Spaced Repetition Schedule

Provenance: written 2026-09-29. Built primarily from signal-frequency-and-boundaries.md §1 (this paper's existing whole-paper frequency table, read in full) and all eleven signal-topic-brief-*.md files in this same folder (each read in full), which supply a per-topic frequency count, mark-tariff pattern and — in one case below — a direct correction to §1's own row, named explicitly rather than silently substituted. Also read directly for this pass: forge-exam-technique-guide.md §1 (the real per-question mark/timing table, reused rather than re-derived) and §2 (the M/A/B mechanics referenced in §4 below); codex-formula-and-method-bank.md's "Master GIVEN vs MEMORIZE table" and forge-battle- card.md (both grepped, confirming the single must-memorize P4 formula and that neither document states a repetition schedule); content/veridian/question-bank/wma14.ts (checked — see §0 below on why this document does not draw from it); paper-anatomy.ts (checked and excluded from the tiering below, for the same reason WMA13's sibling document excludes its own paper-anatomy page — it is a paper-structure lesson, not an examinable spec topic, and has no SIGNAL topic brief to draw a frequency count from). The lesson-audit-log entry in research/veridian/WMA14-verified-facts.md (dated 2026-09-14, under "Lesson-audit log") was read directly to verify the integration-by-parts correction in §2 below rather than taking the topic brief's citation of it on trust. No new primary-source PDF was opened for this document — every fact below reuses a citation already verified elsewhere in this facts bank; this document's own contribution is the repetition-count construction in §3, built on top of those existing citations. The six-cycle Day-0/2/5/10/18/30 widening-interval pattern in §3 is reused, unchanged, from this course's own content/veridian/technique-hub/wbs11/forge-spaced-repetition-schedule.md §3, exactly as the WBS12/13, WMA11, WMA12 and WMA13 siblings already reuse it — flagged here as a reused scheduling convention, not a new finding. No likelihood, probability, or grade-boundary figure appears anywhere below.

#WMA14 — Spaced Repetition Schedule (Unit P4: Pure Mathematics 4)

#0. What this is, and what it deliberately doesn't repeat

This document answers one question: given WMA14's real, uneven distribution of exam coverage across its eleven taught spec topics, how many times should a student revisit each one before the exam, and in what order? It does not re-teach content, and does not reproduce:

• the frequency tables themselves — those live in signal-frequency-and-boundaries.md and the eleven signal-topic-brief-*.md files in this folder, cited here by row, not copied wholesale;
• any formula, given-vs-memorize status, or worked method skeleton — codex-formula-and-method-bank.md and the eleven codex-deep-dive-*.md files;
• any worked exemplar or trap taxonomy — those live in the lesson files themselves, content/veridian/curriculum/wma14/*.ts, and in forge-exam-technique-guide.md's own marked-solution material;
• grade boundaries — no primary Pearson grade-boundary document exists anywhere in this course's WMA14 source review (signal-frequency-and-boundaries.md §2), so none is estimated or implied here either;
• content/veridian/question-bank/wma14.ts — checked directly for this pass and confirmed to hold practice items rather than any frequency or scheduling claim, so it supplies nothing this document could cite.

What it adds: an actual repetition count per taught topic, built from the real sightings-per-topic each SIGNAL topic brief independently established, rather than assuming WMA14's eleven topics deserve equal revision time.

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#1. Why repetition count should track this paper's real, uneven frequency

Three real, paper-specific facts argue against a flat schedule.

First, the eleven topics span a six-fold real range, with one clear leader. Proof by contradiction (spec 1.1) is confirmed in 6 of the 7 WMA14 series this course has mined question-by-question — genuinely ahead of everything else, not tied at the top the way WMA13's two leading topics were [signal-topic-brief-proof-by-contradiction.md]. At the other end, two topics are each confirmed in only 1 of 7: position vectors and the foot of a perpendicular (spec 7.4–7.5), and area under a parametric curve (spec 6.5) [signal-topic-brief-position-vectors-distance-and-foot-of-perpendicular.md; signal-topic-brief-area-under-a-parametric-curve.md]. A flat schedule would spend as much repetition on either thin topic as on proof by contradiction, despite a six-fold gap in how often each has a real, citable anchor.

Second, the two thinnest topics are named directly in this course's own source document as a sourcing artefact, not a rarity signal — and unlike WMA13's parallel thin-topic case, both have a full, real question available to simulate. signal-frequency-and-boundaries.md §1 states this in its own words: "the bottom two rows (1 of 7 each) are a sourcing artefact, not evidence of rarity... Area under a parametric curve (6.5) is a compulsory, explicitly spec-listed skill that had zero citations anywhere in this facts bank until the January 2026 series was reviewed... Do not read either row as 'safe to deprioritise.'" Both thin topics also happen to have a real, fully-sized confirmed question behind their single citation — Oct 2021 Q7 (9 marks) for position vectors/foot of perpendicular, Jan 2026 Q7 (16 marks, the largest confirmed item in the whole facts bank) for area under a parametric curve [forge-exam-technique-guide.md §1]. That changes what a single pass on each should actually look like, worked through in §4 below.

Third, a real correction exists between the whole-paper frequency table and one topic's own brief, and this schedule uses the corrected figure rather than silently picking one. signal-frequency-and-boundaries.md §1 lists integration by parts and substitution (spec 6.2) at 3 of 7 (October 2021, October 2022, January 2024). That topic's own brief re-derives the count directly from this facts bank's lesson-audit log (dated 2026-09-14) and finds a fourth, genuinely real anchor the main table's row omits: June 2022 Q8(b), a mark-scheme-only citation (no examiner's report exists for that series) that was used to fix a dM1-vs-M1 marking error in the live lesson file itself [signal-topic-brief-integration-by-parts-and-substitution.md; lesson-audit-log entry, WMA14-verified- facts.md]. The brief notes this is the same convention this facts bank already applies elsewhere — the separable-differential-equations row counts a mark-scheme-only January 2026 citation the same way — so 4 of 7, not 3, is the count this schedule uses, stated here as a correction rather than a quiet substitution.

None of this licenses skipping a thin topic: every one of the eleven is compulsory spec content [research/veridian/WMA14-verified-facts.md §1]. What it licenses is an honest allocation of repeated practice — a topic with one real citable anchor has a thinner repeatable past-paper pattern to drill against than one with six, though as §4 shows, "thinner pattern" does not always mean "smaller pass."

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#2. The tiers, built from each topic's own real, cited frequency

#Tier 1 — 6 of 7, the clear leader

• Proof by contradiction (spec 1.1) — 6 of 7: January 2021, October 2021, June 2022, January 2024, October 2024, January 2026 [signal-topic-brief-proof-by-contradiction.md]. Not seen in October 2022. The actual claim proven is different every time — consecutive integers, a cube/square parity chain, a divisibility statement, a stationary point, a curve-intersection, a Diophantine-style equation — so there is no single reusable scenario to drill, only the proof structure itself. This is also the one topic examiner reports most consistently flag as weakly answered, so high frequency and low average performance co-occur here, not high frequency and confidence [signal-frequency-and-boundaries.md §1].

#Tier 2 — 5 of 7

• Binomial expansion for rational n (spec 4.1) — 5 of 7: January 2021, October 2021, October 2022, January 2024, October 2024 [signal-frequency-and-boundaries.md §1; signal-topic-brief-binomial-expansion-for-rational-n.md]. Its own brief adds a genuinely additive detail: the estimate-a-surd-or-root extension (using $x=$ a small value in the expanded series to approximate something like $\sqrt[3]{6}$) is confirmed in 3 of the 5 citations — real enough to be the expected second half of the question, not a rare add-on.

#Tier 3 — 4 of 7, four topics genuinely tied

• Implicit and parametric differentiation, tangents and normals (spec 5.1) — 4 of 7: January 2021, October 2021, October 2022, January 2024 [signal-topic-brief-implicit-and-parametric-differentiation-tangents-and-normals.md]. Only one of this topic's five real citations (across those four series — October 2022 supplies two) carries a confirmed total mark tariff (January 2021 Q6, 9 marks, 5+4). A single mechanical step — a mixed term needing the product rule and the chain rule applied together — is the substance of three of the five citations, and the facts bank itself calls the January 2024 instance ($y^2x$) "the single hardest mechanical step in implicit differentiation across the whole archive reviewed."
• Vectors — scalar product, angle, skew and parallel lines (spec 7.6–7.7) — 4 of 7: January 2021, October 2022, January 2024, January 2026 [signal-topic-brief-vectors-scalar-product-and-skew- lines.md]. Joint-second-most-frequently-evidenced topic on the paper after proof by contradiction, and it anchors this paper's real largest confirmed vectors item (Jan 2026 Q9, 11 marks, 3+4+2+2). Two distinct, separately-documented error patterns sit inside this one topic, not one: reporting the acute angle between two lines when the obtuse one was required (Jan 2021, Oct 2022), and — a genuinely different mistake — trying to prove skewness by showing lines are "not perpendicular" instead of "not parallel and not intersecting" (Jan 2021 Q8), or concluding two direction vectors aren't parallel just because they aren't identical, without checking for a scalar multiple (Oct 2022 Q9).
• Separable differential equations and rates of change (spec 5.2, 6.4) — 4 of 7 on the lesson's own bundled count: January 2021, October 2021, January 2024, January 2026 [signal-topic-brief-separable-differential-equations.md]. A narrower count is flagged directly in the same brief and repeated here rather than smoothed over: one of the four, January 2024 Q4, forms a rates-of-change equation from a cone's geometry but is differentiation-only — it is never carried through to a separable equation and solved. A stricter count of spec 6.4 alone (separating, integrating, solving) would be 3 of 7 (Jan 2021, Oct 2021, Jan 2026), not 4. This schedule keeps the topic at Tier 3 on the lesson's own bundled count, since the lesson file teaches both halves together, but a pass on this topic should not assume every one of its four sightings ends in an actual separable-DE solve.
• Integration by parts and substitution (spec 6.2) — 4 of 7, corrected from signal-frequency-and-boundaries.md §1's own "3 of 7" row as explained in §1 above: October 2021, June 2022, October 2022, January 2024 [signal-topic-brief-integration-by-parts-and-substitution.md]. Two structural facts are confirmed without exception across all four real citations, and both are genuinely useful for what a pass should drill: this topic has never appeared as a whole question by itself — every citation is a lettered sub-part of a larger question — and where the tested step is "by parts" specifically, it has never been a single, one-shot application; three of the four state directly that it is a second, dependent application (the June 2022 mark scheme confirms this dependent mark is coded dM1, withheld unless the first M1 was earned), and the fourth is credited via the DI/tabular method built specifically for tracking repeated applications.

#Tier 4 — 3 of 7, three topics tied

• Partial fractions decomposition and integration (spec 2.1, 6.3) — 3 of 7: October 2021, October 2022, January 2024 [signal-frequency-and-boundaries.md §1; signal-topic-brief-partial-fractions-decomposition-and-integration.md]. Genuinely the thinnest data of any topic on this paper in a second sense, beyond frequency: no single citation carries a confirmed total mark tariff at all, so there is no real "this is roughly how big it runs" figure to anchor a pass against, unlike every other topic in this tier.
• Parametric equations — conversion and domain/range (spec 3.1) — 3 of 7: January 2021, October 2021, October 2022 [signal-frequency-and-boundaries.md §1; signal-topic-brief-parametric-equations- conversion-and-domain-range.md]. Each of the three citations documents a genuinely different specific failure, not the same slip attested three times — a real reason to vary what a pass practises rather than drilling one fixed error mode. (A fourth series, January 2026, touches an adjacent skill inside a much larger question whose main content is area under a parametric curve; per this facts bank's own convention that question counts toward 6.5's tally instead, not folded in here.)
• Volume of revolution (spec 6.1) — 3 of 7: January 2021, October 2022, January 2024 [signal-frequency-and-boundaries.md §1; signal-topic-brief-volume-of-revolution.md]. Notably absent from January 2026 despite that series having four question-level citations mined elsewhere in this facts bank (a differential equation, an area/tangent combination, a proof, a vectors question) — an absent citation, not evidence the topic is fading; it remains compulsory spec content regardless.

#Tier 5 — 1 of 7, thinnest confirmed record on the whole paper, for the same reason in both cases

• Position vectors, distance and foot of a perpendicular (spec 7.4–7.5) — 1 of 7: October 2021 only, WMA14/01 Q7 [signal-topic-brief-position-vectors-distance-and-foot-of-perpendicular.md]. Its one real anchor is a genuinely large, chained question — foot of perpendicular, distance, and a reflection, all in one 9-mark, roughly 11-exam-minute item [forge-exam-technique-guide.md §1].
• Area under a parametric curve (spec 6.5) — 1 of 7: January 2026 only, WMA14/01A Q7 [signal-topic-brief-area-under-a-parametric-curve.md]. Had zero citations anywhere in this facts bank before a 2026-09-07 citation-currency audit surfaced this one — the thinnest-evidenced spec point in the whole document until that point. Its one real anchor is the largest confirmed single item in the entire WMA14 facts bank: 16 marks, chaining parametric coordinates (3.1), a tangent/normal (5.1) and the area itself (6.5) together, with a calculator-technology ban printed twice over its four parts.

Both Tier 5 topics are named explicitly in signal-frequency-and-boundaries.md §1 as a sourcing artefact, not a rarity signal — restated here rather than left implicit, since a Tier 5 placement is the one most at risk of being misread as "safe to skip."

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#3. The six-cycle schedule

This reuses the six-cycle, widening-interval pattern (Day 0, 2, 5, 10, 18, 30) already established for this course in wbs11/forge-spaced-repetition-schedule.md §3 — a scheduling convention, stated here as one, not a new cited finding. If fewer than 30 days remain, compress by dropping the latest cycles first and keep Cycle 1 intact, since both Tier 5 topics' only scheduled passes live there.

Reading this as repetition counts rather than a calendar: proof by contradiction gets six passes — one every cycle, matching its clear lead as this paper's single most frequently confirmed topic. Binomial expansion gets four passes. Implicit/parametric differentiation, vectors, separable differential equations and integration by parts each get three passes — the four-way tie at 4 of 7. Partial fractions, parametric conversion and volume of revolution each get two passes — the three-way tie at 3 of 7. Position vectors/foot of perpendicular and area under a parametric curve each get exactly one pass, in Cycle 1 only, and are not scheduled again — consistent with §1 and §2's reasoning, though §4 below states explicitly why that one pass should not be a short one for either topic.

Per-cycle load is 6, 4, 4, 5, 5, 6 topics — close to flat, with Cycle 1 and Cycle 6 carrying one extra item each (both Tier 5 passes land in Cycle 1; Cycle 6 absorbs the third round of three Tier 3 items and the second round of a Tier 4 item), so that the two thinnest topics are drilled early rather than risking a compressed run-up dropping them entirely.

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#4. Judgement calls stated explicitly

Both Tier 5 topics get only one scheduled pass, but that pass should be a full simulated question, not a shortened drill — a genuinely different call from how this course's WMA13 sibling document treated its own thinnest topic. WMA13's reciprocal/inverse-trig case had never anchored more than a single mark of its own on any transcribed paper, so there was no real multi-mark worked example to simulate. WMA14's two Tier 5 topics are the opposite shape: each has exactly one real citation, but that citation is a large, fully-formed question (9 marks for position vectors/foot of perpendicular; 16 marks — the paper's biggest confirmed item — for area under a parametric curve). A student's single pass on either topic is better spent working the real question shape end to end under timed conditions (≈11 minutes and ≈19 minutes respectively, per forge-exam-technique-guide.md §1's real timing figures) than as a quick recognition drill, precisely because a full real anchor exists to simulate.

The integration-by-parts correction in §1 changes this topic's tier, and that has a real knock-on effect worth naming rather than leaving implicit. At the uncorrected "3 of 7," this topic would sit in Tier 4 alongside partial fractions, parametric conversion and volume of revolution, and would be scheduled for two passes rather than three. Using the corrected "4 of 7" instead moves it into Tier 3, and gives it one additional pass (Cycle 6) beyond what the uncorrected count would justify. This schedule uses the corrected figure because the correction itself is grounded in a real, verified mark-scheme anchor (§1) — not because the higher tier was more convenient for a tidier-looking distribution.

Separable differential equations is scheduled at its lesson's own bundled 4-of-7 count, not the stricter 3-of-7 count for spec 6.4 alone. As §2 states, one of the four sightings (Jan 2024 Q4) never reaches an actual separable-equation solve. This schedule does not split the topic into two slots — the lesson file itself teaches the rates-of-change setup and the separable solve as one unit — but a student using this table should know that roughly a quarter of this topic's own scheduled repetition budget draws on a sighting that is genuinely about the differentiation setup, not the integration-and-solve stage the topic is nominally scheduled for.

Vectors' two documented error patterns are different enough that a single pass should not treat them as one drill. The acute-vs-obtuse angle slip (a numerical/interpretation error, applying $\cos^{-1}$ correctly but reporting the wrong one of the two angles a dot product allows) and the skewness-via-"not-perpendicular" slip (a conceptual error about what property actually proves two lines are skew) sit inside the same spec point but are not the same mistake. Each of this topic's three scheduled passes should include both, not alternate between them, since both are real and independently confirmed rather than one being a subset of the other.

The tier boundaries in §2 follow each topic's own real, most-recently-stated count exactly, including where three topics land on an exact tie. Partial fractions, parametric conversion and volume of revolution are all confirmed at exactly 3 of 7; implicit/parametric differentiation, vectors, separable DE and integration by parts are all confirmed at exactly 4 of 7 (the last only after the §1 correction). None of these ties is broken by adjusting one topic up or down to spread topics more evenly across tiers — the real counts are what they are, and this schedule's tier and pass-count structure follows them as reported rather than smoothing them into a more evenly-spread-looking distribution.

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#5. Where this document's scope ends

This document gives a repetition count and an order; it does not give a grade boundary, a likelihood percentage, or a claim about what will appear on any specific future paper — none of those exist in this course's WMA14 source review, and inventing one here would violate this course's own no-fabrication discipline, the same standard the facts bank, SIGNAL, FORGE and CODEX all hold to elsewhere. It also does not address exam-day wellness, logistics, or a final-48-hours countdown — no other WMA14 technique-hub document covers that territory either, so nothing here should be read as filling that specific gap.

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#6. Honesty notes

• Every tier assignment in §2 traces to a real, cited count in one of the eleven signal-topic-brief- *.md files in this folder, or to signal-frequency-and-boundaries.md §1 directly where a topic brief reuses that table's own count without narrowing or correcting it.
• The specific day-intervals and cycle-to-topic assignments in §3 are this course's own scheduling construction, reused from wbs11/forge-spaced-repetition-schedule.md's established pattern — not a cited finding from an examiner report, the specification, or a spacing-effect study. Only the tier weighting (which topics get more or fewer passes) is grounded in this paper's own real exam-frequency data.
• No likelihood percentage and no grade boundary appears anywhere above. No primary Pearson grade-boundary document exists anywhere in this course's WMA14 source review (signal-frequency-and-boundaries.md §2), so none is estimated or implied here either.
• A Tier 4 or Tier 5 assignment is not a recommendation to skip that content — every one of the eleven taught topics is compulsory spec content [research/veridian/WMA14-verified-facts.md §1]. It reflects only that repeated practice against a topic with a thinner confirmed sighting count has less real past-paper pattern to rehearse, so fewer allocated passes is the honest ceiling this schedule gives it — except where, as with both Tier 5 topics here, the one real anchor is large enough that the single pass itself should still be substantial (§4).
• Where a topic brief itself flags an unresolved discrepancy (the integration-by-parts 3-vs-4 correction; the separable-DE 4-vs-3 bundling question) or a genuine internal split (vectors' two distinct error patterns), that flag is repeated here rather than quietly resolved in either direction.
• paper-anatomy.ts is excluded from this schedule because it is a paper-structure overview lesson, not an examinable spec topic, and has no SIGNAL topic brief to draw a frequency count from — stated here rather than silently omitted, consistent with how this course's WMA13 sibling document treats its own paper-anatomy page.

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#Sources used

• All eleven content/veridian/technique-hub/wma14/signal-topic-brief-*.md files — read in full; the primary source for every per-topic frequency count, mark-tariff pattern, internal correction and judgement call above.
• content/veridian/technique-hub/wma14/signal-frequency-and-boundaries.md §1 — read in full, for the whole-paper frequency table these topic briefs individually cross-check against and, in the integration-by-parts case, correct.
• research/veridian/WMA14-verified-facts.md §1 (spec content, confirming all eleven topics are compulsory) and the lesson-audit-log entry dated 2026-09-14 (verifying the integration-by-parts correction directly against its own cited mark-scheme bullets).
• content/veridian/technique-hub/wma14/forge-exam-technique-guide.md §1 — the real per-question mark/timing table, reused directly for the Tier 5 timing figures in §4.
• content/veridian/technique-hub/wma14/codex-formula-and-method-bank.md and forge-battle-card.md — grepped to confirm neither already states a repetition schedule.
• content/veridian/question-bank/wma14.ts — checked directly and confirmed to hold no frequency or scheduling claim.
• content/veridian/technique-hub/wbs11/forge-spaced-repetition-schedule.md — source of the six-cycle Day-0/2/5/10/18/30 scheduling convention reused, unchanged, in §3 above.

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