Topic Brief: Stationary Points and Curve Sketching

Provenance (2026-09-29). Read in full for this pass: research/veridian/WMA12-verified-facts.md (§2's transcription of spec item 7.1; §5's archive-scope note — 20 series with a question paper and mark scheme reviewed, June 2019–January 2026, 17 with a published examiner report; §6.8 in full; §7 and §8's stationary-points entries). Also read in full: content/veridian/curriculum/wma12/stationary-points-and-curve-sketching.ts (every series citation in the file, including its two audit-pass header notes) and codex-deep-dive-stationary-points-and-curve-sketching.md (Parts 1–4 in full, including its own primary-source verification of the two 2025 anchors and its Part 3 synthesis table) and signal-frequency-and-boundaries.md (this topic's row). content/veridian/question-bank/wma12.ts grepped for "stationary" / "curve sketch" / "maxima" / "minima" — one item present, a discriminant/no-turning-points question already matching the lesson's own Oct 2019 Q10 anchor; not reproduced or duplicated below. Not affiliated with or endorsed by Pearson Edexcel. Quotations below are short (under ~15 words) and attributed by name; no full question, mark-scheme extract, or examiner-report passage is reproduced at length.

#SIGNAL Topic Master Brief — Stationary Points and Curve Sketching (WMA12, spec 7.1)

#What this is, and isn't

codex-deep-dive-stationary-points-and-curve-sketching.md already carries a Part 3 synthesis table of every confirmed real anchor, built from its own primary-source verification of the two 2025 papers — that table is not rebuilt here. What it does not state is the course's standard SIGNAL frequency line (seen in N of M series checked) or a pure exam-day "what to expect" summary stripped of mark-scheme mechanism. This document supplies exactly those two things, plus one clarification the CODEX table's own anchor count leaves implicit: how many series, not questions, this topic has actually appeared in.

#Real frequency: seen in 4 of 20 series checked

The archive has 20 series with a question paper and mark scheme read (WMA12-verified-facts.md §5). This topic (spec 7.1) is individually confirmed tested, by named series and question, in 4 of them: October 2019, January 2021, January 2025, June 2025. Two of the five confirmed real question-anchors both fall inside June 2025 — Q8 on the 01A regional variant paper and Q9 on the main series paper — which the facts bank's own archive-scope note (§5) treats as one series with two question papers, not two series; counted that way, June 2025 contributes one series to the frequency total, not two.

#Every real series/question that has tested this topic

#Real mark-tariff pattern

Confirmed totals split cleanly by question shape rather than drifting evenly across the range. The two "find and classify a cubic's stationary points" anchors (Oct 2019 Q10, Jan 2021 Q2) both sit at 7 marks, split 4/3 across two parts. The single "deduce a decreasing region" instance (Jun 2025 Q8a) is a short 2-mark partial-credit part on its own, not a full standalone question — Q8 continues into a factorisation part that belongs to a different topic and is not counted here. The two practical-optimisation anchors are the longest confirmed instances of this topic on the paper, at 10 and 11 marks, each spanning three parts (form the function; find the stationary value; justify it). Where the mark-scheme skeleton is known in structural detail (all five anchors), every one splits "solve your own equation" from "use the value you just found" into separate marks — an independent method mark for the algebra, then a dependent mark for the substitution or discriminant step that follows it.

#Real recurring context/angle across the series checked

• The two confirmed practical-optimisation anchors (Jan 2025 Q3, Jun 2025 Q9) both reduce to a cube, not a quadratic, when the derivative is set to zero — the only sub-pattern of this topic confirmed to do so — and both real examiner reports independently name the identical slip: taking a square root instead of a cube root at that exact step.
• Both confirmed optimisation anchors are dated 2025, with no confirmed instance in any of the 16 earlier series this archive covers. This is a floor, not a trend claim — several earlier series were grepped for keywords but not read in full depth (WMA12-verified-facts.md §8) — but as things stand, this sub-pattern's evidence is recent and thin.
• The independent-method/dependent-follow-up mark split recurs on every anchor with a known skeleton, regardless of whether the question is pure algebra (Jan 2021), a "prove" question (Oct 2019), or a practical context (both 2025 anchors) — the one structural feature shared across every question shape this topic has actually been tested from.

#If this topic appears: what to expect

• Expect either a compact ~7-mark find-and-classify (or prove-no-turning-points) question on a given cubic, or a longer 10–11 mark multi-part optimisation question set in a practical context — the two confirmed shapes, at opposite ends of the tariff range.
• If the context is practical (a container, a constraint, an "eliminate one variable" setup), expect setting the derivative to zero to produce a cube, and check the root-extraction step specifically — both real anchors of this type record the same square-root-instead-of-cube-root slip.
• Expect the step that actually uses an already-found value — substituting into the second derivative, or applying the discriminant — to carry its own separate, dependent mark, not to be bundled into the mark for finding that derivative or forming that equation.
• Check what the question's own rounding instruction attaches to: a stationary point's coordinate on a pure polynomial question is normally kept exact (fraction or surd), while both optimisation anchors explicitly instruct rounding — one to a value of x, the other to the optimised quantity itself.

#What this document deliberately leaves out

No derivation of the second-derivative test, no worked practical-optimisation example, and no mark-scheme skeleton beyond the tariff already tabulated above — all in codex-deep-dive-stationary-points-and-curve-sketching.md, Parts 1–3, and the lesson file's own worked chains and marked solutions. No general exam-timing or self-checklist material (forge-exam-technique-guide.md). No percentage, likelihood, or grade-boundary claim of any kind, per this course's standing discipline.

#Sources used

• research/veridian/WMA12-verified-facts.md — §2, §5, §6.8, §7, §8, read in full.
• content/veridian/curriculum/wma12/stationary-points-and-curve-sketching.ts — read in full for its own series citations and audit-pass header notes.
• codex-deep-dive-stationary-points-and-curve-sketching.md — Parts 1–4 read in full, including its own primary-source verification of the Jan 2025 and Jun 2025 optimisation anchors.
• signal-frequency-and-boundaries.md — this topic's existing row, read to confirm nothing above restates it.
• content/veridian/question-bank/wma12.ts — grepped for "stationary", "curve sketch", "maxima", "minima"; one unrelated-topic item present, not duplicated.