Pure Mathematics 4
Frequency and Boundaries
Provenance: written 2026-09-28, grounded in research/veridian/WMA14-verified-facts.md and
cross-referenced against this pair's own already-verified figures in
content/veridian/technique-hub/wma14/forge-exam-technique-guide.md (§1's real per-question mark
tariffs) and codex-formula-and-method-bank.md (the spec-point/lesson-file grouping). No new primary
document was fetched for this file — it re-analyses the facts bank's existing §5 citations by series,
and does not extend the evidence base beyond what those two documents already established. Every
mark-weight figure below is a single real confirmed question, cited as such, not an average or a
paper-wide weighting — this spec does not publish one (see §1 below).
WMA14 · SIGNAL — Topic Frequency & Grade Boundaries
This is deliberately the narrowest of the three WMA14 reference documents. It answers two questions only: how often has each spec topic actually shown up in the series this course has verified primary documents for, and what do real grade boundaries say. It does not re-teach technique (the 12 curriculum lessons do that) and does not repeat FORGE's exam-craft layer or CODEX's formula masterlist — both are cited, not duplicated.
How to use this document
The frequency table is evidence of past coverage across a small, specific set of series — not a prediction of what will appear on any future paper, and not a substitute for knowing every spec point cold (spec 1.3 and Pearson's own guidance both note IAL papers can, and do, test any listed content in any series). Read "seen in N of M series checked" as exactly that: a count grounded in real citations, against a small, stated denominator — never as a probability, and never rounded into a percentage. Combine this with FORGE (how to play the marking system) and CODEX (the formulae and method skeletons) rather than in place of either.
1. Topic frequency, by spec point
Denominator and what it means. The facts bank has at least one primary document for 11 series, but only 7 of those received real, question-by-question mining — the other five (June 2021 provisional, January 2023, June 2023, October 2023, June 2024) had their mark schemes checked only for the shared general-marking-guidance boilerplate (M/A/B definitions, abbreviations), not analysed question by question, so they contribute no topic-specific citations either way. The honest denominator for a topic frequency claim is therefore the 7 series with question-level findings: January 2021, October 2021, June 2022, October 2022, January 2024, October 2024, January 2026. A topic absent from a series' row below means no citation for it was captured in this course's review of that series — not that the topic was confirmed absent from that paper.
No official per-topic mark weighting exists to check this against. The spec (p.69) publishes only an assessment-objective mark range for P4 out of 75 — AO1 25–30, AO2 25–30, AO3 5–10, AO4 5–10, AO5 5–10 — nothing per spec point. The "marks" column below is therefore a single real confirmed question's size, not a weighting; it is sourced from FORGE §1 rather than re-derived here, and marked "—" where neither source document captured one.
| Spec topic | Lesson file | Series with a real citation | Seen in | Confirmed real item size |
|---|---|---|---|---|
| Proof by contradiction (1.1) | proof-by-contradiction.ts | Jan 2021, Oct 2021, Jun 2022, Jan 2024, Oct 2024, Jan 2026 | 6 of 7 | 4–5 marks (Jun 2022 Q9 = 4; Oct 2024 Q2 = 4; Jan 2026 Q8 = 5) |
| Binomial expansion (4.1) | binomial-expansion-for-rational-n.ts | Jan 2021, Oct 2021, Oct 2022, Jan 2024, Oct 2024 | 5 of 7 | 6 marks (Oct 2024 Q1, 4+2) |
| Implicit/parametric differentiation, tangents & normals (5.1) | implicit-and-parametric-differentiation-tangents-and-normals.ts | Jan 2021, Oct 2021, Oct 2022, Jan 2024 | 4 of 7 | 9 marks (Jan 2021 Q6, 5+4) |
| Scalar product, angle, skew/parallel lines (7.6–7.7) | vectors-scalar-product-and-skew-lines.ts | Jan 2021, Oct 2022, Jan 2024, Jan 2026 | 4 of 7 | 11 marks (Jan 2026 Q9, 3+4+2+2) |
| Separable differential equations & rates of change (5.2, 6.4) | separable-differential-equations.ts | Jan 2021, Oct 2021, Jan 2024, Jan 2026 | 4 of 7 | 8 marks (Jan 2026 Q3, 6+2) |
| Partial fractions, incl. integration via them (2.1, 6.3) | partial-fractions-decomposition-and-integration.ts | Oct 2021, Oct 2022, Jan 2024 | 3 of 7 | — (no single confirmed total captured in either source) |
| Parametric conversion & domain/range (3.1) | parametric-equations-conversion-and-domain-range.ts | Jan 2021, Oct 2021, Oct 2022 | 3 of 7 | 7 marks (Jan 2021 Q4, 5+2) |
| Volume of revolution (6.1) | volume-of-revolution.ts | Jan 2021, Oct 2022, Jan 2024 | 3 of 7 | 10 marks (Jan 2021 Q9, 7+3) |
| Integration by parts & substitution (6.2) | integration-by-parts-and-substitution.ts | Oct 2021, Oct 2022, Jan 2024 | 3 of 7 | part of a 10-mark question (Jun 2022 Q8(b)) |
| Position vectors, foot of perpendicular (7.4–7.5) | position-vectors-distance-and-foot-of-perpendicular.ts | Oct 2021 | 1 of 7 | 9 marks (Oct 2021 Q7, 7+2) |
| Area under a parametric curve (6.5) | area-under-a-parametric-curve.ts | Jan 2026 | 1 of 7 | 16 marks (Jan 2026 Q7, 2+5+6+3) — the largest confirmed item in the whole facts bank |
Two things worth reading correctly rather than over-reading:
- Proof by contradiction's 6-of-7 is a genuine, robust finding — it is also the topic the examiner reports most consistently flag as weakly answered (facts bank §5.1), so high frequency and low average performance co-occur here, not high frequency and confidence.
- The bottom two rows (1 of 7 each) are a sourcing artefact, not evidence of rarity. Area under a parametric curve (6.5) is a compulsory, explicitly spec-listed skill (§1 above) that had zero citations anywhere in this facts bank until the January 2026 series was reviewed — it is the thinnest-evidenced spec point in the whole document, not a topic Pearson rarely tests. The same caution applies to position vectors/foot-of-perpendicular, evidenced by exactly one series. Do not read either row as "safe to deprioritise."
2. Grade boundaries
No real grade-boundary data exists in this course's WMA14 source review. WMA14-verified-facts.md
contains no grade-boundary figures anywhere — it was built from the specification, the formula
booklet, mark schemes and examiner's reports, none of which publish grade boundaries (those are
released separately, per series, on Pearson's results-day boundary documents). A direct search of the
facts bank for boundary-related content this session found only mathematical domain/range boundaries
inside worked questions (e.g. an interval endpoint in a parametric domain), not grade-boundary marks —
confirming the gap is real, not an oversight in searching.
This document does not estimate, interpolate or otherwise invent a boundary figure. Stating a
number here without a primary Pearson grade-boundaries document behind it would violate this course's
own no-fabrication discipline, the same standard the facts bank, FORGE and CODEX all hold to
elsewhere. Real WMA14/P4 grade boundaries, where published, live on Pearson's own results-day
documents (searchable via qualifications.pearson.com's grade boundaries archive, by series and paper
code WMA14/01); fetching and verifying those — the same primary-source discipline used for every other
claim in this facts bank — is future work, not something this pass had in scope or could responsibly
shortcut.
3. Flagged gaps
- The 7-series denominator is this document's own recount, not a figure copied from facts-bank §6 verbatim — §6 states "11 series with at least one document," but only 7 of those yielded real, question-level citations when §5 is read topic by topic (the October 2024 series in particular is cited extensively in §5 but is not named in §6's own 11-series list, an inconsistency in the source document worth flagging rather than silently resolving either way).
- A topic's absence from a series' citation list is not evidence that series omitted it. Restated from §1: five reviewed series contributed no question-level citations for any topic, because their mark schemes were checked only for shared boilerplate.
- No grade-boundary primary source was reviewed this session — see §2. This is a genuine, open gap, not a "checked and found nothing published" result.
Sources used
research/veridian/WMA14-verified-facts.md §5 (per-topic citations, re-tallied by series for this
document), §6 (series/document-count, cross-checked and found incomplete against §5 — see §3 above),
§2 (AO mark-range table, spec p.69). Real mark-weight figures are reused, not re-derived, from
forge-exam-technique-guide.md §1. Spec-point/lesson-file groupings are reused from
codex-formula-and-method-bank.md Part 2. No new primary Pearson document was fetched for this file.
Not affiliated with or endorsed by Pearson Edexcel.