" }, { "id": "07-13-working-3", "type": "working", "target": "07-13#printed-working", "description": "(i),(ii)" }, { "id": "07-12-teacher-note-4", "type": "teacher-note", "target": "07-12#teacher-notes", "description": "Boxed u,du,dv,v and parts formula" }, { "id": "07-13-teacher-note-5", "type": "teacher-note", "target": "07-13#teacher-notes", "description": "x=±π vertical asymptotes" }, { "id": "07-13-diagram-6", "type": "diagram", "target": "07-13#source-diagrams-in-native-form", "description": "two trigonometric curves and ±π asymptotes" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 16, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-16-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 16; title / [Solution] / Answers heading where present" }, { "id": "07-14-question-1", "type": "question", "target": "07-14#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "07-13-working-2", "type": "working", "target": "07-13#printed-working", "description": "(iii)" }, { "id": "07-14-working-3", "type": "working", "target": "07-14#printed-working", "description": "(i),(ii)" }, { "id": "07-13-teacher-note-4", "type": "teacher-note", "target": "07-13#teacher-notes", "description": "Signs on [0,π/2] and (π/2,2π/3]" }, { "id": "07-13-teacher-note-5", "type": "teacher-note", "target": "07-13#teacher-notes", "description": "MF27 cos2A and not-MF27 sec²A, replace A by x/2" }, { "id": "07-14-teacher-note-6", "type": "teacher-note", "target": "07-14#teacher-notes", "description": "Not-MF27 inverse-sine chain rule" }, { "id": "07-14-teacher-note-7", "type": "teacher-note", "target": "07-14#teacher-notes", "description": "GC key sequence 2nd mode→alpha window→4:fnInt→enter" } ], "unresolved": [] }, { "file": "07 Integration tech sol.pdf", "page": 17, "visualChecked": true, "status": "audited-native", "items": [ { "id": "07-solution-17-metadata", "type": "header-footer", "target": "topic-07#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 17; title / [Solution] / Answers heading where present" }, { "id": "07-14-working-1", "type": "working", "target": "07-14#printed-working", "description": "(iii) formal conditional algebra" }, { "id": "07-14-teacher-note-2", "type": "teacher-note", "target": "07-14#teacher-notes", "description": "Parts formula u=arcsin(x²),dv/dx=x²" } ], "unresolved": [] } ], "questions": [ { "id": "07-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "07-14", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." } ], "unresolved": [] }, { "topic": "08", "pages": [ { "file": "08 App of integration.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-1-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 51; title / [Solution] / Answers heading where present" }, { "id": "08-01-question-1", "type": "question", "target": "08-01#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-02-question-2", "type": "question", "target": "08-02#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-03-question-3", "type": "question", "target": "08-03#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-04-question-4", "type": "question", "target": "08-04#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-05-question-5", "type": "question", "target": "08-05#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" } ], "unresolved": [] }, { "file": "08 App of integration.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-2-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 52; title / [Solution] / Answers heading where present" }, { "id": "08-06-question-1", "type": "question", "target": "08-06#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-07-question-2", "type": "question", "target": "08-07#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-06-diagram-3", "type": "diagram", "target": "08-06#source-diagrams-in-native-form", "description": "ellipse,line,R" } ], "unresolved": [] }, { "file": "08 App of integration.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-3-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 53; title / [Solution] / Answers heading where present" }, { "id": "08-08-question-1", "type": "question", "target": "08-08#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-09-question-2", "type": "question", "target": "08-09#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-08-diagram-3", "type": "diagram", "target": "08-08#source-diagrams-in-native-form", "description": "parametric arch,line,A,R" }, { "id": "08-09-diagram-4", "type": "diagram", "target": "08-09#source-diagrams-in-native-form", "description": "C,l,P,Q" } ], "unresolved": [] }, { "file": "08 App of integration.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-4-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 54; title / [Solution] / Answers heading where present" }, { "id": "08-10-question-1", "type": "question", "target": "08-10#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-11-question-2", "type": "question", "target": "08-11#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" } ], "unresolved": [] }, { "file": "08 App of integration.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-5-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 55; title / [Solution] / Answers heading where present" }, { "id": "08-12-question-1", "type": "question", "target": "08-12#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-12-diagram-2", "type": "diagram", "target": "08-12#source-diagrams-in-native-form", "description": "exponential/parabola" }, { "id": "08-12-diagram-3", "type": "diagram", "target": "08-12#source-diagrams-in-native-form", "description": "C,L,S" } ], "unresolved": [] }, { "file": "08 App of integration.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-6-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 56; title / [Solution] / Answers heading where present" }, { "id": "08-13-question-1", "type": "question", "target": "08-13#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-13-diagram-2", "type": "diagram", "target": "08-13#source-diagrams-in-native-form", "description": "logistic R" }, { "id": "08-13-diagram-3", "type": "diagram", "target": "08-13#source-diagrams-in-native-form", "description": "bowl A,B" } ], "unresolved": [] }, { "file": "08 App of integration.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-7-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 57; title / [Solution] / Answers heading where present" }, { "id": "08-14-question-1", "type": "question", "target": "08-14#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-15-question-2", "type": "question", "target": "08-15#printed-question", "description": "Complete printed prompt, all subparts, marks and original exam attribution" }, { "id": "08-14-diagram-3", "type": "diagram", "target": "08-14#source-diagrams-in-native-form", "description": "lower rectangles" }, { "id": "08-15-diagram-4", "type": "diagram", "target": "08-15#source-diagrams-in-native-form", "description": "arctangent rectangle" } ], "unresolved": [] }, { "file": "08 App of integration.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-question-8-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 58; title / [Solution] / Answers heading where present" }, { "id": "08-01-diagram-1", "type": "diagram", "target": "08-01#source-diagrams-in-native-form", "description": "answer-key bell" }, { "id": "08-03-diagram-2", "type": "diagram", "target": "08-03#source-diagrams-in-native-form", "description": "answer-key trough" }, { "id": "08-07-diagram-3", "type": "diagram", "target": "08-07#source-diagrams-in-native-form", "description": "answer-key periodic curve" }, { "id": "08-01-answer-key-4", "type": "answer-key", "target": "08-01#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-02-answer-key-5", "type": "answer-key", "target": "08-02#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-03-answer-key-6", "type": "answer-key", "target": "08-03#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-04-answer-key-7", "type": "answer-key", "target": "08-04#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-05-answer-key-8", "type": "answer-key", "target": "08-05#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-06-answer-key-9", "type": "answer-key", "target": "08-06#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-07-answer-key-10", "type": "answer-key", "target": "08-07#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-08-answer-key-11", "type": "answer-key", "target": "08-08#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-09-answer-key-12", "type": "answer-key", "target": "08-09#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-10-answer-key-13", "type": "answer-key", "target": "08-10#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-11-answer-key-14", "type": "answer-key", "target": "08-11#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-12-answer-key-15", "type": "answer-key", "target": "08-12#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-13-answer-key-16", "type": "answer-key", "target": "08-13#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" }, { "id": "08-15-answer-key-17", "type": "answer-key", "target": "08-15#printed-answer-key", "description": "Printed short answer entry with original numbering anomaly if present" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-1-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 1; title / [Solution] / Answers heading where present" }, { "id": "08-01-question-1", "type": "question", "target": "08-01#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-02-question-2", "type": "question", "target": "08-02#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-01-working-3", "type": "working", "target": "08-01#printed-working", "description": "(i)–(iii)" }, { "id": "08-01-teacher-note-4", "type": "teacher-note", "target": "08-01#teacher-notes", "description": "Area upper-minus-lower on [1,3]" }, { "id": "08-01-teacher-note-5", "type": "teacher-note", "target": "08-01#teacher-notes", "description": "Y-axis volume formula π∫x²dy" }, { "id": "08-01-diagram-6", "type": "diagram", "target": "08-01#source-diagrams-in-native-form", "description": "stationary/intersection sketch" }, { "id": "08-01-diagram-7", "type": "diagram", "target": "08-01#source-diagrams-in-native-form", "description": "two inverse radii and rotation" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-2-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 2; title / [Solution] / Answers heading where present" }, { "id": "08-02-working-1", "type": "working", "target": "08-02#printed-working", "description": "(a),(b)" }, { "id": "08-02-teacher-note-2", "type": "teacher-note", "target": "08-02#teacher-notes", "description": "Accepted exact forms ln√2−π/12 and −½ln½−π/12" }, { "id": "08-02-teacher-note-3", "type": "teacher-note", "target": "08-02#teacher-notes", "description": "Area upper-minus-lower on [1/√2,1]" }, { "id": "08-02-teacher-note-4", "type": "teacher-note", "target": "08-02#teacher-notes", "description": "Black rectangle becomes cylinder radius5,height1.4−0.2" }, { "id": "08-02-diagram-5", "type": "diagram", "target": "08-02#source-diagrams-in-native-form", "description": "Q between reciprocal curves" }, { "id": "08-02-diagram-6", "type": "diagram", "target": "08-02#source-diagrams-in-native-form", "description": "R under y5" }, { "id": "08-02-diagram-7", "type": "diagram", "target": "08-02#source-diagrams-in-native-form", "description": "black cylinder rectangle" }, { "id": "08-02-diagram-8", "type": "diagram", "target": "08-02#source-diagrams-in-native-form", "description": "blue integral region" }, { "id": "08-02-diagram-9", "type": "diagram", "target": "08-02#source-diagrams-in-native-form", "description": "red integral region" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-3-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 3; title / [Solution] / Answers heading where present" }, { "id": "08-03-question-1", "type": "question", "target": "08-03#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-03-working-2", "type": "working", "target": "08-03#printed-working", "description": "(i) derivative and symmetry alternative, (ii)" }, { "id": "08-03-diagram-3", "type": "diagram", "target": "08-03#source-diagrams-in-native-form", "description": "trough sketch y3 asymptote" }, { "id": "08-03-diagram-4", "type": "diagram", "target": "08-03#source-diagrams-in-native-form", "description": "R between line and curve" }, { "id": "08-03-diagram-5", "type": "diagram", "target": "08-03#source-diagrams-in-native-form", "description": "blue triangular cone region" }, { "id": "08-03-diagram-6", "type": "diagram", "target": "08-03#source-diagrams-in-native-form", "description": "red curved excluded region" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-4-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 4; title / [Solution] / Answers heading where present" }, { "id": "08-03-working-1", "type": "working", "target": "08-03#printed-working", "description": "(iii),(iv), cone alternative" }, { "id": "08-03-teacher-note-2", "type": "teacher-note", "target": "08-03#teacher-notes", "description": "Area upper-minus-lower on [0,1]" }, { "id": "08-03-teacher-note-3", "type": "teacher-note", "target": "08-03#teacher-notes", "description": "Printed cylinder note for blue triangle; corrected cone interpretation" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-5-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 5; title / [Solution] / Answers heading where present" }, { "id": "08-04-question-1", "type": "question", "target": "08-04#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-04-working-2", "type": "working", "target": "08-04#printed-working", "description": "cylinder-minus-integral calculation" }, { "id": "08-04-teacher-note-3", "type": "teacher-note", "target": "08-04#teacher-notes", "description": "Red cylinder radius4.5,height1" }, { "id": "08-04-teacher-note-4", "type": "teacher-note", "target": "08-04#teacher-notes", "description": "Green solid π∫y²dx" }, { "id": "08-04-diagram-5", "type": "diagram", "target": "08-04#source-diagrams-in-native-form", "description": "Rational curve, oblique/vertical asymptotes,red/green volume guides" }, { "id": "08-04-table-6", "type": "table", "target": "08-04#printed-working", "description": "calculator display native table" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-6-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 6; title / [Solution] / Answers heading where present" }, { "id": "08-05-question-1", "type": "question", "target": "08-05#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-05-working-2", "type": "working", "target": "08-05#printed-working", "description": "inverse curve and three-piece volume" }, { "id": "08-05-teacher-note-3", "type": "teacher-note", "target": "08-05#teacher-notes", "description": "Rotation about y-axis label and three-solid subtraction" }, { "id": "08-05-diagram-4", "type": "diagram", "target": "08-05#source-diagrams-in-native-form", "description": "rational graph with x2,x3,y⅓,y½" }, { "id": "08-05-diagram-5", "type": "diagram", "target": "08-05#source-diagrams-in-native-form", "description": "purple minus blue minus red solids" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-7-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 7; title / [Solution] / Answers heading where present" }, { "id": "08-06-question-1", "type": "question", "target": "08-06#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-06-working-2", "type": "working", "target": "08-06#printed-working", "description": "(i) quadrant-minus-triangle reduction" }, { "id": "08-06-teacher-note-3", "type": "teacher-note", "target": "08-06#teacher-notes", "description": "Area quadrant ∫ydx, upper ellipse y≥0" }, { "id": "08-06-diagram-4", "type": "diagram", "target": "08-06#source-diagrams-in-native-form", "description": "question ellipse,line and R" }, { "id": "08-06-diagram-5", "type": "diagram", "target": "08-06#source-diagrams-in-native-form", "description": "solution quadrant minus triangle guide" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-8-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 8; title / [Solution] / Answers heading where present" }, { "id": "08-06-working-1", "type": "working", "target": "08-06#printed-working", "description": "(i) substitution chain, (ii) polynomial volume" }, { "id": "08-06-teacher-note-2", "type": "teacher-note", "target": "08-06#teacher-notes", "description": "Substitution formula and change definite limits" }, { "id": "08-06-teacher-note-3", "type": "teacher-note", "target": "08-06#teacher-notes", "description": "Quadrant rotated about y-axis" }, { "id": "08-06-teacher-note-4", "type": "teacher-note", "target": "08-06#teacher-notes", "description": "Triangle becomes cone radiusa,heightb" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-9-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 9; title / [Solution] / Answers heading where present" }, { "id": "08-07-question-1", "type": "question", "target": "08-07#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-07-working-2", "type": "working", "target": "08-07#printed-working", "description": "(a),(b),(c)" }, { "id": "08-07-teacher-note-3", "type": "teacher-note", "target": "08-07#teacher-notes", "description": "Signed area A,−A cancellation" }, { "id": "08-07-teacher-note-4", "type": "teacher-note", "target": "08-07#teacher-notes", "description": "Signed area B,−B cancellation" }, { "id": "08-07-diagram-5", "type": "diagram", "target": "08-07#source-diagrams-in-native-form", "description": "full periodic graph −4a to7a" }, { "id": "08-07-diagram-6", "type": "diagram", "target": "08-07#source-diagrams-in-native-form", "description": "small signed-area cancellation graph" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-10-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 10; title / [Solution] / Answers heading where present" }, { "id": "08-08-question-1", "type": "question", "target": "08-08#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-08-working-2", "type": "working", "target": "08-08#printed-working", "description": "(i),(ii)" }, { "id": "08-08-teacher-note-3", "type": "teacher-note", "target": "08-08#teacher-notes", "description": "Area blue region minus red triangle" }, { "id": "08-08-diagram-4", "type": "diagram", "target": "08-08#source-diagrams-in-native-form", "description": "question parametric arch and line" }, { "id": "08-08-diagram-5", "type": "diagram", "target": "08-08#source-diagrams-in-native-form", "description": "blue-minus-red area guide" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-11-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 11; title / [Solution] / Answers heading where present" }, { "id": "08-09-question-1", "type": "question", "target": "08-09#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-08-working-2", "type": "working", "target": "08-08#printed-working", "description": "(iii),(iv)" }, { "id": "08-09-working-3", "type": "working", "target": "08-09#printed-working", "description": "parameter points and trapezium-minus-area" }, { "id": "08-08-teacher-note-4", "type": "teacher-note", "target": "08-08#teacher-notes", "description": "Triangle becomes cone radiusπ/2−1,height1" }, { "id": "08-09-teacher-note-5", "type": "teacher-note", "target": "08-09#teacher-notes", "description": "Red trapezium area ½h(d1+d2)" }, { "id": "08-08-diagram-6", "type": "diagram", "target": "08-08#source-diagrams-in-native-form", "description": "cone and left inverse-branch guide" }, { "id": "08-09-diagram-7", "type": "diagram", "target": "08-09#source-diagrams-in-native-form", "description": "question C,l,P,Q" }, { "id": "08-09-diagram-8", "type": "diagram", "target": "08-09#source-diagrams-in-native-form", "description": "trapezium d1,d2,h guide" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 12, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-12-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 12; title / [Solution] / Answers heading where present" }, { "id": "08-10-question-1", "type": "question", "target": "08-10#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-10-working-2", "type": "working", "target": "08-10#printed-working", "description": "parameter limits and area setup" }, { "id": "08-10-teacher-note-3", "type": "teacher-note", "target": "08-10#teacher-notes", "description": "Cartesian area first, then parameter; change x to t limits" }, { "id": "08-10-diagram-4", "type": "diagram", "target": "08-10#source-diagrams-in-native-form", "description": "shaded S between verticals" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 13, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-13-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 13; title / [Solution] / Answers heading where present" }, { "id": "08-10-working-1", "type": "working", "target": "08-10#printed-working", "description": "trigonometric substitution calculation" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 14, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-14-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 14; title / [Solution] / Answers heading where present" }, { "id": "08-11-question-1", "type": "question", "target": "08-11#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-11-working-2", "type": "working", "target": "08-11#printed-working", "description": "(a),(b)" }, { "id": "08-11-teacher-note-3", "type": "teacher-note", "target": "08-11#teacher-notes", "description": "Red cylinder and blue even-solid subtraction dimensions" }, { "id": "08-11-diagram-4", "type": "diagram", "target": "08-11#source-diagrams-in-native-form", "description": "negative sine area" }, { "id": "08-11-diagram-5", "type": "diagram", "target": "08-11#source-diagrams-in-native-form", "description": "even region R" }, { "id": "08-11-diagram-6", "type": "diagram", "target": "08-11#source-diagrams-in-native-form", "description": "red cylinder dimensions" }, { "id": "08-11-diagram-7", "type": "diagram", "target": "08-11#source-diagrams-in-native-form", "description": "blue removed solid" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 15, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-15-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 15; title / [Solution] / Answers heading where present" }, { "id": "08-12-question-1", "type": "question", "target": "08-12#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-12-working-2", "type": "working", "target": "08-12#printed-working", "description": "(a)" }, { "id": "08-12-teacher-note-3", "type": "teacher-note", "target": "08-12#teacher-notes", "description": "MF26 cosP−cosQ identity and m=3/2,n=1/2 replacement" }, { "id": "08-12-diagram-4", "type": "diagram", "target": "08-12#source-diagrams-in-native-form", "description": "question exponential/parabola intersection" }, { "id": "08-12-diagram-5", "type": "diagram", "target": "08-12#source-diagrams-in-native-form", "description": "question parametric C,L,S" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 16, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-16-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 16; title / [Solution] / Answers heading where present" }, { "id": "08-12-working-1", "type": "working", "target": "08-12#printed-working", "description": "(b),(c)(i),(ii)" }, { "id": "08-12-teacher-note-2", "type": "teacher-note", "target": "08-12#teacher-notes", "description": "Integral of yC negative below x-axis on [−2√2,−2]" }, { "id": "08-12-diagram-3", "type": "diagram", "target": "08-12#source-diagrams-in-native-form", "description": "washer inverse branches" }, { "id": "08-12-diagram-4", "type": "diagram", "target": "08-12#source-diagrams-in-native-form", "description": "negative area with −2√2,−5/2,−2" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 17, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-17-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 17; title / [Solution] / Answers heading where present" }, { "id": "08-13-question-1", "type": "question", "target": "08-13#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-13-diagram-2", "type": "diagram", "target": "08-13#source-diagrams-in-native-form", "description": "logistic area R" }, { "id": "08-13-diagram-3", "type": "diagram", "target": "08-13#source-diagrams-in-native-form", "description": "logarithmic bowl A,B" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 18, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-18-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 18; title / [Solution] / Answers heading where present" }, { "id": "08-13-working-1", "type": "working", "target": "08-13#printed-working", "description": "(a)(i)–(iii),(b)" }, { "id": "08-13-teacher-note-2", "type": "teacher-note", "target": "08-13#teacher-notes", "description": "Log derivative modulus and positivity" }, { "id": "08-13-teacher-note-3", "type": "teacher-note", "target": "08-13#teacher-notes", "description": "Scaling replaces y by y/2" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 19, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-19-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 19; title / [Solution] / Answers heading where present" }, { "id": "08-14-question-1", "type": "question", "target": "08-14#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-14-working-2", "type": "working", "target": "08-14#printed-working", "description": "geometric sum and area inequality" }, { "id": "08-14-teacher-note-3", "type": "teacher-note", "target": "08-14#teacher-notes", "description": "Rectangles lie below the increasing graph" }, { "id": "08-14-diagram-4", "type": "diagram", "target": "08-14#source-diagrams-in-native-form", "description": "lower rectangles and all symbolic ticks" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 20, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-20-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 20; title / [Solution] / Answers heading where present" }, { "id": "08-15-question-1", "type": "question", "target": "08-15#printed-question", "description": "Repeated printed question block/subparts on solution page" }, { "id": "08-15-working-2", "type": "working", "target": "08-15#printed-working", "description": "(i) inverse differentiation" }, { "id": "08-15-diagram-3", "type": "diagram", "target": "08-15#source-diagrams-in-native-form", "description": "arctangent lower rectangle" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 21, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-21-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 21; title / [Solution] / Answers heading where present" }, { "id": "08-15-working-1", "type": "working", "target": "08-15#printed-working", "description": "(ii),(iii), direct-area and telescoping alternatives" }, { "id": "08-15-teacher-note-2", "type": "teacher-note", "target": "08-15#teacher-notes", "description": "Telescoping cancellation strokes and arctan0=0" } ], "unresolved": [] }, { "file": "08 App of integration sol.pdf", "page": 22, "visualChecked": true, "status": "audited-native", "items": [ { "id": "08-solution-22-metadata", "type": "header-footer", "target": "topic-08#source-metadata", "description": "Repeated 2025 TJC H2 Math (9758) JC2 MSM topic header; printed page 22; title / [Solution] / Answers heading where present" }, { "id": "08-15-working-1", "type": "working", "target": "08-15#printed-working", "description": "translation, inverse branch and volume" }, { "id": "08-15-teacher-note-2", "type": "teacher-note", "target": "08-15#teacher-notes", "description": "Minus inverse branch does not enclose R; choose plus branch" }, { "id": "08-15-diagram-3", "type": "diagram", "target": "08-15#source-diagrams-in-native-form", "description": "original R about x3" }, { "id": "08-15-diagram-4", "type": "diagram", "target": "08-15#source-diagrams-in-native-form", "description": "translated R about y-axis" }, { "id": "08-15-boundary-note", "type": "teacher-note", "target": "08-15#printed-working", "description": "Printed final volume description names x-axis as boundary; preserved and corrected to y-axis from diagram and integration limits" } ], "unresolved": [] } ], "questions": [ { "id": "08-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-14", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." }, { "id": "08-15", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Every relevant question and solution page visually read; all displayed working, formula sidebars, annotations and native geometry transcribed. Mathematical inconsistencies preserved as printed and separately reviewed; equation syntax and numerical validation recorded in topic evidence." } ], "unresolved": [] }, { "topic": "09", "pages": [ { "file": "09 series expansion.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-1", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 1." }, { "id": "09-01-question-1", "type": "question", "target": "09-01#printed-question", "description": "Q1: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-01-working-1", "type": "working", "target": "09-01#printed-working", "description": "Q1 printed working continuation on page 1; equation chains and any printed alternative methods retained." }, { "id": "09-01-note-1-p1", "type": "teacher-note", "target": "09-01#teacher-note-1", "description": "Need to factorise out $4$ to make the constant term 1. Use the law of indices $(AB)^n=A^nB^n$. Then use the binomial theorem" }, { "id": "09-01-note-2-p1", "type": "teacher-note", "target": "09-01#teacher-note-2", "description": "The binomial expansion of $(1+f(x))^n$, where $n$ is a negative integer or fraction, is valid for the range of $x$ given by $|f(x)|<1$." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-2", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 2." }, { "id": "09-02-question-2", "type": "question", "target": "09-02#printed-question", "description": "Q2: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-02-working-2", "type": "working", "target": "09-02#printed-working", "description": "Q2 printed working continuation on page 2; equation chains and any printed alternative methods retained." }, { "id": "09-02-note-1-p2", "type": "teacher-note", "target": "09-02#teacher-note-1", "description": "Since both expansions of $(1-x)^{1/3}$ and $(1+2x)^{-1/3}$ must be valid at the same time, we take the intersection of the 2 regions." }, { "id": "09-02-validity-p2", "type": "diagram", "target": "09-02#diagram-09-02-validity", "description": "Intersection of the two validity intervals; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-3", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 3." }, { "id": "09-03-question-3", "type": "question", "target": "09-03#printed-question", "description": "Q3: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-03-working-3", "type": "working", "target": "09-03#printed-working", "description": "Q3 printed working continuation on page 3; equation chains and any printed alternative methods retained." }, { "id": "09-03-note-1-p3", "type": "teacher-note", "target": "09-03#teacher-note-1", "description": "For expansion of $(1-x)^{-1}$, coefficient of $x^{2008}$ is $-2(1)=-2$. For $(1+x^2)^{-1}=1+(-1)x^2+(-1)^2(x^2)^2+(-1)^3(x^2)^3+\\cdots$, coefficient of $x^{2008}$ is $3(-1)^{1004}=3$." }, { "id": "09-04-question-3", "type": "question", "target": "09-04#printed-question", "description": "Q4: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-04-working-3", "type": "working", "target": "09-04#printed-working", "description": "Q4 printed working continuation on page 3; equation chains and any printed alternative methods retained." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-4", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 4." }, { "id": "09-04-working-4", "type": "working", "target": "09-04#printed-working", "description": "Q4 printed working continuation on page 4; equation chains and any printed alternative methods retained." }, { "id": "09-05-question-4", "type": "question", "target": "09-05#printed-question", "description": "Q5: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-05-working-4", "type": "working", "target": "09-05#printed-working", "description": "Q5 printed working continuation on page 4; equation chains and any printed alternative methods retained." }, { "id": "09-05-note-1-p4", "type": "teacher-note", "target": "09-05#teacher-note-1", "description": "Need to factorise out $2$ to make the constant term 1. Use the law of indices $(AB)^n=A^nB^n$. Then use the binomial theorem" }, { "id": "09-05-note-2-p4", "type": "teacher-note", "target": "09-05#teacher-note-2", "description": "In the coefficient of $x^r$, $(-b-0)(-b-1)\\cdots(-b-(r-1))/r!$: there are $r$ factors in the numerator for $r!$ in the denominator." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-5", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 5." }, { "id": "09-06-question-5", "type": "question", "target": "09-06#printed-question", "description": "Q6: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-06-working-5", "type": "working", "target": "09-06#printed-working", "description": "Q6 printed working continuation on page 5; equation chains and any printed alternative methods retained." }, { "id": "09-06-note-1-p5", "type": "teacher-note", "target": "09-06#teacher-note-1", "description": "Need to factorise out $3$ to make the constant term 1. Use the law of indices $(AB)^n=A^nB^n$. Then use the binomial theorem" }, { "id": "09-06-note-2-p5", "type": "teacher-note", "target": "09-06#teacher-note-2", "description": "At $x=0$, $y=2/\\sqrt3$ and $y'=2/(3\\sqrt3)$. Thus tangent at $x=0$ is $y-2/\\sqrt3=(2/(3\\sqrt3))(x-0)$. The constant and term in $x$ are the first two terms in the expansion of $y$." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-6", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 6." }, { "id": "09-07-question-6", "type": "question", "target": "09-07#printed-question", "description": "Q7: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-07-working-6", "type": "working", "target": "09-07#printed-working", "description": "Q7 printed working continuation on page 6; equation chains and any printed alternative methods retained." }, { "id": "09-07-note-1-p6", "type": "teacher-note", "target": "09-07#teacher-note-1", "description": "Both $(1-2x)^{-2}$ and $(1+x/2)^{-1}$ must be valid at the same time: take the intersection of the 2 regions." }, { "id": "09-07-note-2-p6", "type": "teacher-note", "target": "09-07#teacher-note-2", "description": "$(1-x)^{-2}=1+2x+3x^2+\\cdots$; $(1+x)^{-1}=1+(-1)x+(-1)^2x^2+\\cdots$." }, { "id": "09-07-validity-p6", "type": "diagram", "target": "09-07#diagram-09-07-validity", "description": "Simultaneous validity of the expansions; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-7", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 7." }, { "id": "09-08-question-7", "type": "question", "target": "09-08#printed-question", "description": "Q8: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-08-working-7", "type": "working", "target": "09-08#printed-working", "description": "Q8 printed working continuation on page 7; equation chains and any printed alternative methods retained." }, { "id": "09-08-note-1-p7", "type": "teacher-note", "target": "09-08#teacher-note-1", "description": "For $e^{2x}$, use MF27: $e^x=1+x+x^2/2!+x^3/3!+\\cdots$, where $x$ is replaced by $2x$. Do **not** expand as $\\ln(1+e^{2x})=\\ln[1+1+2x+(2x)^2/2!+\\cdots]=(1+2x+\\cdots)-(1+2x+\\cdots)^2/2+\\cdots$, as each bracketed term contains a constant and terms in $x,x^2,x^3,\\ldots$." }, { "id": "09-08-error-p7", "type": "diagram", "target": "09-08#diagram-09-08-error", "description": "Error in the quadratic logarithm approximation; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-8", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 8." }, { "id": "09-09-question-8", "type": "question", "target": "09-09#printed-question", "description": "Q9: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-09-working-8", "type": "working", "target": "09-09#printed-working", "description": "Q9 printed working continuation on page 8; equation chains and any printed alternative methods retained." }, { "id": "09-09-note-1-p8", "type": "teacher-note", "target": "09-09#teacher-note-1", "description": "Square the equation so that the resulting equation (1) is easier to handle for repeated differentiation using implicit differentiation and product rule." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-9", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 9." }, { "id": "09-09-working-9", "type": "working", "target": "09-09#printed-working", "description": "Q9 printed working continuation on page 9; equation chains and any printed alternative methods retained." }, { "id": "09-09-note-2-p9", "type": "teacher-note", "target": "09-09#teacher-note-2", "description": "Use implicit differentiation and product rule:" }, { "id": "09-09-note-3-p9", "type": "teacher-note", "target": "09-09#teacher-note-3", "description": "From MF27, $\\cos x=1-x^2/2!+x^4/4!-\\cdots$. For $e^{x/2}$ replace $x$ by $x/2$ in $e^x=1+x+x^2/2!+\\cdots$." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-10", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 10." }, { "id": "09-10-question-10", "type": "question", "target": "09-10#printed-question", "description": "Q10: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-10-working-10", "type": "working", "target": "09-10#printed-working", "description": "Q10 printed working continuation on page 10; equation chains and any printed alternative methods retained." }, { "id": "09-10-note-1-p10", "type": "teacher-note", "target": "09-10#teacher-note-1", "description": "From MF27 replace $x$ by $3x$ in $\\sin x=x-x^3/3!+\\cdots$ to obtain the expansion for $\\sin3x$. For $e^{\\sin3x}$, replace $x$ by $\\sin3x=3x-9x^3/2+\\cdots$ in $e^x=1+x+x^2/2!+x^3/3!+\\cdots$." } ], "unresolved": [] }, { "file": "09 series expansion.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "09-metadata-09 series expansion.pdf-11", "type": "header-footer", "target": "topic-09#source-metadata", "description": "Running topic header; printed page 11." }, { "id": "09-10-working-11", "type": "working", "target": "09-10#printed-working", "description": "Q10 printed working continuation on page 11; equation chains and any printed alternative methods retained." }, { "id": "09-11-question-11", "type": "question", "target": "09-11#printed-question", "description": "Q11: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "09-11-working-11", "type": "working", "target": "09-11#printed-working", "description": "Q11 printed working continuation on page 11; equation chains and any printed alternative methods retained." }, { "id": "09-11-note-1-p11", "type": "teacher-note", "target": "09-11#teacher-note-1", "description": "Need to factorise out $k$ to make the constant term 1. Apply rule of logarithms $\\ln(ab)=\\ln a+\\ln b$. From MF27, use $\\ln(1+x)=x-x^2/2+x^3/3-\\cdots$, where $-132$ (temperature of kitchen), hence $\\theta-32>0$ and constant of proportionality is negative." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-10", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 10." }, { "id": "10-08-working-10", "type": "working", "target": "10-08#printed-working", "description": "Q8 printed working continuation on page 10; equation chains and any printed alternative methods retained." }, { "id": "10-08-note-2-p10", "type": "teacher-note", "target": "10-08#teacher-note-2", "description": "Given $d\\theta/dt=f(\\theta)$, integrate $\\int d\\theta/f(\\theta)=\\int1dt$." }, { "id": "10-08-note-3-p10", "type": "teacher-note", "target": "10-08#teacher-note-3", "description": "Note $t\\ge0$; do not sketch a curve for $t<0$. As $t\\to\\infty$, $(37/42)^{t/15}\\to0$, thus $\\theta\\to32$. Horizontal asymptote $\\theta=32$." }, { "id": "10-08-note-4-p10", "type": "teacher-note", "target": "10-08#teacher-note-4", "description": "Since pie is cooling and removed from the oven at 1 pm at 200 °C, it first reaches 60 °C in the danger zone. Pie is removed at 1 pm." }, { "id": "10-08-cooling-p10", "type": "diagram", "target": "10-08#diagram-10-08-cooling", "description": "Cooling pie; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-11", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 11." }, { "id": "10-09-question-11", "type": "question", "target": "10-09#printed-question", "description": "Q9: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "10-09-working-11", "type": "working", "target": "10-09#printed-working", "description": "Q9 printed working continuation on page 11; equation chains and any printed alternative methods retained." }, { "id": "10-09-note-1-p11", "type": "teacher-note", "target": "10-09#teacher-note-1", "description": "Given $dG/dt=f(G)$." }, { "id": "10-09-note-2-p11", "type": "teacher-note", "target": "10-09#teacher-note-2", "description": "Neo’s glucose level falls below the healthy range when $G\\le70$ (source wording; the reviewed strict crossing is distinguished below)." }, { "id": "10-09-note-3-p11", "type": "teacher-note", "target": "10-09#teacher-note-3", "description": "Given $dG/dt=f(G)$, integrate $\\int dG/f(G)=\\int1dt$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 12, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-12", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 12." }, { "id": "10-09-working-12", "type": "working", "target": "10-09#printed-working", "description": "Q9 printed working continuation on page 12; equation chains and any printed alternative methods retained." }, { "id": "10-09-note-4-p12", "type": "teacher-note", "target": "10-09#teacher-note-4", "description": "As $t\\to\\infty$, $G\\to200\\mu$. $70<200\\mu<100$ would put the long-term equilibrium in the interior of the healthy range." }, { "id": "10-10-question-12", "type": "question", "target": "10-10#printed-question", "description": "Q10: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "10-10-rod-p12", "type": "diagram", "target": "10-10#diagram-10-10-rod", "description": "Slipping rod XY; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 13, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-13", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 13." }, { "id": "10-10-working-13", "type": "working", "target": "10-10#printed-working", "description": "Q10 printed working continuation on page 13; equation chains and any printed alternative methods retained." }, { "id": "10-10-note-1-p13", "type": "teacher-note", "target": "10-10#teacher-note-1", "description": "Since $y$ decreases as $t$ increases, $dy/dt<0$. Since $y>0$, the constant of proportionality is negative for $dy/dt<0$." }, { "id": "10-10-note-2-p13", "type": "teacher-note", "target": "10-10#teacher-note-2", "description": "Given a DE of form $dx/dt=f(x)$, rearrange before integrating with respect to $t$: $\\frac1{f(x)}\\frac{dx}{dt}=1$, hence $\\int\\frac1{f(x)}dx=\\int1dt$." }, { "id": "10-10-note-3-p13", "type": "teacher-note", "target": "10-10#teacher-note-3", "description": "Note $t\\ge0$; do not sketch any curve for $t<0$." }, { "id": "10-10-solution-p13", "type": "diagram", "target": "10-10#diagram-10-10-solution", "description": "Position of the lower rod end; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 14, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-14", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 14." }, { "id": "10-11-question-14", "type": "question", "target": "10-11#printed-question", "description": "Q11: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "10-11-working-14", "type": "working", "target": "10-11#printed-working", "description": "Q11 printed working continuation on page 14; equation chains and any printed alternative methods retained." }, { "id": "10-11-note-1-p14", "type": "teacher-note", "target": "10-11#teacher-note-1", "description": "Note number of flying foxes $N$ is in **thousands**." }, { "id": "10-11-note-2-p14", "type": "teacher-note", "target": "10-11#teacher-note-2", "description": "Given $dN/dt=f(N)$. Integrate $\\int dN/f(N)=\\int1dt$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 15, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-15", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 15." }, { "id": "10-11-working-15", "type": "working", "target": "10-11#printed-working", "description": "Q11 printed working continuation on page 15; equation chains and any printed alternative methods retained." }, { "id": "10-11-population-p15", "type": "diagram", "target": "10-11#diagram-10-11-population", "description": "Flying fox population; faithful native D3 vector redraw, labels and mathematical parameters retained." }, { "id": "10-12-question-15", "type": "question", "target": "10-12#printed-question", "description": "Q12: complete printed question wording, equations, subparts, marks and attribution." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 16, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-16", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 16." }, { "id": "10-12-working-16", "type": "working", "target": "10-12#printed-working", "description": "Q12 printed working continuation on page 16; equation chains and any printed alternative methods retained." }, { "id": "10-12-note-1-p16", "type": "teacher-note", "target": "10-12#teacher-note-1", "description": "$dx/dt=\\text{rate of increase}-\\text{rate of decrease}$. Population remains constant when $x=p$, so $dx/dt=0$ when $x=p$." }, { "id": "10-12-note-2-p16", "type": "teacher-note", "target": "10-12#teacher-note-2", "description": "Given $dx/dt=kf(x)$, $k$ constant, rearrange: $(1/f(x))dx/dt=k$, $\\int dx/f(x)=\\int kdt$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 17, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-17", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 17." }, { "id": "10-12-working-17", "type": "working", "target": "10-12#printed-working", "description": "Q12 printed working continuation on page 17; equation chains and any printed alternative methods retained." }, { "id": "10-12-note-3-p17", "type": "teacher-note", "target": "10-12#teacher-note-3", "description": "Population decreases over time: as $t$ increases, $x$ decreases. Since $x=(5-p)e^{3t/p}+p$ and $e^{3t/p}>0$ increases with $t\\ge0$, $5-p<0$. Time cannot be negative, so $t\\ge0$; no sketch for $t<0$." }, { "id": "10-12-extinction-p17", "type": "diagram", "target": "10-12#diagram-10-12-extinction", "description": "Tree population before depletion; faithful native D3 vector redraw, labels and mathematical parameters retained." }, { "id": "10-13-question-17", "type": "question", "target": "10-13#printed-question", "description": "Q13: complete printed question wording, equations, subparts, marks and attribution." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 18, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-18", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 18." }, { "id": "10-13-working-18", "type": "working", "target": "10-13#printed-working", "description": "Q13 printed working continuation on page 18; equation chains and any printed alternative methods retained." }, { "id": "10-13-note-1-p18", "type": "teacher-note", "target": "10-13#teacher-note-1", "description": "$dQ/dt$ is the rate of change of pollutants in the tank at time $t$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 19, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-19", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 19." }, { "id": "10-13-working-19", "type": "working", "target": "10-13#printed-working", "description": "Q13 printed working continuation on page 19; equation chains and any printed alternative methods retained." }, { "id": "10-13-note-2-p19", "type": "teacher-note", "target": "10-13#teacher-note-2", "description": "Given a DE of form $dx/dt=f(x)$, rearrange before integrating with respect to $t$: $\\frac1{f(x)}\\frac{dx}{dt}=1$, hence $\\int\\frac1{f(x)}dx=\\int1dt$. Used result: $\\int f'(x)/f(x)dx=\\ln|f(x)|+c$." }, { "id": "10-13-note-3-p19", "type": "teacher-note", "target": "10-13#teacher-note-3", "description": "Fish pollute water in the tank at a constant rate of 5 units per day." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 20, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-20", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 20." }, { "id": "10-14-question-20", "type": "question", "target": "10-14#printed-question", "description": "Q14: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "10-14-working-20", "type": "working", "target": "10-14#printed-working", "description": "Q14 printed working continuation on page 20; equation chains and any printed alternative methods retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 21, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-21", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 21." }, { "id": "10-14-working-21", "type": "working", "target": "10-14#printed-working", "description": "Q14 printed working continuation on page 21; equation chains and any printed alternative methods retained." }, { "id": "10-14-note-1-p21", "type": "teacher-note", "target": "10-14#teacher-note-1", "description": "Method 1: partial fractions. $1/[x(15-x)]=A/x+B/(15-x)$. Thus $1=A(15-x)+Bx$. Let $x=0$: $A=1/15$; let $x=15$: $B=1/15$. Therefore $1/[x(15-x)]=(1/15)[1/x+1/(15-x)]$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 22, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-22", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 22." }, { "id": "10-14-working-22", "type": "working", "target": "10-14#printed-working", "description": "Q14 printed working continuation on page 22; equation chains and any printed alternative methods retained." }, { "id": "10-15-question-22", "type": "question", "target": "10-15#printed-question", "description": "Q15: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "10-15-working-22", "type": "working", "target": "10-15#printed-working", "description": "Q15 printed working continuation on page 22; equation chains and any printed alternative methods retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 23, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-23", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 23." }, { "id": "10-15-working-23", "type": "working", "target": "10-15#printed-working", "description": "Q15 printed working continuation on page 23; equation chains and any printed alternative methods retained." }, { "id": "10-15-note-1-p23", "type": "teacher-note", "target": "10-15#teacher-note-1", "description": "Using partial fractions: $1/[x(100-x)]=A/x+B/(100-x)$; $1=A(100-x)+Bx$. Let $x=0$, $A=1/100$; let $x=100$, $B=1/100$. Thus $1/[x(100-x)]=(1/100)[1/x+1/(100-x)]$. **Printed sidebar typo:** its last fraction’s left side uses $x(15-x)$; context requires $x(100-x)$." }, { "id": "10-16-question-23", "type": "question", "target": "10-16#printed-question", "description": "Q16: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "10-16-working-23", "type": "working", "target": "10-16#printed-working", "description": "Q16 printed working continuation on page 23; equation chains and any printed alternative methods retained." }, { "id": "10-16-note-1-p23", "type": "teacher-note", "target": "10-16#teacher-note-1", "description": "$dM/dt$ is the overall net change in the number of mudskippers $M$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 24, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-24", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 24." }, { "id": "10-16-working-24", "type": "working", "target": "10-16#printed-working", "description": "Q16 printed working continuation on page 24; equation chains and any printed alternative methods retained." }, { "id": "10-16-note-2-p24", "type": "teacher-note", "target": "10-16#teacher-note-2", "description": "Given $dM/dt=f(M)$, $(1/f(M))dM/dt=1$. Integrate $\\int dM/f(M)=\\int1dt$." }, { "id": "10-16-note-3-p24", "type": "teacher-note", "target": "10-16#teacher-note-3", "description": "Complete the square: $(C-800)^2\\ge0$, so $-0.005(C-800)^2\\le0$ and $dC/dt\\le3200$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 25, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-25", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 25." }, { "id": "10-16-working-25", "type": "working", "target": "10-16#printed-working", "description": "Q16 printed working continuation on page 25; equation chains and any printed alternative methods retained." }, { "id": "10-16-note-4-p25", "type": "teacher-note", "target": "10-16#teacher-note-4", "description": "Since coefficient of $C^2$ is negative, this quadratic curve has a maximum. For a quadratic, max/min occurs at the midpoint of the $x$-intercepts." }, { "id": "10-16-note-5-p25", "type": "teacher-note", "target": "10-16#teacher-note-5", "description": "$1/[C(1600-C)]=A/C+B/(1600-C)$; $1=A(1600-C)+BC$. At $C=0$, $A=1/1600$; at $C=1600$, $B=1/1600$. Cover-up rule gives the same values." }, { "id": "10-16-growth-p25", "type": "diagram", "target": "10-16#diagram-10-16-growth", "description": "Crab growth-rate maximum; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 26, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-26", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 26." }, { "id": "10-16-working-26", "type": "working", "target": "10-16#printed-working", "description": "Q16 printed working continuation on page 26; equation chains and any printed alternative methods retained." }, { "id": "10-16-note-6-p26", "type": "teacher-note", "target": "10-16#teacher-note-6", "description": "As $t\\to\\infty$, $e^{-8t}\\to0$, so $C\\to1600$." }, { "id": "10-16-population-p26", "type": "diagram", "target": "10-16#diagram-10-16-population", "description": "Crab population; faithful native D3 vector redraw, labels and mathematical parameters retained." }, { "id": "10-17-question-26", "type": "question", "target": "10-17#printed-question", "description": "Q17: complete printed question wording, equations, subparts, marks and attribution." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 27, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-27", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 27." }, { "id": "10-17-working-27", "type": "working", "target": "10-17#printed-working", "description": "Q17 printed working continuation on page 27; equation chains and any printed alternative methods retained." }, { "id": "10-17-note-1-p27", "type": "teacher-note", "target": "10-17#teacher-note-1", "description": "$dV/dt=dV_{\\rm in}/dt-dV_{\\rm out}/dt$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 28, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-28", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 28." }, { "id": "10-17-working-28", "type": "working", "target": "10-17#printed-working", "description": "Q17 printed working continuation on page 28; equation chains and any printed alternative methods retained." }, { "id": "10-17-note-2-p28", "type": "teacher-note", "target": "10-17#teacher-note-2", "description": "Given $dh/dt=f(h)$, integrate $\\int dh/f(h)=\\int1dt$. Used result: $\\int f'(x)/(f(x)^2-a^2)dx=\\frac1{2a}\\ln|(f(x)-a)/(f(x)+a)|+c$." }, { "id": "10-17-note-3-p28", "type": "teacher-note", "target": "10-17#teacher-note-3", "description": "As $t\\to\\infty$, $e^{-11t/20}\\to0$, so $h\\to10$. Horizontal asymptote $h=10$." }, { "id": "10-17-height-p28", "type": "diagram", "target": "10-17#diagram-10-17-height", "description": "Formal tank height; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 29, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-29", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 29." }, { "id": "10-18-question-29", "type": "question", "target": "10-18#printed-question", "description": "Q18: complete printed question wording, equations, subparts, marks and attribution." }, { "id": "10-18-working-29", "type": "working", "target": "10-18#printed-working", "description": "Q18 printed working continuation on page 29; equation chains and any printed alternative methods retained." }, { "id": "10-18-note-1-p29", "type": "teacher-note", "target": "10-18#teacher-note-1", "description": "Given $dI/dt=f(I)$, $t=\\int dI/f(I)$. Let $1/[kI(N-I)]=(1/k)[A/I+B/(N-I)]$; $1=A(N-I)+BI$. At $I=0$, $A=1/N$; at $I=N$, $B=1/N$. Hence $1/[kI(N-I)]=(1/(kN))[1/I+1/(N-I)]$." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 30, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-30", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 30." }, { "id": "10-18-working-30", "type": "working", "target": "10-18#printed-working", "description": "Q18 printed working continuation on page 30; equation chains and any printed alternative methods retained." }, { "id": "10-18-note-2-p30", "type": "teacher-note", "target": "10-18#teacher-note-2", "description": "Complete the square for $kI(N-I)=-k(I^2-NI)$, where $k,N$ are constants." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 31, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-31", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 31." }, { "id": "10-18-working-31", "type": "working", "target": "10-18#printed-working", "description": "Q18 printed working continuation on page 31; equation chains and any printed alternative methods retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 32, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-32", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 32." }, { "id": "10-18-working-32", "type": "working", "target": "10-18#printed-working", "description": "Q18 printed working continuation on page 32; equation chains and any printed alternative methods retained." }, { "id": "10-18-note-3-p32", "type": "teacher-note", "target": "10-18#teacher-note-3", "description": "For Diagram 1, sketch $y=1/[99(33^{-t/12})+1]$ and $y=0.5$. On GC go to `2nd [calc] → 5:intersect` to find intersection between the 2 curves." }, { "id": "10-18-GC-intersection-p32", "type": "diagram", "target": "10-18#diagram-10-18-gc-intersection", "description": "GC Diagram 1: intersection with 0.5; faithful native D3 vector redraw, labels and mathematical parameters retained." }, { "id": "10-18-GC-zero-p32", "type": "diagram", "target": "10-18#diagram-10-18-gc-zero", "description": "GC Diagram 2: zero of shifted fraction; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] }, { "file": "10 DE sol.pdf", "page": 33, "visualChecked": true, "status": "audited-native", "items": [ { "id": "10-metadata-10 DE sol.pdf-33", "type": "header-footer", "target": "topic-10#source-metadata", "description": "Running topic header; printed page 33." }, { "id": "10-18-working-33", "type": "working", "target": "10-18#printed-working", "description": "Q18 printed working continuation on page 33; equation chains and any printed alternative methods retained." }, { "id": "10-18-population-p33", "type": "diagram", "target": "10-18#diagram-10-18-population", "description": "Flu infection population; faithful native D3 vector redraw, labels and mathematical parameters retained." } ], "unresolved": [] } ], "questions": [ { "id": "10-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-14", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-15", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-16", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-17", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." }, { "id": "10-18", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "All printed content read from rendered page; source equations and marks manually transcribed. Prior independent algebra/numerics preserved in evidence/review-10.md. Native expanded equation chains and sidebar rules rechecked in this pass; printed issues explicitly preserved/qualified." } ], "unresolved": [] }, { "topic": "11", "pages": [ { "file": "11 vectors sol.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-1-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 1." }, { "id": "11-01-question-sol-p1", "type": "question", "target": "11-01#question", "description": "Repeated full question in the solution document" }, { "id": "11-01-work-p1", "type": "working", "target": "11-01#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 1" }, { "id": "11-01-diagram-p1", "type": "diagram", "target": "11-01#native-diagrams", "description": "collinear A–B–C and ratio/perpendicular triangle" }, { "id": "11-01-note-p1", "type": "teacher-note", "target": "11-01#teacher-notes", "description": "collinearity alternatives, segment-produced terminology, dot-product angle" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-2-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 2." }, { "id": "11-01-work-p2", "type": "working", "target": "11-01#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 2" }, { "id": "11-01-diagram-p2", "type": "diagram", "target": "11-01#native-diagrams", "description": "height triangle, parallelogram, kite" }, { "id": "11-01-note-p2", "type": "teacher-note", "target": "11-01#teacher-notes", "description": "consecutive parallelogram labels and all kite properties" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-3-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 3." }, { "id": "11-02-question-sol-p3", "type": "question", "target": "11-02#question", "description": "Repeated full question in the solution document" }, { "id": "11-02-work-p3", "type": "working", "target": "11-02#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 3" }, { "id": "11-02-diagram-p3", "type": "diagram", "target": "11-02#native-diagrams", "description": "external-section ratio and intersection F" }, { "id": "11-02-note-p3", "type": "teacher-note", "target": "11-02#teacher-notes", "description": "R outside PQ; two OF expressions and intersection alternative" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-4-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 4." }, { "id": "11-03-question-sol-p4", "type": "question", "target": "11-03#question", "description": "Repeated full question in the solution document" }, { "id": "11-03-work-p4", "type": "working", "target": "11-03#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 4" }, { "id": "11-03-diagram-p4", "type": "diagram", "target": "11-03#native-diagrams", "description": "perpendicular foot and line direction" }, { "id": "11-03-note-p4", "type": "teacher-note", "target": "11-03#teacher-notes", "description": "position/direction line vectors; third-equation check; perpendicular-foot conditions" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-5-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 5." }, { "id": "11-04-question-sol-p5", "type": "question", "target": "11-04#question", "description": "Repeated full question in the solution document" }, { "id": "11-04-work-p5", "type": "working", "target": "11-04#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 5" }, { "id": "11-04-diagram-p5", "type": "diagram", "target": "11-04#native-diagrams", "description": "projection length and perpendicular foot" }, { "id": "11-04-note-p5", "type": "teacher-note", "target": "11-04#teacher-notes", "description": "projection derivation, foot C, same direction when positive dot product" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-6-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 6." }, { "id": "11-05-question-sol-p6", "type": "question", "target": "11-05#question", "description": "Repeated full question in the solution document" }, { "id": "11-04-work-p6", "type": "working", "target": "11-04#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 6" }, { "id": "11-05-work-p6", "type": "working", "target": "11-05#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 6" }, { "id": "11-04-diagram-p6", "type": "diagram", "target": "11-04#native-diagrams", "description": "reflected line diagram" }, { "id": "11-04-note-p6", "type": "teacher-note", "target": "11-04#teacher-notes", "description": "midpoint/ratiotheorem reflected B′" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-7-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 7." }, { "id": "11-06-question-sol-p7", "type": "question", "target": "11-06#question", "description": "Repeated full question in the solution document" }, { "id": "11-05-work-p7", "type": "working", "target": "11-05#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 7" }, { "id": "11-06-work-p7", "type": "working", "target": "11-06#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 7" }, { "id": "11-05-diagram-p7", "type": "diagram", "target": "11-05#native-diagrams", "description": "rhombus with triangle altitude" }, { "id": "11-06-diagram-p7", "type": "diagram", "target": "11-06#native-diagrams", "description": "perpendicular distance, equal-area and margin parallelograms" }, { "id": "11-05-note-p7", "type": "teacher-note", "target": "11-05#teacher-notes", "description": "cross-product rhombus area derivation" }, { "id": "11-06-note-p7", "type": "teacher-note", "target": "11-06#teacher-notes", "description": "perpendicular distance, area-height identity, cross-product angle reasoning" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-8-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 8." }, { "id": "11-07-question-sol-p8", "type": "question", "target": "11-07#question", "description": "Repeated full question in the solution document" }, { "id": "11-07-work-p8", "type": "working", "target": "11-07#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 8" }, { "id": "11-07-diagram-p8", "type": "diagram", "target": "11-07#native-diagrams", "description": "shortest-distance triangle" }, { "id": "11-07-note-p8", "type": "teacher-note", "target": "11-07#teacher-notes", "description": "line equation and perpendicular-distance derivation" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-9-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 9." }, { "id": "11-08-question-sol-p9", "type": "question", "target": "11-08#question", "description": "Repeated full question in the solution document" }, { "id": "11-08-work-p9", "type": "working", "target": "11-08#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 9" }, { "id": "11-08-diagram-p9", "type": "diagram", "target": "11-08#native-diagrams", "description": "ratio and projection triangle" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-10-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 10." }, { "id": "11-08-work-p10", "type": "working", "target": "11-08#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 10" }, { "id": "11-08-diagram-p10", "type": "diagram", "target": "11-08#native-diagrams", "description": "cosine graph" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-11-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 11." }, { "id": "11-09-question-sol-p11", "type": "question", "target": "11-09#question", "description": "Repeated full question in the solution document" }, { "id": "11-09-work-p11", "type": "working", "target": "11-09#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 11" }, { "id": "11-09-diagram-p11", "type": "diagram", "target": "11-09#native-diagrams", "description": "parallelogram with 120-degree angle" }, { "id": "11-09-note-p11", "type": "teacher-note", "target": "11-09#teacher-notes", "description": "dot product cos∠AOB; swapped cross-product magnitudes" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 12, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-12-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 12." }, { "id": "11-10-question-sol-p12", "type": "question", "target": "11-10#question", "description": "Repeated full question in the solution document" }, { "id": "11-10-work-p12", "type": "working", "target": "11-10#source-working", "description": "All intermediate calculations, alternatives and printed conclusions on page 12" }, { "id": "11-10-note-p12", "type": "teacher-note", "target": "11-10#teacher-notes", "description": "define angle, show dot symbol, GC instructions, cross normals and simple point" } ], "unresolved": [] }, { "file": "11 vectors sol.pdf", "page": 13, "visualChecked": true, "status": "audited-native", "items": [ { "id": "11-solution-13-metadata", "type": "header-footer", "target": "topic-11#document-metadata", "description": "Printed running header where present, section title where present, original footer 13." }, { "id": 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Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Source question pages1–3,key11 and all solution pages1–16 visually inspected. Expanded every printed calculation and alternative. Native specific geometries, perpendicular/equality marks and notes retain source labels. KaTeX and geometry assertions checked; integrated render QA is root-owned." }, { "id": "11-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-14", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-15", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-16", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-17", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-18", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-19", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-20", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-21", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-22", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." }, { "id": "11-23", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Original question pages4–12 and all solution pages17–44 visually inspected. Printed intermediate triples/dot/cross products, all alternative methods and teacher notes transcribed; SVG render compared with source labels, relationships and dimensions; correction separately marked." } ], "unresolved": [] }, { "topic": "12", "pages": [ { "file": "12 APGP.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q01-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 89; bold topic heading on first page." }, { "id": "12-q01-01-question", "type": "question", "target": "12-01#printed-question", "description": "Q1 printed question / subparts / marks / attribution" }, { "id": "12-q01-02-question", "type": "question", "target": "12-02#printed-question", "description": "Q2 printed question / subparts / marks / attribution" }, { "id": "12-q01-03-question", "type": "question", "target": "12-03#printed-question", "description": "Q3 printed question / subparts / marks / attribution" }, { "id": "12-q01-04-question", "type": "question", "target": "12-04#printed-question", "description": "Q4 printed question / subparts / marks / attribution" }, { "id": "12-q01-05-question", "type": "question", "target": "12-05#printed-question", "description": "Q5 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "12 APGP.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q02-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 90; bold topic heading on first page." }, { "id": "12-q02-06-question", "type": "question", "target": "12-06#printed-question", "description": "Q6 printed question / subparts / marks / attribution" }, { "id": "12-q02-07-question", "type": "question", "target": "12-07#printed-question", "description": "Q7 printed question / subparts / marks / attribution" }, { "id": "12-q02-08-question", "type": "question", "target": "12-08#printed-question", "description": "Q8 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "12 APGP.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q03-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 91; bold topic heading on first page." }, { "id": "12-q03-09-question", "type": "question", "target": "12-09#printed-question", "description": "Q9 printed question / subparts / marks / attribution" }, { "id": "12-q03-10-question", "type": "question", "target": "12-10#printed-question", "description": "Q10 printed question / subparts / marks / attribution" }, { "id": "12-q03-11-question", "type": "question", "target": "12-11#printed-question", "description": "Q11 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "12 APGP.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q04-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 92; bold topic heading on first page." }, { "id": "12-q04-12-question", "type": "question", "target": "12-12#printed-question", "description": "Q12 printed question / subparts / marks / attribution" }, { "id": "12-q04-13-question", "type": "question", "target": "12-13#printed-question", "description": "Q13 printed question / subparts / marks / attribution" }, { "id": "12-q04-14-question", "type": "question", "target": "12-14#printed-question", "description": "Q14 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "12 APGP.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q05-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 93; bold topic heading on first page." }, { "id": "12-q05-15-question", "type": "question", "target": "12-15#printed-question", "description": "Q15 printed question / subparts / marks / attribution" }, { "id": "12-q05-16-question", "type": "question", "target": "12-16#printed-question", "description": "Q16 printed question / subparts / marks / attribution" }, { "id": "12-q05-17-question", "type": "question", "target": "12-17#printed-question", "description": "Q17 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "12 APGP.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q06-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 94; bold topic heading on first page." }, { "id": "12-q06-17-question", "type": "question", "target": "12-17#printed-question", "description": "Q17 printed question / subparts / marks / attribution" }, { "id": "12-q06-18-question", "type": "question", "target": "12-18#printed-question", "description": "Q18 printed question / subparts / marks / attribution" }, { "id": "12-q06-19-question", "type": "question", "target": "12-19#printed-question", "description": "Q19 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "12 APGP.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q07-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 95; bold topic heading on first page." }, { "id": "12-q07-20-question", "type": "question", "target": "12-20#printed-question", "description": "Q20 printed question / subparts / marks / attribution" }, { "id": "12-q07-diagram-20", "type": "diagram", "target": "12-20#source-diagrams-redrawn", "description": "Q20 original question diagram; repeated graph mapped to same native source geometry" } ], "unresolved": [] }, { "file": "12 APGP.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-q08-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 96; bold topic heading on first page." }, { "id": "12-q08-01-answer-key", "type": "answer-key", "target": "12-01#printed-answer-key", "description": "Q1 short-answer entry" }, { "id": "12-q08-02-answer-key", "type": "answer-key", "target": "12-02#printed-answer-key", "description": "Q2 short-answer entry" }, { "id": "12-q08-03-answer-key", "type": "answer-key", "target": "12-03#printed-answer-key", "description": "Q3 short-answer entry" }, { "id": "12-q08-04-answer-key", "type": "answer-key", "target": "12-04#printed-answer-key", "description": "Q4 short-answer entry" }, { "id": "12-q08-05-answer-key", "type": "answer-key", "target": "12-05#printed-answer-key", "description": "Q5 short-answer entry" }, { "id": "12-q08-06-answer-key", "type": "answer-key", "target": "12-06#printed-answer-key", "description": "Q6 short-answer entry" }, { "id": "12-q08-07-answer-key", "type": "answer-key", "target": "12-07#printed-answer-key", "description": "Q7 short-answer entry" }, { "id": "12-q08-08-answer-key", "type": "answer-key", "target": "12-08#printed-answer-key", "description": "Q8 short-answer entry" }, { "id": "12-q08-09-answer-key", "type": "answer-key", "target": "12-09#printed-answer-key", "description": "Q9 short-answer entry" }, { "id": "12-q08-10-answer-key", "type": "answer-key", "target": "12-10#printed-answer-key", "description": "Q10 short-answer entry" }, { "id": "12-q08-11-answer-key", "type": "answer-key", "target": "12-11#printed-answer-key", "description": "Q11 short-answer entry" }, { "id": "12-q08-12-answer-key", "type": "answer-key", "target": "12-12#printed-answer-key", "description": "Q12 short-answer entry" }, { "id": "12-q08-13-answer-key", "type": "answer-key", "target": "12-13#printed-answer-key", "description": "Q13 short-answer entry" }, { "id": "12-q08-14-answer-key", "type": "answer-key", "target": "12-14#printed-answer-key", "description": "Q14 short-answer entry" }, { "id": "12-q08-15-answer-key", "type": "answer-key", "target": "12-15#printed-answer-key", "description": "Q15 short-answer entry" }, { "id": "12-q08-16-answer-key", "type": "answer-key", "target": "12-16#printed-answer-key", "description": "Q16 short-answer entry" }, { "id": "12-q08-17-answer-key", "type": "answer-key", "target": "12-17#printed-answer-key", "description": "Q17 short-answer entry" }, { "id": "12-q08-18-answer-key", "type": "answer-key", "target": "12-18#printed-answer-key", "description": "Q18 short-answer entry" }, { "id": "12-q08-19-answer-key", "type": "answer-key", "target": "12-19#printed-answer-key", "description": "Q19 short-answer entry" }, { "id": "12-q08-20-answer-key", "type": "answer-key", "target": "12-20#printed-answer-key", "description": "Q20 short-answer entry" } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s01-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 1; bold topic heading on first page." }, { "id": "12-s01-teacher-note-1", "type": "teacher-note", "target": "12-01#teacher-notes", "description": "Q1 teacher-note content: GP: the sum to infinity exists when $|r|<1$, i.e. $-10$. Change the inequality sign when dividing/multiplying both sides by a negative value; $\\ln(\\frac34)<0$.\n\nSince $a,r$ are posit" }, { "id": "12-s01-q01-statement", "type": "question", "target": "12-01#printed-question", "description": "Repeated source Q1 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s01-q02-statement", "type": "question", "target": "12-02#printed-question", "description": "Repeated source Q2 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s01-q01-working-1", "type": "working", "target": "12-01#printed-working", "description": "Q1: ratio inequalities; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s01-q01-working-2", "type": "working", "target": "12-01#printed-working", "description": "Q1: sum-to-infinity substitution; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s01-q02-working-1", "type": "working", "target": "12-02#printed-working", "description": "Q2: absolute-error derivation; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s01-q02-working-2", "type": "working", "target": "12-02#printed-working", "description": "Q2: logarithmic threshold; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s02-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 2; bold topic heading on first page." }, { "id": "12-s02-teacher-note-1", "type": "teacher-note", "target": "12-02#teacher-notes", "description": "Q2 teacher-note content: $|ab|=|a||b|$; $|-b|=b$ for $b>0$. Change the inequality sign when dividing/multiplying both sides by a negative value; $\\ln(\\frac34)<0$.\n\nSince $a,r$ are posit" }, { "id": "12-s02-teacher-note-2", "type": "teacher-note", "target": "12-03#teacher-notes", "description": "Q3 teacher-note content: GP terms: $a,a+7d,a+12d$; common ratio $\\frac{a+7d}a=\\frac{a+12d}{a+7d}$." }, { "id": "12-s02-q03-statement", "type": "question", "target": "12-03#printed-question", "description": "Repeated source Q3 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s02-q02-working-1", "type": "working", "target": "12-02#printed-working", "description": "Q2: alternative positive-tail derivation; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s02-q03-working-1", "type": "working", "target": "12-03#printed-working", "description": "Q3: (a) ratio equations; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s02-q03-working-2", "type": "working", "target": "12-03#printed-working", "description": "Q3: (b) convergence and sum; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s03-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 3; bold topic heading on first page." }, { "id": "12-s03-q03-working-1", "type": "working", "target": "12-03#printed-working", "description": "Q3: (c) a-variable quadratic; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s03-q03-working-2", "type": "working", "target": "12-03#printed-working", "description": "Q3: (c) d-variable alternative; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s03-q03-working-3", "type": "working", "target": "12-03#printed-working", "description": "Q3: (d) 98% tail inequality; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s04-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 4; bold topic heading on first page." }, { "id": "12-s04-teacher-note-1", "type": "teacher-note", "target": "12-04#teacher-notes", "description": "Q4 teacher-note content: $S_n=u_1+\\cdots+u_n$, $S_{n-1}=u_1+\\cdots+u_{n-1}$, so $u_n=S_n-S_{n-1}$. Replace $n$ by $n-1$ to obtain an expression for $u_n$.\n\nTo show AP, prove $u_n-u_{n-1" }, { "id": "12-s04-table-1", "type": "table", "target": "12-03#source-tables-and-calculator-displays", "description": "Q3 table content: Alternative GC table:\n\n| $k$ | $1-(5/7)^k$ |\n|---:|---:|\n|11|0.97531 (<0.98)|\n|12|0.98236 (>0.98)|\n\nLeast $k=12$." }, { "id": "12-s04-q04-statement", "type": "question", "target": "12-04#printed-question", "description": "Repeated source Q4 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s04-q03-working-1", "type": "working", "target": "12-03#printed-working", "description": "Q3: (d) alternative GC table; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s04-q04-working-1", "type": "working", "target": "12-04#printed-working", "description": "Q4: (a)(i) consecutive sums; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s04-q04-working-2", "type": "working", "target": "12-04#printed-working", "description": "Q4: (a)(ii) general differences; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s04-q04-working-3", "type": "working", "target": "12-04#printed-working", "description": "Q4: (a)(iii) odd-term sequence; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s05-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 5; bold topic heading on first page." }, { "id": "12-s05-teacher-note-1", "type": "teacher-note", "target": "12-04#teacher-notes", "description": "Q4 teacher-note content: $S_n=u_1+\\cdots+u_n$, $S_{n-1}=u_1+\\cdots+u_{n-1}$, so $u_n=S_n-S_{n-1}$. Replace $n$ by $n-1$ to obtain an expression for $u_n$.\n\nTo show AP, prove $u_n-u_{n-1" }, { "id": "12-s05-table-1", "type": "table", "target": "12-04#source-tables-and-calculator-displays", "description": "Q4 table content: | $n$ | Odd-term sum |\n|---:|---:|\n|6|469.68 <500|\n|7|651.4 >500|" }, { "id": "12-s05-diagram-1", "type": "diagram", "target": "12-04#source-diagrams-redrawn", "description": "Q4 diagram content: ![12-04](/diagrams/native-12-04-odd-sum.svg)" }, { "id": "12-s05-q04-working-1", "type": "working", "target": "12-04#printed-working", "description": "Q4: (a)(iii) numerical table; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s05-q04-working-2", "type": "working", "target": "12-04#printed-working", "description": "Q4: (a)(iii) graphical alternative; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s05-q04-working-3", "type": "working", "target": "12-04#printed-working", "description": "Q4: (b)(i) convergence; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s06-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 6; bold topic heading on first page." }, { "id": "12-s06-teacher-note-1", "type": "teacher-note", "target": "12-04#teacher-notes", "description": "Q4 teacher-note content: $S_n=u_1+\\cdots+u_n$, $S_{n-1}=u_1+\\cdots+u_{n-1}$, so $u_n=S_n-S_{n-1}$. Replace $n$ by $n-1$ to obtain an expression for $u_n$.\n\nTo show AP, prove $u_n-u_{n-1" }, { "id": "12-s06-q05-statement", "type": "question", "target": "12-05#printed-question", "description": "Repeated source Q5 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s06-q04-working-1", "type": "working", "target": "12-04#printed-working", "description": "Q4: (b)(ii) method 1 tail difference; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s06-q04-working-2", "type": "working", "target": "12-04#printed-working", "description": "Q4: (b)(ii) method 2 eighth-term tail; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s07-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 7; bold topic heading on first page." }, { "id": "12-s07-teacher-note-1", "type": "teacher-note", "target": "12-05#teacher-notes", "description": "Q5 teacher-note content: For GP G, $G_n=ar^{n-1}$. AP terms $A_1,A_2,A_3$ are $G_5,G_{10},G_{20}=ar^4,ar^9,ar^{19}$. Equal differences: $A_2-A_1=A_3-A_2$.\n\nAP odd-indexed terms $A_1,A_3" }, { "id": "12-s07-q05-working-1", "type": "working", "target": "12-05#printed-working", "description": "Q5: (i) r^5 reduction and roots; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s07-q05-working-2", "type": "working", "target": "12-05#printed-working", "description": "Q5: (ii) infinite sum; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s07-q05-working-3", "type": "working", "target": "12-05#printed-working", "description": "Q5: (iii) odd-index AP sum; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s08-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 8; bold topic heading on first page." }, { "id": "12-s08-teacher-note-1", "type": "teacher-note", "target": "12-06#teacher-notes", "description": "Q6 teacher-note content: The full GP sum is $T_1+\\cdots+T_n+T_{n+1}+\\cdots$; the first bracket is $S_n$, the remaining bracket is the remaining-tail sum.\n\nEven-indexed GP terms $u_2,u_4" }, { "id": "12-s08-q06-statement", "type": "question", "target": "12-06#printed-question", "description": "Repeated source Q6 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s08-q06-working-1", "type": "working", "target": "12-06#printed-working", "description": "Q6: (a) half-tail derivation; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s08-q06-working-2", "type": "working", "target": "12-06#printed-working", "description": "Q6: (b) even-index GP sum; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s09-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 9; bold topic heading on first page." }, { "id": "12-s09-teacher-note-1", "type": "teacher-note", "target": "12-06#teacher-notes", "description": "Q6 teacher-note content: The full GP sum is $T_1+\\cdots+T_n+T_{n+1}+\\cdots$; the first bracket is $S_n$, the remaining bracket is the remaining-tail sum.\n\nEven-indexed GP terms $u_2,u_4" }, { "id": "12-s09-q07-statement", "type": "question", "target": "12-07#printed-question", "description": "Repeated source Q7 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s09-q06-working-1", "type": "working", "target": "12-06#printed-working", "description": "Q6: (b) logarithmic AP proof; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s09-q07-working-1", "type": "working", "target": "12-07#printed-working", "description": "Q7: (i) elimination and real roots; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s10-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 10; bold topic heading on first page." }, { "id": "12-s10-teacher-note-1", "type": "teacher-note", "target": "12-08#teacher-notes", "description": "Q8 teacher-note content: G converges when $|r|<1$.\n\nEven-indexed terms $T_2,T_4,T_6,\\ldots=-e^{1+\\alpha},-e^{1+3\\alpha},-e^{1+5\\alpha},\\ldots$ form a GP with first term $-e^{1+\\alpha}$ " }, { "id": "12-s10-diagram-1", "type": "diagram", "target": "12-08#source-diagrams-redrawn", "description": "Q8 diagram content: ![12-08-exp](/diagrams/native-12-08-exponential.svg)\n\n![12-08-quad](/diagrams/native-12-08-quadratic.svg)\n\n![12-08-product](/diagrams/native-12-08-product.svg)" }, { "id": "12-s10-q08-statement", "type": "question", "target": "12-08#printed-question", "description": "Repeated source Q8 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s10-q07-working-1", "type": "working", "target": "12-07#printed-working", "description": "Q7: (ii) tail bound; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s10-q07-working-2", "type": "working", "target": "12-07#printed-working", "description": "Q7: (ii) alternative tail formula; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s10-q08-working-1", "type": "working", "target": "12-08#printed-working", "description": "Q8: (i) convergence; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s10-q08-working-2", "type": "working", "target": "12-08#printed-working", "description": "Q8: (ii) even-term negative sum; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s11-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 11; bold topic heading on first page." }, { "id": "12-s11-teacher-note-1", "type": "teacher-note", "target": "12-08#teacher-notes", "description": "Q8 teacher-note content: G converges when $|r|<1$.\n\nEven-indexed terms $T_2,T_4,T_6,\\ldots=-e^{1+\\alpha},-e^{1+3\\alpha},-e^{1+5\\alpha},\\ldots$ form a GP with first term $-e^{1+\\alpha}$ " }, { "id": "12-s11-diagram-1", "type": "diagram", "target": "12-08#source-diagrams-redrawn", "description": "Q8 diagram content: ![12-08-exp](/diagrams/native-12-08-exponential.svg)\n\n![12-08-quad](/diagrams/native-12-08-quadratic.svg)\n\n![12-08-product](/diagrams/native-12-08-product.svg)" }, { "id": "12-s11-q08-working-1", "type": "working", "target": "12-08#printed-working", "description": "Q8: (iii) exponential product; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s11-q08-working-2", "type": "working", "target": "12-08#printed-working", "description": "Q8: (iii) quadratic interval; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s11-q08-working-3", "type": "working", "target": "12-08#printed-working", "description": "Q8: (iii) alternative graph; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s11-product-diagram", "type": "diagram", "target": "12-08#source-diagrams-redrawn", "description": "Second alternative product-exponential plot with y=15000 and labelled intersections 11.39,56.275 (separate from first quadratic sign chart)." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 12, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s12-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 12; bold topic heading on first page." }, { "id": "12-s12-teacher-note-1", "type": "teacher-note", "target": "12-09#teacher-notes", "description": "Q9 teacher-note content: $S_n=T_1+\\cdots+T_n$, $S_{n-1}=T_1+\\cdots+T_{n-1}$, so $T_n=S_n-S_{n-1}$.\n\nFor a GP, prove $T_n/T_{n-1}$ or $T_{n+1}/T_n$ constant using **general terms**; the " }, { "id": "12-s12-q09-statement", "type": "question", "target": "12-09#printed-question", "description": "Repeated source Q9 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s12-q09-working-1", "type": "working", "target": "12-09#printed-working", "description": "Q9: successive sums and GP ratio; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 13, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s13-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 13; bold topic heading on first page." }, { "id": "12-s13-teacher-note-1", "type": "teacher-note", "target": "12-09#teacher-notes", "description": "Q9 teacher-note content: $S_n=T_1+\\cdots+T_n$, $S_{n-1}=T_1+\\cdots+T_{n-1}$, so $T_n=S_n-S_{n-1}$.\n\nFor a GP, prove $T_n/T_{n-1}$ or $T_{n+1}/T_n$ constant using **general terms**; the " }, { "id": "12-s13-q09-working-1", "type": "working", "target": "12-09#printed-working", "description": "Q9: (i) bracket term count; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s13-q09-working-2", "type": "working", "target": "12-09#printed-working", "description": "Q9: (ii) middle index; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s13-q09-working-3", "type": "working", "target": "12-09#printed-working", "description": "Q9: (iii) convergence range; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s13-q09-working-4", "type": "working", "target": "12-09#printed-working", "description": "Q9: (iii) infinite sum and alternative; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s13-q09-working-5", "type": "working", "target": "12-09#printed-working", "description": "Q9: (iii) n² relative error; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 14, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s14-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 14; bold topic heading on first page." }, { "id": "12-s14-teacher-note-1", "type": "teacher-note", "target": "12-10#teacher-notes", "description": "Q10 teacher-note content: GP formulas $S_n=a(1-r^n)/(1-r)$, $S_{\\infty}=a/(1-r)$, here $a=p,r=q/p$.\n\nAP sum $\\frac n2(a+l)$, where $a$ is first, $l$ is last; for counting preceding rows " }, { "id": "12-s14-q10-statement", "type": "question", "target": "12-10#printed-question", "description": "Repeated source Q10 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s14-q10-working-1", "type": "working", "target": "12-10#printed-working", "description": "Q10: (a) tail equality proof; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s14-q10-working-2", "type": "working", "target": "12-10#printed-working", "description": "Q10: (b)(i) first-term count; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s14-q10-working-3", "type": "working", "target": "12-10#printed-working", "description": "Q10: (b)(i) alternative successive-row differences; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 15, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s15-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 15; bold topic heading on first page." }, { "id": "12-s15-teacher-note-1", "type": "teacher-note", "target": "12-11#teacher-notes", "description": "Q11 teacher-note content: AP $S_n=\\frac n2[2a+(n-1)d]$, here $a=4,d=0.5$, or $\\frac n2(a+u_n)$ with $u_n=4+(n-1)0.5$.\n\nGC roots: **apps → 9:PlySmlt2 → 1:Polynomial Root Finder → Order 2 " }, { "id": "12-s15-table-1", "type": "table", "target": "12-11#source-tables-and-calculator-displays", "description": "Q11 table content: | Pump A | Amount ($\\mathrm m^3$) |\n|---|---|\n|1st|4|\n|2nd|$4+0.5$|\n|3rd|$4+2(0.5)$|\n|…|…|\n|$n$th|$4+(n-1)(0.5)$|\n\n| Pump B | Amount ($\\mathrm m^3$) |\n|---|---|" }, { "id": "12-s15-diagram-1", "type": "diagram", "target": "12-11#source-diagrams-redrawn", "description": "Q11 diagram content: ![12-11](/diagrams/native-12-11-capacity.svg)" }, { "id": "12-s15-q11-statement", "type": "question", "target": "12-11#printed-question", "description": "Repeated source Q11 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s15-q10-working-1", "type": "working", "target": "12-10#printed-working", "description": "Q10: (b)(ii) row sum; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s15-q11-working-1", "type": "working", "target": "12-11#printed-working", "description": "Q11: (i) pump-A AP and capacity inequality; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 16, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s16-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 16; bold topic heading on first page." }, { "id": "12-s16-teacher-note-1", "type": "teacher-note", "target": "12-11#teacher-notes", "description": "Q11 teacher-note content: AP $S_n=\\frac n2[2a+(n-1)d]$, here $a=4,d=0.5$, or $\\frac n2(a+u_n)$ with $u_n=4+(n-1)0.5$.\n\nGC roots: **apps → 9:PlySmlt2 → 1:Polynomial Root Finder → Order 2 " }, { "id": "12-s16-table-1", "type": "table", "target": "12-11#source-tables-and-calculator-displays", "description": "Q11 table content: | Pump A | Amount ($\\mathrm m^3$) |\n|---|---|\n|1st|4|\n|2nd|$4+0.5$|\n|3rd|$4+2(0.5)$|\n|…|…|\n|$n$th|$4+(n-1)(0.5)$|\n\n| Pump B | Amount ($\\mathrm m^3$) |\n|---|---|" }, { "id": "12-s16-q11-working-1", "type": "working", "target": "12-11#printed-working", "description": "Q11: (i) 52nd-pump overflow; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s16-q11-working-2", "type": "working", "target": "12-11#printed-working", "description": "Q11: (ii)(a) pump-B finite sum; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s16-q11-working-3", "type": "working", "target": "12-11#printed-working", "description": "Q11: (ii)(b) theoretical capacity; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 17, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s17-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 17; bold topic heading on first page." }, { "id": "12-s17-teacher-note-1", "type": "teacher-note", "target": "12-12#teacher-notes", "description": "Q12 teacher-note content: Amy: AP, first term 160, common difference −8; $u_n=a+(n-1)d$ is the $n$th length and must be positive.\n\nBala: GP, first term 160, ratio $p$, infinite sum $a/(1" }, { "id": "12-s17-q12-statement", "type": "question", "target": "12-12#printed-question", "description": "Repeated source Q12 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s17-q12-working-1", "type": "working", "target": "12-12#printed-working", "description": "Q12: (a) positive-piece bound; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s17-q12-working-2", "type": "working", "target": "12-12#printed-working", "description": "Q12: (b) limiting total; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s17-q12-working-3", "type": "working", "target": "12-12#printed-working", "description": "Q12: (b) 9.5m inequality; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s17-q12-working-4", "type": "working", "target": "12-12#printed-working", "description": "Q12: (c) total roll length; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 18, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s18-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 18; bold topic heading on first page." }, { "id": "12-s18-q13-statement", "type": "question", "target": "12-13#printed-question", "description": "Repeated source Q13 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s18-q13-working-1", "type": "working", "target": "12-13#printed-working", "description": "Q13: (i) sprinter AP; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s18-q13-working-2", "type": "working", "target": "12-13#printed-working", "description": "Q13: (ii) marathon GP; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s18-q13-working-3", "type": "working", "target": "12-13#printed-working", "description": "Q13: (iii) logarithmic threshold; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 19, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s19-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 19; bold topic heading on first page." }, { "id": "12-s19-table-1", "type": "table", "target": "12-13#source-tables-and-calculator-displays", "description": "Q13 table content: | $n$ | Marathon total seconds |\n|---:|---:|\n|24|2345 <2400|\n|25|2498.8 >2400|\n|26|2658.7 >2400|\n\n| $n$ | $1500(1.04^n-1)$ | $3n^2+53n$ |\n|---:|---:|---:|\n|3|18" }, { "id": "12-s19-diagram-1", "type": "diagram", "target": "12-13#source-diagrams-redrawn", "description": "Q13 diagram content: ![12-13](/diagrams/native-12-13-race.svg)" }, { "id": "12-s19-q13-working-1", "type": "working", "target": "12-13#printed-working", "description": "Q13: (iii) alternative table; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s19-q13-working-2", "type": "working", "target": "12-13#printed-working", "description": "Q13: (iv) race winner; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s19-q13-working-3", "type": "working", "target": "12-13#printed-working", "description": "Q13: (v) table comparison; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s19-q13-working-4", "type": "working", "target": "12-13#printed-working", "description": "Q13: (v) graphical intersection; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s19-table-13-2", "type": "table", "target": "12-13#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 2 for Q13; all rows/displayed truncated digits retained in native table section." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 20, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s20-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 20; bold topic heading on first page." }, { "id": "12-s20-teacher-note-1", "type": "teacher-note", "target": "12-14#teacher-notes", "description": "Q14 teacher-note content: AP sum $S_n=\\frac n2(u_1+u_n)$ with $n=671,u_1=3,u_n=3(671)$.\n\nRequired integer sum = sum of all integers in $\\{1,2,\\ldots,2014\\}$ − sum of its multiples of 3.\n" }, { "id": "12-s20-diagram-1", "type": "diagram", "target": "12-14#source-diagrams-redrawn", "description": "Q14 diagram content: ![12-14](/diagrams/native-12-14-bounces.svg)" }, { "id": "12-s20-q14-statement", "type": "question", "target": "12-14#printed-question", "description": "Repeated source Q14 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s20-q14-working-1", "type": "working", "target": "12-14#printed-working", "description": "Q14: (a) multiples count and sum; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s20-q14-working-2", "type": "working", "target": "12-14#printed-working", "description": "Q14: (b)(i) rebound height; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 21, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s21-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 21; bold topic heading on first page." }, { "id": "12-s21-teacher-note-1", "type": "teacher-note", "target": "12-14#teacher-notes", "description": "Q14 teacher-note content: AP sum $S_n=\\frac n2(u_1+u_n)$ with $n=671,u_1=3,u_n=3(671)$.\n\nRequired integer sum = sum of all integers in $\\{1,2,\\ldots,2014\\}$ − sum of its multiples of 3.\n" }, { "id": "12-s21-q15-statement", "type": "question", "target": "12-15#printed-question", "description": "Repeated source Q15 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s21-q14-working-1", "type": "working", "target": "12-14#printed-working", "description": "Q14: (b)(ii) bounce inequality; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s21-q14-working-2", "type": "working", "target": "12-14#printed-working", "description": "Q14: (b)(iii) total distance; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 22, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s22-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 22; bold topic heading on first page." }, { "id": "12-s22-q15-working-1", "type": "working", "target": "12-15#printed-working", "description": "Q15: (i) weeks; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s22-q15-working-2", "type": "working", "target": "12-15#printed-working", "description": "Q15: (ii) weekly earnings and GP; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s22-q15-working-3", "type": "working", "target": "12-15#printed-working", "description": "Q15: (iii) weekly costs and AP; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s22-q15-working-4", "type": "working", "target": "12-15#printed-working", "description": "Q15: (iv) profit inequality; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 23, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s23-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 23; bold topic heading on first page." }, { "id": "12-s23-teacher-note-1", "type": "teacher-note", "target": "12-15#teacher-notes", "description": "Q15 teacher-note content: GC: enter expression in **Y=**; **2nd window → TblStart:1, ΔTbl:1 → 2nd graph**. Scroll down to the rows where values change from negative to positive." }, { "id": "12-s23-table-1", "type": "table", "target": "12-15#source-tables-and-calculator-displays", "description": "Q15 table content: | $k$ | Profit expression |\n|---:|---:|\n|21|−139.6 <0|\n|22|62.669 >0|\n|23|249.31 >0|" }, { "id": "12-s23-q16-statement", "type": "question", "target": "12-16#printed-question", "description": "Repeated source Q16 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s23-q15-working-1", "type": "working", "target": "12-15#printed-working", "description": "Q15: (iv) table and divisor restriction; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s23-q16-working-1", "type": "working", "target": "12-16#printed-working", "description": "Q16: (a)(i) eliminate a; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 24, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s24-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 24; bold topic heading on first page." }, { "id": "12-s24-teacher-note-1", "type": "teacher-note", "target": "12-16#teacher-notes", "description": "Q16 teacher-note content: Eliminate $a$ first. Then eliminate $b,d$ simultaneously by dividing (4) by (5); the final equation contains $r$ only.\n\nOdd-indexed GP terms $T_1,T_3,T_5,\\ldots" }, { "id": "12-s24-table-1", "type": "table", "target": "12-16#source-tables-and-calculator-displays", "description": "Q16 table content: | $n$ | $Y$ |\n|---:|---:|\n|53|59.171 <60|\n|54|60.084 >60|\n|55|60.987 >60|" }, { "id": "12-s24-diagram-1", "type": "diagram", "target": "12-16#source-diagrams-redrawn", "description": "Q16 diagram content: ![12-16-gap](/diagrams/native-12-16-gap.svg)\n\n![12-16](/diagrams/native-12-16-chase.svg)" }, { "id": "12-s24-q16-working-1", "type": "working", "target": "12-16#printed-working", "description": "Q16: (a)(i) eliminate b,d; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s24-q16-working-2", "type": "working", "target": "12-16#printed-working", "description": "Q16: (a)(ii) odd GP sum; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s24-q16-working-3", "type": "working", "target": "12-16#printed-working", "description": "Q16: (b)(i) catch-up totals and table; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s24-q16-working-4", "type": "working", "target": "12-16#printed-working", "description": "Q16: (b)(ii) stop count and maximum; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 25, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s25-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 25; bold topic heading on first page." }, { "id": "12-s25-table-1", "type": "table", "target": "12-17#source-tables-and-calculator-displays", "description": "Q17 table content: Plan A:\n\n| End of | Amount invested | Bonus in account |\n|---|---:|---|\n|Jan 2021|$k$|5|\n|Feb 2021|$2k$|$5+2(5)$|\n|…|…|…|\n|Dec 2022|$24k$|$5+2(5)+\\cdots+24(5)$|" }, { "id": "12-s25-q17-statement", "type": "question", "target": "12-17#printed-question", "description": "Repeated source Q17 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s25-q17-working-1", "type": "working", "target": "12-17#printed-working", "description": "Q17: (a) bonus AP; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s25-q17-working-2", "type": "working", "target": "12-17#printed-working", "description": "Q17: (b)(i) interest; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s25-q17-working-3", "type": "working", "target": "12-17#printed-working", "description": "Q17: (b)(ii) 24-month GP; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s25-table-17-2", "type": "table", "target": "12-17#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 2 for Q17; all rows/displayed truncated digits retained in native table section." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 26, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s26-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 26; bold topic heading on first page." }, { "id": "12-s26-table-1", "type": "table", "target": "12-18#source-tables-and-calculator-displays", "description": "Q18 table content: | Month | Amount at beginning | Amount at end |\n|---|---|---|\n|1|$200000(1.005)$|$200000(1.005)-x$|\n|2|$200000(1.005)^2-(1.005)x$|$200000(1.005)^2-(1.005)x-x$|\n" }, { "id": "12-s26-q18-statement", "type": "question", "target": "12-18#printed-question", "description": "Repeated source Q18 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s26-q17-working-1", "type": "working", "target": "12-17#printed-working", "description": "Q17: (b)(iii) n-month sum and crossing day; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s26-q18-working-1", "type": "working", "target": "12-18#printed-working", "description": "Q18: (i) balance table and unrolling; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 27, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s27-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 27; bold topic heading on first page." }, { "id": "12-s27-table-1", "type": "table", "target": "12-18#source-tables-and-calculator-displays", "description": "Q18 table content: | Month | Amount at beginning | Amount at end |\n|---|---|---|\n|1|$200000(1.005)$|$200000(1.005)-x$|\n|2|$200000(1.005)^2-(1.005)x$|$200000(1.005)^2-(1.005)x-x$|\n" }, { "id": "12-s27-q18-working-1", "type": "working", "target": "12-18#printed-working", "description": "Q18: (ii) repayment inequality; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s27-q18-working-2", "type": "working", "target": "12-18#printed-working", "description": "Q18: (ii) alternative table; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s27-q18-working-3", "type": "working", "target": "12-18#printed-working", "description": "Q18: (ii) last debt/payment/date; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s27-q18-working-4", "type": "working", "target": "12-18#printed-working", "description": "Q18: (iii) cent-rounding condition; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 28, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s28-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 28; bold topic heading on first page." }, { "id": "12-s28-table-1", "type": "table", "target": "12-19#source-tables-and-calculator-displays", "description": "Q19 table content: | Term | Year | Operational cost ($) |\n|---|---|---|\n|1st|2011|120|\n|2nd|2012|$120+40$|\n|3rd|2013|$120+40(2)$|\n|…|…|…|\n|$n$th||$120+40(n-1)$|\n\n| Term | Year | F" }, { "id": "12-s28-q19-statement", "type": "question", "target": "12-19#printed-question", "description": "Repeated source Q19 statement, all premises, printed subparts/marks and attribution." }, { "id": "12-s28-q19-working-1", "type": "working", "target": "12-19#printed-working", "description": "Q19: (i) operating-cost table and AP; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 29, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s29-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 29; bold topic heading on first page." }, { "id": "12-s29-table-1", "type": "table", "target": "12-19#source-tables-and-calculator-displays", "description": "Q19 table content: | Term | Year | Operational cost ($) |\n|---|---|---|\n|1st|2011|120|\n|2nd|2012|$120+40$|\n|3rd|2013|$120+40(2)$|\n|…|…|…|\n|$n$th||$120+40(n-1)$|\n\n| Term | Year | F" }, { "id": "12-s29-q19-working-1", "type": "working", "target": "12-19#printed-working", "description": "Q19: (ii) fishing-income table and bounded sum; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s29-q19-working-2", "type": "working", "target": "12-19#printed-working", "description": "Q19: (iii) boat-sale table and total income; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s29-q19-working-3", "type": "working", "target": "12-19#printed-working", "description": "Q19: (iv) profit comparison table; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s29-table-19-2", "type": "table", "target": "12-19#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 2 for Q19; all rows/displayed truncated digits retained in native table section." }, { "id": "12-s29-table-19-3", "type": "table", "target": "12-19#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 3 for Q19; all rows/displayed truncated digits retained in native table section." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 30, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s30-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 30; bold topic heading on first page." }, { "id": "12-s30-diagram-1", "type": "diagram", "target": "12-20#source-diagrams-redrawn", "description": "Q20 diagram content: ![12-20](/diagrams/native-12-20-circuit.svg)\n\n![12-20-rate](/diagrams/native-12-20-growth.svg)" }, { "id": "12-s30-q20-statement", "type": "question", "target": "12-20#printed-question", "description": "Repeated source Q20 statement, all premises, printed subparts/marks and attribution." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 31, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s31-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 31; bold topic heading on first page." }, { "id": "12-s31-table-1", "type": "table", "target": "12-20#source-tables-and-calculator-displays", "description": "Q20 table content: | $n$ | $T_n$ |\n|---:|---:|\n|79|19900 <20000|\n|80|20150 >20000|\n|81|20400 >20000|\n\n| $n$ | Total stage distance expansion |\n|---|---|\n|1|$2(50)$|\n|2|$2(50)+2(15" }, { "id": "12-s31-q20-working-1", "type": "working", "target": "12-20#printed-working", "description": "Q20: (i) AP session/table; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s31-q20-working-2", "type": "working", "target": "12-20#printed-working", "description": "Q20: (i) algebraic alternative; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s31-q20-working-3", "type": "working", "target": "12-20#printed-working", "description": "Q20: (ii) stage table and GP; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s31-table-20-2", "type": "table", "target": "12-20#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 2 for Q20; all rows/displayed truncated digits retained in native table section." } ], "unresolved": [] }, { "file": "12 APGP sol.pdf", "page": 32, "visualChecked": true, "status": "audited-native", "items": [ { "id": "12-s32-header", "type": "header-footer", "target": "topic-12#source-metadata", "description": "Running topic header and printed page 32; bold topic heading on first page." }, { "id": "12-s32-table-1", "type": "table", "target": "12-20#source-tables-and-calculator-displays", "description": "Q20 table content: | $n$ | $T_n$ |\n|---:|---:|\n|79|19900 <20000|\n|80|20150 >20000|\n|81|20400 >20000|\n\n| $n$ | Total stage distance expansion |\n|---|---|\n|1|$2(50)$|\n|2|$2(50)+2(15" }, { "id": "12-s32-diagram-1", "type": "diagram", "target": "12-20#source-diagrams-redrawn", "description": "Q20 diagram content: ![12-20](/diagrams/native-12-20-circuit.svg)\n\n![12-20-rate](/diagrams/native-12-20-growth.svg)" }, { "id": "12-s32-q20-working-1", "type": "working", "target": "12-20#printed-working", "description": "Q20: (iii) stage table and remaining outward leg; displayed equalities/inequalities and conclusion retained." }, { "id": "12-s32-q20-working-2", "type": "working", "target": "12-20#printed-working", "description": "Q20: (iv) training-rate inequality and graph; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] } ], "questions": [ { "id": "12-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-14", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-15", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-16", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-17", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-18", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-19", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "12-20", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." } ], "unresolved": [], "counts": { "question": 41, "working": 90, "answer-key": 20, "teacher-note": 22, "table": 19, "diagram": 11, "header-footer": 40 } }, { "topic": "13", "pages": [ { "file": "13 Recurrence relations.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-q01-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 97; bold topic heading on first page." }, { "id": "13-q01-01-question", "type": "question", "target": "13-01#printed-question", "description": "Q1 printed question / subparts / marks / attribution" }, { "id": "13-q01-02-question", "type": "question", "target": "13-02#printed-question", "description": "Q2 printed question / subparts / marks / attribution" }, { "id": "13-q01-03-question", "type": "question", "target": "13-03#printed-question", "description": "Q3 printed question / subparts / marks / attribution" }, { "id": "13-q01-04-question", "type": "question", "target": "13-04#printed-question", "description": "Q4 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "13 Recurrence relations.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-q02-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 98; bold topic heading on first page." }, { "id": "13-q02-05-question", "type": "question", "target": "13-05#printed-question", "description": "Q5 printed question / subparts / marks / attribution" }, { "id": "13-q02-06-question", "type": "question", "target": "13-06#printed-question", "description": "Q6 printed question / subparts / marks / attribution" }, { "id": "13-q02-07-question", "type": "question", "target": "13-07#printed-question", "description": "Q7 printed question / subparts / marks / attribution" }, { "id": "13-q02-diagram-7", "type": "diagram", "target": "13-07#source-diagrams-redrawn", "description": "Q7 original question diagram; repeated graph mapped to same native source geometry" } ], "unresolved": [] }, { "file": "13 Recurrence relations.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-q03-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 99; bold topic heading on first page." }, { "id": "13-q03-08-question", "type": "question", "target": "13-08#printed-question", "description": "Q8 printed question / subparts / marks / attribution" }, { "id": "13-q03-09-question", "type": "question", "target": "13-09#printed-question", "description": "Q9 printed question / subparts / marks / attribution" }, { "id": "13-q03-10-question", "type": "question", "target": "13-10#printed-question", "description": "Q10 printed question / subparts / marks / attribution" }, { "id": "13-q03-11-question", "type": "question", "target": "13-11#printed-question", "description": "Q11 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "13 Recurrence relations.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-q04-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 100; bold topic heading on first page." }, { "id": "13-q04-12-question", "type": "question", "target": "13-12#printed-question", "description": "Q12 printed question / subparts / marks / attribution" }, { "id": "13-q04-13-question", "type": "question", "target": "13-13#printed-question", "description": "Q13 printed question / subparts / marks / attribution" }, { "id": "13-q04-diagram-12", "type": "diagram", "target": "13-12#source-diagrams-redrawn", "description": "Q12 original question diagram; repeated graph mapped to same native source geometry" }, { "id": "13-q04-diagram-13", "type": "diagram", "target": "13-13#source-diagrams-redrawn", "description": "Q13 original question diagram; repeated graph mapped to same native source geometry" } ], "unresolved": [] }, { "file": "13 Recurrence relations.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-q05-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 101; bold topic heading on first page." }, { "id": "13-q05-01-answer-key", "type": "answer-key", "target": "13-01#printed-answer-key", "description": "Q1 short-answer entry" }, { "id": "13-q05-02-answer-key", "type": "answer-key", "target": "13-02#printed-answer-key", "description": "Q2 short-answer entry" }, { "id": "13-q05-03-answer-key", "type": "answer-key", "target": "13-03#printed-answer-key", "description": "Q3 short-answer entry" }, { "id": "13-q05-04-answer-key", "type": "answer-key", "target": "13-04#printed-answer-key", "description": "Q4 short-answer entry" }, { "id": "13-q05-05-answer-key", "type": "answer-key", "target": "13-05#printed-answer-key", "description": "Q5 short-answer entry" }, { "id": "13-q05-06-answer-key", "type": "answer-key", "target": "13-06#printed-answer-key", "description": "Q6 short-answer entry" }, { "id": "13-q05-07-answer-key", "type": "answer-key", "target": "13-07#printed-answer-key", "description": "Q7 short-answer entry" }, { "id": "13-q05-08-answer-key", "type": "answer-key", "target": "13-08#printed-answer-key", "description": "Q8 short-answer entry" }, { "id": "13-q05-09-answer-key", "type": "answer-key", "target": "13-09#printed-answer-key", "description": "Q9 short-answer entry" }, { "id": "13-q05-10-answer-key", "type": "answer-key", "target": "13-10#printed-answer-key", "description": "Q10 short-answer entry" }, { "id": "13-q05-11-answer-key", "type": "answer-key", "target": "13-11#printed-answer-key", "description": "Q11 short-answer entry" }, { "id": "13-q05-12-answer-key", "type": "answer-key", "target": "13-12#printed-answer-key", "description": "Q12 short-answer entry" }, { "id": "13-q05-13-answer-key", "type": "answer-key", "target": "13-13#printed-answer-key", "description": "Q13 short-answer entry" } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s01-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 1; bold topic heading on first page." }, { "id": "13-s01-q01-statement", "type": "question", "target": "13-01#printed-question", "description": "Repeated source Q1 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s01-q02-statement", "type": "question", "target": "13-02#printed-question", "description": "Repeated source Q2 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s01-q01-working-1", "type": "working", "target": "13-01#printed-working", "description": "Q1: (i) consecutive sums; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s01-q01-working-2", "type": "working", "target": "13-01#printed-working", "description": "Q1: (ii) recurrence; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s01-q02-working-1", "type": "working", "target": "13-02#printed-working", "description": "Q2: (i) next terms; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s01-q02-working-2", "type": "working", "target": "13-02#printed-working", "description": "Q2: (ii) conjecture; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s02-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 2; bold topic heading on first page." }, { "id": "13-s02-teacher-note-1", "type": "teacher-note", "target": "13-03#teacher-notes", "description": "Q3 teacher-note content: Using GC:\n\n1. Press **mode**, scroll to **SEQ** (sequence mode).\n2. Press **Y=**. You will see **nMin = 1**. Enter $u(n)=3-0.5u(n-1)$. Press **2nd 7** for “u” a" }, { "id": "13-s02-table-1", "type": "table", "target": "13-03#source-tables-and-calculator-displays", "description": "Q3 table content: Calculator table for $c=5$ (display precision retained):\n\n| $n$ | $u$ |\n|---:|---:|\n|10|1.9941|\n|11|2.0029|\n|12|1.9985|\n|13|2.0007|\n|14|1.9996|\n|15|2.0002|\n|16|" }, { "id": "13-s02-q03-statement", "type": "question", "target": "13-03#printed-question", "description": "Repeated source Q3 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s02-q03-working-1", "type": "working", "target": "13-03#printed-working", "description": "Q3: (a)(i)(A) decreasing oscillation table; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s02-q03-working-2", "type": "working", "target": "13-03#printed-working", "description": "Q3: (a)(i)(B) constant table; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s02-table-3-2", "type": "table", "target": "13-03#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 2 for Q3; all rows/displayed truncated digits retained in native table section." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s03-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 3; bold topic heading on first page." }, { "id": "13-s03-q04-statement", "type": "question", "target": "13-04#printed-question", "description": "Repeated source Q4 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s03-q03-working-1", "type": "working", "target": "13-03#printed-working", "description": "Q3: (a)(ii) solve c; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s03-q03-working-2", "type": "working", "target": "13-03#printed-working", "description": "Q3: (b)(i) relation c+p; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s03-q03-working-3", "type": "working", "target": "13-03#printed-working", "description": "Q3: (b)(ii) solve p; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s03-q04-working-1", "type": "working", "target": "13-04#printed-working", "description": "Q4: (i) solve p,q; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s04-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 4; bold topic heading on first page." }, { "id": "13-s04-teacher-note-1", "type": "teacher-note", "target": "13-04#teacher-notes", "description": "Q4 teacher-note content: Observe the pattern in the series: **do not simplify to numerical values**. Leave $\\left(\\frac52\\right)^2(2)+\\frac52(2)+2$ instead of $\\frac{25}2+5+2=\\frac{39}2" }, { "id": "13-s04-teacher-note-2", "type": "teacher-note", "target": "13-05#teacher-notes", "description": "Q5 teacher-note content: Sequence converges to $L$ means its limit is a finite value $L$. As $n\\to\\infty$, both $u_n\\to L$ and $u_{n+1}\\to L$. Substitute these in the recurrence formula" }, { "id": "13-s04-q05-statement", "type": "question", "target": "13-05#printed-question", "description": "Repeated source Q5 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s04-q04-working-1", "type": "working", "target": "13-04#printed-working", "description": "Q4: (ii) unrolled GP; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s04-q05-working-1", "type": "working", "target": "13-05#printed-working", "description": "Q5: (a) finite-limit contradiction; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s05-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 5; bold topic heading on first page." }, { "id": "13-s05-teacher-note-1", "type": "teacher-note", "target": "13-06#teacher-notes", "description": "Q6 teacher-note content: Use the recurrence formula to obtain $u_n$ in terms of $u_{n-1}$. Repeat to obtain $u_{n-1}$ in terms of $u_{n-2}$ and so on until a pattern can be observed; th" }, { "id": "13-s05-q06-statement", "type": "question", "target": "13-06#printed-question", "description": "Repeated source Q6 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s05-q05-working-1", "type": "working", "target": "13-05#printed-working", "description": "Q5: (b)(i) next four terms; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s05-q05-working-2", "type": "working", "target": "13-05#printed-working", "description": "Q5: (b)(ii) fourfold composition; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s05-q06-working-1", "type": "working", "target": "13-06#printed-working", "description": "Q6: unrolling; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s05-q06-working-2", "type": "working", "target": "13-06#printed-working", "description": "Q6: AP and GP sums; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s05-q06-working-3", "type": "working", "target": "13-06#printed-working", "description": "Q6: increasing divergence; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s06-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 6; bold topic heading on first page." }, { "id": "13-s06-diagram-1", "type": "diagram", "target": "13-07#source-diagrams-redrawn", "description": "Q7 diagram content: ![13-07](/diagrams/native-13-07-increment.svg)" }, { "id": "13-s06-q07-statement", "type": "question", "target": "13-07#printed-question", "description": "Repeated source Q7 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s06-q07-working-1", "type": "working", "target": "13-07#printed-working", "description": "Q7: (i) GC roots; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s06-q07-working-2", "type": "working", "target": "13-07#printed-working", "description": "Q7: (ii) fixed-point limit; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s06-q07-working-3", "type": "working", "target": "13-07#printed-working", "description": "Q7: (iii) maximum bound; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s07-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 7; bold topic heading on first page." }, { "id": "13-s07-q08-statement", "type": "question", "target": "13-08#printed-question", "description": "Repeated source Q8 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s07-q09-statement", "type": "question", "target": "13-09#printed-question", "description": "Repeated source Q9 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s07-q08-working-1", "type": "working", "target": "13-08#printed-working", "description": "Q8: (i) square-root fixed point; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s07-q08-working-2", "type": "working", "target": "13-08#printed-working", "description": "Q8: (ii) square difference; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s07-q08-working-3", "type": "working", "target": "13-08#printed-working", "description": "Q8: (iii) factor/sign proof; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s08-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 8; bold topic heading on first page." }, { "id": "13-s08-diagram-1", "type": "diagram", "target": "13-09#source-diagrams-redrawn", "description": "Q9 diagram content: ![13-09](/diagrams/native-13-09-increment.svg)" }, { "id": "13-s08-q10-statement", "type": "question", "target": "13-10#printed-question", "description": "Repeated source Q10 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s08-q09-working-1", "type": "working", "target": "13-09#printed-working", "description": "Q9: (i) fixed-point roots; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s08-q09-working-2", "type": "working", "target": "13-09#printed-working", "description": "Q9: (ii) graph sign; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s08-q09-working-3", "type": "working", "target": "13-09#printed-working", "description": "Q9: (ii) alternative completion of square; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s08-q09-working-4", "type": "working", "target": "13-09#printed-working", "description": "Q9: (iii) convergence readout; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s09-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 9; bold topic heading on first page." }, { "id": "13-s09-q11-statement", "type": "question", "target": "13-11#printed-question", "description": "Repeated source Q11 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s09-q10-working-1", "type": "working", "target": "13-10#printed-working", "description": "Q10: (a)(i) limit; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s09-q10-working-2", "type": "working", "target": "13-10#printed-working", "description": "Q10: (a)(ii) two inequalities; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s09-q10-working-3", "type": "working", "target": "13-10#printed-working", "description": "Q10: (a)(iii) behaviour; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s09-q10-working-4", "type": "working", "target": "13-10#printed-working", "description": "Q10: (b)(i) ratio proof; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s09-q10-working-5", "type": "working", "target": "13-10#printed-working", "description": "Q10: (b)(ii) GP expression; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s10-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 10; bold topic heading on first page." }, { "id": "13-s10-diagram-1", "type": "diagram", "target": "13-11#source-diagrams-redrawn", "description": "Q11 diagram content: ![13-11](/diagrams/native-13-11-increment.svg)" }, { "id": "13-s10-q11-working-1", "type": "working", "target": "13-11#printed-working", "description": "Q11: (i) quadratic roots; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s10-q11-working-2", "type": "working", "target": "13-11#printed-working", "description": "Q11: (ii) two graph inequalities; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 11, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s11-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 11; bold topic heading on first page." }, { "id": "13-s11-teacher-note-1", "type": "teacher-note", "target": "13-12#teacher-notes", "description": "Q12 teacher-note content: If $00$. Replace $x$ by $x_n$ in this inequality." }, { "id": "13-s11-diagram-1", "type": "diagram", "target": "13-12#source-diagrams-redrawn", "description": "Q12 diagram content: ![13-12](/diagrams/native-13-12-increment.svg)" }, { "id": "13-s11-q12-statement", "type": "question", "target": "13-12#printed-question", "description": "Repeated source Q12 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s11-q12-working-1", "type": "working", "target": "13-12#printed-working", "description": "Q12: (i) exact root; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s11-q12-working-2", "type": "working", "target": "13-12#printed-working", "description": "Q12: (ii) increment sign; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 12, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s12-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 12; bold topic heading on first page." }, { "id": "13-s12-diagram-1", "type": "diagram", "target": "13-13#source-diagrams-redrawn", "description": "Q13 diagram content: ![13-13-poly](/diagrams/native-13-13-polynomial.svg)\n\n![13-13](/diagrams/native-13-13-cobweb.svg)" }, { "id": "13-s12-q13-statement", "type": "question", "target": "13-13#printed-question", "description": "Repeated source Q13 statement, all premises, printed subparts/marks and attribution." }, { "id": "13-s12-q12-working-1", "type": "working", "target": "13-12#printed-working", "description": "Q12: (iii) printed convergence argument; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "13 Recurrence relation sol.pdf", "page": 13, "visualChecked": true, "status": "audited-native", "items": [ { "id": "13-s13-header", "type": "header-footer", "target": "topic-13#source-metadata", "description": "Running topic header and printed page 13; bold topic heading on first page." }, { "id": "13-s13-table-1", "type": "table", "target": "13-13#source-tables-and-calculator-displays", "description": "Q13 table content: GC polynomial-root finder setup: **ORDER 1 2 3 4 5 6 7 8 9 10** (5 selected); **REAL / a+bi / re^(θi)** (a+bi selected); **DEC / FRAC**; **NORMAL / SCI / ENG**;" }, { "id": "13-s13-diagram-1", "type": "diagram", "target": "13-13#source-diagrams-redrawn", "description": "Q13 diagram content: ![13-13-poly](/diagrams/native-13-13-polynomial.svg)\n\n![13-13](/diagrams/native-13-13-cobweb.svg)" }, { "id": "13-s13-q13-working-1", "type": "working", "target": "13-13#printed-working", "description": "Q13: (i) root and GC displays; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s13-q13-working-2", "type": "working", "target": "13-13#printed-working", "description": "Q13: (ii) fixed-point argument; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s13-q13-working-3", "type": "working", "target": "13-13#printed-working", "description": "Q13: (iii) diagram proof; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s13-q13-working-4", "type": "working", "target": "13-13#printed-working", "description": "Q13: (iv) oscillation; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s13-q13-working-5", "type": "working", "target": "13-13#printed-working", "description": "Q13: (v) repeated source solution block; displayed equalities/inequalities and conclusion retained." }, { "id": "13-s13-solver-graph", "type": "diagram", "target": "13-13#source-diagrams-redrawn", "description": "GC polynomial graph / intersection panel; its equation and intersection X=1.3915028,Y=0 mapped to native polynomial SVG and numeric display table." }, { "id": "13-s13-table-13-2", "type": "table", "target": "13-13#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 2 for Q13; all rows/displayed truncated digits retained in native table section." }, { "id": "13-s13-table-13-3", "type": "table", "target": "13-13#source-tables-and-calculator-displays", "description": "Separate displayed source table/panel 3 for Q13; all rows/displayed truncated digits retained in native table section." } ], "unresolved": [] } ], "questions": [ { "id": "13-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "13-13", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." } ], "unresolved": [], "counts": { "question": 26, "working": 42, "answer-key": 13, "teacher-note": 5, "table": 5, "diagram": 10, "header-footer": 18 } }, { "topic": "14", "pages": [ { "file": "14 Sigma notation.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-q01-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 102; bold topic heading on first page." }, { "id": "14-q01-01-question", "type": "question", "target": "14-01#printed-question", "description": "Q1 printed question / subparts / marks / attribution" }, { "id": "14-q01-02-question", "type": "question", "target": "14-02#printed-question", "description": "Q2 printed question / subparts / marks / attribution" }, { "id": "14-q01-03-question", "type": "question", "target": "14-03#printed-question", "description": "Q3 printed question / subparts / marks / attribution" }, { "id": "14-q01-04-question", "type": "question", "target": "14-04#printed-question", "description": "Q4 printed question / subparts / marks / attribution" }, { "id": "14-q01-05-question", "type": "question", "target": "14-05#printed-question", "description": "Q5 printed question / subparts / marks / attribution" }, { "id": "14-q01-06-question", "type": "question", "target": "14-06#printed-question", "description": "Q6 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "14 Sigma notation.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-q02-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 103; bold topic heading on first page." }, { "id": "14-q02-07-question", "type": "question", "target": "14-07#printed-question", "description": "Q7 printed question / subparts / marks / attribution" }, { "id": "14-q02-08-question", "type": "question", "target": "14-08#printed-question", "description": "Q8 printed question / subparts / marks / attribution" }, { "id": "14-q02-09-question", "type": "question", "target": "14-09#printed-question", "description": "Q9 printed question / subparts / marks / attribution" }, { "id": "14-q02-10-question", "type": "question", "target": "14-10#printed-question", "description": "Q10 printed question / subparts / marks / attribution" }, { "id": "14-q02-11-question", "type": "question", "target": "14-11#printed-question", "description": "Q11 printed question / subparts / marks / attribution" }, { "id": "14-q02-12-question", "type": "question", "target": "14-12#printed-question", "description": "Q12 printed question / subparts / marks / attribution" } ], "unresolved": [] }, { "file": "14 Sigma notation.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-q03-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 104; bold topic heading on first page." }, { "id": "14-q03-01-answer-key", "type": "answer-key", "target": "14-01#printed-answer-key", "description": "Q1 short-answer entry" }, { "id": "14-q03-02-answer-key", "type": "answer-key", "target": "14-02#printed-answer-key", "description": "Q2 short-answer entry" }, { "id": "14-q03-03-answer-key", "type": "answer-key", "target": "14-03#printed-answer-key", "description": "Q3 short-answer entry" }, { "id": "14-q03-04-answer-key", "type": "answer-key", "target": "14-04#printed-answer-key", "description": "Q4 short-answer entry" }, { "id": "14-q03-05-answer-key", "type": "answer-key", "target": "14-05#printed-answer-key", "description": "Q5 short-answer entry" }, { "id": "14-q03-06-answer-key", "type": "answer-key", "target": "14-06#printed-answer-key", "description": "Q6 short-answer entry" }, { "id": "14-q03-07-answer-key", "type": "answer-key", "target": "14-07#printed-answer-key", "description": "Q7 short-answer entry" }, { "id": "14-q03-08-answer-key", "type": "answer-key", "target": "14-08#printed-answer-key", "description": "Q8 short-answer entry" }, { "id": "14-q03-09-answer-key", "type": "answer-key", "target": "14-09#printed-answer-key", "description": "Q9 short-answer entry" }, { "id": "14-q03-10-answer-key", "type": "answer-key", "target": "14-10#printed-answer-key", "description": "Q10 short-answer entry" } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s01-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 1; bold topic heading on first page." }, { "id": "14-s01-teacher-note-1", "type": "teacher-note", "target": "14-01#teacher-notes", "description": "Q1 teacher-note content: LHS is an AP sum:\n$$\\sum_{r=3}^a(2r+a)=(6+a)+(8+a)+\\cdots+(2a+a).$$\nFirst term $6+a$; common difference 2; number of terms $(a-3)+1=(\\text{upper limit}-\\text{lo" }, { "id": "14-s01-diagram-1", "type": "diagram", "target": "14-01#source-diagrams-redrawn", "description": "Q1 diagram content: ![14-01](/diagrams/native-14-01-sign.svg)" }, { "id": "14-s01-q01-statement", "type": "question", "target": "14-01#printed-question", "description": "Repeated source Q1 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s01-q02-statement", "type": "question", "target": "14-02#printed-question", "description": "Repeated source Q2 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s01-q01-working-1", "type": "working", "target": "14-01#printed-working", "description": "Q1: AP method; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s01-q01-working-2", "type": "working", "target": "14-01#printed-working", "description": "Q1: alternative two-sum method; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s02-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 2; bold topic heading on first page." }, { "id": "14-s02-teacher-note-1", "type": "teacher-note", "target": "14-02#teacher-notes", "description": "Q2 teacher-note content: **EXPAND!** Use the sum of an AP with $a=1,d=1,n$ terms for $\\sum r$, and $n$ copies for $\\sum1$.\n\nAlternative: $\\sum_{r=1}^n(-4r+1)=-3-7-11-\\cdots-(4n-1)$ is a" }, { "id": "14-s02-q02-working-1", "type": "working", "target": "14-02#printed-working", "description": "Q2: (i) expanded squares; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s02-q02-working-2", "type": "working", "target": "14-02#printed-working", "description": "Q2: (i) alternative AP; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s02-q02-working-3", "type": "working", "target": "14-02#printed-working", "description": "Q2: (ii) lower/upper limits and subtraction; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 3, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s03-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 3; bold topic heading on first page." }, { "id": "14-s03-teacher-note-1", "type": "teacher-note", "target": "14-03#teacher-notes", "description": "Q3 teacher-note content: $\\sum_{r=1}^n(8r+3)=11+19+26+\\cdots+(8n+3)$ **as printed**. It is an AP with first term 11, common difference 8, $n$ terms, $S_n=\\frac n2(u_1+u_n)$.\n\nThe displa" }, { "id": "14-s03-q03-statement", "type": "question", "target": "14-03#printed-question", "description": "Repeated source Q3 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s03-q04-statement", "type": "question", "target": "14-04#printed-question", "description": "Repeated source Q4 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s03-q03-working-1", "type": "working", "target": "14-03#printed-working", "description": "Q3: expanded polynomial AP; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s03-q03-working-2", "type": "working", "target": "14-03#printed-working", "description": "Q3: 25–75 block sum; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 4, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s04-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 4; bold topic heading on first page." }, { "id": "14-s04-teacher-note-1", "type": "teacher-note", "target": "14-04#teacher-notes", "description": "Q4 teacher-note content: $\\sum_{r=1}^k(-\\frac12)^{r+1}=(-\\frac12)^2+(-\\frac12)^3+(-\\frac12)^4+\\cdots$ is geometric, with first term $\\frac14$, common ratio $-\\frac12$." }, { "id": "14-s04-teacher-note-2", "type": "teacher-note", "target": "14-05#teacher-notes", "description": "Q5 teacher-note content: Formula found in list MF27: $\\sin^2x=\\frac{1-\\cos2x}2$." }, { "id": "14-s04-q05-statement", "type": "question", "target": "14-05#printed-question", "description": "Repeated source Q5 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s04-q04-working-1", "type": "working", "target": "14-04#printed-working", "description": "Q4: (i) GP and log-factorial; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s04-q04-working-2", "type": "working", "target": "14-04#printed-working", "description": "Q4: (ii) limiting divergence; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s04-q05-working-1", "type": "working", "target": "14-05#printed-working", "description": "Q5: double-angle and block subtraction; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 5, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s05-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 5; bold topic heading on first page." }, { "id": "14-s05-diagram-1", "type": "diagram", "target": "14-06#source-diagrams-redrawn", "description": "Q6 diagram content: ![14-06](/diagrams/native-14-06-convergence.svg)" }, { "id": "14-s05-q06-statement", "type": "question", "target": "14-06#printed-question", "description": "Repeated source Q6 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s05-q06-working-1", "type": "working", "target": "14-06#printed-working", "description": "Q6: (a) telescoping log; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s05-q06-working-2", "type": "working", "target": "14-06#printed-working", "description": "Q6: (b)(i) graphical method; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 6, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s06-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 6; bold topic heading on first page." }, { "id": "14-s06-teacher-note-1", "type": "teacher-note", "target": "14-06#teacher-notes", "description": "Q6 teacher-note content: For $x=0.25$, this is a GP with first term $\\frac35$ and common ratio $\\frac35$." }, { "id": "14-s06-q07-statement", "type": "question", "target": "14-07#printed-question", "description": "Repeated source Q7 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s06-q06-working-1", "type": "working", "target": "14-06#printed-working", "description": "Q6: (b)(i) squared-inequality method; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s06-q06-working-2", "type": "working", "target": "14-06#printed-working", "description": "Q6: (b)(ii) GP method; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s06-q06-working-3", "type": "working", "target": "14-06#printed-working", "description": "Q6: (b)(ii) algebraic formula method; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 7, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s07-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 7; bold topic heading on first page." }, { "id": "14-s07-teacher-note-1", "type": "teacher-note", "target": "14-07#teacher-notes", "description": "Q7 teacher-note content: To use the given result (lower limit $r=1$), re-express $\\sum_{r=5}^{\\infty}f(r)=\\sum_{r=1}^{\\infty}f(r)-\\sum_{r=1}^4f(r)$. Note $\\sum_{r=1}^{\\infty}f(r)=\\lim_{" }, { "id": "14-s07-q08-statement", "type": "question", "target": "14-08#printed-question", "description": "Repeated source Q8 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s07-q07-working-1", "type": "working", "target": "14-07#printed-working", "description": "Q7: limit minus prefix; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s07-q08-working-1", "type": "working", "target": "14-08#printed-working", "description": "Q8: (a) factorial limits; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s07-q08-working-2", "type": "working", "target": "14-08#printed-working", "description": "Q8: (b) shifted-index sum; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 8, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s08-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 8; bold topic heading on first page." }, { "id": "14-s08-teacher-note-1", "type": "teacher-note", "target": "14-09#teacher-notes", "description": "Q9 teacher-note content: “Within” is strictly “$<$” and does **not** include “$=$”.\n\nFactorise $4r^2-1$ and compare $(2r-1)(2r+1)$ with $(2r+3)(2r+5)$ to find the replacement for $r$. R" }, { "id": "14-s08-q09-statement", "type": "question", "target": "14-09#printed-question", "description": "Repeated source Q9 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s08-q10-statement", "type": "question", "target": "14-10#printed-question", "description": "Repeated source Q10 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s08-q09-working-1", "type": "working", "target": "14-09#printed-working", "description": "Q9: (i) strict tail threshold; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s08-q09-working-2", "type": "working", "target": "14-09#printed-working", "description": "Q9: (ii) shifted/factored summand; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 9, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s09-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 9; bold topic heading on first page." }, { "id": "14-s09-teacher-note-1", "type": "teacher-note", "target": "14-10#teacher-notes", "description": "Q10 teacher-note content: To use the given result, rewrite $f(n)$ to match its summand. $\\sum_{n=2}^{N+1}T_n=\\sum_{n=1}^{N+1}T_n-T_1$, where $T_n=\\frac{3^n(2n-1)}{2n(n+1)}$." }, { "id": "14-s09-teacher-note-2", "type": "teacher-note", "target": "14-11#teacher-notes", "description": "Q11 teacher-note content: Remember to change $r$ to $r-1$ for the upper limit too. $\\sum_{r=1}^{2501}T_r=\\sum_{r=1}^{2500}T_r+T_{2501}$.\n\nSource typographic slip: its penultimate denomin" }, { "id": "14-s09-q11-statement", "type": "question", "target": "14-11#printed-question", "description": "Repeated source Q11 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s09-q10-working-1", "type": "working", "target": "14-10#printed-working", "description": "Q10: re-index and subtract first term; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s09-q11-working-1", "type": "working", "target": "14-11#printed-working", "description": "Q11: shifted radical sum; displayed equalities/inequalities and conclusion retained." }, { "id": "14-s09-q11-working-2", "type": "working", "target": "14-11#printed-working", "description": "Q11: extra term and lower bound; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] }, { "file": "14 Sigma notation sol.pdf", "page": 10, "visualChecked": true, "status": "audited-native", "items": [ { "id": "14-s10-header", "type": "header-footer", "target": "topic-14#source-metadata", "description": "Running topic header and printed page 10; bold topic heading on first page." }, { "id": "14-s10-q12-statement", "type": "question", "target": "14-12#printed-question", "description": "Repeated source Q12 statement, all premises, printed subparts/marks and attribution." }, { "id": "14-s10-q12-working-1", "type": "working", "target": "14-12#printed-working", "description": "Q12: root-test absolute limit; displayed equalities/inequalities and conclusion retained." } ], "unresolved": [] } ], "questions": [ { "id": "14-01", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-02", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-03", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-04", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-05", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-06", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-07", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-08", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-09", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-10", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-11", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." }, { "id": "14-12", "questionComplete": true, "workingComplete": true, "notesComplete": true, "diagramsComplete": true, "review": "Rendered question/solution page comparison; printed working distinguished from independent mathematical qualifications. Native equations checked with KaTeX and plotted SVG equations evaluated from source." } ], "unresolved": [], "counts": { "question": 24, "working": 24, "answer-key": 10, "teacher-note": 10, "table": 0, "diagram": 2, "header-footer": 13 } }, { "topic": "15", "pages": [ { "file": "15 complex numbers.pdf", "page": 1, "visualChecked": true, "status": "audited-native", "items": [ { "id": "15-question-1-metadata", "type": "header-footer", "target": "topic-15#document-metadata", "description": "Printed topic header when present, document page footer 105; original title COMPLEX NUMBERS on first page." }, { "id": "15-01-q-p1", "type": "question", "target": "15-01#question", "description": "Printed question, instructions, every subpart and mark allocation" }, { "id": "15-02-q-p1", "type": "question", "target": "15-02#question", "description": "Printed question, instructions, every subpart and mark allocation" }, { "id": "15-03-q-p1", "type": "question", "target": "15-03#question", "description": "Printed question, instructions, every subpart and mark allocation" }, { "id": "15-04-q-p1", "type": "question", "target": "15-04#question", "description": "Printed question, instructions, every subpart and mark allocation" }, { "id": "15-05-q-p1", "type": "question", "target": "15-05#question", "description": "Printed question, instructions, every subpart and mark allocation" }, { "id": "15-06-q-p1", "type": "question", "target": "15-06#question", "description": "Printed question, instructions, every subpart and mark allocation" } ], "unresolved": [] }, { "file": "15 complex numbers.pdf", "page": 2, "visualChecked": true, "status": "audited-native", "items": [ { "id": "15-question-2-metadata", "type": "header-footer", "target": "topic-15#document-metadata", "description": "Printed topic header when present, document page footer 106; 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