Source review · Differential equations
All source-review topics · Coverage and provenance · Student practice
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18 question records
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10 · Differential equations
Edition metadata →10-01 · A removable extension of the differential equationQuestion pp.1 / Solution pp.1
Question and explanations → · Complete native source article →
[2010/MI/Prelim/I/11(b) (modified)]. Printed/task labels inventoried: i, ii, iii.
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2 page-item records.
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- source-compared
- Mathematical correctness
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- 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.
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The original equation is undefined at x=0. The requested initial condition uses the smooth extension y′=2x/(1+x²); this interpretation follows the printed working rather than treating the displayed equation as defined there.
Essential answer conditions and source qualifications
Original DE requires on each connected interval.
Uses the intended smooth extension through 0.
Exact private source page references
- 10 DE.pdf · p.1
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.1
10-02 · A second-order equation needs two constantsQuestion pp.1 / Solution pp.1
Question and explanations → · Complete native source article →
[modified 2011/RVHS/Promo/12ai]. Printed/task labels inventoried: general solution.
Question / subparts
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2 page-item records.
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Source comparison recorded
2 page-item records.
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Source comparison recorded
1 page-item record.
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No item inventoried — owner check needed
0 page-item records.
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No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
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Essential answer conditions and source qualifications
On intervals where .
Exact private source page references
- 10 DE.pdf · p.1
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.1
10-03 · The product substitution absorbs a linear termQuestion pp.1 / Solution pp.2
Question and explanations → · Complete native source article →
[2012/RVHS/Prelim/II/1 (modified)]. Printed/task labels inventoried: substitution, general solution, i, ii.
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2 page-item records.
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2 page-item records.
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2 page-item records.
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0 page-item records.
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Source comparison recorded
4 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
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Essential answer conditions and source qualifications
; includes .
Exact private source page references
- 10 DE.pdf · p.1
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.2
10-04 · Bacteria growth after a product substitutionQuestion pp.1 / Solution pp.3
Question and explanations → · Complete native source article →
[2012/NJC/Prelim/I/4]. Printed/task labels inventoried: i, ii, iii.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
2 page-item records.
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Source comparison recorded
2 page-item records.
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No item inventoried — owner check needed
0 page-item records.
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No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
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Essential answer conditions and source qualifications
in hours.
Exact private source page references
- 10 DE.pdf · p.1
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.3
10-05 · Draining a sphere: height is not volumeQuestion pp.1 / Solution pp.4
Question and explanations → · Complete native source article →
[2019/NYJC/Prelim/I/7]. Printed/task labels inventoried: i, ii, iii.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
2 page-item records.
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Source comparison recorded
3 page-item records.
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No item inventoried — owner check needed
0 page-item records.
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No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
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Essential answer conditions and source qualifications
No separate condition recorded. Check the full question, native working and printed assumptions.
Exact private source page references
- 10 DE.pdf · p.1
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.4
10-06 · Drag models approach different terminal speedsQuestion pp.2 / Solution pp.5, 6, 7, 8
Question and explanations → · Complete native source article →
[2024/TJC/Prelim/I/11]. Printed/task labels inventoried: a.i, a.ii, b.i, b.ii.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
5 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
2 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
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Essential answer conditions and source qualifications
Positive equilibrium approached from rest; .
Exact private source page references
- 10 DE.pdf · p.2
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.5
- 10 DE sol.pdf · p.6
- 10 DE sol.pdf · p.7
- 10 DE sol.pdf · p.8
10-07 · Calibrate exponential decayQuestion pp.2 / Solution pp.8, 9
Question and explanations → · Complete native source article →
[modified 2015/YJC/Promo/9]. Printed/task labels inventoried: DE, i, ii, iii.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
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3 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
2 page-item records.
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No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
2 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
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Essential answer conditions and source qualifications
No separate condition recorded. Check the full question, native working and printed assumptions.
Exact private source page references
- 10 DE.pdf · p.2
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.8
- 10 DE sol.pdf · p.9
10-08 · Cooling toward ambient temperatureQuestion pp.2 / Solution pp.9, 10
Question and explanations → · Complete native source article →
[2023/RI/Prelim/I/6]. Printed/task labels inventoried: a, b, c.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
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3 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
4 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
2 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
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Essential answer conditions and source qualifications
Under the exercise rule, store before the 60°C crossing (t≈212.04 min).
Exact private source page references
- 10 DE.pdf · p.2
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.9
- 10 DE sol.pdf · p.10
10-09 · Constant input shifts a decay equilibriumQuestion pp.3 / Solution pp.11, 12
Question and explanations → · Complete native source article →
[2022/RI/Prelim/I/10]. Printed/task labels inventoried: i, ii, iii, iv, v.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
3 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
4 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
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Printed solution p.12 / question answer p.8 uses 0.35<μ<0.5. Inclusive healthy bounds permit both endpoints. Counterexamples μ=0.35 and μ=0.5 remain within the interval for every finite t; exclude them only if the limiting equilibrium must also be strictly interior.
Essential answer conditions and source qualifications
Source prints strict bounds. Inclusive healthy limits admit both endpoints; exclude them only if the limiting equilibrium must also be strictly interior.
Exact private source page references
- 10 DE.pdf · p.3
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.11
- 10 DE sol.pdf · p.12
10-10 · An exponential height law makes the rod never landQuestion pp.3 / Solution pp.13
Question and explanations → · Complete native source article →
[2012/HCI/I/8]. Printed/task labels inventoried: i, ii, iii, iv.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
2 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
3 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
4 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
- 10 DE.pdf · p.3
- 10 DE.pdf · p.8
- 10 DE sol.pdf · p.12
- 10 DE sol.pdf · p.13
10-11 · Keep population units consistentQuestion pp.4 / Solution pp.14, 15
Question and explanations → · Complete native source article →
[2019/RVHS/Prelim/I/10]. Printed/task labels inventoried: i, ii, iii, iv, v.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
3 page-item records.
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Source comparison recorded
2 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
2 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
- 10 DE.pdf · p.4
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.14
- 10 DE sol.pdf · p.15
10-12 · A decreasing forest model stops at extinctionQuestion pp.4 / Solution pp.16, 17
Question and explanations → · Complete native source article →
[2020/CJC/Prelim/II/4]. Printed/task labels inventoried: i, ii, iii.
Question / subparts
Source comparison recorded
2 page-item records.
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Source comparison recorded
3 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
3 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
2 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
Population interpretation only .
Exact private source page references
- 10 DE.pdf · p.4
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.15
- 10 DE sol.pdf · p.16
- 10 DE sol.pdf · p.17
10-13 · A square-root removal law has an implicit solutionQuestion pp.5 / Solution pp.18, 19
Question and explanations → · Complete native source article →
[2023/RVHS/Prelim/I/12]. Printed/task labels inventoried: i, ii, iii, iv.
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Source comparison recorded
2 page-item records.
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Source comparison recorded
3 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
3 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
.
Exact private source page references
- 10 DE.pdf · p.5
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.17
- 10 DE sol.pdf · p.18
- 10 DE sol.pdf · p.19
10-14 · Product substitution and a logistic epidemicQuestion pp.5 / Solution pp.20, 21, 22
Question and explanations → · Complete native source article →
[2017/RVHS/Promo/10]. Printed/task labels inventoried: a.substitution, a.solution, b.DE, b.solution.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
4 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
1 page-item record.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
; includes lost by division.
Exact private source page references
- 10 DE.pdf · p.5
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.20
- 10 DE sol.pdf · p.21
- 10 DE sol.pdf · p.22
10-15 · Compare unbounded growth with a carrying capacityQuestion pp.6 / Solution pp.22, 23
Question and explanations → · Complete native source article →
[2020/ACJC/Prelim/II/2]. Printed/task labels inventoried: i, ii, iii.
Question / subparts
Source comparison recorded
2 page-item records.
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3 page-item records.
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Source comparison recorded
1 page-item record.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
No item inventoried — owner check needed
0 page-item records.
Inspect native target →- 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
- 10 DE.pdf · p.6
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.22
- 10 DE sol.pdf · p.23
10-16 · A declining species and an increasing logistic speciesQuestion pp.6 / Solution pp.23, 24, 25, 26
Question and explanations → · Complete native source article →
[2021/TJC/Prelim/I/10]. Printed/task labels inventoried: a.i, a.ii, b.i, b.ii.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
5 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
6 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
3 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
Stop the population model at extinction.
Exact private source page references
- 10 DE.pdf · p.6
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.23
- 10 DE sol.pdf · p.24
- 10 DE sol.pdf · p.25
- 10 DE sol.pdf · p.26
10-17 · Separate the formal model from inconsistent pump directionsQuestion pp.6 / Solution pp.27, 28
Question and explanations → · Complete native source article →
[2022/ASRJC/Prelim/I/11]. Printed/task labels inventoried: i, ii, iii.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
3 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
3 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
2 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
Question PDF p.6 (printed73), solution pp.27–28: the printed k=−11/50 is algebraically consistent with the given derivative datum but incompatible with positive inflow ∝h² and positive outflow ∝h. The original wording and solution are preserved; the logistic interpretation is explicitly conditional.
Essential answer conditions and source qualifications
Incompatible with positive printed inflow∝h² and outflow∝h; no positive physical constants satisfy all data.
Conditional algebraic model, not a physically consistent solution of the printed pump description.
Exact private source page references
- 10 DE.pdf · p.6
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.26
- 10 DE sol.pdf · p.27
- 10 DE sol.pdf · p.28
10-18 · Logistic proportions and the first whole weekQuestion pp.7 / Solution pp.29, 30, 31, 32, 33
Question and explanations → · Complete native source article →
[2021/HCI/Prelim/I/10]. Printed/task labels inventoried: i, ii, iii, iv, v.
Question / subparts
Source comparison recorded
2 page-item records.
Inspect native target →Solution steps
Source comparison recorded
6 page-item records.
Inspect native target →Teacher notes
Source comparison recorded
3 page-item records.
Inspect native target →Tables
No item inventoried — owner check needed
0 page-item records.
Inspect native target →Diagrams
Source comparison recorded
4 page-item records. Native SVG generated; rendering is checked separately
Inspect native target →- 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
- 10 DE.pdf · p.7
- 10 DE.pdf · p.9
- 10 DE sol.pdf · p.29
- 10 DE sol.pdf · p.30
- 10 DE sol.pdf · p.31
- 10 DE sol.pdf · p.32
- 10 DE sol.pdf · p.33
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.