PorismaSource review

Your source-to-article checklist

Source review · Series expansion

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

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.

Find a question, topic or source page

23 question records

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

09 · Series expansion

Edition metadata →

09-01 · Normalize before expandingQuestion pp.1 / Solution pp.1

Question and explanations → · Complete native source article →

[2022/EJC/Prelim/II/1]. 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

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

$-4/3<x<4/3$ .

Smaller omitted powers support this particular estimate; no universal error bound.

Exact private source page references

09 series expansion.pdf · p.1
09 seriex expansion sol.pdf · p.1

09-02 · Multiply two binomial seriesQuestion pp.2 / Solution pp.2

Question and explanations → · Complete native source article →

[2009/IJC/Prelim/I/7]. Printed/task labels inventoried: expansion, comparison, approximation.

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers. Source p.2 has a product-line typo (1−2x) in place of (1+2x); the actual binomial expansion and result use the plus sign.

Essential answer conditions and source qualifications

expansion

$|x|<1/2$ .

comparison

A truncation heuristic, not a rigorous bound.

Exact private source page references

09 series expansion.pdf · p.2
09 seriex expansion sol.pdf · p.2

09-03 · Use partial fractions for distant coefficientsQuestion pp.3 / Solution pp.3

Question and explanations → · Complete native source article →

[2008/HCI/Prelim/I/6]. Printed/task labels inventoried: partial fractions, expansion, coefficient.

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

expansion

$|x|<1$ .

Exact private source page references

09 series expansion.pdf · p.3
09 seriex expansion sol.pdf · p.3

09-04 · Compare coefficients without full expansionsQuestion pp.3 / Solution pp.3, 4

Question and explanations → · Complete native source article →

[2020/HCI/Prelim/I/2]. Printed/task labels inventoried: coefficient equation.

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

No item inventoried — owner check needed

0 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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.3
09 series expansion.pdf · p.4
09 seriex expansion sol.pdf · p.3
09 seriex expansion sol.pdf · p.4

09-05 · Recover parameters and a general coefficientQuestion pp.4 / Solution pp.4

Question and explanations → · Complete native source article →

[ACJC/2009/Prelim/II/2]. 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

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

Integer $r\ge0$ ; $|x|<2/3$ .

Exact private source page references

09 series expansion.pdf · p.4
09 seriex expansion sol.pdf · p.4

09-06 · Read a tangent from the first two coefficientsQuestion pp.5 / Solution pp.5

Question and explanations → · Complete native source article →

[modified DHS/2008/Prelim/I/5]. Printed/task labels inventoried: expansion, validity, tangent.

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.5
09 seriex expansion sol.pdf · p.5

09-07 · Repeated poles and general coefficientsQuestion pp.6 / Solution pp.6

Question and explanations → · Complete native source article →

[2009/SAJC/JCT/8]. Printed/task labels inventoried: partial fractions, 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

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

$|x|<1/2$ .

Integer $r\ge0$ .

Exact private source page references

09 series expansion.pdf · p.6
09 seriex expansion sol.pdf · p.6

09-08 · Check an approximation by its error functionQuestion pp.7 / Solution pp.7

Question and explanations → · Complete native source article →

[2018/DHS/Prelim/I/2]. 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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

Strict error less than 0.3; rounded endpoints are illustrative.

Exact private source page references

09 series expansion.pdf · p.7
09 seriex expansion sol.pdf · p.7

09-09 · Two routes to the same square-root seriesQuestion pp.8 / Solution pp.8, 9

Question and explanations → · Complete native source article →

[2020/MI/Prelim/I/6]. 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

4 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

6 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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

iii

Real square-root branch near 0, where $\cos x>0$ .

Exact private source page references

09 series expansion.pdf · p.8
09 series expansion.pdf · p.9
09 seriex expansion sol.pdf · p.8
09 seriex expansion sol.pdf · p.9

09-10 · A vanishing cubic term does not make an integral exactQuestion pp.10 / Solution pp.10, 11

Question and explanations → · Complete native source article →

[2023/DHS/Prelim/P1/6]. 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

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.10
09 series expansion.pdf · p.11
09 seriex expansion sol.pdf · p.10
09 seriex expansion sol.pdf · p.11

09-11 · Integration can leave the convergence rangeQuestion pp.11 / Solution pp.11, 12

Question and explanations → · Complete native source article →

[2020/NYJC/Prelim/I/9]. 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

4 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

6 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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.11
09 series expansion.pdf · p.12
09 seriex expansion sol.pdf · p.11
09 seriex expansion sol.pdf · p.12

09-12 · Derivatives from a nonlinear differential identityQuestion pp.12 / Solution pp.13

Question and explanations → · Complete native source article →

[2008/RJC/Prelim /II/5(c)]. Printed/task labels inventoried: derivative, series.

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.12
09 series expansion.pdf · p.13
09 seriex expansion sol.pdf · p.12
09 seriex expansion sol.pdf · p.13

09-13 · An even function has no linear termQuestion pp.13 / Solution pp.13, 14

Question and explanations → · Complete native source article →

[2008/AJC/Prelim/I/4]. Printed/task labels inventoried: identity, series, approximation.

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

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.13
09 series expansion.pdf · p.14
09 seriex expansion sol.pdf · p.13
09 seriex expansion sol.pdf · p.14

09-14 · Factor a logarithm argumentQuestion pp.14 / Solution pp.14, 15

Question and explanations → · Complete native source article →

[2010/MI/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

4 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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.14
09 series expansion.pdf · p.15
09 seriex expansion sol.pdf · p.14
09 seriex expansion sol.pdf · p.15

09-15 · Use one series to recover its companionQuestion pp.15 / Solution pp.15, 16

Question and explanations → · Complete native source article →

[2022/DHS/Prelim/I/6]. 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

4 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

6 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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.15
09 series expansion.pdf · p.16
09 seriex expansion sol.pdf · p.15
09 seriex expansion sol.pdf · p.16

09-16 · Compose sine and logarithm carefullyQuestion pp.16 / Solution pp.16, 17, 18

Question and explanations → · Complete native source article →

[2022/ACJC/Prelim/I/7]. 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

6 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

6 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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.16
09 series expansion.pdf · p.17
09 series expansion.pdf · p.18
09 seriex expansion sol.pdf · p.16
09 seriex expansion sol.pdf · p.17
09 seriex expansion sol.pdf · p.18

09-17 · Small-angle series in a triangleQuestion pp.18 / Solution pp.18, 19

Question and explanations → · Complete native source article →

[2022/ASRJC/Prelim/I/4]. 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

4 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

6 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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

iii

Small angles in radians; geometry $0<\theta<\pi/4$ .

Exact private source page references

09 series expansion.pdf · p.18
09 series expansion.pdf · p.19
09 seriex expansion sol.pdf · p.18
09 seriex expansion sol.pdf · p.19

09-18 · Sine rule and a percentage-error intervalQuestion pp.20 / Solution pp.20, 21

Question and explanations → · Complete native source article →

[2023/SAJC/Prelim/P2/2]. 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

4 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

6 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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

iii

Physical domain $0<\theta<\pi/6$ ; error strictly below 5%.

Exact private source page references

09 series expansion.pdf · p.20
09 series expansion.pdf · p.21
09 seriex expansion sol.pdf · p.20
09 seriex expansion sol.pdf · p.21

09-19 · A sector arc contributes a linear termQuestion pp.22 / Solution pp.22

Question and explanations → · Complete native source article →

[2018/AJC/Prelim/I/2]. Printed/task labels inventoried: perimeter.

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

perimeter

Small positive $\theta$ in radians; PR is the minor arc.

Exact private source page references

09 series expansion.pdf · p.22
09 seriex expansion sol.pdf · p.22

09-20 · Differentiate only after keeping enough termsQuestion pp.22 / Solution pp.22, 23

Question and explanations → · Complete native source article →

[2009/MI/PU2 Promo/I/7]. Printed/task labels inventoried: identity, i, ii, integral.

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

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

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 rendered question requests two derivative-series terms, not three. The earlier compact transcription misread this request; it has been corrected during the complete native audit. The printed two-term solution is not missing a requested term. The quadratic integral estimate is a truncation, without a small-error guarantee over the full interval.

Essential answer conditions and source qualifications

integral

Requested quadratic truncation; small error is not guaranteed over the entire interval. The source requests only two derivative terms.

Exact private source page references

09 series expansion.pdf · p.22
09 series expansion.pdf · p.23
09 seriex expansion sol.pdf · p.22
09 seriex expansion sol.pdf · p.23

09-21 · An inverse tangent generates a reciprocal seriesQuestion pp.24 / Solution pp.24

Question and explanations → · Complete native source article →

[2008/HCI/Prelim P2/1]. Printed/task labels inventoried: identity, series, reciprocal.

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.24
09 seriex expansion sol.pdf · p.24

09-22 · A shifted cotangent is analytic at zeroQuestion pp.25 / Solution pp.25, 26

Question and explanations → · Complete native source article →

[modified 2009/ACJC/Prelim/I/11]. 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

4 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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.25
09 series expansion.pdf · p.26
09 seriex expansion sol.pdf · p.25
09 seriex expansion sol.pdf · p.26

09-23 · Integrate a chain-rule derivative firstQuestion pp.26 / Solution pp.26, 27

Question and explanations → · Complete native source article →

[2010/SAJC/Prelim P1/9]. Printed/task labels inventoried: i, ii, iii, iv.a, iv.b.

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

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

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

Both Topic 09 PDFs are identical and include full solutions beside the questions; opening source pages reveals answers.

Essential answer conditions and source qualifications

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

Exact private source page references

09 series expansion.pdf · p.26
09 series expansion.pdf · p.27
09 seriex expansion sol.pdf · p.26
09 seriex expansion sol.pdf · p.27

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.