Technique Masterclasses

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 topicLesson fileSeries with a real citationSeen inConfirmed real item size
Proof by contradiction (1.1)proof-by-contradiction.tsJan 2021, Oct 2021, Jun 2022, Jan 2024, Oct 2024, Jan 20266 of 74–5 marks (Jun 2022 Q9 = 4; Oct 2024 Q2 = 4; Jan 2026 Q8 = 5)
Binomial expansion (4.1)binomial-expansion-for-rational-n.tsJan 2021, Oct 2021, Oct 2022, Jan 2024, Oct 20245 of 76 marks (Oct 2024 Q1, 4+2)
Implicit/parametric differentiation, tangents & normals (5.1)implicit-and-parametric-differentiation-tangents-and-normals.tsJan 2021, Oct 2021, Oct 2022, Jan 20244 of 79 marks (Jan 2021 Q6, 5+4)
Scalar product, angle, skew/parallel lines (7.6–7.7)vectors-scalar-product-and-skew-lines.tsJan 2021, Oct 2022, Jan 2024, Jan 20264 of 711 marks (Jan 2026 Q9, 3+4+2+2)
Separable differential equations & rates of change (5.2, 6.4)separable-differential-equations.tsJan 2021, Oct 2021, Jan 2024, Jan 20264 of 78 marks (Jan 2026 Q3, 6+2)
Partial fractions, incl. integration via them (2.1, 6.3)partial-fractions-decomposition-and-integration.tsOct 2021, Oct 2022, Jan 20243 of 7— (no single confirmed total captured in either source)
Parametric conversion & domain/range (3.1)parametric-equations-conversion-and-domain-range.tsJan 2021, Oct 2021, Oct 20223 of 77 marks (Jan 2021 Q4, 5+2)
Volume of revolution (6.1)volume-of-revolution.tsJan 2021, Oct 2022, Jan 20243 of 710 marks (Jan 2021 Q9, 7+3)
Integration by parts & substitution (6.2)integration-by-parts-and-substitution.tsOct 2021, Oct 2022, Jan 20243 of 7part 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.tsOct 20211 of 79 marks (Oct 2021 Q7, 7+2)
Area under a parametric curve (6.5)area-under-a-parametric-curve.tsJan 20261 of 716 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:

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

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.

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