Technique Masterclasses

Pure Mathematics 3

Spaced Repetition Schedule

Provenance: compiled 2026-09-29. Built primarily from signal-frequency-and-boundaries.md Part 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 internal sub-topic split that in several cases narrows or corrects signal-frequency-and-boundaries.md's own row — every such case is named explicitly in §2 below, not silently substituted. Also read directly for this pass: research/veridian/WMA13-verified- facts.md §3 (the formula-booklet-vs-memorise split, verified verbatim from the actual booklet PDF) and §7 ("topics with enough verified material for a genuine standalone lesson"), used in §1 as a secondary weighting signal. forge-forty-eight-hour-checklist.md (this folder) was read in full and is the direct reason this document exists: its own "Flagged gaps" section states plainly that it gives no topic-by-topic time allocation because no prior WMA13 document had topic-tagged enough of the archive to support one — that gap is what §2 below fills, using the eleven topic briefs that did not yet exist when that checklist was written. forge-exam-technique-guide.md and codex-formula-and-method-bank.md were grepped to confirm neither already states a repetition schedule; neither does. The eleven curriculum lesson files in content/veridian/curriculum/wma13/ and content/veridian/question-bank/ wma13.ts were checked by filename and by what each topic brief already reports finding there (mostly zero or one matched item), not re-read line by line — their own worked exemplars are not reproduced here. paper-anatomy.ts, the twelfth file in that curriculum folder, is a paper-structure overview lesson rather than an examinable spec-content topic and has no matching SIGNAL topic brief; it is excluded from the tiering in §2 for that reason, stated here rather than silently omitted. No new primary-source PDF was opened for this document — everything below is a repetition-count construction built on top of facts eleven other documents in this hub already independently established. 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 and WMA12 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.

WMA13 — Spaced Repetition Schedule (Unit P3: Pure Mathematics 3)

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

This document answers one question: given WMA13'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:

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 WMA13's eleven topics deserve equal revision time. No other WMA13 technique-hub document does this — the 48-hour checklist says so directly, in its own words, in its "Flagged gaps" section: "No topic-by-topic time allocation is given ... because no pass of this course's WMA13 research has topic-tagged all 75 marks of enough series to support a real weighting." That gap existed because, at the time that checklist was written, the eleven per-topic SIGNAL briefs this document leans on had not yet been built for every topic. They now have, and this document is what filling that gap actually looks like.

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

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

First, the eleven topics span roughly a nine-fold real range, with no single runaway leader at the top. Two topics are confirmed in 9 of the 13 series checked — Functions, composition and inverses (spec 1.2) and Numerical methods (spec 6.1–6.2) — genuinely tied, not one narrowly ahead of the other [signal-topic-brief-functions-composition-and-inverses.md; signal-topic-brief-numerical- methods.md]. At the other end, Reciprocal and inverse trigonometric functions (spec 2.1–2.2) anchors a dedicated mark in only 1 of 13, and Harmonic form — the one specific R cos/sin(θ±α) construction inside the broader spec 2.3 bucket — anchors a real, transcribed question in only 1 of the 11 series whose mark schemes were checked for general topic coverage [signal-topic-brief-reciprocal-and-inverse- trigonometric-functions.md; signal-topic-brief-harmonic-form.md]. A flat schedule would spend as much repetition on either thin topic as on Functions or Numerical methods, despite an order-of-magnitude gap in how often each has a real, citable anchor.

Second, frequency and per-appearance weight point in different directions for the two thinnest topics — for two genuinely different reasons, not one. Reciprocal/inverse trig is confirmed as load-bearing inside a real question in 4 of 13 series, but has never once anchored more than a single mark of its own on any transcribed WMA13 paper — its own brief states this as the ceiling directly: "this spec item has never anchored more than 1 mark of its own on any transcribed WMA13 paper, and has never anchored a full question by itself." Harmonic form is the opposite shape: thin on sightings (1 of 11), but the one time it does appear, it is never a token add-on — it structures an entire 9-mark question, split 3 (construct R and α) + 2 (apply to a real-world extreme) + 4 (solve for the original variable) [signal-topic-brief-harmonic-form.md]. Treating both as "thin, so drill lightly" would be wrong for harmonic form specifically: its thinness is a sighting-count fact, not a low-stakes one, and §2 below schedules the two very differently for exactly this reason.

Third, several of WMA13's eleven taught lessons bundle two spec sub-items at genuinely different real frequencies, and the pass count below follows the lesson as taught while flagging which half deserves more of each pass's time. modulus-and-graph-transformations.ts teaches spec 1.3 (the modulus function, confirmed in 5 of 13) and spec 1.4 (combined transformations, confirmed in only 2 of 13) together — six series total, but a clear 5-vs-2 internal split [signal-topic-brief-modulus-and-graph-transformations.md]. differentiation-rules.ts teaches spec 4.2 (product/quotient/chain, 7 of 13) alongside spec 4.3 (dy/dx = 1/(dx/dy), 4 of 13, every instance a subset of the same seven series) [signal-topic-brief-differentiation-rules.md]. exponentials-and- logarithmic-graphs.ts teaches the real-world modelling half (spec 3.1–3.2, 8 of 13) alongside log-linear parameter estimation (spec 3.3, 2 of 13) [signal-topic-brief-exponentials-and- logarithmic-graphs.md]. None of these three lessons gets split into two separate schedule slots below — they are taught as one lesson each, and a student revises them as one — but §2 states, per lesson, which half is carrying the real frequency.

Fourth, a real, checkable secondary signal exists for three specific pieces of content: whether the formula is on the exam's own formula sheet at all. WMA13-verified-facts.md §3 verifies, directly from the booklet PDF, that the double-angle forms themselves (sin2A, cos2A, tan2A) are not printed and must be memorised, even though the compound-angle sum/difference forms feeding into them are printed; that d/dx(aˣ) = aˣ ln a — the one specifically spec-named result for exponential growth and decay (4.4) — is not printed; and that the standard differentiation results (sin kx, cos kx, eᵏˣ, ln x, plus the product/chain/sum rules) are not printed, even though the quotient-rule formula and the cosec/cot/sec derivatives are. These three facts do not change any topic's tier below — they are not independently confirmed frequency evidence — but they are a real reason the compound-and-double-angle, exponential-growth-and-decay, and differentiation-rules passes in §3 should include active recall of the specific memorised result, not just re-solving a past-paper question with the formula sheet open, since the real exam gives you no such sheet for exactly that piece.

None of this licenses skipping a thin topic: every one of the eleven is compulsory spec content [WMA13-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 nine, and a topic whose core result isn't on the formula sheet deserves active recall alongside worked practice, not instead of it.

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

Tier 1 — 9 of 13, genuinely tied at the top

Tier 2 — 8 of 13

Tier 3 — 7 of 13

Tier 4 — 6 of 13

Tier 5 — 5 of 13

Tier 6 — 4 of 13

Tier 7 — thinnest confirmed record on the whole paper, for two different reasons

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 7 topics' only scheduled passes live there.

CycleDayTier 1 (every cycle)Tier 2Tier 3Tier 4Tier 5Tier 6Tier 7
10Functions (1st); Numerical methods (1st)Exp/log modelling (1st)————Harmonic form — only pass; Reciprocal/inverse trig — only pass
22Functions (2nd); Numerical methods (2nd)—Differentiation rules (1st)Exp growth/decay (1st)———
35Functions (3rd); Numerical methods (3rd)Exp/log modelling (2nd)—Modulus + transformations (1st)Compound/double angle (1st)——
410Functions (4th); Numerical methods (4th)—Differentiation rules (2nd)——Rational expressions (1st); Integration by recognition (1st)—
518Functions (5th); Numerical methods (5th)Exp/log modelling (3rd)—Exp growth/decay (2nd)Compound/double angle (2nd)——
630Functions (6th); Numerical methods (6th)—Differentiation rules (3rd)Modulus + transformations (2nd)—Rational expressions (2nd); Integration by recognition (2nd)—

Reading this as repetition counts rather than a calendar: Functions and Numerical methods each get six passes — the most of anything, matching their tied status as this paper's two most frequently confirmed topics. Exponentials/log modelling and Differentiation rules each get three passes. Exponential growth/decay, Modulus+transformations, and Compound/double angle each get two passes. Rational expressions and Integration by recognition each get two passes. Harmonic form and Reciprocal/inverse trig each get exactly one pass, in Cycle 1 only, and are not scheduled again — consistent with §1 and §2's reasoning, though for the two different reasons already named: one because its thin sighting count leaves little repeatable pattern to drill beyond its single anchor, the other because it has never once justified more than a single accessible mark.

Per-cycle load is 5, 4, 5, 5, 5, 6 topics — close to flat, with Cycle 1 and Cycle 6 carrying one extra item each (both Tier 7 passes land in Cycle 1; Cycle 6 absorbs the third round of two Tier-3/4/6 items each) rather than a perfectly even split, so that the two thinnest topics are drilled early rather than risking a compressed run-up dropping them entirely.

4. Judgement calls stated explicitly

Harmonic form's one pass and part of Compound/double angle's own passes can, in practice, share the same source material — a real, citable overlap, not a coincidence manufactured for convenience. Harmonic form's single confirmed anchor is October 2020 Q7; three of Compound/double angle's five confirmed anchors are also October 2020 (Q1, Q5, Q7) — the same series [signal-topic-brief-harmonic-form.md; signal-topic-brief-compound-and-double-angle-formulae.md]. A student working through the real October 2020 paper during Cycle 1 is, in effect, covering Harmonic form's only scheduled pass and a meaningful share of Compound/double angle's first pass in one sitting. This document states that as a scheduling efficiency worth knowing, not as a new primary-source finding — both underlying facts were already independently established elsewhere in this hub; connecting them for scheduling purposes is this document's own construction.

Modulus+transformations and Differentiation rules are each scheduled as one lesson, but the two halves inside each should not get equal attention within a pass. Modulus (1.3, 5 of 13) is confirmed more than twice as often as Transformations (1.4, 2 of 13) inside the same lesson; Differentiation's product/quotient/chain half (4.2, 7 of 13) is confirmed nearly twice as often as its dy/dx=1/(dx/dy) half (4.3, 4 of 13, itself a strict subset of the same seven series). This schedule does not split either lesson into two slots — no sibling document in this hub does that either, and the lesson files themselves teach both halves together — but a student using this table should weight time inside each pass toward the higher-frequency half, not split it evenly.

Numerical methods is scheduled at 9 of 13, its own brief's committed figure, despite that same brief flagging a possible tenth series. Resolving whether Jun 2022 Q8(c) belongs to a genuine tenth citation would require re-checking the Jun 2022 primary source specifically for this topic — not done in this pass or the topic brief's own pass. Since 9 and 10 would not change Numerical methods' Tier-1 placement either way (it would remain tied with or slightly ahead of Functions), this schedule uses the stated 9 and repeats the flag rather than resolving it unverified.

Reciprocal/inverse trig's single scheduled pass should look different in kind from every other topic's passes, not just shorter. Because this spec item has never anchored more than one mark of its own on any transcribed paper, there is no real multi-mark worked example to rehearse the way there is for, say, Harmonic form's one pass. Its Cycle-1 pass is better spent as a fast recognition drill (state the reciprocal identity cleanly, without a coefficient sliding inside it — the one real, confirmed error mode) than as a simulated full question, because no full question built on this spec item alone exists in the record to simulate.

The tier boundaries in §2 follow each topic's own real, most-recently-stated count exactly, including where two adjacent tiers are close. Exp/log modelling (8) and Differentiation (7) are one series apart; Exp growth/decay and Modulus+transformations are tied at 6; Rational expressions and Integration by recognition are tied at 4. None of these near-ties or exact ties is adjusted 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 tidier-looking distribution.

5. Where this document's scope ends

This document exists specifically to fill the gap forge-forty-eight-hour-checklist.md names in its own "Flagged gaps" section — a topic-by-topic time allocation, which that document explicitly declines to guess at. It does not replace that checklist's own countdown, cross-topic habits list, or "confirmed repeat offenders" list, and a student should still read that document for the final 48 hours specifically — this schedule's own six cycles are a longer-run-up complement to it, not a substitute. Nor does this document address exam-day wellness, logistics, or anything beyond an ordered repetition count — no document in this course's WMA13 research addresses that territory, and nothing here should be read as covering it.

6. Honesty notes

Sources used