A Star Gap Analysis

Provenance (2026-09-29). This is a synthesis/index document, not new primary-source research — no raw Pearson PDF was opened this session. Read in full this session: forge-level-threshold-guide.md (source of Part 0's holistic-band-absence finding, Part 1's gate vocabulary, and Part 2's nine-anchor synthesis in its own §3); forge-error-pattern-tracker.md (source of every "seen in N of 5" count reused in Parts 3–4); forge-exam-technique-guide.md (read in full, §§1–6 — checked directly for a "danger-phrases" section: neither the word "danger" nor "phrase" appears anywhere in that file outside a lesson-file's own trap-id text, so no such section exists to read from); and forge-battle-card.md §4, the "Top 5 danger warnings, ranked," used in Parts 3–4 in place of the non-existent "danger-phrases" section, exactly as this course's sibling WMA13 gap-analysis document already did for its own paper. signal-frequency-and-boundaries.md §2 supplies Part 0's grade-boundary finding. research/veridian/WMA14-verified-facts.md was not re-opened directly for new material this session; every citation below is reused, with its original attribution preserved, from one of the four technique-hub documents just named. content/veridian/curriculum/wma14/ (all twelve lesson files) and the rest of content/veridian/technique-hub/wma14/ were checked as directory listings, to confirm this document doesn't duplicate an existing one — this is the eighth paper in this course to receive a document of this exact name and shape (wbs11, wbs12, wbs13, wbs14, wec14, wma12, wma13); none of them cover WMA14. No new diagnostic category is introduced anywhere below; every category already exists, cited, in one of the four sources. Not affiliated with or endorsed by Pearson Edexcel.

#WMA14 (Pure Mathematics 4) — A* Gap Analysis: Self-Diagnostic

#What this document is, and isn't

This is not new research. Every document that measures why WMA14 marks are lost — the level-threshold guide's mark-by-mark ladders, the error-pattern tracker's trap watchlist, the exam-technique guide's checklists, the battle card's danger warnings — already exists in this folder. What doesn't exist yet is one place that filters all of that for the specific question a candidate already producing mostly-correct scripts actually asks: of everything already documented, which parts are about the gap between a strong answer and a fully-clean one, as opposed to the gap between not knowing the method and knowing it at all? This document answers that by re-reading the four source documents with that filter and indexing what survives it. It invents nothing: every citation below already appears, in the same words, in one of the four sources.

#Part 0 — Unlike WMA13, this paper has neither a grade boundary nor a holistic band to anchor a gap analysis against

Two honest facts, stated first because together they change what "gap analysis" can even mean for this specific paper.

No grade-boundary figure exists anywhere in this course's WMA14 review. signal-frequency-and-boundaries.md §2 confirms this directly: the facts bank was built from the specification, the formula booklet, mark schemes and examiner's reports — none of which publish grade boundaries — and a direct search of the facts bank for boundary-related content found only mathematical domain/range boundaries inside worked questions, not grade boundaries. This is the opposite finding from the sibling WMA13 document, which opens by naming real A* boundaries running from 58 to 68 raw marks across 13 series. No boundary figure is stated or estimated anywhere below.

WMA14 also has no holistic level-descriptor scale at all. forge-level-threshold-guide.md §0 states this as its own governing constraint: there is no examiner reading a whole answer and placing it in a band — every mark is a discrete, named M/A/B or dependent-mark line, gated on a specific, checkable condition. So this document's "top band" cannot be a raw-mark threshold the way WMA13's could be; it can only be the internal mark-to-mark gates inside a single question's own scheme — the boundary between M1 and M0, between a dependent mark earned and withheld. That is the frame every part below inherits, not works around.

#Part 1 — The real gate vocabulary, read as self-diagnostic checks

forge-level-threshold-guide.md §1 defines these gates more precisely than any other document in this course's WMA14 material, because its own worked ladders depend on the distinctions being exact. Read each as a question to ask about a mark you think you've earned, not as a definition to memorise.

• M1 — is a power-shift (or equivalent method step) actually visible anywhere in the working, even with a later arithmetic slip, or is the original expression simply asserted with a final value attached?
• A1 cannot stand without its own M1. The clean real anchor: Oct 2024 Q1's misread index caps the whole script at "B1M1A0A0 M0A0" — the shape of the method survives, but every A mark gated on the correct index is lost even though everything after that point is internally consistent.
• B1 is unconditional, but not undemanding. Jan 2021 Q6(b)'s corrected reading: the B1 for $y=\frac32$ is earned regardless of whether the extraneous root is explicitly discarded — a genuine, documented correction against over-tightening a B mark into an A-mark-style "show your reasoning" test it was never gated on.
• Is a dependent mark (dM1, or a chain running to ddM1) actually linked to the specific earlier mark it depends on, not just numerically consistent with it? Jan 2026 Q7's $M1A1\to dM1\to ddM1,A1$ chain is this paper's richest real example: a correct gradient formula evaluated at the wrong parameter value breaks the chain at the dM1, and the ddM1 above it is then unrecoverable however perfectly the rest is executed.
• Which of three different senses of "independent" does a given ft actually carry — a flat two-mark deduction for a genuine misread, a named cap specific to one question (Oct 2024 Q1 above), or a B1ft that follows the candidate's own earlier numbers rather than one fixed pair (Jan 2026 Q7(c))?
• cao vs. cso is the sharpest, and most asymmetric, real distinction on this paper. An A1* on a "show that" line functions as cso even unlabelled: Jun 2022 Q9's own line requires "all working must have been correct" before the final mark is available at all. Set directly against Jan 2026 Q9(a)'s cao A1, where the scheme explicitly allows "no-working scores all 3" — the opposite extreme of the same spectrum, on the same paper.
• Is the exact-answer default actually in force, or has this specific mark named a condoned exception? Jan 2026 Q3(b) is the real, quotable exception: its A1ft explicitly condones the decimal $1.5625$ alongside the exact $\frac{25}{16}$, because that particular value was never asked for in exact form. Every other "condone [decimal]" note is a deliberate, scheme-authored carve-out, not evidence the general rule has softened.
• Have you checked whether an "unusual" method is actually credited on equal footing, before assuming it scores less? Jan 2026 Q8 scores three structurally different proof routes — divisor-pair, parity, substitution — on the identical $M1\to A1\to dM1\to A1^{*}$ skeleton. The threshold is written at the level of what is established, not which specific path reached it.

#Part 2 — The nine-anchor synthesis: what a "just misses" costs, in the level-threshold guide's own words

forge-level-threshold-guide.md §3 is titled, almost exactly, this document's own question — "what actually separates a 'just misses' from a 'just clears,' read across all nine anchors" — and its finding is the single most load-bearing citation in this whole document: across every real near-miss it documents, the mathematics itself is essentially never what fails; what fails is "the exact linking step the mark is actually checking." Four concrete, real instances it names:

• Dotting the wrong object. Oct 2021 Q7's most consequential real "just misses": the line's general point is dotted directly against the direction vector, skipping the subtraction that forms the true $\overrightarrow{AX}$. This is genuinely solvable — it yields a specific, plausible wrong $\lambda=\frac{37}{50}$ against the correct $\frac25$ — so the mark is lost to which object enters the dot product, not to algebraic competence.
• Checking one factor pair instead of both. Jan 2026 Q8's dM1 requires attempting both valid pairs (46×1 and 23×2); a candidate who checks one, reaches a correct non-integer $p$, and stops has not cleared this specific dependent mark, even though that one checked pair is flawless.
• Defaulting to the acute angle on a question that names an interior one. Jan 2026 Q9(b)'s final A1 is cso-gated on reporting $70.5°$ specifically; reaching $109.5°$ and simply writing "therefore $70.5°$" scores A0 unless a genuine supporting argument accompanies it — the opposite convention from an ordinary angle-between-lines question, where the acute value is usually the safe default.
• Inverting a fraction term-by-term instead of as a whole. Jan 2026 Q3's sharpest "just misses": a candidate who correctly finds the constant of integration but then inverts $\frac1{c-\frac15t^{-1}}$ term-by-term rather than as a single fraction reaches a plausible-looking but structurally wrong expression for $h$ — costing that M1 and the final cao A1 while the four earlier marks stay intact.

Read together, these four are the closest thing this paper has to a top-band-specific gap: none of them reflects a missing technique, and all four are documented at the level of an individual mark's own gate, not a whole question's difficulty.

#Part 3 — The calculator-jump risk: this paper's own version of "correct but scores almost nothing"

forge-level-threshold-guide.md §2.1 cross-references a real, precise breakdown for Oct 2024 Q2 (curves $C_1$, $C_2$ don't intersect, 4 marks): a calculator-only jump straight to the roots keeps the independent B1 but forfeits the M1 and both dependent A marks — one of four marks kept for a numerically correct final line with the required algebraic reduction skipped. forge-error-pattern-tracker.md's T-PROOF-6 confirms this is not a one-off: the same mechanism — a calculator used to state roots with no shown method, then a weak or missing concluding sentence — is independently confirmed across 2 of 5 series (Jan 2024 Q8 and Oct 2024 Q2).

This connects forward to forge-battle-card.md §4's fifth ranked danger: Jan 2026 Q7, the paper's largest confirmed item at 16 marks, prints "Solutions relying on calculator technology are not acceptable" twice, covering all four parts. A numerically-correct final answer with no algebraic working scores nothing on a question carrying that rubric, regardless of the paper's general calculator-allowed policy.

The shape worth naming explicitly: this is a strong-candidate risk more than a weak-candidate one. A script that genuinely cannot do the algebra has no calculator shortcut available to it in the first place; the candidate who can see the answer, and is confident enough to reach for the calculator instead of writing the reduction out, is exactly the one this rule catches.

#Part 4 — Cross-cutting meta-traps, and which of them are pass-level rather than top-band-specific

forge-error-pattern-tracker.md's cross-cutting section (§12) names two meta-traps that recur across unrelated spec topics: T-GEN-1, fudged-reverse-fit (working "adjusted" to land on a printed target after a mistake, documented independently in proof, parametric elimination, and separable differential equations, all Jan 2021), and T-GEN-2, a convenient nearby object substituted for the one the question's geometry actually requires (the origin instead of the named point, Jan 2021 Q6; a line's own general point instead of the true difference vector, Oct 2021 Q7). Both sit closer to Part 2's "linking step" failure mode than to a knowledge gap — T-GEN-2 is, in fact, the same Oct 2021 Q7 anchor already named there.

Set against these, forge-battle-card.md §4's other three ranked dangers are better read as pass-level risks than top-band ones, on the tracker's own evidence: T-VEC-1, the wrong pair of vectors used for a named angle, is the single most robustly confirmed specific error in the whole tracker — 3 of 5 series (Jan 2021 Q2a, Oct 2022 Q3b, Jan 2024 Q6c); T-VEC-2, the acute angle reported where the obtuse one is required, is confirmed across 2 of 5 (Jan 2021 Q2a, Oct 2022 Q3b); and rounding an exact answer early (danger #2) rests on a standing mark-scheme rule, not a series count, but is general enough to cost marks at any script strength. A trap common enough to be confirmed across three of five series is a risk to any script reaching that question, not narrowly a problem for scripts otherwise scoring near-full marks — which is a different profile from Part 3's calculator-jump risk above.

#Part 5 — Using this as a diagnostic, not just a reading list

This document adds no new tracking mechanism of its own — forge-error-pattern-tracker.md already has the fillable log (its Part 2 table) and the tallying method (its Part 3). What this document adds is a filter to apply before logging a lost mark as a plain "silly mistake": check it first against Part 1's gate vocabulary and Part 2's four named "just misses" instances. A mark lost to a dependent-chain gate (Part 1) or a linking-step failure (Part 2) is a different category of problem from a mark lost to not knowing a method at all, and the fix is different — reading the specific mark's own gate correctly, not repeating practice of mathematics that, by definition, was already right.

#Flagged gaps — what this document does not claim

• No new primary-source reading happened this session. Every citation is reused, with its original attribution intact, from forge-level-threshold-guide.md, forge-error-pattern-tracker.md, forge-exam-technique-guide.md, or forge-battle-card.md.
• No grade-boundary figure is stated anywhere above. signal-frequency-and-boundaries.md §2 confirms none exists in this course's WMA14 review at all — this is a genuine open gap for this paper, unlike WMA13, and Part 0 states it rather than working around it.
• forge-exam-technique-guide.md has no section named or shaped as "danger-phrases" — checked directly, not assumed. forge-battle-card.md §4's "Top 5 danger warnings, ranked" is used in its place in Parts 3–4, and that substitution is stated here rather than made silently, exactly as the sibling WMA13 document already disclosed for its own paper.
• forge-level-threshold-guide.md's own nine anchors are unevenly verified — some (Jan 2026 Q7, Q9) have every mark confirmed, others (Jun 2022 Q9, Jan 2021 Q4/Q6/Q9) only partially. This document inherits that unevenness rather than smoothing it; Parts 1–2 above cite only what the guide itself verifies, not a reconstructed full ladder.
• The January 2026 series (Q3, Q7, Q8, Q9) has no published examiner's report yet. Every "just misses" example drawn from it in Parts 2–3 is built from the mark scheme's own stated exclusions and generosity notes, never from a documented candidate error — matching the discipline the source documents themselves already hold to.
• No likelihood, percentage, or "confirmed in every series without exception" claim appears anywhere in this document. Every series count above is reused, unchanged, from forge-error-pattern-tracker.md.
• This document does not extend coverage by opening any further primary source; it is bounded by what the four named technique-hub documents have already established.

#Sources used

• content/veridian/technique-hub/wma14/forge-level-threshold-guide.md — read in full; source of Part 0's holistic-band-absence finding (§0), Part 1's gate vocabulary (§1), and Part 2's nine-anchor synthesis (§3), plus the Oct 2024 Q2 calculator-jump cross-reference reused in Part 3 (§2.1).
• content/veridian/technique-hub/wma14/forge-error-pattern-tracker.md — read in full; source of every "seen in N of 5" count reused in Parts 3–4 (T-PROOF-6, T-VEC-1, T-VEC-2, T-GEN-1, T-GEN-2).
• content/veridian/technique-hub/wma14/forge-exam-technique-guide.md — read in full, §§1–6; checked directly for a "danger-phrases" section (none exists) and cited for the Jan 2026 Q7 calculator-rubric wording reused in Part 3.
• content/veridian/technique-hub/wma14/forge-battle-card.md §4 — read in full; source of the "Top 5 danger warnings, ranked" used in Parts 3–4 in place of a non-existent "danger-phrases" section.
• content/veridian/technique-hub/wma14/signal-frequency-and-boundaries.md §2 — read in full; sole source of Part 0's grade-boundary-absence finding.
• content/veridian/curriculum/wma14/ and content/veridian/technique-hub/wma14/ — both checked as directory listings, to confirm no existing lesson file or technique-hub document already covers this synthesis.

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