Coverage & provenance · Applications of differentiation
All coverage topics · Student practice
Indexing is not transcription, and transcription is not mathematical review. This page keeps those stages visible.
18 of 18 groups have authored prompts and authored interactive lessons; 0 await conversion. 18 have mathematical review recorded. Review includes documented qualifications where the printed source is inconsistent or depends on an unstated assumption. This is a first authoring and mathematical review pass, not independent expert certification. Difficulty ratings remain unassigned. The ledger below distinguishes these states.
Inventory reconciliation: Inequalities Q13–14 are on question PDF page 3, printed page 22. Their extra indentation caused the initial scan to stop at Q12. The corrected topic count is 14 and the overall count is 248; original source bytes are unchanged.
Collection-wide source ledger
248 complete-source articles and 15 topic metadata articles cover 468 original page instances. Source transcription, mathematical review and browser acceptance are recorded separately.
Download the native page-by-item ledger →Topic ledger
| Topic | Groups | Authored explanations | Maths review | Source pages |
|---|---|---|---|---|
| 06 · Applications of differentiation | 18 | 18 / 18 | 18 / 18 | 9 question / 29 solution |
Source qualifications and cautions
The original pages remain unchanged. Corrections, interpretation choices and necessary domain conditions are recorded alongside the authored working.
06-01 · reviewed
An undefined slope is not automatically a vertical tangent at every singularity. Here the nonzero implicit gradient verifies it.
06-02 · reviewed with nonzero-parameter qualification
The answer list prints only one sign in part (iii); both x-axis intersections require a normal. Closedness supplies the unstated n≠0 condition.
06-03 · reviewed
Dividing by b would lose the two horizontal normals.
06-04 · reviewed
ln(x²) is defined for negative x too; replacing it by 2ln x discards the branch containing Q.
06-05 · reviewed
A tangent can touch at one parameter and intersect again elsewhere; do not infer the second meeting from tangency alone.
06-06 · reviewed with source-domain discrepancy
Printed greatest value assumes an unstated domain restriction. Keep the local answer and unrestricted conclusion distinct.
06-07 · reviewed
The Cartesian equation alone includes an unattained origin; retain a≠0. Do not divide by t(t+2) when deriving a formula valid at horizontal tangents.
06-08 · reviewed
The midpoint locus is not an ordinary ellipse in x,y: reciprocal coordinates satisfy the ellipse identity.
06-09 · reviewed
Do not integrate from t=0 as if the entire path and axis enclosed one positive region; the early curve doubles back in x.
06-10 · reviewed
Use degree mode for this model. The approaching target travels towards the origin, so its distance decreases.
06-11 · reviewed
Using x+1 for the outer base side misses one wall; using h+2 adds a lid the design does not have.
06-12 · reviewed
Do not count the joined circular cone base as exposed area, and do not omit the floor.
06-13 · reviewed
The surface-area bound is a limiting value for nonzero cylinder height; distinguish a supremum from an attained maximum.
06-14 · reviewed
Do not mistake the interior stationary maximum for the minimum on a closed interval.
06-15 · reviewed
The printed range A>−1/27 must be read alongside its original A≠0 assumption. At the discriminant boundary the derivative is 0/0.
06-16 · reviewed
Radius changes as the water rises; it is not the constant full-container radius 9 cm.
06-17 · reviewed
The source line has x=2y+4, not 2y+2; one intermediate printed line contains the latter typo but its final Q is correct.
06-18 · reviewed
The shrinking cylinder height makes the radius increase; keep dx/dt negative.
Series expansion topic 09 has byte-identical question and solution PDFs. Their printed solutions are transcribed once; the provenance ledger accounts for both file instances.
Exam references
2025 TJC H2 Maths (9758), JC2 MSM. Individual exam references are retained on question pages; original question and solution page numbers are kept independently. Source margin notes, short keys, tables and diagrams are transcribed into native articles. All 468 original page instances map to 2,703 native item records. Diagrams are source-specific D3 SVGs.
Owner reports that the source contributor has permission to republish. Original attribution and source-page provenance are retained. Originals are preserved privately for quality checks and are excluded from the delivered site.
Byte verification
Original ZIP: 11,692,621 bytes.
SHA-256: 39645f7e5aee1f8d870eca9267920157747d43725a1cc8b0486cb43ca532b1cc
30 PDFs / 468 PDF pages. Every PDF has its own byte length and SHA-256 in the manifest.
Question-by-question status
| Question | Conversion | Mathematical review | Question PDF pages |
|---|---|---|---|
| 06-01 · Source review | authored | reviewed | 1 |
| 06-02 · Source review | authored | reviewed with nonzero-parameter qualification | 1 |
| 06-03 · Source review | authored | reviewed | 1 |
| 06-04 · Source review | authored | reviewed | 1 |
| 06-05 · Source review | authored | reviewed | 2 |
| 06-06 · Source review | authored | reviewed with source-domain discrepancy | 2 |
| 06-07 · Source review | authored | reviewed | 2 |
| 06-08 · Source review | authored | reviewed | 3 |
| 06-09 · Source review | authored | reviewed | 3 |
| 06-10 · Source review | authored | reviewed | 4 |
| 06-11 · Source review | authored | reviewed | 5 |
| 06-12 · Source review | authored | reviewed | 5 |
| 06-13 · Source review | authored | reviewed | 6 |
| 06-14 · Source review | authored | reviewed | 6 |
| 06-15 · Source review | authored | reviewed | 6 |
| 06-16 · Source review | authored | reviewed | 7 |
| 06-17 · Source review | authored | reviewed | 7 |
| 06-18 · Source review | authored | reviewed | 8 |