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Source review · Applications of differentiation

All source-review topics · Coverage and provenance · Student practice

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18 question records

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06 · Applications of differentiation

Edition metadata →

06-01 · A vertical tangent forms a squareQuestion pp.1 / Solution pp.1

Question and explanations → · Complete native source article →

2012/NYJC/Prelim/I/3. Printed/task labels inventoried: derivative, i, ii, geometry.

Question / subparts

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2 page-item records.

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Solution steps

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2 page-item records.

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Teacher notes

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2 page-item records.

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Tables

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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

An undefined slope is not automatically a vertical tangent at every singularity. Here the nonzero implicit gradient verifies it.

Essential answer conditions and source qualifications

Derivative

At regular points where denominator is nonzero.

Exact private source page references

06 App of diff.pdf · p.1
06 App of diff.pdf · p.8
06 App of diff sol.pdf · p.1

06-02 · Vertical tangents on a tilted ellipseQuestion pp.1 / Solution pp.2, 3

Question and explanations → · Complete native source article →

2009/IJC/Prelim/I/11. Printed/task labels inventoried: i, ii, iii.

Question / subparts

Source comparison recorded

2 page-item records.

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Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

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2 page-item records.

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Tables

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0 page-item records.

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Diagrams

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0 page-item records.

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Short answer: source-compared
Mathematical correctness: reviewed with nonzero-parameter 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 answer list prints only one sign in part (iii); both x-axis intersections require a normal. Closedness supplies the unstated n≠0 condition.

Essential answer conditions and source qualifications

Closed-curve assumption requires n≠0.

iii

Both x-axis intersections require a normal; n≠0.

Exact private source page references

06 App of diff.pdf · p.1
06 App of diff.pdf · p.8
06 App of diff sol.pdf · p.2
06 App of diff sol.pdf · p.3

06-03 · All ellipse normals through a fixed pointQuestion pp.1 / Solution pp.3, 4, 5

Question and explanations → · Complete native source article →

2023/MI/Prelim/II/4. Printed/task labels inventoried: i, ii, iii.

Question / subparts

Source comparison recorded

2 page-item records.

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Solution steps

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4 page-item records.

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Teacher notes

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1 page-item record.

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Tables

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0 page-item records.

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Diagrams

Source comparison recorded

3 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

Dividing by b would lose the two horizontal normals.

Essential answer conditions and source qualifications

$y\ne0$ .

iii

Retain both axis-point normals; dividing by b would lose them.

Exact private source page references

06 App of diff.pdf · p.1
06 App of diff.pdf · p.8
06 App of diff sol.pdf · p.3
06 App of diff sol.pdf · p.4
06 App of diff sol.pdf · p.5

06-04 · Two tangents to an exponential-logarithmic curveQuestion pp.1 / Solution pp.5, 6

Question and explanations → · Complete native source article →

2022/HCI/Prelim/I/9. Printed/task labels inventoried: i, ii, iii.

Question / subparts

Source comparison recorded

2 page-item records.

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Solution steps

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3 page-item records.

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Teacher notes

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3 page-item records.

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Tables

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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

ln(x²) is defined for negative x too; replacing it by 2ln x discards the branch containing Q.

Essential answer conditions and source qualifications

$x\ne0$ .

Exact private source page references

06 App of diff.pdf · p.1
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.5
06 App of diff sol.pdf · p.6

06-05 · Horizontal and vertical parametric tangentsQuestion pp.2 / Solution pp.7, 8

Question and explanations → · Complete native source article →

modified 2011/SRJC/Prelim/II/3. Printed/task labels inventoried: i, ii, iii, iv.

Question / subparts

Source comparison recorded

2 page-item records.

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Solution steps

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3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

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2 page-item records.

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Tables

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0 page-item records.

Inspect native target → I compared this with the original

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

A tangent can touch at one parameter and intersect again elsewhere; do not infer the second meeting from tangency alone.

Essential answer conditions and source qualifications

$0\le\theta\le2\pi$ ; distinct from the tangent point θ=π/6.

Exact private source page references

06 App of diff.pdf · p.2
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.7
06 App of diff sol.pdf · p.8

06-06 · Decreasing curves and the largest tangent interceptQuestion pp.2 / Solution pp.9, 10

Question and explanations → · Complete native source article →

2011/NYJC/Prelim/I/9. Printed/task labels inventoried: i, ii, iii.

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

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0 page-item records.

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Tables

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

3 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 source-domain discrepancy. 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

Printed greatest value assumes an unstated domain restriction. Keep the local answer and unrestricted conclusion distinct.

Essential answer conditions and source qualifications

iii — greatest value

h→∞ as x→−∞. If x≥0 (or x>1) is intended, the maximum is 4e⁻² at x=2.

Exact private source page references

06 App of diff.pdf · p.2
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.9
06 App of diff sol.pdf · p.10

06-07 · A normal intersection and a midpoint locusQuestion pp.2 / Solution pp.10, 11, 12

Question and explanations → · Complete native source article →

2022/NYJC/Prelim/I/7. Printed/task labels inventoried: i, ii, iii.

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

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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

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. 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 Cartesian equation alone includes an unattained origin; retain a≠0. Do not divide by t(t+2) when deriving a formula valid at horizontal tangents.

Essential answer conditions and source qualifications

$a\ne0,t\ne-1$ ; formula also covers horizontal-tangent parameters 0 and −2.

iii

a≠0.

Exact private source page references

06 App of diff.pdf · p.2
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.10
06 App of diff sol.pdf · p.11
06 App of diff sol.pdf · p.12

06-08 · Ellipse tangent intercepts and their midpointQuestion pp.3 / Solution pp.12, 13

Question and explanations → · Complete native source article →

2023/ACJC/Promo/7. Printed/task labels inventoried: a, b, c, d.

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

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

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

The midpoint locus is not an ordinary ellipse in x,y: reciprocal coordinates satisfy the ellipse identity.

Essential answer conditions and source qualifications

$0<p<\pi/2$ .

These conditions select the actual midpoint locus.

Exact private source page references

06 App of diff.pdf · p.3
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.12
06 App of diff sol.pdf · p.13

06-09 · A particle switches from a curve to its normalQuestion pp.3 / Solution pp.14, 15

Question and explanations → · Complete native source article →

2017/SRJC/Prelim/I/10. Printed/task labels inventoried: i, ii, iii, iv, v.

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

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

3 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

Do not integrate from t=0 as if the entire path and axis enclosed one positive region; the early curve doubles back in x.

Essential answer conditions and source qualifications

No y-axis intersection; follows curve until t=2, then its normal to A.

The enclosed region begins at the curve’s x-axis crossing, not the free launch endpoint.

Exact private source page references

06 App of diff.pdf · p.3
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.14
06 App of diff sol.pdf · p.15

06-10 · Two launch angles for an approaching targetQuestion pp.4 / Solution pp.16, 17

Question and explanations → · Complete native source article →

Not printed in supplied question. Printed/task labels inventoried: i, ii, iii, iv.

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

2 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

3 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

Use degree mode for this model. The approaching target travels towards the origin, so its distance decreases.

Essential answer conditions and source qualifications

Use the specified rounded launch angle 22.7° and degree mode.

Exact private source page references

06 App of diff.pdf · p.4
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.16
06 App of diff sol.pdf · p.17

06-11 · Minimise material in a thick lidless containerQuestion pp.5 / Solution pp.18

Question and explanations → · Complete native source article →

2009/MJC/Prelim/I/11. 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

2 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

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

Using x+1 for the outer base side misses one wall; using h+2 adds a lid the design does not have.

Essential answer conditions and source qualifications

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

Exact private source page references

06 App of diff.pdf · p.5
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.18

06-12 · A cone-roof model with least surface areaQuestion pp.5 / Solution pp.19, 20

Question and explanations → · Complete native source article →

2022/NYJC/Prelim/I/Q2. 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

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

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

Do not count the joined circular cone base as exposed area, and do not omit the floor.

Essential answer conditions and source qualifications

Optimal dimensions

$k>0$ ; includes the circular floor but excludes the joined cone base.

Exact private source page references

06 App of diff.pdf · p.5
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.19
06 App of diff sol.pdf · p.20

06-13 · A cylinder inscribed in a coneQuestion pp.6 / Solution pp.20, 21

Question and explanations → · Complete native source article →

2010/NYJC/Prelim/II/Q2. 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

1 page-item record.

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

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

The surface-area bound is a limiting value for nonzero cylinder height; distinguish a supremum from an attained maximum.

Essential answer conditions and source qualifications

Surface-area bound

$c>0,0<x<2c$ ; equality only in the zero-height limiting cylinder.

Exact private source page references

06 App of diff.pdf · p.6
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.20
06 App of diff sol.pdf · p.21

06-14 · The best seat for the viewing angleQuestion pp.6 / Solution pp.22, 23

Question and explanations → · Complete native source article →

2008/RJC/Prelim/I/11(b). Printed/task labels inventoried: i, ii, iii.

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

2 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

3 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

Do not mistake the interior stationary maximum for the minimum on a closed interval.

Essential answer conditions and source qualifications

$x>0$ .

Exact private source page references

06 App of diff.pdf · p.6
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.22
06 App of diff sol.pdf · p.23

06-15 · Stationary points of an implicit cubicQuestion pp.6 / Solution pp.23, 24

Question and explanations → · Complete native source article →

2023/EJC/Prelim/II/4. Printed/task labels inventoried: a, b, c.

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

1 page-item record.

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. 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 range A>−1/27 must be read alongside its original A≠0 assumption. At the discriminant boundary the derivative is 0/0.

Essential answer conditions and source qualifications

b — coordinates

Real cube roots; ordinate y=3x².

b — parameter range

At A=−1/27 the repeated candidate is singular, not a regular stationary point.

Exact private source page references

06 App of diff.pdf · p.6
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.23
06 App of diff sol.pdf · p.24

06-16 · Water rises through a conical containerQuestion pp.7 / Solution pp.25

Question and explanations → · Complete native source article →

2009/SRJC/Prelim/II/1. 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

1 page-item record.

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

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

Radius changes as the water rises; it is not the constant full-container radius 9 cm.

Essential answer conditions and source qualifications

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

Exact private source page references

06 App of diff.pdf · p.7
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.25

06-17 · Vertical and horizontal gaps to a parabolaQuestion pp.7 / Solution pp.26, 27, 28

Question and explanations → · Complete native source article →

2017/ACJC/Prelim/I/8. Printed/task labels inventoried: i, ii, iii, iv.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

4 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

2 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

The source line has x=2y+4, not 2y+2; one intermediate printed line contains the latter typo but its final Q is correct.

Essential answer conditions and source qualifications

Minimum AB=31/16.

Minimum PQ=31/8.

Exact private source page references

06 App of diff.pdf · p.7
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.26
06 App of diff sol.pdf · p.27
06 App of diff sol.pdf · p.28

06-18 · A capsule changes inside a fixed coneQuestion pp.8 / Solution pp.28, 29

Question and explanations → · Complete native source article →

2008/AJC/Prelim/I/7. 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

Source comparison recorded

3 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

The shrinking cylinder height makes the radius increase; keep dx/dt negative.

Essential answer conditions and source qualifications

For a genuine cylinder 0<r<9/2.

Exact private source page references

06 App of diff.pdf · p.8
06 App of diff.pdf · p.9
06 App of diff sol.pdf · p.28
06 App of diff sol.pdf · p.29

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.