Pure Mathematics 1

Vocabulary Precision List

#WMA11 — Vocabulary Precision List

#Pearson Edexcel IAL Mathematics, Unit 1: Pure Mathematics P1

Provenance: written 2026-09-29. Primary source for every citation below is research/veridian/WMA11-verified-facts.md (read in full; grepped specifically for "hence", "state", "write down", "show that", "condone", "exact", "simplest form", "sketch", "given that", "critical value" and "period"/"domain" before this document's entries were drafted, and the surrounding context of every hit read in full rather than judged from the grep line alone). Cross-checked against the other three WMA11 technique-hub documents already in this directory (forge-exam-technique-guide.md, codex-formula-and-method-bank.md, codex-deep-dive-surds-manipulation-and-exact-answers.md, codex-deep-dive-trig-graphs-period-and-domain.md) and against content/veridian/question-bank/wma11.ts, to keep every entry below genuinely additive rather than a restatement of ground those documents already cover in depth — see §0 for exactly where the boundary sits. No new primary-source PDF was fetched for this pass; every quotation below is inherited from the facts bank's own already-verified extractions (themselves taken directly from pdftotext -layout/-raw output of real Pearson QP/MS/ER PDFs, per that document's own §0 methodology), re-checked here only for correct attribution, word-count-under-15 compliance on direct quotes, and fit to this document's stated purpose.

#0. What this document is, and what it deliberately does not repeat

This is a glossary of command words and technical terms, not mark-scheme abbreviations and not a topic-by-topic deep dive. Three things it does not reproduce, because a fuller, better-suited treatment of each already exists elsewhere in this course:

Mark-code abbreviations (bod, ft, cao, cso, isw, awrt, SC, oe, dep/indep) and the R-vs-variable inequality trap are already defined and cited in forge-exam-technique-guide.md §2.6–2.7. Not repeated here.
The general "exact value, not a decimal" convention, traced across five spec strands, is already synthesised in codex-deep-dive-surds-manipulation-and-exact-answers.md Part 7. This document's own exact/simplest-form/specified-form entry (§4 below) is a different, narrower cut of the same evidence — a three-way distinction the deep dive states in passing but doesn't itself organise as its own entry — not a re-derivation of that document's synthesis.
Period vs. domain/range, as a full worked concept, is already covered at length in codex-deep-dive-trig-graphs-period-and-domain.md §1 and §6. §9 below gives only the glossary-length version, with a pointer.

Everything else below — "hence," the fact that "state" does not by itself guarantee a no-method mark, answer-given (ag) marks, "given that" as a binding restriction, critical values vs. inequalities, "condone," and what "sketch" does and doesn't require — is not written up as its own entry anywhere else in this course's WMA11 material at the time of writing. Where a citation below has also been quoted once in passing inside another technique-hub document, this document's own contribution is the definition and the cross-topic pattern, not the citation itself.

Every entry follows the same hard rule as the rest of this course: a real, sourced mark-scheme or examiner-report citation, or the document says so and stops rather than inventing one. Direct quotations are kept under roughly fifteen words with attribution; everything longer is paraphrased.

#1. "Hence" — building on a given result, not solving from scratch

A "hence" instruction is not stylistic. It names the route a mark scheme credits, and a mathematically correct answer reached by the wrong route can score zero on that part.

Jan 2023 Q5(b) (hidden-quadratic substitution: part (a) shows $3\times9^x+3^{x+2}=1+3^{x-1}$ can be written as $9p^2+26p-3=0$ ; part (b) says "hence solve" the original equation). Examiner report, verbatim: candidates who "ignored the 'Hence' and attempted to solve the original equation" directly "could score no marks in this part" — regardless of whether the x-value they eventually reached was correct. The mark scheme's M1 for part (b) requires solving the quadratic named in part (a); an equation solved by any other route, even to the right answer, is not what that mark is checking for.

This is the one series where the exact phrasing was directly re-verified against the primary mark scheme and examiner report this pass; it is not claimed to recur at a stated frequency across the wider corpus. The distinction it establishes generalises regardless: "hence" ties the required method to a named earlier result, and "hence, or otherwise" (not sighted in this specific form on this paper in the material checked) would be the version that relaxes that tie — the two are not interchangeable, and this paper's own examiner reports treat "hence" literally.

#2. "State" / "write down" — a command verb that does not, by itself, guarantee a no-method mark

The instinct that "state" or "write down" means "just give the answer, no working needed" is correct on some WMA11 questions and wrong on others, and the mark scheme — not the verb alone — decides which.

Where it does mean no method (B1, genuinely independent). A B mark itself is defined, verbatim, in the General Marking Guidance printed at the start of the real mark schemes: Jan 2023's own wording is "independent accuracy marks where there is no method"; Jan 2024 phrases the identical convention as "B marks are unconditional accuracy marks (independent of M marks)." Three real "state"/"write down" questions fit that description directly:

Jan 2023 Q6(b): "state" angle AOB, worth a single B1 — the value follows immediately from AOD being a straight line, with nothing left to derive once part (a) is done.
Oct 2020 Q3(b)(ii): an arc-length B1, similarly awarded with no method line, because the angle it depends on was already found and fixed in part (a).
June 2023 Q2: the real question text itself reads, verbatim, "write down an equation linking x and y" — twice, each worth a single B1 — direct transcription of a stated fact (the pitch's perimeter, then its area) into algebra, with no solving involved yet.

Where the same verb still requires a shown method (M1/A1). Jan 2023 Q10(a)'s real question text reads, verbatim, "state the values of x for which f(x) > 0" — 2 marks — but the real mark scheme is M1 (attempt at one correct inequality) then A1 (both inequalities correct), not a B mark at all. The examiner report confirms candidates were marked down for exactly this: partial or missing working cost the M1 as much as a wrong final answer would.

The distinction that costs marks when blurred: a question is only a B-mark "state" when the requested fact is already sitting directly on the page — read off a diagram, or handed over from an earlier part with nothing left to compute. The moment "state" is asking a candidate to extract something from given information (a sign pattern from a factorised expression, in Q10(a)'s case), the mark scheme reverts to the ordinary method-then-accuracy structure, and working that isn't shown is working that isn't credited — exactly as if the question had said "find" instead.

#3. "Show that" and the answer-given (ag) mark — a target you must reach honestly, not one you may reach backwards

"Show that" and "prove" questions carry a distinct mark-scheme mechanism: the final mark is tagged ag (answer given), and it is explicitly withheld from a solution that reaches the stated target by working backwards from it rather than forwards to it.

Oct 2021 Q7(a) ("show that θ = 1.64", 4 marks): the final mark is tagged A1* for fully correct work reaching the given answer with no rounding errors, and the mark scheme's own note explicitly withholds it from a candidate who states an intermediate angle and simply doubles it to reach 1.64 without showing the genuine intermediate method.
Oct 2020 Q3(a) ("show that α = 1.6", 2 marks): the same mechanism — the final mark is again A1*, requiring a correct proof with at least one genuine intermediate line and no errors — a target reached with no visible intermediate step does not satisfy it even if 1.6 is the number written down.

Seen in two independently-checked series with the same mechanism (Oct 2021, Oct 2020): on a "show that" question, the given answer functions as a target to verify your route against, not as a number you are free to manufacture a plausible-looking path toward. A "find" question and a "show that" question asking for the same numeric fact are not scored the same way — the second one is checking the journey, and a candidate who already knows the destination can still score zero on the ag mark for arriving there dishonestly.

#4. "Exact" vs. "simplest form" vs. "in the form …" — three different levels of answer-form precision

These three instructions are often treated as synonyms for "don't leave it messy." On this paper's mark schemes they are three genuinely different bars, confirmed at increasing levels of strictness:

"Exact" / no instruction on form at all — any algebraically-equivalent exact expression is accepted, decimals are not. Oct 2021 Q2's final accuracy mark is stated as $x=\pm\tfrac{1}{\sqrt5}$ "or exact equivalent" — an unrationalised surd is explicitly fine, because the question never specified a target shape.
"Giving your answer in simplest form" — a specific instruction that the general "exact" leniency above does not cover. Splitting-fractions Q3 (Jan 2023) asks for the answer "giving your answer in simplest form"; the examiner report records marks lost for "not simplifying fully" even where the underlying integration was correct — the exact-equivalent allowance in point 1 above does not rescue an answer that is exact but not fully reduced.
"Giving your answer in the form p + q√3" — the strictest of the three: the answer must match the stated algebraic shape, not merely be exact or simplified. Summer 2024 Q2(ii) states this explicitly, and the mark scheme's own worked "insufficient" example shows a response that reaches the correct value with no expansion step shown scoring one accuracy mark short — because the intermediate rationalising line, not just the destination, is what the specified form is checking for.

The general convention behind all three, verified verbatim across the General Marking Guidance: "marks will normally be lost if the candidate resorts to using rounded decimals." The distinction that costs marks when the three are treated as one instruction: "exact" alone is the most forgiving of the three (any equivalent form), "simplest form" adds a completeness requirement on top of exactness, and a stated target form is the least forgiving — matching that exact shape is itself part of what earns the mark, independent of whether the value is correct.

#5. "Given that …" as a binding restriction, not scene-setting

A "given that" clause stating a domain restriction is not throat-clearing before the real question starts — it overrides the paper's usual default of finding every algebraically valid solution.

Jan 2025 Q5(c) (curve $y=4x^3+2/x+9$ , $x>0$ stated in the question's own opening line; part (b) derives $12x^4+5x^2-2=0$ , part (c) asks for $k$ ): the examiner report records that a common way to lose the final A mark was substituting "a negative value of x... despite 'x > 0'" in the question's own wording, producing a second, unwanted value of $k$ . The default instinct on this paper — keep every sign a quadratic-in- $x^2$ produces — is the wrong one here, because the question's own stated restriction has already ruled half the algebra out before the final substitution step. The same report, on the same question, separately documents the opposite failure (stopping at $x^2$ without ever taking the square root) — the two errors run in opposite directions on the identical question, which is itself evidence that neither is a one-off slip: the "given that" clause has to be actively checked against the final answer, not read once and set aside.

#6. "Critical value" vs. "the inequality" — a number is not a solution set

Two independently-documented series confirm the same conflation: candidates who correctly find the boundary number(s) of an inequality, then stop, without ever writing the inequality itself.

Jan 2023 Q10(a) examiner report, verbatim: candidates "wrote down one or more critical values only, not realising... inequalities were required."
Jan 2019 Q4 examiner report, on a related region-defining question: candidates who "solved the equation correctly but stated no inequalities" scored nothing on that part.

A critical value is an input to the answer, not the answer. On a question asking "for which values of x is f(x) positive" or "state the inequalities that define this region," a fully correct piece of algebra that stops at "x = 16" or "x = 3/2" — with no ">" or "<" ever written — is, on this paper's mark schemes, indistinguishable from having done no algebra at all: both score the same zero on the accuracy mark that only exists to check the relational statement, not the number inside it.

#7. "Condone" — a mark scheme's own technical use of the word, not blanket leniency

"Condone" appears repeatedly across WMA11 mark schemes, and it is tempting to read it as general examiner goodwill. In every real instance checked, it names one specific, stated alternative — not an open invitation to be imprecise more broadly.

Jan 2023 Q9(a): "Period is π (radians) but condone 180° or just 180." — one named alternative unit, nothing else.
Oct 2021 Q6(a): "Condone with no axes and condone cusp like appearance for the turning points" — two named, specific leniencies (missing axes; a cusp-shaped turning point), on this one question's shape-method mark only.
Jan 2023 Q4 (discriminant with a parameter): "Condone attempts where the ''6'' isn't squared" — condoned for that one method mark only; the same slip costs the next mark, because the dependent mark (§ discriminant entries in the facts bank) requires the correct value to carry forward.
June 2022 Q5(a) (reconstructing a quadratic from its turning point): the mark scheme's first method mark is described in the facts bank as condoning specific named slips — incorrect squaring, or setting the leading multiplier to ±1 — for that one mark only, not the question as a whole. (Paraphrase, not a direct quote: the facts bank does not present this particular clause in the mark scheme's own quotation marks, unlike the three entries above.)

Seen in four separate instances across four series (Jan 2023 twice, Oct 2021, June 2022), always with the same shape: "condone X" means the scheme has pre-decided that this one specific, named substitute earns the mark exactly as the "correct" form would — it is not evidence that the marker will accept an unspecified range of near-misses on that mark, and it says nothing about any other mark in the same question.

#8. "Sketch" — what it requires, and what it explicitly doesn't

Two real findings on this paper, read together rather than in isolation, draw the actual boundary of what a WMA11 "sketch" instruction is checking for.

What is explicitly not required. Oct 2021 Q6(a)'s own mark scheme states outright that the shape-method mark should condone with no axes — a sketch without drawn/scaled axes at all can still earn full marks on this question, and a cusp-shaped turning point (mathematically wrong on every polynomial graph) is separately condoned on the same mark.

What is required regardless. The same question's examiner report records that a "surprising number" of otherwise-correct sketches lost a mark for failing to label the y-intercept — a mark the "no axes" leniency above does not extend to. Separately, Jan 2019 Q5 (sketching $\sin x$ on axes already drawn for $\cos 2x$ , no scale supplied) reports that the missing scale correlated with candidates "not sketching [sin x] carefully enough" — a precision cost, on a different question, where scale genuinely mattered to the shape being assessed.

The distinction: "sketch" does not, by default, require an accurately scaled drawing — a scheme may explicitly condone missing axes and imprecise curvature at a turning point. What it does not excuse, on the one series that tested it directly, is failing to mark and label the specific coordinate points the question names (an axis intercept). Read the two findings together, not as a contradiction: a sketch is checked for its labelled key features, not for its draughtsmanship.

#9. "Period" vs. "domain" / "range" / "interval" — glossary entry only

A period is a repeat-length (the smallest positive $T$ with $f(x+T)=f(x)$ ); a domain is the set of $x$ -values a function is defined on; a range is the set of $y$ -values it outputs. These are three different kinds of mathematical object, and confusing any pair of them is a real, heavily-documented error on this exact paper.

Jan 2023 Q9(a) ("state the period of tan x," 1 mark): the examiner report states plainly that fewer than half the cohort answered correctly, and that a recurring wrong answer was an interval such as $-\pi/2 < x < \pi/2$ — attributed by the report itself to "confusion between period and domain/range."

This entry is deliberately kept to a glossary paragraph: the general theory (how period scales under $f(kx)$ , the distinct domain restriction $\tan x$ carries that $\sin x$ / $\cos x$ don't, and every other real exam angle found for this spec point) is already given in full in codex-deep-dive-trig-graphs-period-and-domain.md §1 and §6, and is not reproduced here.

#10. Honest limits of this document

Every citation above traces to a specific series' mark scheme or examiner report, independently re-checked against research/veridian/WMA11-verified-facts.md rather than assumed from memory. None of the counts above are claimed as a frequency across the full WMA11 corpus — where an entry rests on one series (§1, §5), that is stated as such; where it rests on two or more independently (§3, §6, §9), that is stated too, and four is the largest count claimed (§7). No likelihood percentage and no grade boundary appears anywhere in this document, per this course's own standing rule. Genuinely absent from the material checked: a documented "hence, or otherwise" instance on this paper (only plain "hence" was found), and any WMA11-specific examiner-report commentary distinguishing "deduce" from "find" or "verify" from "show" — those pairs may exist on other Pearson units, but no real WMA11 citation for either was located in this pass, and this document accordingly ends here rather than filling them in from general mathematics-exam convention.