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This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "07-13", "topic": "07", "number": 13, "title": "Locate the crossing before taking the absolute area", "questionPages": [ 3 ], "solutionPages": [ 15, 16 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "07 Integration tech.pdf · p.3", "07 Integration tech.pdf · p.5", "07 Integration tech sol.pdf · p.15", "07 Integration tech sol.pdf · p.16" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "07-13#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "07-13#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 3, "status": "Source comparison recorded", "target": "07-13#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "07-13" }, { "type": "diagram", "label": "Diagrams", "itemCount": 2, "status": "Source comparison recorded", "target": "07-13#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "07-14", "topic": "07", "number": 14, "title": "Check whether the given equality can hold", "questionPages": [ 4 ], "solutionPages": [ 16, 17 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "07 Integration tech.pdf · p.4", "07 Integration tech.pdf · p.5", "07 Integration tech sol.pdf · p.16", "07 Integration tech sol.pdf · p.17" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "07-14#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "07-14#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 3, "status": "Source comparison recorded", "target": "07-14#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "07-14" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "07-14" } ], "mathematicalReview": "reviewed with source inconsistency", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "i", "text": "$-10$." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "08-07", "topic": "08", "number": 7, "title": "Cancel whole periods before integrating", "questionPages": [ 2 ], "solutionPages": [ 9 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "a", "b", "c" ], "sourcePages": [ "08 App of integration.pdf · p.2", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.9" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-07#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "08-07#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "08-07#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-07" }, { "type": "diagram", "label": "Diagrams", "itemCount": 3, "status": "Source comparison recorded", "target": "08-07#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "a", "text": "$a>0$; join the given tangent/sine pieces continuously." }, { "part": "c", "text": "Signed integral, not total area." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "This asks for signed integration, not total shaded area. Positive and negative lobes cancel.", "unresolved": [] }, { "id": "08-08", "topic": "08", "number": 8, "title": "Keep the parameter branch when eliminating t", "questionPages": [ 3 ], "solutionPages": [ 10, 11 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "i", "ii", "iii", "iv" ], "sourcePages": [ "08 App of integration.pdf · p.3", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.10", "08 App of integration sol.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-08#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "08-08#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "08-08#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-08" }, { "type": "diagram", "label": "Diagrams", "itemCount": 4, "status": "Source comparison recorded", "target": "08-08#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed with source branch qualification", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "iii", "text": "Valid 0≤t≤π/2 only. 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Question PDF p.3 (printed53); solution PDF p.11 explicitly adds the rising-arc restriction.", "unresolved": [] }, { "id": "08-09", "topic": "08", "number": 9, "title": "Use y as the monotone coordinate", "questionPages": [ 3 ], "solutionPages": [ 11 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "main" ], "sourcePages": [ "08 App of integration.pdf · p.3", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-09#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "08-09#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "08-09#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-09" }, { "type": "diagram", "label": "Diagrams", "itemCount": 3, "status": "Source comparison recorded", "target": "08-09#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed with depicted-region qualification", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "Area", "text": "Source-selected arc −1/2≤t≤1. Full real-parameter curve also meets the line at t=7, giving a different additional region." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "The full real-parameter curve has a third intersection at t=7, outside the depicted arc. The article explicitly selects the region shown in the source diagram; the original wording “at two points” is preserved in the PDF.", "unresolved": [] }, { "id": "08-10", "topic": "08", "number": 10, "title": "Carry negative parameter bounds through the substitution", "questionPages": [ 4 ], "solutionPages": [ 12, 13 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "limits", "area" ], "sourcePages": [ "08 App of integration.pdf · p.4", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.12", "08 App of integration sol.pdf · p.13" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-10#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "08-10#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "08-10#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-10" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "08-10#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "08-11", "topic": "08", "number": 11, "title": "Use unsigned area and subtract the rotating core", "questionPages": [ 4 ], "solutionPages": [ 14 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "a", "b" ], "sourcePages": [ "08 App of integration.pdf · p.4", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.14" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-11#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "08-11#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "08-11#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-11" }, { "type": "diagram", "label": "Diagrams", "itemCount": 4, "status": "Source comparison recorded", "target": "08-11#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "b", "text": "Finite region −π/3≤x≤π/3." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "08-12", "topic": "08", "number": 12, "title": "Use identities for integration and geometry for the regions", "questionPages": [ 5 ], "solutionPages": [ 15, 16 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "a", "b", "c.i", "c.ii" ], "sourcePages": [ "08 App of integration.pdf · p.5", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.15", "08 App of integration sol.pdf · p.16" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-12#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "08-12#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "08-12#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-12" }, { "type": "diagram", "label": "Diagrams", "itemCount": 6, "status": "Source comparison recorded", "target": "08-12#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "a", "text": "On intervals with sin2x≠0." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "08-13", "topic": "08", "number": 13, "title": "Take the infinite limit and use the bowl radius", "questionPages": [ 6 ], "solutionPages": [ 18 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "a.i", "a.ii", "a.iii", "b" ], "sourcePages": [ "08 App of integration.pdf · p.6", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.17", "08 App of integration sol.pdf · p.18" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-13#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "08-13#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "08-13#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-13" }, { "type": "diagram", "label": "Diagrams", "itemCount": 4, "status": "Source comparison recorded", "target": "08-13#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed with notation qualification", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "a(iii)", "text": "Printed 2q is the total only if q denotes the limiting area; the question definesq from the finite-n integral." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "Notation qualification in (a)(iii): q is defined in the question as a finite-n integral, while R extends to infinity. The printed “2q” is recorded separately from the total area 2ln2. 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This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "08-15", "topic": "08", "number": 15, "title": "Sum local area inequalities, then shift the axis", "questionPages": [ 7 ], "solutionPages": [ 20, 21, 22 ], "attribution": "2025 TJC H2 Maths (9758) JC2 MSM · original exercise attribution retained on source pages", "labels": [ "i", "ii", "iii", "translation", "volume" ], "sourcePages": [ "08 App of integration.pdf · p.7", "08 App of integration.pdf · p.8", "08 App of integration sol.pdf · p.20", "08 App of integration sol.pdf · p.21", "08 App of integration sol.pdf · p.22" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "08-15#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 4, "status": "Source comparison recorded", "target": "08-15#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 3, "status": "Source comparison recorded", "target": "08-15#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "08-15" }, { "type": "diagram", "label": "Diagrams", "itemCount": 4, "status": "Source comparison recorded", "target": "08-15#source-diagrams-in-native-form", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "ii", "text": "$n\\ge1$; unit-width rectangle lies below the decreasing curve." }, { "part": "iii", "text": "Positive integer n; right-hand differences telescope." }, { "part": "Rotation volume", "text": "Source right-hand region 1≤x≤3; rotate about x=3." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "09-01", "topic": "09", "number": 1, "title": "Normalize before expanding", "questionPages": [ 1 ], "solutionPages": [ 1 ], "attribution": "[2022/EJC/Prelim/II/1]", "labels": [ "a", "b", "c" ], "sourcePages": [ "09 series expansion.pdf · p.1", "09 seriex expansion sol.pdf · p.1" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "09-01#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "09-01#printed-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 4, "status": "Source comparison recorded", "target": "09-01#teacher-note-1" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "09-01" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "09-01" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "a", "text": "$-4/30$." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "10-15", "topic": "10", "number": 15, "title": "Compare unbounded growth with a carrying capacity", "questionPages": [ 6 ], "solutionPages": [ 22, 23 ], "attribution": "[2020/ACJC/Prelim/II/2]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "10 DE.pdf · p.6", "10 DE.pdf · p.9", "10 DE sol.pdf · p.22", "10 DE sol.pdf · p.23" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "10-15#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "10-15#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "10-15#teacher-note-1" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "10-15" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "10-15" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "10-16", "topic": "10", "number": 16, "title": "A declining species and an increasing logistic species", "questionPages": [ 6 ], "solutionPages": [ 23, 24, 25, 26 ], "attribution": "[2021/TJC/Prelim/I/10]", "labels": [ "a.i", "a.ii", "b.i", "b.ii" ], "sourcePages": [ "10 DE.pdf · p.6", "10 DE.pdf · p.9", "10 DE sol.pdf · p.23", "10 DE sol.pdf · p.24", "10 DE sol.pdf · p.25", "10 DE sol.pdf · p.26" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "10-16#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 5, "status": "Source comparison recorded", "target": "10-16#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 6, "status": "Source comparison recorded", "target": "10-16#teacher-note-1" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "10-16" }, { "type": "diagram", "label": "Diagrams", "itemCount": 3, "status": "Source comparison recorded", "target": "10-16#diagram-10-16-population", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "a.ii", "text": "Stop the population model at extinction." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "10-17", "topic": "10", "number": 17, "title": "Separate the formal model from inconsistent pump directions", "questionPages": [ 6 ], "solutionPages": [ 27, 28 ], "attribution": "[2022/ASRJC/Prelim/I/11]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "10 DE.pdf · p.6", "10 DE.pdf · p.9", "10 DE sol.pdf · p.26", "10 DE sol.pdf · p.27", "10 DE sol.pdf · p.28" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "10-17#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "10-17#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 3, "status": "Source comparison recorded", "target": "10-17#teacher-note-1" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "10-17" }, { "type": "diagram", "label": "Diagrams", "itemCount": 2, "status": "Source comparison recorded", "target": "10-17#diagram-10-17-height", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "ii", "text": "Incompatible with positive printed inflow∝h² and outflow∝h; no positive physical constants satisfy all data." }, { "part": "iii", "text": "Conditional algebraic model, not a physically consistent solution of the printed pump description." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "Question PDF p.6 (printed73), solution pp.27–28: the printed k=−11/50 is algebraically consistent with the given derivative datum but incompatible with positive inflow ∝h² and positive outflow ∝h. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "11-01", "topic": "11", "number": 1, "title": "A perpendicular foot organizes four shapes", "questionPages": [ 1 ], "solutionPages": [ 1, 2 ], "attribution": "[modified 2017/DHS/Promo/6]", "labels": [ "collinearity", "i", "ii", "iii", "iv" ], "sourcePages": [ "11 vectors sol.pdf · p.1", "11 vectors sol.pdf · p.2", "11 vectors.pdf · p.1", "11 vectors.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "11-01#question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "11-01#source-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "11-01#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-01" }, { "type": "diagram", "label": "Diagrams", "itemCount": 2, "status": "Source comparison recorded", "target": "11-01#native-diagrams", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed: independent vector calculation compared with rendered question and answer pages", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "11-02", "topic": "11", "number": 2, "title": "An extended segment and coefficient comparison", "questionPages": [ 1 ], "solutionPages": [ 3 ], "attribution": "[2018/EJC/Prelim/I/5]", "labels": [ "i", "ii" ], "sourcePages": [ "11 vectors sol.pdf · p.3", "11 vectors.pdf · p.1", "11 vectors.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "11-02#question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "11-02#source-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "11-02#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-02" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "11-02#native-diagrams", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed: independent vector calculation compared with rendered question and answer pages", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "ii", "text": "$\\lambda>0$." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "11-03", "topic": "11", "number": 3, "title": "Skew lines and a perpendicular foot", "questionPages": [ 1 ], "solutionPages": [ 4 ], "attribution": "[modified 2009/NYJC/Prelim/I/3]", "labels": [ "i", "ii" ], "sourcePages": [ "11 vectors sol.pdf · p.4", "11 vectors.pdf · p.1", "11 vectors.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "11-03#question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "11-03#source-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "11-03#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-03" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "11-03#native-diagrams", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed: independent vector calculation compared with rendered question and answer pages", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "11-04", "topic": "11", "number": 4, "title": "Projection followed by line reflection", "questionPages": [ 1 ], "solutionPages": [ 5, 6 ], "attribution": "[2010/ACJC/Prelim/I/9]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "11 vectors sol.pdf · p.5", "11 vectors sol.pdf · p.6", "11 vectors.pdf · p.1", "11 vectors.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "11-04#question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "11-04#source-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "11-04#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-04" }, { "type": "diagram", "label": "Diagrams", "itemCount": 2, "status": "Source comparison recorded", "target": "11-04#native-diagrams", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed: independent vector calculation compared with rendered question and answer pages", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "11-05", "topic": "11", "number": 5, "title": "Equal radii make a midpoint perpendicular", "questionPages": [ 1 ], "solutionPages": [ 6, 7 ], "attribution": "[2010/NJC/Prelim/I/3]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "11 vectors sol.pdf · p.6", "11 vectors sol.pdf · p.7", "11 vectors.pdf · p.1", "11 vectors.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "11-05#question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "11-05#source-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "11-05#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-05" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "11-05#native-diagrams", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed: independent vector calculation compared with rendered question and answer pages", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "iii", "text": "$A\\ne B$; for a genuine rhombus the sides must also be nonparallel." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "11-06", "topic": "11", "number": 6, "title": "Area identities and a cross-product degeneracy", "questionPages": [ 2 ], "solutionPages": [ 7 ], "attribution": "[2018/DHS/Prelim/II/1]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "11 vectors sol.pdf · p.7", "11 vectors.pdf · p.2", "11 vectors.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "11-06#question" }, { "type": "working", "label": "Solution steps", "itemCount": 2, "status": "Source comparison recorded", "target": "11-06#source-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "11-06#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-06" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "11-06#native-diagrams", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed with source qualification; see warning and topic review evidence", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "iii", "text": "The printed $a=k(2b+3d)$ omits the valid case $2b+3d=0$." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. 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This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "11-08", "topic": "11", "number": 8, "title": "Orthogonality and an angle maximisation", "questionPages": [ 2 ], "solutionPages": [ 9, 10 ], "attribution": "[2017/ACJC/Prelim/I/9]", "labels": [ "i", "ii", "iii", "iv" ], "sourcePages": [ "11 vectors sol.pdf · p.9", "11 vectors sol.pdf · p.10", "11 vectors.pdf · p.2", "11 vectors.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "11-08#question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "11-08#source-working" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-08" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "11-08" }, { "type": "diagram", "label": "Diagrams", "itemCount": 2, "status": "Source comparison recorded", "target": "11-08#native-diagrams", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed with source qualification; see warning and topic review evidence", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "iv", "text": "The explicit coordinate paths are circular; the printed fixed-line motion description is inconsistent." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "The printed motion description names line segments, but the prescribed coordinate paths are circular. 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This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "12-01", "topic": "12", "number": 1, "title": "A variable geometric ratio", "questionPages": [ 1 ], "solutionPages": [ 1 ], "attribution": "[2020/DHS/Prelim/I/1]", "labels": [], "sourcePages": [ "12 APGP.pdf · p.1", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.1" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-01#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "12-01#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "12-01#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-01" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-01" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "12-02", "topic": "12", "number": 2, "title": "A relative geometric-tail error", "questionPages": [ 1 ], "solutionPages": [ 1, 2 ], "attribution": "[2022/RVHS/Promo/3(ii)]", "labels": [], "sourcePages": [ "12 APGP.pdf · p.1", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.1", "12 APGP sol.pdf · p.2" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-02#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 4, "status": "Source comparison recorded", "target": "12-02#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "12-02#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-02" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-02" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "main", "text": "Percentage error assumes a nonzero positive total." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "The percentage statement implicitly concerns a nonzero positive total; a zero GP cannot have a strict error less than zero.", "unresolved": [] }, { "id": "12-03", "topic": "12", "number": 3, "title": "Link an AP with a convergent GP", "questionPages": [ 1 ], "solutionPages": [ 2, 3, 4 ], "attribution": "[2022/YIJC/Promo/8]", "labels": [ "a", "b", "c", "d" ], "sourcePages": [ "12 APGP.pdf · p.1", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.2", "12 APGP sol.pdf · p.3", "12 APGP sol.pdf · p.4" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-03#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 7, "status": "Source comparison recorded", "target": "12-03#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "12-03#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 1, "status": "Source comparison recorded", "target": "12-03#source-tables-and-calculator-displays" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-03" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "12-04", "topic": "12", "number": 4, "title": "Odd-indexed terms and an alternating tail", "questionPages": [ 1 ], "solutionPages": [ 4, 5, 6 ], "attribution": "[2023/ACJC/Promo/8]", "labels": [ "a.i", "a.ii", "a.iii", "b.i", "b.ii" ], "sourcePages": [ "12 APGP.pdf · p.1", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.4", "12 APGP sol.pdf · p.5", "12 APGP sol.pdf · p.6" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-04#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 9, "status": "Source comparison recorded", "target": "12-04#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 3, "status": "Source comparison recorded", "target": "12-04#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 1, "status": "Source comparison recorded", "target": "12-04#source-tables-and-calculator-displays" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "12-04#source-diagrams-redrawn", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "12-05", "topic": "12", "number": 5, "title": "Selected GP terms form an AP", "questionPages": [ 1 ], "solutionPages": [ 6, 7 ], "attribution": "TJC JC2 2025 H2 Maths MSM; no separate exam attribution printed for Q5", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "12 APGP.pdf · p.1", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.6", "12 APGP sol.pdf · p.7" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-05#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 4, "status": "Source comparison recorded", "target": "12-05#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "12-05#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-05" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-05" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "The printed solution divides by r^4 and thereby omits the zero-ratio GP. The displayed main answer follows its intended nondegenerate branch.", "unresolved": [] }, { "id": "12-06", "topic": "12", "number": 6, "title": "Half the infinite sum and alternate indices", "questionPages": [ 2 ], "solutionPages": [ 8, 9 ], "attribution": "[2009/NYJC/Prelim/I/9]", "labels": [ "a", "b" ], "sourcePages": [ "12 APGP.pdf · p.2", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.8", "12 APGP sol.pdf · p.9" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-06#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 4, "status": "Source comparison recorded", "target": "12-06#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "12-06#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-06" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-06" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "b", "text": "Literal infinite-GP wording also allows the constant GP: even-indexed series diverges and log-AP difference is 0." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "An infinite GP need not have a finite sum. The printed solution supplies a convergence assumption absent from part (b) wording.", "unresolved": [] }, { "id": "12-07", "topic": "12", "number": 7, "title": "Eliminate two progression parameters", "questionPages": [ 2 ], "solutionPages": [ 9, 10 ], "attribution": "[2024/NJC/Prelim/II/2]", "labels": [ "i", "ii" ], "sourcePages": [ "12 APGP.pdf · p.2", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.9", "12 APGP sol.pdf · p.10" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-07#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 4, "status": "Source comparison recorded", "target": "12-07#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-07" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-07" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-07" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "ii", "text": "$n\\in\\mathbb Z^+$; use the unrounded root." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "12-08", "topic": "12", "number": 8, "title": "Alternating terms, even terms and products", "questionPages": [ 2 ], "solutionPages": [ 10, 11 ], "attribution": "[2009/IJC/Prelim/I/12]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "12 APGP.pdf · p.2", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.10", "12 APGP sol.pdf · p.11" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-08#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 6, "status": "Source comparison recorded", "target": "12-08#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "12-08#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-08" }, { "type": "diagram", "label": "Diagrams", "itemCount": 3, "status": "Source comparison recorded", "target": "12-08#source-diagrams-redrawn", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "12-09", "topic": "12", "number": 9, "title": "Odd-sized groups of geometric terms", "questionPages": [ 3 ], "solutionPages": [ 12, 13 ], "attribution": "[modified 2011/AJC/Prelim/I/12]", "labels": [ "intro", "i", "ii", "iii" ], "sourcePages": [ "12 APGP.pdf · p.3", "12 APGP.pdf · p.8", "12 APGP sol.pdf · p.12", "12 APGP sol.pdf · p.13" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "12-09#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 7, "status": "Source comparison recorded", "target": "12-09#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 2, "status": "Source comparison recorded", "target": "12-09#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-09" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "12-09" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "intro", "text": "$a\\ne0,1$." }, { "part": "iii", "text": "The printed $01$." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "Finding possible limits does not prove convergence; every logarithm requires $x_n$>1.", "unresolved": [] }, { "id": "13-08", "topic": "13", "number": 8, "title": "A square-root iteration crosses its limit", "questionPages": [ 3 ], "solutionPages": [ 7 ], "attribution": "[2012/IJC/Prelim/II/3]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "13 Recurrence relations.pdf · p.3", "13 Recurrence relations.pdf · p.5", "13 Recurrence relation sol.pdf · p.7" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "13-08#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 4, "status": "Source comparison recorded", "target": "13-08#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-08" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-08" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-08" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "iii", "text": "For the prescribed positive, defined sequence." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "The source has a square root over $10-3x_n$; plain text extraction loses it. The recurrence is assumed defined and positive at every step.", "unresolved": [] }, { "id": "13-09", "topic": "13", "number": 9, "title": "A rational map approaches two", "questionPages": [ 3 ], "solutionPages": [ 7, 8 ], "attribution": "[2011/TPJC/Prelim/I/2]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "13 Recurrence relations.pdf · p.3", "13 Recurrence relations.pdf · p.5", "13 Recurrence relation sol.pdf · p.7", "13 Recurrence relation sol.pdf · p.8" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "13-09#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 5, "status": "Source comparison recorded", "target": "13-09#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-09" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-09" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "13-09#source-diagrams-redrawn", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "", "unresolved": [] }, { "id": "13-10", "topic": "13", "number": 10, "title": "Halve the error at every step", "questionPages": [ 3 ], "solutionPages": [ 8, 9 ], "attribution": "[2011/TJC/Promo/14]", "labels": [ "a.i", "a.ii", "a.iii", "b.i", "b.ii" ], "sourcePages": [ "13 Recurrence relations.pdf · p.3", "13 Recurrence relations.pdf · p.5", "13 Recurrence relation sol.pdf · p.8", "13 Recurrence relation sol.pdf · p.9" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "13-10#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 6, "status": "Source comparison recorded", "target": "13-10#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-10" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-10" }, { "type": "diagram", "label": "Diagrams", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-10" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "Use $v_{n+1}=v_n/2$ rather than dividing by $v_n$, which could be zero.", "unresolved": [] }, { "id": "13-11", "topic": "13", "number": 11, "title": "A conditional limit in a two-cycle map", "questionPages": [ 3 ], "solutionPages": [ 9, 10 ], "attribution": "[2011/CJC/Prelim/I/2]", "labels": [ "i", "ii" ], "sourcePages": [ "13 Recurrence relations.pdf · p.3", "13 Recurrence relations.pdf · p.5", "13 Recurrence relation sol.pdf · p.9", "13 Recurrence relation sol.pdf · p.10" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "13-11#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 3, "status": "Source comparison recorded", "target": "13-11#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-11" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-11" }, { "type": "diagram", "label": "Diagrams", "itemCount": 1, "status": "Source comparison recorded", "target": "13-11#source-diagrams-redrawn", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "i", "text": "The convergence premise forces the constant sequence: F∘F is the identity, so nonconstant admissible sequences form two-cycles." }, { "part": "ii", "text": "This one-step comparison does not imply convergence." } ], "interaction": "Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.", "nativeVisual": "Settled source-content screenshots reviewed", "warning": "The printed question assumes convergence only in (i). Do not infer convergence of every sequence from the one-step inequalities.", "unresolved": [] }, { "id": "13-12", "topic": "13", "number": 12, "title": "An exponential denominator creates a stable limit", "questionPages": [ 4 ], "solutionPages": [ 11, 12 ], "attribution": "[2011/YJC/Prelim/I/1]", "labels": [ "i", "ii", "iii" ], "sourcePages": [ "13 Recurrence relations.pdf · p.4", "13 Recurrence relations.pdf · p.5", "13 Recurrence relation sol.pdf · p.11", "13 Recurrence relation sol.pdf · p.12" ], "categories": [ { "type": "question", "label": "Question / subparts", "itemCount": 2, "status": "Source comparison recorded", "target": "13-12#printed-question" }, { "type": "working", "label": "Solution steps", "itemCount": 4, "status": "Source comparison recorded", "target": "13-12#printed-answer-key" }, { "type": "teacher-note", "label": "Teacher notes", "itemCount": 1, "status": "Source comparison recorded", "target": "13-12#teacher-notes" }, { "type": "table", "label": "Tables", "itemCount": 0, "status": "No item inventoried — owner check needed", "target": "13-12" }, { "type": "diagram", "label": "Diagrams", "itemCount": 2, "status": "Source comparison recorded", "target": "13-12#source-diagrams-redrawn", "generated": "Native SVG generated; rendering is checked separately" } ], "mathematicalReview": "reviewed", "mathLimit": "Recorded mathematical review is a first pass; it is not independent expert certification.", "answerFirst": "source-compared", "answerConditions": [ { "part": "iii", "text": "$0