Technique Masterclasses

Pure Mathematics 4

Error Pattern Tracker

Provenance: compiled 2026-09-29, grounded entirely in research/veridian/WMA14-verified-facts.md §5 (per-topic verified examiner and mark-scheme findings, all seven sub-sections) and cross-referenced against this same folder's forge-exam-technique-guide.md (§3's self-mark checklist and §4's common-error digest) and signal-frequency-and-boundaries.md (the "seen in N of M series checked" denominator convention this document reuses). No new primary-source fetching was done for this document — every trap below already exists, verbatim-sourced, in the facts bank; this document's own contribution is re-organising them into a loggable, fillable tracking format, not new research. The facts bank's own lesson-audit-log entries (corrections made to the curriculum .ts files' internal wording — a backwards vector identity, a mislabelled dependent mark, a fabricated exemplar caught before publication) are course-QA history, not evidence of real candidate behaviour, and are deliberately excluded from Part 1 below for that reason. Nothing in this document states a likelihood, a percentage, or a grade boundary — only "seen in N of M series checked," per this course's standing rule.

WMA14 (Pure Mathematics 4) — Error Pattern Tracker

How to use this document

This is a tracking tool, not a teaching document. For the explanation of any trap named below — why it happens, the full mark-scheme mechanism, a worked fix — see forge-exam-technique-guide.md or the named lesson file in content/veridian/curriculum/wma14/; this document deliberately does not re-teach them. What it adds instead:

  1. Part 1 is a single-page checklist of every real, examiner-report-sourced WMA14 error pattern this course has confirmed, grouped by spec topic, each with a stable trap ID and its real evidence count.
  2. Part 2 is a blank log table with the same columns every time — keep adding rows after every timed past paper or mock, and record exactly what went wrong against a trap ID from Part 1, or flag it as new.
  3. Part 3 is how to turn a stack of filled-in logs into an actual revision priority list, and how to promote a mistake that isn't in Part 1 yet into your own tracked trap.

Run it after every timed paper: mark the paper against the real mark scheme, fill in one log row per mark lost, tick the matching Part 1 box, then move on. One paper's log tells you little; four or five start showing which of the paper's known traps are also your traps, and which mistakes are yours alone.

The evidence base, stated once here rather than repeated on every row. WMA14 has confirmed examiner-report material from 5 series: four full Examiners' Reports (January 2021, October 2021, October 2022, January 2024) plus one single-question extract (October 2024, covering only its own Q1 and Q2). Every "seen in N of 5" count below is against that denominator. A topic's real question paper and mark scheme can exist for a series with no examiner's report reviewed yet (January 2026 is the current case) — those items verify real mark-scheme mechanics only and are listed separately at the end of Part 1, never folded into a trap's "seen in" count, matching the discipline the facts bank and forge-exam-technique-guide.md §4 already hold to.

Part 1 — The known-trap watchlist

Tick a box the first time you can confirm, from a real mock or past paper you've marked, that you've made that mistake yourself.

1. Proof by contradiction (spec 1.1)

The facts bank's own cross-series finding: across three independent reports (Jan 2021, Oct 2021, Jan 2024), candidates can usually do the algebra but consistently fail to write the logical scaffolding — the individual traps below are that failure broken into its specific, loggable forms.

Full mechanism and worked fixes: proof-by-contradiction.ts.

2. Partial fractions, incl. integration via them (spec 2.1, 6.3)

Process note, not an error to log: substitution (x = specific roots) scored more reliably than full simultaneous-equation expansion on the same question — Jan 2024 Q2(a). Full mechanism: partial-fractions-decomposition-and-integration.ts.

3. Parametric equations — conversion, domain, range (spec 3.1)

Full mechanism: parametric-equations-conversion-and-domain-range.ts.

4. Binomial expansion for rational n (spec 4.1)

Full mechanism: binomial-expansion-for-rational-n.ts.

5. Implicit/parametric differentiation, tangents & normals; rates of change (spec 5.1, 5.2)

Full mechanism: implicit-and-parametric-differentiation-tangents-and-normals.ts.

6. Integration by parts and by substitution (spec 6.2)

Process note, not an error: a second application of integration by parts is a dependent method mark on the real mark scheme, not an independent one — a slip on the first application costs both (Jun 2022 Q8(b), mark-scheme mechanics). The Pearson-credited "DI"/tabular method is an accepted alternative route, not an informal shortcut — Jan 2024 Q5(a). Full mechanism: integration-by-parts-and-substitution.ts.

7. Volume of revolution (spec 6.1)

Full mechanism: volume-of-revolution.ts.

8. Area under a parametric curve (spec 6.5) — no tracked traps yet

The only real question located for this spec point is January 2026 Q7 (16 marks), and no examiner's report has been published for that series yet (checked directly — the same URL pattern used for its mark scheme and question paper 404s for a report). This is genuinely the thinnest-evidenced spec point in the whole facts bank: there is a verified mark scheme and question paper, but zero documented candidate misconceptions, in either direction. Two real mechanics from that mark scheme are worth being deliberate about even without a documented failure attached: converting the given x-limits into the matching θ-limits before integrating, and not dropping the dx/dθ factor when setting up ∫y (dx/dθ) dθ. Log any real mistake you make here under "NEW" in Part 2 rather than against an invented ID — this section should stay empty of ticked boxes until a real examiner's report is published and reviewed.

9. Separable differential equations & rates of change (spec 5.2, 6.4)

Full mechanism: separable-differential-equations.ts.

10. Vectors — scalar product, angle-finding, skew/parallel/intersecting lines (spec 7.6–7.7)

Full mechanism: vectors-scalar-product-and-skew-lines.ts.

11. Position vectors, distance, foot of perpendicular (spec 7.4–7.5)

Full mechanism: position-vectors-distance-and-foot-of-perpendicular.ts.

12. Cross-cutting — not tied to one spec topic

Items with verified mark-scheme mechanics but no documented candidate error yet

The January 2026 series (Q3, Q7, Q8, Q9) has a real, independently verified question paper and mark scheme, but no published examiner's report — checked directly, the report URL 404s for this series. These items are real and useful to practise correctly, but are deliberately not given a trap ID or a "seen in N of 5" count, because no documented candidate misconception exists for them: the exhaustion-based proof needing every factor pair checked (Q8); converting a closed-rational solution's own leading coefficients into a limiting value rather than hunting for a stationary point that doesn't exist (Q3); the calculator-only-working ban printed twice on one question (Q7); crediting either sinθ or the component cross product for a vector-defined area (Q9). If you genuinely get one of these wrong on a real paper, log it under "NEW" in Part 2 — you would be contributing the first real evidence this course has for that specific mistake, not confirming an existing one.

Part 2 — The fillable log

Fill in one row per mark (or per mark-losing moment) after marking a timed paper. Use a trap ID from Part 1 where it fits; write your own short description and mark it NEW if it doesn't match anything above.

#DatePaper/series practisedQ. no.Spec topicTrap IDMarks lostWhat I actually wrote / didFix for next time
DEMO—Jan 2021 (real past paper)Q2(a)7.7 Scalar product / angleT-VEC-1 + T-VEC-22 of 4Found angle ABC using AC·BC instead of BA·BC, then reported the acute value (67.35°) without checking whether ABC was actually obtuseBefore setting up the dot product, write down which two vertices the named angle sits at and which two vectors share that vertex — then check whether the diagram/context calls for the acute or the obtuse result before writing a final answer

The DEMO row is a worked example built from a real, already-documented trap — delete it before you start logging your own papers, or keep adding real rows underneath it.

Part 3 — Turning the log into a revision priority list

Do this after every 3–5 timed papers, not after every single one — one paper's worth of data is too little to tell a real pattern from a one-off slip.

  1. Tally your own Trap ID column. Any ID that appears twice or more across your logged papers has stopped being "a thing the paper does to people in general" and become a thing you specifically keep doing. That is your revision priority, above anything you only got wrong once.
  2. Cross-check against how well-evidenced the trap already is in Part 1. A trap you've now hit twice that is also confirmed across multiple real series (T-VEC-1, T-VEC-2, T-PF-3, T-PROOF-6) is worth fixing first — it is both a real risk on the actual exam and a risk you've shown you're personally exposed to. A trap seen in only 1 of 5 series so far (most of the list) is real, but treat it as "worth knowing exists," not as something to drill as hard as the multi-series items.
  3. If the same mistake shows up twice in your log and isn't in Part 1 at all, it's a real personal trap this course's examiner-report review hasn't independently documented — write it as its own new row at the bottom of the relevant Part 1 section, in the same "what it looks like + how many times you've actually seen it" format, sourced as "mine, logged on [dates]" rather than attributed to an examiner report it didn't come from. Don't invent a series count for it — it's your data, not the paper's.
  4. Re-read the fuller mechanism, not just this tracker's one-line summary, for anything you've ticked twice — forge-exam-technique-guide.md §3–4 or the named lesson file, both cited against every trap ID in Part 1.
  5. For section 8 (area under a parametric curve) and any Jan 2026 mechanics-only item, treat a real mistake you log there as genuinely new information, not confirmation of something already known — there is no existing examiner-report baseline for either yet.

Genuine gaps and honest limits

Sources

Not affiliated with or endorsed by Pearson Edexcel. Every quoted fragment above is under fifteen words with its own series/question attribution; all longer commentary is this course's own, built on — not reproduced from — the cited primary documents.