PorismaSource review

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Source review · Inequalities

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.

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14 question records

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

03 · Inequalities

Edition metadata →

03-01 · Keep the denominator sign in viewQuestion pp.1 / Solution pp.1

Question and explanations → · Complete native source article →

[2009/JJC/Prelim/I/6b]. Printed/task labels inventoried: first, hence.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.1
03 Inequalities sol.pdf · p.1

03-02 · A positive square denominator still has a holeQuestion pp.1 / Solution pp.2

Question and explanations → · Complete native source article →

[modified 2011/RI/Prelim/I/1]. 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

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.1
03 Inequalities sol.pdf · p.2

03-03 · Replace the input by its magnitudeQuestion pp.1 / Solution pp.3

Question and explanations → · Complete native source article →

[2008/RJC/J1/T3 CT/9]. Printed/task labels inventoried: a.first, a.hence, b.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.1
03 Inequalities sol.pdf · p.3

03-04 · A range proof needs degenerate casesQuestion pp.1 / Solution pp.4, 5

Question and explanations → · Complete native source article →

[2018/ACJC/Prelim/I/8]. Printed/task labels inventoried: a.first, a.hence, 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

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-with-source-correction. 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

Source discrepancy to review: solution PDF pp.4–5 applies the discriminant formula to all −1≤k≤1 without checking k=0 or cancelled roots at k=±1. Porisma separates those cases; the printed source remains available.

Essential answer conditions and source qualifications

For 0<|k|<1. If k=0: (−∞,−1]∪(0,∞). If k=±1: ℝ excluding 0 and −1/2.

Exact private source page references

03 Inequalities.pdf · p.1
03 Inequalities sol.pdf · p.4
03 Inequalities sol.pdf · p.5

03-05 · Split at the absolute-value boundaryQuestion pp.1 / Solution pp.6

Question and explanations → · Complete native source article →

[modified 2008/ACJC/Prelim/I/5]. Printed/task labels inventoried: first, hence.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.1
03 Inequalities sol.pdf · p.6

03-06 · Use the double-angle identity before solvingQuestion pp.1 / Solution pp.7

Question and explanations → · Complete native source article →

[2018/DHS/Prelim/I/4]. Printed/task labels inventoried: simplify, solve.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.1
03 Inequalities sol.pdf · p.7

03-07 · Strict positivity requires a strict discriminant boundQuestion pp.2 / Solution pp.8

Question and explanations → · Complete native source article →

[2008/TPJC/Prelim/I/4]. Printed/task labels inventoried: positivity, parameter.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.2
03 Inequalities sol.pdf · p.8

03-08 · A chained inequality means an intersectionQuestion pp.2 / Solution pp.9

Question and explanations → · Complete native source article →

[2011/MJC/Prelim/I/6a]. Printed/task labels inventoried: chain.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.2
03 Inequalities sol.pdf · p.9

03-09 · A repeated factor does not disappear from a strict inequalityQuestion pp.2 / Solution pp.10, 11

Question and explanations → · Complete native source article →

[modified 2008/RJC/Prelim/II/1]. Printed/task labels inventoried: factorization, solve, deduce.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.2
03 Inequalities sol.pdf · p.10
03 Inequalities sol.pdf · p.11

03-10 · Square substitution preserves an excluded zeroQuestion pp.2 / Solution pp.11, 12

Question and explanations → · Complete native source article →

[2009/NJC/Prelim/I/1]. Printed/task labels inventoried: first, hence.

Question / subparts

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.2
03 Inequalities sol.pdf · p.11
03 Inequalities sol.pdf · p.12

03-11 · Reciprocals reverse negative interval orderQuestion pp.2 / Solution pp.12, 13

Question and explanations → · Complete native source article →

[2014/ACJC/Promo/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

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.2
03 Inequalities sol.pdf · p.12
03 Inequalities sol.pdf · p.13

03-12 · Fold the rational graph above the axisQuestion pp.2 / Solution pp.13, 14

Question and explanations → · Complete native source article →

[2020/YIJC/Prelim/I/4]. Printed/task labels inventoried: i, ii.sketch, ii.solve.

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.2
03 Inequalities.pdf · p.4
03 Inequalities sol.pdf · p.13
03 Inequalities sol.pdf · p.14

03-13 · A downward absolute-value graph with parametersQuestion pp.3 / Solution pp.14, 15

Question and explanations → · Complete native source article →

[2020/ACJC/Prelim/I/4]. Printed/task labels inventoried: i, ii.a, ii.b.sketch, ii.b.solve, ii.b.deduce.

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

Essential answer conditions and source qualifications

ii(b) — sketch

$a<b<-1$ .

Exact private source page references

03 Inequalities.pdf · p.3
03 Inequalities.pdf · p.4
03 Inequalities sol.pdf · p.14
03 Inequalities sol.pdf · p.15

03-14 · An exponential reflected at its zeroQuestion pp.3 / Solution pp.16

Question and explanations → · Complete native source article →

[2022/ACJC/Prelim/I/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

1 page-item record.

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

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

Essential answer conditions and source qualifications

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

Exact private source page references

03 Inequalities.pdf · p.3
03 Inequalities.pdf · p.4
03 Inequalities sol.pdf · p.16

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.