Technique Masterclasses

Pure Mathematics 2

Frequency and Boundaries

Provenance: written 2026-09-28, against forge-exam-technique-guide.md and codex-formula-and-method-bank.md (both read in full) and research/veridian/WMA12-verified-facts.md (read in full, §1–§9, specifically §5 for the archive's real scope — 20 series with question paper + mark scheme reviewed, June 2019–January 2026; 17 of those with an examiner report — and §6/§7 for the per-topic citations the frequency table below is built from). Grade boundaries are not in the facts bank at all (checked directly: zero matches for "grade", "boundary", "UMS", or "threshold" anywhere in that document) — that half of this document instead comes from seven official Pearson grade-boundary PDFs fetched and read directly in this session (pdftotext -layout), listed with their URLs in Part 2 below.

WMA12 — Topic Frequency and Grade Boundaries

What this document is, and isn't

This is the SIGNAL-equivalent layer for WMA12: two narrow, real tables — how often each spec topic has been individually confirmed tested in the reviewed archive, and what Pearson has actually published as this unit's grade boundaries. It is not exam technique (that's forge-exam-technique-guide.md) and not a formula/method reference (that's codex-formula-and-method-bank.md). Nothing below is a prediction.


Part 1 — Topic frequency

What "N of 20" means here, precisely. The archive has 20 series with a question paper and mark scheme read (June 2019–January 2026, per the facts bank's own §5). No pass to date — including this one — has topic-tagged all 75 marks of all 20 papers. The counts below are a floor: the number of series in which this course's own research (the facts bank, FORGE, or CODEX) found and cited a specific, named question confirming that topic. A low count does not mean a topic is rare — every row below is a compulsory, recurring spec area (spec P2.3) that a candidate should expect most series — it means only that many series have been individually verified by citation so far. Treat this as "confirmed present at least this often," never as a probability, and never round it into a percentage.

Spec topic (lesson file)Seen in N of 20 series checkedNamed instances (series, Q#)Real mark-weight observed
Proof — exhaustion/counter-example/general (proof.ts)6Jun 2019 Q1; Jun 2022 Q3(i); Oct 2021 Q9; Oct 2022 Q1; Oct 2023 Q1; Jun 2025 Q102–4 marks; usually opens or closes the paper
Factor & remainder theorems (factor-and-remainder-theorems.ts)≥4 (facts bank §7; 3 individually named here)Jan 2024 Q1; Oct 2023 Q4; Jun 2025 Q43–9 marks
The circle (the-circle.ts)≥5 (facts bank §7; 3 individually named here)Jan 2021 Q9; Jan 2023 Q6; Jun 2025 Q27–10 marks
Arithmetic sequences & series (sequences-and-arithmetic-series.ts)4Jun 2019 (general); Jan 2020 Q8(i); Oct 2020 (general); Jan 2022 (mixed context)~3 marks for the standard sum-formula proof
Geometric series, incl. sum to infinity (geometric-series.ts)2Jan 2022 (mixed with arithmetic); Jan 2024 Q5(i)Usually embedded in a multi-part question, not isolated
Binomial expansion (binomial-expansion.ts)2 series / 3 papersJan 2024 Q2; Jun 2025 Q1 (main paper) and Q7 (01R regional variant)3–7 marks
Exponentials & logarithms (logarithms-and-exponentials.ts)5Jan 2021 Q3(i)/Q3(ii); Jan 2023 Q4(i)/(ii); Jun 2023 Q5; Jun 2024 Q3(i); Jun 2025 Q6(i)3–10 marks
Trigonometric equations (trigonometric-equations.ts)4Oct 2021 Q10(i); Oct 2022 Q5; Oct 2023 Q3; Jun 2025 Q83–8 marks
Differentiation — stationary points/curve sketching (stationary-points-and-curve-sketching.ts)4Jan 2021 Q2; Oct 2019 Q10; Jan 2025 Q3; Jun 2025 Q8 (01A)/Q94–11 marks
Definite integrals & areas (definite-integrals-and-areas.ts)3Jan 2020 Q4; Jan 2023 Q(c); Jun 2025 Q35–6 marks
Trapezium rule (the-trapezium-rule.ts)6Oct 2020; Jan 2023; Jun 2024; Oct 2023 (facts bank §6.9's own "at least four series"); Jan 2025 (novel log context); Jun 2025 Q55–6 marks, often combined with a definite integral

One fully mapped series, reused rather than re-derived

FORGE's own Part 1 independently extracted and topic-tagged every question of June 2025 against the real mark scheme (wma12-01-rms-20250814.pdf), summing correctly to 75 — the only series in the archive mapped question-by-question so far. Reused here rather than re-verified:

QTopicMarks
1Binomial expansion6
2The circle7
3Area between a curve and a line5
4Factor/remainder theorem9
5Trapezium rule + definite integral6
6Logarithms10
7(not read this session — FORGE's own flagged gap)9
8Trigonometric equations8
93-D shape optimisation (differentiation)11
10Proof by exhaustion4

Note what this one series does not show: no dedicated arithmetic/geometric-series question was identified among Q1–Q6 or Q8–Q10 — it may be folded into the unread Q7, or genuinely absent that series. Sequences/series is still a compulsory spec area (confirmed tested directly in four other named series above); one series' mapping is not evidence it was skipped.


Part 2 — Grade boundaries

Real, published data exists. It is not in the facts bank (confirmed absent, per the provenance note above) — it comes from seven official Pearson "International AS/A Level grade boundaries" PDFs, fetched and read directly in this session. WMA12 is graded as an AS-level unit in these tables (Unit 2 of six), so the scale is A–E + U — there is no A* at unit level (A* exists only for the combined, six-unit International A-Level Mathematics qualification, not for this single paper). Two paper codes appear per series — the main paper and a same-boundary regional/retake variant (named "P2R" in 2024, "Unit 2A" from mid-2025) — and in every series checked here, the two carry identical raw-mark boundaries.

SeriesMax rawABCDEUSource
Oct 20237555474033260Pearson PDF
Jan 20247553463932250Pearson PDF
Jun 20247548423732270Pearson PDF
Oct 20247554474034280Pearson PDF
Jan 20257554474034280Pearson PDF
Jun 20257553474135290Pearson PDF
Jan 20267551453933280Pearson PDF

UMS conversion (identical across all seven series, printed directly beneath each raw-mark row): A=80, B=70, C=60, D=50, E=40, U=0, out of a maximum 100 UMS.

What this table doesn't cover. Only the WMA12 unit boundary is shown. The overall International A-Level Mathematics qualification grade (which does carry an A*) is set from combined UMS across all six units, not from this paper alone, and is not covered here. Series before October 2023 were not fetched for this pass — the seven above were chosen to cover the most recent two years plus January 2024 and October 2023, which FORGE and CODEX already use as anchor series elsewhere in this technique hub; extending further back is a real but bounded gap, not a claim that no earlier data exists.


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