Pure Mathematics 3

Error Pattern Tracker

Provenance: compiled 2026-09-29, grounded entirely in research/veridian/WMA13-verified-facts.md (13 real WMA13 series checked, Oct 2020–Jun 2026: 8 read start-to-finish with full mark schemes and examiner reports — Oct 2020, Oct 2021, Jan 2022, Jun 2022, Oct 2022, Jun 2023, Jan 2024, Jan 2025 — plus 5 more checked for specific topics only — Jan 2023, Oct 2023, Jun 2024, Oct 2024, Jun 2026), cross-referenced against this same folder's forge-exam-technique-guide.md (§5.1's per-lesson trap table and §5.2's six newly-mined patterns) and the trap names as they actually appear in content/veridian/curriculum/wma13/*.ts. No new primary-source fetching was done for this document — every trap below already exists, verbatim-sourced, in one of those two places; this document's own contribution is re-organising them into a loggable tracking format, not new research. Where the underlying source gives an exact series count ("confirmed across N series"), that exact count is reused here rather than re-derived. Nothing below states a likelihood or a probability — only "seen in N of M series checked," per this course's standing rule.

#WMA13 (Pure Mathematics 3) — 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 exact mark-scheme mechanism, a worked fix — see forge-exam-technique-guide.md (§5) or the named lesson file in content/veridian/curriculum/wma13/; this document deliberately does not re-explain them. What it adds instead:

Part 1 is a single-page checklist of every real, sourced WMA13 error pattern this course has confirmed, grouped by spec topic, each with a stable trap ID and its real evidence count.
Part 2 is a blank log table with the same columns every time — photocopy it (or just 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.
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, fill in one log row per mark lost, tick the matching Part 1 box, then move on. The value is cumulative — 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.

#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. A box ticked twice or more is a real personal pattern, not a one-off — see Part 3.

#1. Algebra and functions (spec 1.1–1.4)

T-ALG-1 — combined fraction not fully justified. Reaching the correct simplified rational expression but not showing the factorise-and-cancel (or equivalent) step a "show that" question demands. Seen in 3 of 13 series checked: Oct 2020 Q9(a), Jan 2024, Jan 2025 Q4(a). Full mechanism: rational-expressions-and-algebraic-division.ts.
T-ALG-2 — domain of the inverse function omitted. f⁻¹(x) itself correct, but its domain missing or wrong. The single most consistently tested sub-topic in the whole archive; the research file's own cross-topic tally (§6) puts this at confirmed across at least 4 series — explicitly quoted in Jun 2022, Jan 2022, and Oct 2021 Q1(b), and independently in Jan 2023 Q1(c) per the lesson's own trap catalogue. Full mechanism: functions-composition-and-inverses.ts, trap domain-of-inverse-omitted.
T-ALG-3 — range of f derived from scratch instead of recognised as the domain of f⁻¹. They are the same set; several reports note candidates re-deriving it needlessly. Oct 2022 Q2(b).
T-ALG-4 — composed algebraic argument not collapsed via a stated domain constraint. A composed argument that is itself an expression (not a bare number), needing a condition like "a > 0" applied before an equation can even be set up. Seen once so far — Jun 2026 Q2(d).
T-ALG-5 — only one branch of a modulus equation/inequality solved, or the wrong combined region selected at the end. Confirmed across 3+ series: Jan 2022 Q7, Oct 2020 Q4(c), Jun 2023 Q6(c). Full mechanism: modulus-and-graph-transformations.ts.
T-ALG-6 — a combined transformation only partially applied (e.g. one coordinate shifted, the other not). Jan 2024 Q1.
T-ALG-7 — the wrong point transformed — a freshly-computed value (e.g. a turning point just found in an earlier part) transformed instead of a different point the question separately names. Zero marks even with flawless transformation arithmetic. Seen once — Summer 2026 Q3(c).
T-ALG-8 — a range stated in x-notation instead of y/f(x)-notation. Numerically correct, scored zero anyway. Seen once — Jan 2023 Q1(a). (forge-exam-technique-guide.md §5.2(c).)

#2. Trigonometry (spec 2.1–2.3)

T-TRIG-1 — cosec written as the reciprocal of cosine (confused with sec). Jan 2022 Q2.
T-TRIG-2 — a coefficient folded into the reciprocal, e.g. writing 3cosecθ = 1/(3sinθ). Scored B0 unless the plain identity is separately stated. Seen once, Jan 2022 Q2 — a genuinely distinct slip from T-TRIG-1, not the same mistake restated.
T-TRIG-3 — an extra genuine solution found but not rejected, when the question asks for a specific one ("the smallest," "the first"). Seen once — Jan 2022 Q2(b), where the accuracy mark is explicitly "ONLY."
T-TRIG-4 — forgetting to halve (or otherwise convert) when recovering θ from a solved multiple of θ (e.g. reporting the solved 2θ value, not θ). Seen once — same Jan 2022 Q2(b) report.
T-TRIG-5 — wrong double-angle cosine form chosen, or a missing bracket that changes the equation's meaning (e.g. 4cos²x − 2 = 2cosx losing the brackets around (2cos²x − 1)). Oct 2020 Q1.
T-TRIG-6 — "show that" proof missing an intermediate line, even when every line present is correct. Confirmed across 4+ series: Oct 2020, Jan 2022, Jun 2023, Jan 2024.
T-TRIG-7 — degrees/radians mismatch, a missing second solution in range, or an extra out-of-range solution included. Confirmed across 5+ series: Oct 2020, Jan 2022, Jun 2022, Jun 2023, Jan 2024.
T-TRIG-8 — harmonic-form R given as a decimal instead of an exact surd, or α given in the wrong angle unit, on the construction marks themselves (not just the final solved angle). Seen once, on the only head-on harmonic-form question located — Oct 2020 Q7(a).

#3. Exponentials and logarithms (spec 3.1–3.3, plus 4.4 where the two overlap)

T-EXP-1 — a correct numeric modelling answer missing its unit or a required context word (£, tonnes, m², "loss," "decreasing"). Verified across at least 4 separate series with near-identical wording each time: Oct 2021 Q3(b), Jan 2022 Q4(c), Oct 2022 Q5(a), Jan 2025 Q2(a). The single best-documented trap in this entire tracker.
T-EXP-2 — a calculator's built-in equation solver used instead of shown algebraic log/exponential manipulation. Confirmed across at least 4 series: Oct 2022, Jun 2022, Jan 2024, Jan 2025 — with examiner reports explicitly warning this will be penalised more, not less, in future series.
T-EXP-3 — the wrong log base used on a log-log graph (base 10 or ln substituted for the question's own stated base). Seen once — Jun 2023 Q2.
T-EXP-4 — the "eliminate logs from a linear log-equation" step not properly understood, even when the graph-reading step beforehand was fine. Jun 2023 Q2(b) — named in the examiner report as "where things often went wrong."
T-EXP-5 — interpreting a model's constant (e.g. b in H = ab^t) in words, but missing one of the three required components (direction, percentage, and "per year"/"per annum"). Seen once — Jun 2026 Q5(b); the scheme's own reject list shows how easy it is to get the general idea right and still lose the mark.
T-EXP-6 — a domain-restriction "why is there no solution" question answered with an ambiguous or wrong statement (e.g. "logs can't be negative" or "the maximum is 10," both explicitly rejected) instead of naming the actual restriction. Jan 2024 Q5(d).

#4. Differentiation (spec 4.1–4.4)

T-DIFF-1 — the differentiation rule not quoted as its own line before being applied. The single most repeated piece of technique advice in the whole archive, confirmed across 5 series: Oct 2020 Q3, Oct 2021 Q9(a), Jan 2022 Q6(a), Jun 2023 Q10(a), Jan 2024 Q7(a).
T-DIFF-2 — dx/dy found correctly but then used as if it were dy/dx, or not converted back into x-terms. Oct 2020 Q8(ii).
T-DIFF-3 — on a dy/dx = 1/(dx/dy) turning point, the reciprocal itself set equal to zero (rather than its denominator, dx/dy, set to zero directly) — invalid algebra that the real mark scheme scores zero for, even when it happens to land on the right number for that particular curve. Seen once, independently re-verified against the primary Oct 2024 mark scheme.
T-DIFF-4 — a "rate of change" question answered by substitution alone, with no differentiation. Confirmed across 3 series: Jan 2022 Q8(c), Jun 2023 Q7(b), Jan 2024 Q5(c).
T-DIFF-5 — the sign lost when differentiating a negative exponent (e.g. N₀e^(−Bt)). Confirmed strictly across 2 series (Jan 2022 Q8(c), Jan 2024 Q5(c)), with a third, weaker related instance during rearrangement rather than differentiation itself (Jan 2025 Q5(c)) — log this third one separately if it's what actually happened.
T-DIFF-6 — the power rule applied to a variable exponent instead of a^x → a^x ln a. Treating N = 100 × 2.24^t as if 2.24 were the variable and t the fixed power. Seen once, Oct 2024 Q4(c) — the wrong rule entirely, not a slip within the right one.
T-DIFF-7 — two exponential terms with different rate constants not combined into one solvable equation before logs are taken, on a sum-of-two-exponentials maximum/minimum question. A calculator-only route here scores only 2 of 5 marks regardless of the final number's accuracy. Seen once, Oct 2024 Q8(c).

#5. Integration (spec 5.1–5.2)

T-INT-1 — the constant of integration omitted on an indefinite integral, otherwise fully correct. Confirmed across at least 2 series with direct quotes (Oct 2021 Q5(ii), Jan 2022 Q3(i)); the source describes the pattern as recurring more broadly still.
T-INT-2 — the modulus sign dropped in logarithmic integration, leading to an attempt to evaluate ln of a negative number. Confirmed across 2 series: Oct 2020 Q9(c), Jun 2023 Q9(c).
T-INT-3 — a formula-booklet result re-derived from scratch (e.g. by substitution) instead of recognised and used directly. Costs time, not marks outright. Seen once, Jun 2023 Q9(c).

#6. Numerical methods (spec 6.1–6.2)

T-NUM-1 — "continuity" not named; "sign change" alone stated as the reason a root exists. The single most repeated specific error in the entire archive — the mark scheme requires the word (or a clear equivalent) as its own component, separate from the sign-change values and the "hence root" conclusion. Named explicitly in the examiner reports for at least 4 of the series checked: Jan 2022 Q5(a), Oct 2022 (itself describing a pattern across several prior series), Jan 2024, and Jan 2025 Q1(a) — the first series where the source notes this finally seems to be improving.
T-NUM-2 — an iterate given to fewer decimal places than asked, or rounded prematurely partway through a chain of iterations. At least 3 series per the source, two named directly: Oct 2020 Q6(c), Jan 2024 Q2(c)(ii).
T-NUM-3 — the substitution into an iterative formula not shown, relying silently on a calculator's ANS key. Seen once, Jun 2022 Q8(c) — the mark scheme treats this as insufficient method evidence even with correct final values.
T-NUM-4 — an algebraic division terminated early, left with a remaining linear term (still containing x) standing in for a genuine constant remainder against a quadratic divisor. Seen once, Oct 2024 Q9(c).

#7. Cross-cutting — not tied to one spec topic

T-GEN-1 — a "show that" question's final line reached without every intermediate step shown. Confirmed across algebra, trigonometry, differentiation and numerical-methods questions alike (research file §6, cross-topic pattern 1) — this is the same underlying habit as T-TRIG-6 and T-DIFF-1, just tracked once here because it recurs outside those two topics too.
T-GEN-2 — a calculator-only method used with no algebra shown, on a question that either carries the explicit "solutions relying entirely on calculator technology are not acceptable" instruction or otherwise requires shown working. Confirmed paper-wide, independently, across at least six separately audited lessons and topics (differentiation, exponential modelling, log-graphs, modulus/transformations, numerical methods, algebraic division) — see forge-exam-technique-guide.md §3 for the full list and the exact worked mark-loss example (1,1,0,0,0 out of 5).

#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.

#	Date	Paper/series practised	Q. no.	Spec topic	Trap ID	Marks lost	What I actually wrote / did	Fix for next time
DEMO	—	Jan 2022 (real past paper)	Q5(a)	6.1 Numerical methods	T-NUM-1	1 of 2	Wrote "f(1) < 0 and f(2) > 0, so there is a root between x=1 and x=2" — no mention of continuity anywhere	Add a fixed sentence template: "f is continuous on [a,b], and since f(a) and f(b) have opposite signs, by the change-of-sign rule there is a root in (a,b)" — write it in full every single time, not just when it "feels needed"

The DEMO row is a worked example of how to fill the table in, built from a real, already-documented trap — delete it before you start logging your own papers, or just 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.

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.
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 4–5+ real series (T-EXP-1, T-DIFF-1, T-NUM-1, T-TRIG-6/7, T-ALG-2, T-GEN-2) 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 that's only ever been seen in one series so far (most of the T-*-3 through T-*-8 entries above) is real, but treat it as "worth knowing exists," not as something to drill as hard.
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 research hasn't independently documented from the examiner reports — 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.
Re-read the fuller mechanism, not just this tracker's one-line summary, for anything you've ticked twice — forge-exam-technique-guide.md §5 or the named lesson file, both cited against every trap ID in Part 1.

#Genuine gaps and honest limits

Every count above of the form "N of 13 series" is exactly the count already established in research/veridian/WMA13-verified-facts.md, not independently re-tallied for this document — where that file says "at least," this document keeps "at least," because the underlying series-by-series check was not exhaustive for every topic (see that file's own §8).
Most of the traps under 1.4, 2.1–2.2 (beyond the two named), 3.3, 4.3, 4.4's newest entry, 5.2's booklet-recognition point, and all of numerical methods' T-NUM-3/T-NUM-4 are single-series findings. They are real and verbatim-sourced, not guesses — but a single occurrence is not yet a confirmed recurring pattern the way T-NUM-1 or T-DIFF-1 are. Part 1 states the count for every entry so this distinction is never hidden.
This tracker does not include topic-frequency or grade-boundary data — that is signal-frequency-and-boundaries.md's job, not this document's; a trap appearing on this list says nothing about how likely it is to reappear on a specific future paper, only that it has genuinely happened before and been named in a real mark scheme or examiner report.
No trap here has an attached likelihood, percentage, or "commonly worth X marks" claim beyond what a cited mark scheme states outright for that exact question — per this course's standing rule against inventing likelihoods.

#Sources

research/veridian/WMA13-verified-facts.md — §5 (per-topic verified examiner findings, all six sub-sections), §6 (cross-topic patterns), §7 (topics with the richest evidence) — the primary source for every trap's evidence count in Part 1.
content/veridian/technique-hub/wma13/forge-exam-technique-guide.md — §5.1 (the existing per-lesson trap table, cross-referenced by trap ID) and §5.2 (the six newly-mined, single-series patterns T-ALG-4, T-ALG-8, T-TRIG-3, T-TRIG-4, T-DIFF-3, T-DIFF-6, T-NUM-4 are drawn from).
content/veridian/curriculum/wma13/*.ts — exact trap names (domain-of-inverse-omitted, rule-not-quoted-before-use, continuity-statement-omitted, and others) reused verbatim from each lesson's own misconception/commonWrongPath fields, not renamed for this document.
content/veridian/question-bank/wma13.ts — the two Oct 2024 marked-solution items underlying T-DIFF-7 and its calculator-only commonWrongPath.