Pure Mathematics 3
Frequency and Boundaries
Provenance: compiled 2026-09-28. Topic-frequency data is drawn from research/veridian/WMA13-verified-facts.md (13 real WMA13 series, Oct 2020–Jun 2026 — 8 read start-to-finish with full mark schemes and examiner reports: Oct 2020, Oct 2021, Jan 2022, Jun 2022, Oct 2022, Jun 2023, Jan 2024, Jan 2025; 5 more checked for specific topics only: Jan 2023, Oct 2023, Jun 2024, Oct 2024, Jun 2026) and its companion documents forge-exam-technique-guide.md and codex-formula-and-method-bank.md in this same folder. Grade-boundary data is not in the research file — it was independently fetched this pass directly from Pearson's own published grade-boundary PDFs (qualifications.pearson.com/.../Grade-boundaries/International-A-level/*.pdf, one per session), each converted with pdftotext -layout and read for the WMA13 row specifically; every session's boundaries appeared twice in the same PDF (a landscape and a portrait table) and the two extractions agreed in every case checked. Full source list at the bottom.
WMA13 (Pure Mathematics 3) — Topic Frequency & Grade Boundaries
How to use this
This is a two-fact reference, not a technique guide — for exam technique and mark-scheme conventions, see forge-exam-technique-guide.md; for formulas and worked-method skeletons, see codex-formula-and-method-bank.md. Use the table below to gauge which spec topics have shown up most often in the 13 series actually checked, and use the grade-boundary table to see how much a raw mark is actually worth — not to predict a specific future paper. Every "N of 13" figure below is a count of series with a located, citable question on that topic, not an estimate of probability; a topic's absence from a series may mean it genuinely wasn't tested, or may mean that series was only checked for a different topic (5 of the 13 series were checked for specific things only, not read end-to-end — see the provenance note).
1. Topic frequency and typical mark-weight
| Spec item | Topic | Seen in (of 13 series checked) | Typical marks, when tested |
|---|---|---|---|
| 1.1 | Algebraic division / rational expressions | 4 — Oct 2020, Jan 2024, Jan 2025, Oct 2024 | The "show a given constant" step is usually 2 marks inside a larger 7–9 mark question |
| 1.2 | Functions — composition, inverse, domain/range | 9 — Oct 2021, Jan 2022, Jun 2022, Oct 2022, Jun 2023, Jan 2024, Jan 2023, Oct 2024, Jun 2026 | 6 marks as a compact opener; up to 8–9 with a second composition or an algebraic argument |
| 1.3 | The modulus function (equations/inequalities/graphs) | 5 — Oct 2020, Jan 2022, Jun 2023, Jan 2024, Oct 2023 | A single "solve |linear| > linear" part is ~4 marks |
| 1.4 | Combined transformations | 2 — Jan 2024, Jun 2026 | A few marks inside a larger multi-part question; not usually a standalone question |
| 2.1–2.2 | Reciprocal & inverse trig (sec/cosec/cot, arcsin/arccos/arctan) | Embedded as a first step inside larger questions in most series (not separately tallied); one full standalone worked anchor located, Jan 2022 | 1–3 marks, usually the accessible opening step of a bigger question |
| 2.3 | Double angle, compound angle, harmonic form (R cos/sin(θ±α)) | 5 — Oct 2020, Jan 2022, Jun 2022, Jun 2023, Jan 2024 (described in the research as anchoring a full question in nearly every series reviewed) | 8–9 marks as a full question; harmonic form specifically only confirmed head-on once (Oct 2020 Q7, 9 marks) |
| 3.1–3.2 | Exponential/log real-world modelling | 8 — Oct 2021, Jan 2022, Jun 2022, Oct 2022, Jun 2023, Jan 2024, Jan 2025, Jun 2026 (7 of the 8 full-review series had a modelling question) | Often the paper's largest single question, 9–12 marks |
| 3.3 | Log-linear graph parameter estimation | 2 — Jun 2023, Jun 2026 | 6–7 marks |
| 4.2 | Product / quotient / chain rule | 7 — Oct 2020, Oct 2021, Jan 2022, Jun 2023, Jan 2024, Oct 2024, Jun 2026 | 4 marks for a "show that f′(x)=…" alone; up to 10 across a full question |
| 4.3 | dy/dx = 1/(dx/dy) | 4 — Oct 2020, Jan 2022, Jun 2023, Oct 2024 | ~5 marks across two parts |
| 4.4 | Exponential growth/decay (differentiation, rate of change) | 6 — Jan 2022, Jun 2023, Jan 2024, Jan 2025, Oct 2024, Jun 2026 | Often paper's largest question, 9–12 marks total; the differentiation-specific part alone is often ~5 |
| 5.1–5.2 | Integration (standard + by recognition) | 4 — Oct 2020, Oct 2021, Jan 2022, Jun 2023 | Not separately tallied by tariff in the source material; typically part of a 5–9 mark question |
| 6.1–6.2 | Numerical methods (sign-change + iteration) | 9 — Oct 2020, Oct 2021, Jan 2022, Jun 2023, Jan 2024, Jan 2025, Oct 2022, Oct 2023, Jun 2026 | A clean 5 marks in at least two series; can extend to 8 with a third part |
Numerical methods (6.1–6.2) and functions (1.2) are the two most consistently evidenced topics in the archive — both are described in the research file as appearing as Q1 or Q2 in nearly every series reviewed. Exponential/log modelling (3) is the most consistently large question when it appears.
2. Grade boundaries
Real, Pearson-published data exists and is used here — this is not the case for every WMA13 support document in this course; a sibling paper's technique guide found no verified figure and said so. Raw marks are out of 75 (the whole paper); UMS boundaries are fixed by Pearson's design (A*=90, A=80, B=70, C=60, D=50, E=40, all out of 100) and do not vary by session, so only the raw-mark table below is informative.
| Series | A* | A | B | C | D | E |
|---|---|---|---|---|---|---|
| Oct 2020 | 64 | 53 | 42 | 31 | 20 | 9 |
| Oct 2021 | 63 | 50 | 39 | 28 | 18 | 8 |
| Jan 2022 | 63 | 50 | 39 | 28 | 18 | 8 |
| Jun 2022 | 60 | 47 | 39 | 31 | 23 | 16 |
| Oct 2022 | 60 | 47 | 39 | 31 | 23 | 16 |
| Jan 2023 | 58 | 45 | 37 | 30 | 23 | 16 |
| Jun 2023 | 68 | 61 | 54 | 47 | 40 | 34 |
| Oct 2023 | 66 | 59 | 52 | 45 | 38 | 32 |
| Jan 2024 | 68 | 61 | 54 | 47 | 40 | 34 |
| Jun 2024 | 68 | 62 | 56 | 50 | 44 | 38 |
| Oct 2024 | 65 | 59 | 53 | 47 | 41 | 36 |
| Jan 2025 | 65 | 59 | 53 | 47 | 41 | 36 |
| Jun 2026 | 63 | 57 | 51 | 45 | 39 | 33 |
Each figure is the minimum raw mark (out of 75) needed for that grade; U runs from 0 up to one below the E boundary. The A* boundary alone has ranged from 58 (Jan 2023, the hardest-graded series in this set) to 68 (Jun 2023, Jan 2024, and Jun 2024) — an 10-mark swing on a 75-mark paper. Treat any single series' boundary as informative about that sitting only, not as a stable target.
One unresolved detail, flagged rather than guessed at: Pearson's grade-boundary documents from June 2025 onward print a second WMA13 row, "Unit 3A: Pure Mathematics 3," with boundaries a few marks lower than the "Unit 3" row used above (e.g. Jun 2026: Unit 3A A*=61 vs Unit 3's 63). What distinguishes "Unit 3" from "Unit 3A" was not established in this pass — the table above consistently uses the "Unit 3" row, matching the WMA13 code used throughout the rest of this course's research.
Sources
research/veridian/WMA13-verified-facts.md— topic-frequency evidence, all counts in §1 traceable to its §5 (per-topic findings) and §7.forge-exam-technique-guide.md,codex-formula-and-method-bank.md(this folder) — mark-tariff figures reused from the FORGE guide's own §1 timing table.- Pearson grade-boundary PDFs, one per session,
qualifications.pearson.com/content/dam/pdf/Support/Grade-boundaries/International-A-level/(exact filenames vary by session, e.g.2306-ial-subject-grade-boundaries.pdffor Jun 2023,grade-boundaries-june-2026-international-advanced-level.pdffor Jun 2026,grade-boundaries-november-2020-ial.pdffor the Oct 2020 series) — downloaded and read directly this pass withpdftotext -layout, not carried over from any prior document.