PorismaSource review

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Source review · Differentiation

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Every question has a place in the ledger. That does not prove every item is accurate or complete. Use these links to compare the native question, subparts, working, teaching notes, tables and diagrams with your private originals.

“Source comparison recorded” means a visual source-comparison pass is documented. “Mapped” or “generated” describes an ingestion step. Mathematical review, browser interaction tests and settled screenshot review are separate checks.

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7 question records

Optional ticks record your own inspection in this browser only. They do not change the conversion or mathematical-review claims.

05 · Differentiation

Edition metadata →

05-01 · Nested derivatives and increasing intervalsQuestion pp.1 / Solution pp.1

Question and explanations → · Complete native source article →

2009/DHS/Prelim/I/4. Printed/task labels inventoried: a, b.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

3 page-item records.

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Tables

No item inventoried — owner check needed

0 page-item records.

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Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: 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.
Rendered source content: Settled source-content screenshots reviewed

Do not omit the derivative of g. A squared denominator is positive only where nonzero.

Essential answer conditions and source qualifications

Radians.

Exact private source page references

05 Differentiation (Gradient function).pdf · p.1
05 Differentiation (Gradient function).pdf · p.4
05 Differentiation sol.pdf · p.1

05-02 · An inverse-trigonometric identity and its endpointsQuestion pp.1 / Solution pp.2

Question and explanations → · Complete native source article →

2009/YJC/Prelim/I/5(a). Printed/task labels inventoried: i, ii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed with endpoint qualification. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: 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.
Rendered source content: Settled source-content screenshots reviewed

The printed derivative includes endpoints without saying one-sided. The identity itself holds on the closed interval.

Essential answer conditions and source qualifications

For −1<x<1. Inward one-sided derivatives at ±1 are −1; unrestricted two-sided derivatives do not exist there.

Identity holds throughout −1≤x≤1.

Exact private source page references

05 Differentiation (Gradient function).pdf · p.1
05 Differentiation (Gradient function).pdf · p.4
05 Differentiation sol.pdf · p.2

05-03 · Turn a curve sketch into its gradient graphQuestion pp.1 / Solution pp.3

Question and explanations → · Complete native source article →

modified 2010/RVHS/Prelim/II/1. Printed/task labels inventoried: none recorded; check the question itself.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

4 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

4 page-item records. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: 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.
Rendered source content: Settled source-content screenshots reviewed

Roots of f need not be roots of its derivative.

Essential answer conditions and source qualifications

Derivative sketch

A′ has positive slope ordinate, C′ negative; their numerical ordinates are unspecified. Limits follow the particular source sketch.

Exact private source page references

05 Differentiation (Gradient function).pdf · p.1
05 Differentiation (Gradient function).pdf · p.4
05 Differentiation sol.pdf · p.3

05-04 · Read stationary points and slope limitsQuestion pp.2 / Solution pp.4

Question and explanations → · Complete native source article →

modified 2010/ACJC/Prelim/I/3. Printed/task labels inventoried: none recorded; check the question itself.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

4 page-item records. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: 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.
Rendered source content: Settled source-content screenshots reviewed

A value f(x)=2 at one point does not imply zero derivative. Read the actual slope behaviour.

Essential answer conditions and source qualifications

Derivative sketch

Positive for x<−2 and −2<x<3; negative for x>3. Turning-point coordinates beyond this are unspecified.

Exact private source page references

05 Differentiation (Gradient function).pdf · p.2
05 Differentiation (Gradient function).pdf · p.4
05 Differentiation sol.pdf · p.4

05-05 · Recover a rational curve from its asymptotesQuestion pp.2 / Solution pp.5, 6

Question and explanations → · Complete native source article →

2008/NJC/Prelim/I/11(i). Printed/task labels inventoried: none recorded; check the question itself.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

6 page-item records.

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Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

4 page-item records. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: 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.
Rendered source content: Settled source-content screenshots reviewed

No stationary points alone gives c≥−1; the stated vertical asymptote excludes equality.

Essential answer conditions and source qualifications

Derivative sketch

$x\ne0$ , c>−1.

Exact private source page references

05 Differentiation (Gradient function).pdf · p.2
05 Differentiation (Gradient function).pdf · p.4
05 Differentiation sol.pdf · p.5
05 Differentiation sol.pdf · p.6

05-06 · Increasing and concave down from a derivative sketchQuestion pp.3 / Solution pp.6

Question and explanations → · Complete native source article →

2009/HCI/Prelim/I/3. Printed/task labels inventoried: i, ii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

2 page-item records. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: 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.
Rendered source content: Settled source-content screenshots reviewed

A derivative zero alone does not establish a maximum or minimum.

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

05 Differentiation (Gradient function).pdf · p.3
05 Differentiation (Gradient function).pdf · p.4
05 Differentiation sol.pdf · p.6

05-07 · Recover the signs hidden by an absolute valueQuestion pp.3 / Solution pp.7

Question and explanations → · Complete native source article →

2021/DHS/Promo/7. Printed/task labels inventoried: i, ii.a, ii.b, iii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

5 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

6 page-item records. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed with endpoint convention qualification. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: 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.
Rendered source content: Settled source-content screenshots reviewed

A minimum of |f| need not be a minimum of f. Closed endpoints describe full branches, not strict derivative inequalities.

Essential answer conditions and source qualifications

ii(a)

The derivative is strictly negative only for x<0 or x>3; stationary endpoints may be included when naming whole branches.

ii(b)

Strict f″>0 only on −1<x<2; f″=0 at −1, and x=2 is excluded.

Exact private source page references

05 Differentiation (Gradient function).pdf · p.3
05 Differentiation (Gradient function).pdf · p.4
05 Differentiation sol.pdf · p.7

An empty omission list is not a completeness certificate. Add any issue you find to the article or page-item record before calling that part finished.