Pure Mathematics 2
Topic Brief: The Trapezium Rule
Provenance (2026-09-29): written against research/veridian/WMA12-verified-facts.md (read in full, §1–§9 — §5 for the archive's real scope, §6.9 for this topic's own citations, and the §9 lesson-audit pass anchored on October 2023 Q6), content/veridian/curriculum/wma12/the-trapezium-rule.ts (read in full, 896 lines, to confirm nothing below duplicates its worked chains, diagram, or marked solution), and the other WMA12 technique-hub documents already built for this paper — codex-deep-dive-the-trapezium-rule.md, codex-formula-and-method-bank.md, signal-frequency-and-boundaries.md — all read in full so this brief adds a genuinely narrower "what to expect" layer rather than restating their tables. content/veridian/question-bank/wma12.ts was grepped for "trapez": no matches, nothing to cross-check there. No new primary-source PDFs were opened for this pass; every citation below traces to the facts bank or the CODEX deep-dive.
SIGNAL Topic Master Brief: The Trapezium Rule (WMA12, spec 8.3)
What this is
A revision-facing "what to expect" briefing for spec item 8.3 specifically — narrower than signal-frequency-and-boundaries.md's single-row, whole-paper table, and pattern-facing rather than method-teaching (that is codex-deep-dive-the-trapezium-rule.md's job; nothing here re-derives the formula or repeats a worked example). One confusion worth naming once: "trapezium" also appears in this archive as a plain geometry fact — a curve-and-line region that happens to be trapezium-shaped (June 2025 Q3, spec 8.2) — which is a different topic solved by ordinary integration, not the numerical method below. That anchor belongs to the sibling area/integrals brief, not here.
Every real series confirmed testing this topic
Seen in 6 of 20 series checked (the archive's full scope of question-paper-plus-mark-scheme series, per the facts bank §5 — a floor on individually-cited series, never a percentage or likelihood).
| Series | What's confirmed | Q# / marks established? |
|---|---|---|
| October 2020 | Strip-width-from-point-count error; endpoint/interior doubling error, named "the commonest error" | Series confirmed; no Q# or mark total survives in the facts bank |
| January 2023 | Bracket closed early after the first pair of terms, losing all credit | Series confirmed; no Q# or mark total survives |
| June 2024 | Grouped with the above two under the facts bank's own "at least four series" sharing this error taxonomy | Series confirmed only by that grouped citation — no unique quote isolated to it |
| October 2023, Q6 | River cross-section from a graph; area (3), real-world flow-rate use of that area (2), over/underestimate reasoning (1) | Fully established: 6 marks, B1/M1/A1 skeleton, verbatim mark-scheme and examiner-report text |
| January 2025 | "A novel way of testing the trapezium rule via logarithms" (part i) | Series and novelty confirmed; the facts bank's own source quote is truncated, no Q# or mark total survives |
| June 2025, Q5 | "Trapezium rule + definite integral", per FORGE's full question-by-question mapping of this series | Q5, 6 marks; sub-part split not established in this course's sources |
Only two of the six citations — October 2023 and June 2025 — carry an established question number and mark total; the other four are confirmed real by direct examiner-report quotation but without a surviving Q# or mark-scheme skeleton in this course's sources. That asymmetry is real and worth flagging on its own: this topic is confirmed more often than it is confirmed in full detail.
The real mark-tariff pattern
Both fully-documented anchors total 6 marks, and neither tests the trapezium-rule calculation alone: October 2023 pairs it with a real-world rate calculation, June 2025 pairs it with a separate definite-integral part. Where a mark breakdown survives (October 2023), the estimate itself is worth more than any single follow-on step (3 of 6), the reasoning mark is worth exactly 1 — never split into two — and it is explicitly named as the hardest single mark on that entire paper.
The recurring context and angle
- Rarely tested in isolation. Of the six confirmed citations, three are explicitly combined with something else — real-world flow rate (October 2023), logarithms (January 2025), a definite integral (June 2025) — against zero confirmed instances of a bare "here is a table, apply the rule, stop" question.
- The same two structural errors recur across four named series (October 2020, January 2023, June 2024, October 2023): miscounting the strip width from the number of ordinates rather than the number of gaps between them, and doubling the wrong ordinates (endpoints instead of interior values).
- Graph-based ordinate reading, not table- or formula-based reading, is the confirmed harder input format — October 2023's own report distinguishes it directly, and separately names the two zero-valued endpoint ordinates on that question as an added, specific source of difficulty.
- The over/underestimate reasoning mark is a single combined requirement, not a label mark plus a separate reason mark: the mark scheme's own wording is "states underestimate AND gives a valid reason."
If this topic appears, here's what to expect
- Expect roughly 6 marks when this is a question's main role, most likely split into the estimate itself (the larger share) plus one further part that reuses that estimate rather than a second, separate calculation.
- Expect the ordinates to arrive one of three ways — stated directly, given as a table, or plotted on a labelled graph — and treat the graph format as the one worth extra care, including checking for zero-valued endpoints that are easy to drop.
- Before finalising an answer, re-derive h from the number of gaps (not the number of points), and check that only the strictly-interior ordinates are doubled.
- Keep the compressed formula's bracket as one bracket all the way through the final ½h multiplication; closing it early after the first pair of terms is a confirmed, no-credit error.
- If asked to justify over- or under-estimate, write one sentence that states the direction and names how the curve bends to cause it — the direction alone repeats the question rather than answering it, and is confirmed to earn nothing on its own.
- Don't assume the rule stands alone: be ready for an extra step first (rearranging a given relationship, as in the logarithm case) or a second part that asks you to use — not recompute — the estimate you already found.
What remains genuinely unverified for this topic
No confirmed real WMA12 anchor asks for a numeric error estimate or an explicit multi-strip-count comparison as its own gradable step — every confirmed "how far off" question tests the qualitative direction only. June 2024's and January 2025's own question content, and October 2020's and January 2023's own Q#s and full mark schemes, are not established beyond the grouped or truncated citations quoted above; nothing in this brief fills those gaps with invented specifics. October 2025 and January 2026 examiner reports do not yet exist in any archive this course has searched, so if this topic appeared in either sitting, no commentary on it is available yet.