Topic Brief: Numerical Methods

Provenance: compiled 2026-09-29, from research/veridian/WMA13-verified-facts.md (this course's primary, provenance-checked WMA13 source — 13 real series checked in total: 8 read start-to-finish with full mark schemes and examiner reports, 3 more mark-schemes-only for general topic-coverage cross-checking, and 2 more checked for other, unrelated topics only — except Jun 2026, whose mark scheme was independently re-pulled specifically for this topic during the numerical-methods.ts citation-currency audit, so it does contribute a real anchor here despite being logged as an "other topic" series overall). Cross-checked against this folder's signal-frequency-and-boundaries.md, forge-exam-technique-guide.md, and codex-formula-and-method-bank.md so this brief does not restate their content. No new primary-source material was pulled for this pass — this is a synthesis, narrowed to the series-by-series citation ledger and mark-tariff pattern, of what those documents already establish.

#SIGNAL Topic Master Brief: Numerical Methods (WMA13, spec 6.1–6.2)

#What this document is, and how it differs from its siblings

signal-frequency-and-boundaries.md gives a one-line frequency count for this topic inside a full-paper topic table; codex-formula-and-method-bank.md gives the method skeleton (§6.1–6.2); forge-exam-technique-guide.md gives exam-technique advice and a timing-table row. numerical-methods.ts is the taught lesson, with a VERIDIAN-original worked chain and its own trap taxonomy. None of the four assembles the series-by-series citation ledger — which question, which marks, which real function — in one place, or characterises the recurring shape of the tested function across series. That is this document's only job.

#Frequency

Seen in at least 9 of the 13 WMA13 series checked in this course's research, per signal-frequency-and-boundaries.md's own tally: Oct 2020, Oct 2021, Jan 2022, Oct 2022, Jun 2023, Oct 2023, Jan 2024, Jan 2025, Jun 2026. One flagged discrepancy, not silently resolved: WMA13-verified-facts.md §6 also quotes a Jun 2022 Q8(c) examiner-report line on this exact topic (the iteration/ANS-key trap, quoted below) — a series the sibling document's 9-series list omits. Whether this reflects a genuine tenth series or a citation that belongs to a different question type was not re-checked against the Jun 2022 primary source in this pass; it is reported here as an open flag rather than folded into a revised count.

#Series-by-series citation ledger

Blank cells are left blank deliberately, per this course's rule against padding a real citation with an invented number.

#Mark-tariff pattern

Where a full breakdown is confirmed (Jan 2022 Q5, Oct 2023 Q1, Jan 2025 Q1), the shape is identical: 2 marks for sign-change/continuity (a lenient M1 for the substitutions, a single dependent A1 bundling both correct values, the continuity-naming reason, and the conclusion) plus 3 marks for iteration (an M1A1 pair for the first produced iterate, then one further dependent accuracy mark for each value after that) — 5 marks total, confirmed identically in at least two series (Jan 2022, Oct 2023) and matched again in a third (Jan 2025). Jun 2026 shows the same question can be extended to 8 marks by adding a third part, without changing the underlying 2-then-3 shape of the first two parts. No series in this course's sources shows the topic tested for fewer than 5 marks when a full breakdown is available.

#Recurring context and angle type

Every series where the actual function is recorded in this course's sources combines a transcendental term with a polynomial term — never a pure polynomial alone: Jan 2022's cubic-plus-log; Oct 2023's $x^2-5x+e^x$; Jan 2025's $2\sec x+6x-3$; Jun 2026's $4xe^{2x}+6x-2x^2-5$. Four confirmed instances, four different transcendental families (log, $e^x$, $\sec x$, $xe^{2x}$), the same underlying shape each time — a function no simple algebraic technique solves exactly, which is the entire reason the topic exists on this paper. A second recurring pattern, confirmed across every series with a full breakdown: the question is always split into exactly two parts, root-location then iteration, testing the same underlying $f$.

Question position is a strong tendency, not a rule. Most confirmed instances place this topic at Q1 or Q2 (Oct 2023 Q1, Jan 2025 Q1, Jun 2026 Q1, Jan 2024 Q2, Jan 2022 Q5 being the nearest exception among the fully-detailed set) — but Jan 2022's own Q5 and the flagged Jun 2022 Q8(c) citation both sit later in the paper, so "always the opener" would overstate what these sources show.

#If this topic appears — what to expect

Expect a two-part question: locate a root by sign change on a stated interval, then produce two or more iterates from a given (or derivable) rearrangement $x=g(x)$. Expect the interval endpoints to be given to at least 1 significant figure of leeway on the method mark, but expect the accuracy mark to require all three of correct values, an explicit continuity statement, and a "hence root" conclusion — dropping the word "continuous" is, across this course's entire evidence base, the single most repeated way to lose it. Expect the tested $f(x)$ to mix a transcendental term with a polynomial one, not to be a bare polynomial. Expect each iterate after the first to carry its own separate accuracy mark, contingent on the method mark for the first — except that a converged final value is occasionally, not always, made independent of that chain (Jun 2026), so writing down a best estimate for it is worth doing even after a fumbled earlier step.

#Honest gaps

Several citations above (Oct 2020 Q6, Oct 2021's hedged Q9(c), Oct 2022, Jun 2023 Q1, Jan 2024 Q2) are confirmed as real anchors for this topic but without a full mark breakdown or exact function reaching this course's sources — reported as partial rather than filled in with an invented number or interval. The Jun 2022 discrepancy (§ Frequency) is flagged, not resolved. No percentage, likelihood, or grade-boundary claim is made anywhere above; every frequency and count figure is traceable to WMA13-verified-facts.md §6/§9 or signal-frequency-and-boundaries.md §1 directly.

#Sources

• research/veridian/WMA13-verified-facts.md — §6 for the per-series examiner-report quotes and the "Q1 or Q2" pattern claim; the numerical-methods.ts lesson-audit entries (§9) for the Jan 2022/Oct 2023/Jan 2025/Jun 2026 question-level mark breakdowns and function forms.
• signal-frequency-and-boundaries.md (this folder) — the "9 of 13" series count this brief cites rather than recomputes.
• forge-exam-technique-guide.md (this folder) — the 5-mark/8-mark tariff figures and the "Q1 or Q2… strong tendency, not a rule" caution, reused rather than restated in full.
• codex-formula-and-method-bank.md (this folder) — §6.1–6.2 for the method skeleton, not reproduced here.
• content/veridian/curriculum/wma13/numerical-methods.ts — the taught lesson, VERIDIAN-original worked chain, and trap taxonomy, not reproduced here.