Technique Masterclasses

Statistics 1

Flashcard Bank

Provenance: written 2026-09-29. This document is a reformatting exercise, not new research. Every flashcard below is a front/back reformatting of a sentence, formula, table row, or worked micro-example already present in the fifteen existing CODEX files in this folder: codex-formula-and-method-bank.md, codex-complete-worked-paper.md, and the thirteen codex-deep-dive-*.md files (elementary probability and conditional notation; conditional probability, independence vs. mutually exclusive; sampling, tree diagrams and Venn diagrams; discrete random variables/probability function; expectation and variance of linear transformations; mathematical modelling in probability and statistics; measures of location and dispersion; the Normal distribution/standardisation and conditional probability; outliers, box plots and comparing distributions; reading and comparing distributions; regression gradient interpretation and extrapolation; the correlation coefficient and regression calculation; and "show that" answer discipline). No new claim, formula, percentage, grade boundary, or exam finding is introduced here — every card's back is traceable to a real sentence, table row, formula, or worked value in one of those files, cited by document (and section, where the source numbers its own sections) after each card. Quotations from a Pearson mark scheme or examiner report are kept under 15 words with attribution, exactly as the source CODEX files themselves quote them; everything longer is paraphrased. Where a source document itself flags a fact as unverified, a genuine gap, or an honest limit of the evidence, this document repeats that same hedge rather than upgrading it to a plain fact — no likelihood, percentage, or grade-boundary figure is invented anywhere below, matching the standing rule already stated in every source file that no such data exists for WST01.

CODEX · WST01 Flashcard Bank

Pearson Edexcel IAL Statistics 1 (WST01/01)

One flashcard per term, formula, or result — front (the term, formula, or question), then back (the real definition, formula, or worked micro-example already in the CODEX files), organised by spec topic. Cards are numbered FC-001 upward for reference. Several cards point to a real exam anchor by series/question rather than reproducing its full working, since that full working already lives in the cited CODEX file; where a fact is explicitly flagged in its source as unconfirmed, a derivation rather than an exam-attested pattern, or a genuine gap, the card repeats that flag rather than dropping it.

Section 0 — What the formula booklet gives you, and what it doesn't

FC-001 — Front: What does "MEMORISE" mean on this paper's formula status, and what does "GIVEN" mean? Back: MEMORISE = spec-listed as a formula students must produce from memory; not printed in the Mathematical Formulae and Statistical Tables booklet. GIVEN = printed in the booklet — you look it up, but must know how to use it under time pressure. Source: codex-formula-and-method-bank.md §Part 1 intro

FC-002 — Front: What does "RULE GIVEN IN Q" mean, and give one example of a formula tagged this way. Back: No formula to memorise or look up, because the spec guidance explicitly states the exam question will supply it every time — e.g. the outlier fences (lower = Q₁ − k×IQR, upper = Q₃ + k×IQR): "any rule to identify outliers will be specified in the question." Source: codex-formula-and-method-bank.md §1.1

FC-003 — Front: What is explicitly stated as "NOT required" for the Normal distribution, and where does this come from? Back: Knowledge of the p.d.f. of the Normal distribution; derivation of its mean, variance, or CDF; and interpolation within the Normal tables — the spec guidance states all three outright. Source: codex-formula-and-method-bank.md §1.5

FC-004 — Front: Does hypothesis testing (H₀/H₁, test statistic, critical value) exist anywhere on this paper? Back: No — confirmed twice directly in spec guidance (items 2.2 and 4.3) and by a full-text search of the facts bank returning nothing under "hypothesis," "H0," "H1," "critical value," or "test statistic" beyond that guidance line. Source: codex-formula-and-method-bank.md §1.5

Section 1 — Mathematical models in probability and statistics (spec 1.1)

FC-005 — Front: What is the five-step modelling chain this spec point tests? Back: Assumption → distributional family the assumption implies → parameters → calculation → refinement (when evidence contradicts the assumption). Source: codex-deep-dive-mathematical-modelling-in-probability-and-statistics.md §1

FC-006 — Front: How often does spec 1.1 anchor a standalone WST01 question, across the full archive reviewed? Back: 0 of 14 series' question papers — it never anchors a question in its own right; its AO3 marks arrive embedded as sub-parts riding on other questions (e.g. a probability question built on a stated assumption). Source: codex-deep-dive-mathematical-modelling-in-probability-and-statistics.md §1, §3

FC-007 — Front: Fair 12-sided die, numbered 1–12, rolled once, scored as D. What family does "fair die" license, and what is P(D is a multiple of 3)? Back: D is discrete uniform on {1,…,12}. P(D ∈ {3,6,9,12}) = 4/12 = 1/3. Source: codex-deep-dive-mathematical-modelling-in-probability-and-statistics.md §2.1

FC-008 — Front: What is the "self-imposed assumption" failure mode, and what is the real, cited diagnosis for it? Back: A candidate manufactures their own unlicensed model — inventing an "independent" assumption the question never granted — rather than reading off the one actually licensed. Pearson's own general diagnosis one series: "candidates often assume independence when an appropriate conditional probability should be used instead" (Jun 2022). Source: codex-deep-dive-mathematical-modelling-in-probability-and-statistics.md §2.2

FC-009 — Front: In a "critique this model" refinement answer, what earns credit and what earns nothing? Back: Credit: naming the specific evidence given (which value was over/under-represented) and its specific consequence for the model. Nothing: a generic, true-sounding statement (e.g. "real spinners are never perfectly fair"), however reasonable it sounds, because it isn't tied to the evidence actually given. Source: codex-formula-and-method-bank.md §2.1

Section 2.1 — Reading histograms, stem-and-leaf diagrams, and box plots

FC-010 — Front: What does a histogram's vertical axis actually represent, and what is the frequency formula? Back: Frequency density, fd = f/w. Rearranged, frequency f = fd × w — the bar's area, not its height. Source: codex-formula-and-method-bank.md §2.2; codex-deep-dive-reading-and-comparing-distributions.md §1.1

FC-011 — Front: When does comparing histogram bar heights directly correctly rank frequencies, and why? Back: Only when every class shares the same width w = c — then f = fd × c for every class, so height ratios equal frequency ratios exactly, because the shared factor c cancels. Source: codex-deep-dive-reading-and-comparing-distributions.md §1.1

FC-012 — Front: What real error confirms the height-vs-area trap, and which series? Back: Jan 2023 Q1(a): most unsuccessful candidates read bar heights straight off the axis and reported them as class frequencies, producing wrong totals. Source: codex-formula-and-method-bank.md §2.2; codex-deep-dive-reading-and-comparing-distributions.md §1.1

FC-013 — Front: On a back-to-back stem-and-leaf diagram, how is the left-hand flank's leaf order related to its true rank order? Back: Reversed — for L leaves printed left to right as ℓ₁,…,ℓ_L, the leaf at page-position k is the (L−k+1)-th smallest value in that row. The right-hand flank needs no reversal: the leaf at position k is simply the k-th smallest value directly. Source: codex-deep-dive-reading-and-comparing-distributions.md §1.2

FC-014 — Front: What real error does the left-flank reversal rule explain, and which series? Back: Jun 2024 Q1(b): a cross-series description of students reading the diagram in the wrong direction and misidentifying which value was Q₁ and which was Q₃ — a failure to apply the k → L−k+1 reversal on the left flank while correctly leaving the right flank unreversed. Source: codex-deep-dive-reading-and-comparing-distributions.md §1.2

FC-015 — Front: What are the rank positions for the median, Q₁, and Q₃ of an ordered list of n values? Back: Median at (n+1)/2; Q₁ at (n+1)/4; Q₃ at 3(n+1)/4 — the live-lesson convention, tolerated alongside the n-based positions (n/2, n/4, 3n/4). Source: codex-deep-dive-reading-and-comparing-distributions.md §1.2

FC-016 — Front: For an even-n ranked list, is there a confirmed convention for interpolating Q₁/Q₃ between two ranks? Back: No confirmed convention was found in the reviewed archive — only the median (position (n+1)/2, a whole-or-half number) has a settled convention for the even-n case (average the two middle ranks); no equivalent quartile-interpolation rule for a ranked list is confirmed. Source: codex-deep-dive-reading-and-comparing-distributions.md §1.2

Section 2.2/2.3 — Measures of location, coding, dispersion, and interpolation

FC-017 — Front: Mean formula for a bare list, and for a frequency table. Back: Bare list: x̄ = Σx/n. Frequency table: x̄ = Σfx/Σf — divide by the total frequency Σf, never the number of classes. Source: codex-formula-and-method-bank.md §1.1

FC-018 — Front: Why does a grouped table use class midpoints for x in the mean formula? Back: No exact value is known for any single data point inside a class — only which class it fell into — so the class midpoint stands in for every value in that class, on the explicit modelling assumption that values are spread evenly enough across the class for its centre to represent it fairly. Source: codex-deep-dive-measures-of-location-and-dispersion.md §1.1

FC-019 — Front: Are the median and mode calculated from a summation formula? Back: No — median and mode are "TECHNIQUE, not a formula": positional (median, middle value by rank) or highest-frequency (mode) identification, with no computed-statistic formula for either. Source: codex-formula-and-method-bank.md §1.1

FC-020 — Front: State both forms of variance, and the rule for combining them. Back: σ² = Σf(x−x̄)²/n (deviation form) = Σfx²/n − x̄² (computational form) — algebraically identical. Divide by n before subtracting x̄²; the square root wraps the whole result, taken once, last. Source: codex-formula-and-method-bank.md §1.1

FC-021 — Front: Derive the computational variance formula from the definitional one. Back: Expanding Σf(x−x̄)² gives Σfx² − 2x̄Σfx + x̄²Σf. Since x̄ = Σfx/Σf, the middle term equals −2x̄²Σf, which combines with the last term to give −x̄²Σf. So Σf(x−x̄)² = Σfx² − x̄²Σf, and dividing by n = Σf gives Σfx²/n − x̄². Source: codex-deep-dive-measures-of-location-and-dispersion.md §1.2

FC-022 — Front: Is a /(n−1) "sample standard deviation" form ever credited on this paper? Back: Confirmed on one series only (Jan 2023 Q1(d)), where the mark scheme credited both the /n population form and the /(n−1) form for the same 2 marks. Checking June 2023 alongside it found no equivalent credit — not a general licence; the /n form is the safe default. Source: codex-formula-and-method-bank.md §1.1

FC-023 — Front: IQR formula, and its formula-booklet status. Back: IQR = Q₃ − Q₁ — MEMORISE, explicitly grouped with mean/SD on the spec's "expected from memory" list. Source: codex-formula-and-method-bank.md §1.1

FC-024 — Front: How is a quartile located inside a grouped/continuous frequency table? Back: Locate the class containing the target cumulative position (using either the n-based or (n+1)-based convention — both tolerated), then interpolate proportionally across that class's width. Neither source reviewed prints a single prescribed algebraic form for this — spec guidance only says "simple interpolation may be required." Source: codex-formula-and-method-bank.md §1.1, §2.2

FC-025 — Front: How do you recover Σx² given only a mean and a standard deviation? Back: Σx² = n(σ² + x̄²) — square the SD first, then add x̄², then multiply by n. Source: codex-formula-and-method-bank.md §1.1

FC-026 — Front: Under the coding Y = (X−a)/b or Y = b(X−a), how does the mean decode, and how does the variance decode? Back: The mean decodes by reversing the coding step; the variance decodes by the square of the scaling constant, in the opposite direction (i.e. divide the coded variance by b², never multiply). Source: codex-formula-and-method-bank.md §1.1

FC-027 — Front: What real error confirms the coding-variance trap, and how many distinct wrong paths did it produce on one series? Back: Jun 2022 Q3(e) (assumed mean 255, scale factor 0.5): three distinct wrong paths — the constant left un-squared, the constant squared but multiplied instead of divided, and the variable not decoded at all. Source: codex-deep-dive-measures-of-location-and-dispersion.md §3

FC-028 — Front: What real error involves forgetting to square a standard deviation when recovering Σx² for a group, and which series? Back: Jan 2021 Q6(c): candidates "forgot to square the standard deviation of 2" when recovering Σx² for that group. Source: codex-deep-dive-measures-of-location-and-dispersion.md §3

FC-029 — Front: What is the equal-width giveaway for the "wrong mean shortcut" trap, and why does it fail on unequal widths? Back: Using Σ(width×f)/Σf in place of Σfx/Σf always collapses to exactly the constant class width when every class shares the same width — a self-evident giveaway. On unequal widths the wrong shortcut instead produces a number that sits comfortably inside the data's own range, so it no longer advertises itself as suspicious. Source: codex-deep-dive-measures-of-location-and-dispersion.md §2.3

FC-030 — Front: What real "show that" failure is documented for interpolating a quartile, and which series? Back: Oct 2021 Q3(b): some candidates invented two plausible-looking values that happen to produce the given IQR, rather than genuinely interpolating from the data. Source: codex-formula-and-method-bank.md §2.2; codex-deep-dive-measures-of-location-and-dispersion.md §3

FC-031 — Front: Is the grouped median found by interpolation a confirmed exam angle on this paper? Back: No worked example testing this exact combination (grouped median specifically, found by interpolation using position n/2) was found in the reviewed archive — it is a genuine, previously unworked application of an already-confirmed interpolation method, not confirmed past-paper content. Source: codex-deep-dive-measures-of-location-and-dispersion.md §2.4, §4

FC-032 — Front: Is a named interpercentile range wider than the IQR (e.g. the 10th–90th percentile range) confirmed as tested content? Back: No citation anywhere in the reviewed archive confirms a WST01 question naming a specific interpercentile range other than the IQR by name — the method is a direct generalisation of the confirmed IQR technique, but not itself confirmed as tested. Source: codex-deep-dive-measures-of-location-and-dispersion.md §2.5, §4

Section 2.4 — Outliers, box plots, skewness, and comparing distributions

FC-033 — Front: General outlier fence formula, and its formula-booklet status. Back: Lower fence = Q₁ − k×IQR; upper fence = Q₃ + k×IQR. RULE GIVEN IN Q — "any rule to identify outliers will be specified in the question." There is no default k = 1.5 to memorise for this paper. Source: codex-formula-and-method-bank.md §1.1

FC-034 — Front: Which direction do the outlier fences point, and what confirmed error reverses this? Back: Fences point outward from the box (subtract for the lower fence, add for the upper), never the reverse — a confirmed, separately-documented direction error (Jan 2021 Q2). Source: codex-formula-and-method-bank.md §1.1

FC-035 — Front: What real error substitutes a remembered multiplier for the one the question actually gave, and which series? Back: Jun 2022 Q1(b): "a small number of candidates opted to apply the more commonly used outlier formula" instead of the k the question stated. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §2.1

FC-036 — Front: What is the taught safe-default rule for where a box-plot whisker ends? Back: A whisker's end is always a real, non-outlier data value — never the fence itself. If a value is flagged beyond a fence, that whisker stops short at the most extreme value that is NOT itself flagged. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §1

FC-037 — Front: What genuine asymmetry does the real Jan 2021 Q2 mark scheme show about crediting a whisker at the fence versus the real value? Back: It credits the lower whisker at EITHER the real value (54) or the fence itself (50), but the upper whisker only ever at the real value (97), never at its fence (98) — evidence the fence is an unreliable shortcut, not a second valid method to rely on. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §2.2

FC-038 — Front: If a data correction shifts Q₁ while Q₃ stays fixed, by how much does the upper fence shift, in general? Back: F_upper,new − F_upper,old = k×(Q₁,old − Q₁,new) — the upper fence, anchored to Q₃ which never moved, shifts anyway by exactly k times the change in the other quartile, because the width term feeding it (the IQR) changed. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §1

FC-039 — Front: What real error confirms this recompute-cascade rule, and which series? Back: June 2019 Q2(c): after one correction moved Q₁ from 33 to 35 (Q₃ untouched), "the major problem was that few candidates realised that the lower quartile would change" — and, once it does, the untouched-side fence has to be rebuilt from scratch, not patched. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §2.4

FC-040 — Front: For a "show that N outliers exist" instruction, what must the answer contain beyond the fences themselves? Back: The values themselves must be listed and individually checked against the fence — a confirmed real failure finds the correct fences but never lists the outliers (Oct 2021 Q3(c): "some did not list the 3 outliers in this part"). Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §2.3

FC-041 — Front: How is skewness tested on this paper — as a computed coefficient or a comparative judgement? Back: As a checkable inequality, not a formula: positive (right) skew signal, (Q₃ − median) > (median − Q₁); negative (left) skew signal, (median − Q₁) > (Q₃ − median). No skewness coefficient appears in the formula booklet or on the "expected to know" list. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §1

FC-042 — Front: Is skewness a confirmed past-paper exam angle on this paper? Back: No — a full-text search of the facts bank for "skew"/"skewed"/"skewness" returns exactly one hit, the spec's own guidance line. No examiner-report quote, mark-scheme line, or past-paper question part citing skewness was found anywhere in the 14-series archive reviewed — currently unevidenced, not merely under-evidenced. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §2.5

FC-043 — Front: Why does the mean move when a single data value changes, but the median doesn't? Back: x̄ = (1/n)Σxᵢ is a linear function of every value, so a change of δ in one value changes x̄ by exactly δ/n — small but never zero. The median is an order statistic, fixed by rank alone; a change that doesn't alter a value's rank leaves the median completely unchanged, however large that change is. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §1

FC-044 — Front: What is the three-part discipline for a credited "compare two distributions" answer? Back: (1) Identify which comparison the question asks for (difference, similarity, or a named statistic). (2) Name a specific statistic (mean, median, IQR, range — not "the average," unqualified). (3) State its value for both groups being compared. Source: codex-formula-and-method-bank.md §2.2

FC-045 — Front: What real, chronic misconception treats one measure of location as "more accurate" than another, and which series? Back: Jun 2022 Q1(e): "A very common misconception was that the mean is more accurate than the median" — the credited contrast is structural ("the mean uses every value; the median does not"), not a claim that one is a better estimate of some true value. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §1, §3

FC-046 — Front: What real error gives a bare comparison with no supporting figures, and which series? Back: Jun 2024 Q1(e): "surprisingly too many students failed to give supporting figures" — a bare qualitative claim with no numbers is confirmed to lose the mark even when the direction stated is correct. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §2.6

FC-047 — Front: What real error answers the wrong half of a comparison question, and which series? Back: Oct 2021 Q3(e): "few comments referring to the distribution... were seen" — discussing similarities when the question asked for differences (or vice versa) scores nothing even when the observation made is true. Source: codex-deep-dive-outliers-boxplots-comparing-distributions.md §2.6

Section 3.1/3.2 — Elementary probability and conditional notation

FC-048 — Front: Classical probability formula for equally likely outcomes. Back: P(A) = n(A)/n(Ω). Source: codex-formula-and-method-bank.md §1.2

FC-049 — Front: Complement rule, and its formula-booklet status. Back: P(A′) = 1 − P(A) — MEMORISE, explicitly on the spec's "will not appear in the booklet" list. Source: codex-formula-and-method-bank.md §1.2

FC-050 — Front: General addition law, and its formula-booklet status. Back: P(A∪B) = P(A) + P(B) − P(A∩B) — GIVEN, printed in the booklet. Source: codex-formula-and-method-bank.md §1.2

FC-051 — Front: What does the general addition law collapse to when A and B are mutually exclusive, and why? Back: P(A∪B) = P(A) + P(B) — because P(A∩B) = 0, so the "−P(A∩B)" correction term (which undoes the double-count from adding the two marginal probabilities) is already zero. Source: codex-formula-and-method-bank.md §1.2; codex-deep-dive-elementary-probability-and-conditional-notation.md §2.2

FC-052 — Front: General multiplication law, and its formula-booklet status. Back: P(A∩B) = P(A)P(B|A) — GIVEN, printed in the booklet. This is the general, non-independent form — do not confuse with the independence-specific simplification, which is memorise-only. Source: codex-formula-and-method-bank.md §1.2

FC-053 — Front: Conditional probability definition, and its formula-booklet status. Back: P(A|B) = P(A∩B)/P(B), for P(B) > 0 — GIVEN, printed in ratio form on the formula sheet. Source: codex-formula-and-method-bank.md §1.2; codex-deep-dive-elementary-probability-and-conditional-notation.md §2.3

FC-054 — Front: Prove that the raw ratio P(A)/P(B) can never fall short of the true P(A|B). Back: Since A∩B ⊆ A, P(A∩B) ≤ P(A) always, so P(A|B) = P(A∩B)/P(B) ≤ P(A)/P(B), with equality iff A is entirely contained in B. In every other case the raw ratio strictly overshoots the true conditional probability. Source: codex-deep-dive-elementary-probability-and-conditional-notation.md §2.3

FC-055 — Front: Sample space partitions into four regions with P(region 1)=0.1, P(B)=0.3, P(region 3)=0.2, P(region 4)=0.4. Find P(B′). Back: P(B′) = 0.1 + 0.2 + 0.4 = 0.7 — the complement of a compound event is the sum of every other region in the partition, not a single subtraction from a single number. Source: codex-deep-dive-elementary-probability-and-conditional-notation.md §3, sub-case 3.2

FC-056 — Front: What real error collapses a compound conditional probability P(A|B′) into a raw ratio of marginals, and which series? Back: Jan 2021 Q1(c): the examiner report records candidates occasionally writing "0.35/0.4" — reconstructed as P(A)/P(B′) standing in for the correct P(A∩B′)/P(B′) = 0.15/0.4 = 3/8. Source: codex-deep-dive-elementary-probability-and-conditional-notation.md §3 sub-case 3.5, §4

FC-057 — Front: On a multi-branch tree diagram, what real error builds the numerator from too few routes, and which series? Back: Oct 2021 Q4(c): the examiner report records a numerator built from a product of two branches "rather than 3" needed — count how many branches genuinely contribute to the numerator event before multiplying. Source: codex-deep-dive-elementary-probability-and-conditional-notation.md §3 sub-case 3.6, §4

FC-058 — Front: What is the corrected characterisation of the Jan 2023 Q2(d) tree-diagram conditional-probability error? Back: Both quoted wrong answers use the correct denominator throughout — the real fault is a spurious extra copy of that same value added or multiplied into the numerator, not a missing conditioning denominator (a 2026-08-28 re-verification against the actual mark-scheme PDF corrected an earlier mischaracterisation). Source: codex-deep-dive-elementary-probability-and-conditional-notation.md §4

FC-059 — Front: For P(A|B') = 0.15/0.4, what answer form does the real mark scheme require, and what does it explicitly refuse? Back: It must be reduced to 3/8 or 0.375 — the mark scheme explicitly refuses the accuracy mark for 0.15/0.4 left unsimplified. Source: codex-deep-dive-elementary-probability-and-conditional-notation.md §4

Section 3.3 — Independence vs. mutually exclusive events

FC-060 — Front: State the three independence-specific forms, and their formula-booklet status. Back: P(B|A) = P(B); P(A|B) = P(A); P(A∩B) = P(A)P(B) — MEMORISE, the "independence-specific forms only" students must produce unprompted; any one of the three implies the others. Source: codex-formula-and-method-bank.md §1.2

FC-061 — Front: Prove that the three independence forms are one fact, not three separate ones to memorise. Back: Start from P(A|B) = P(A) and substitute the conditional-probability formula: P(A∩B)/P(B) = P(A), which rearranges to P(A∩B) = P(A)P(B) — the third form. Running the same substitution from P(B|A) = P(A∩B)/P(A) reaches the identical product form. So any one, once true, forces the other two. Source: codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md §1

FC-062 — Front: Can two events with P(A) > 0 and P(B) > 0 be both mutually exclusive and independent? Back: Never — mutually exclusive gives P(A∩B) = 0 from one definition, while independent gives P(A∩B) = P(A)P(B) > 0 from the other; these cannot both hold. Source: codex-formula-and-method-bank.md §1.2; codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md §1

FC-063 — Front: For two events with positive probability, what are the three (not two) possible relationships? Back: Mutually exclusive (never independent); independent (never mutually exclusive); or neither — genuinely overlapping, genuinely dependent, and only settled by running the product-rule calculation. Source: codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md §1

FC-064 — Front: What real error judges independence "by eye" (visual overlap) instead of by calculation, and which series? Back: Oct 2021 Q1(b): the examiner report names it "the usual confusion" and quotes a student line, "they are not independent as they overlap." Source: codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md §3

FC-065 — Front: What is Pearson's own paper-wide diagnosis about independence and conditional probability, and which series? Back: Jun 2022 (general comment): candidates "often assume independence when an appropriate conditional probability should be used instead." Source: codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md §3; codex-deep-dive-mathematical-modelling-in-probability-and-statistics.md §2.2

FC-066 — Front: P(A) = 0.2, A and B independent, P(A∩B) = 0.06. Find P(B). Back: Since independent, P(A∩B) = P(A)×P(B), so 0.06 = 0.2×P(B), giving P(B) = 0.3. Source: codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md §2.3

Section 3.4 — Sampling, tree diagrams, and Venn diagrams

FC-067 — Front: What does a tree diagram's product law and sum law each represent? Back: Product law: multiply along a path (successive conditional probabilities, P(A∩B) = P(A)P(B|A) applied branch by branch). Sum law: add across complete, mutually-exclusive paths — distinct complete paths cannot both occur on the same trial. Source: codex-formula-and-method-bank.md §1.2; codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §1

FC-068 — Front: With replacement, what stays the same across successive draws, and why? Back: Composition and totals are unchanged between draws — every branch leaving a given outcome carries the same fraction as the branch before it, because the conditioning event genuinely doesn't change anything about the sample space. Source: codex-formula-and-method-bank.md §1.2; codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §2.1

FC-069 — Front: Without replacement, what two things must change on every subsequent draw? Back: Both the running total (denominator) and the count of whatever was just removed (numerator) — a confirmed real error holds the denominator fixed across draws. Source: codex-formula-and-method-bank.md §1.2

FC-070 — Front: What real error holds the denominator fixed across four genuine without-replacement draws, and which series? Back: Jun 2022 Q3(d): "the most common response was scoring 1 mark for the special case using (62/88)⁴" instead of decreasing denominators across all four draws. Source: codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §4

FC-071 — Front: What real error reuses an earlier branch's probability after the item it represents has already been removed, and which series? Back: Jan 2023 Q2 (general): candidates repeated "the 4/8... onto the branches following the 1st was blue" — reusing a first-container fraction on a later branch after removal. Source: codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §2.2, §4

FC-072 — Front: Container starts with 4 red and 2 blue counters. One red and one blue counter are transferred in from elsewhere, in either order. Why does the final composition not depend on which arrives first? Back: A container's composition after a transfer depends only on the multiset of items moved in, not the sequence — forming the new count is addition, and addition is commutative. Final composition is 5 red, 3 blue either way. Source: codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §2.3

FC-073 — Front: Derive the two-event addition law from the four disjoint regions of a Venn diagram. Back: P(A) = P(A-only) + P(A∩B) and P(B) = P(B-only) + P(A∩B). Adding these double-counts A∩B: P(A)+P(B) = P(A-only)+P(B-only)+2P(A∩B). But P(A∪B) counts A∩B only once, so P(A)+P(B) = P(A∪B)+P(A∩B), which rearranges to P(A∪B) = P(A)+P(B)−P(A∩B). Source: codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §3.1

FC-074 — Front: On a Venn diagram, is a blank region ever read as zero? Back: No — a confirmed, specific presentation trap (Jun 2022 Q4(c) examiner report): "blank spaces are not assumed to be 0s in Venn diagrams." Every region, including a genuinely zero one, must have a value written in. Source: codex-formula-and-method-bank.md §2.3; codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §3.2

FC-075 — Front: What real error substitutes the independence product P(A)P(B) for a Venn diagram's own P(A∩B) region, and which series? Back: Jun 2022 Q4(b): "common errors were to assume independence" instead of testing whether the diagram's own intersection region actually agreed with the product. Source: codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §3.3

FC-076 — Front: Are real three-event Venn diagrams on this paper always drawn as a fixed 8-region template? Back: No — two confirmed anchors (Jan 2021 Q1, Oct 2021 Q1) are each genuinely differently-shaped: Jan 2021's diagram has no drawn A∩C region at all, and Oct 2021's has a genuine three-way overlap but no drawn B∩C-only region. A real diagram is drawn to fit the specific scenario, not stamped from a generic template. Source: codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md §3.4

Section 4.1/4.2 — Regression: fitting the line, interpreting the gradient, extrapolation

FC-077 — Front: Sₓₓ and S_yy formulas (deviation and computational forms), and their status. Back: Sₓₓ = Σ(x−x̄)² = Σx² − (Σx)²/n; S_yy is the same shape with y. GIVEN — both forms are printed. Using x̄² in place of (Σx)²/n is a confirmed substitution trap, not a rounding variant — a genuinely different number. Source: codex-formula-and-method-bank.md §1.3

FC-078 — Front: S_xy formula, and one common substitution error. Back: S_xy = Σxy − (Σx)(Σy)/n — GIVEN. Σxy alone is not S_xy; the correction term must be subtracted first. Source: codex-formula-and-method-bank.md §1.3

FC-079 — Front: Regression coefficients b and a, and the final line's required answer form. Back: b = S_xy/Sₓₓ; a = ȳ − bx̄; ŷ = a + bx — GIVEN. The final line must be in decimal form: "fractions are not... appropriate" for a and b as final estimates (Jun 2022 Q2(c)). Source: codex-formula-and-method-bank.md §1.3

FC-080 — Front: What confirmed real errors occur at the b/a-fitting step, and which series? Back: Oct 2021 Q2(c): the fraction inverted (Sₓₓ/S_xy instead of S_xy/Sₓₓ), and raw totals substituted for means inside the a formula. Source: codex-formula-and-method-bank.md §1.3

FC-081 — Front: What is the three-part template for interpreting a regression gradient in context? Back: (1) Name both variables, in the words the question uses. (2) State the rate: "for each extra [one unit of x], [y] changes by b [correct unit of y], on average" — not a bare direction statement. (3) Check the scale: what does "1 unit of x" actually mean in this question's own units? Source: codex-formula-and-method-bank.md §2.4

FC-082 — Front: Name the four different confirmed real gradient-interpretation slips, and their series. Back: A hundred-fold scale misread, vsvs/100 (Oct 2021 Q2(d)); stopping at "positive correlation" instead of stating a rate (Jun 2022 Q2(d)); mismatched units (Jan 2023 Q6(a)); reversed direction (Jun 2024 Q4(d)). Source: codex-formula-and-method-bank.md §2.4

FC-083 — Front: What is the three-step template for judging the reliability of an extrapolated prediction? Back: (1) State whether the x-value used falls inside or outside the range the data covers. (2) If outside: name the specific predicted value and the specific reference point the question's own data supplies (a stated min/max, or — if only summary statistics are given — x̄ and the spread Sₓₓ implies). (3) Never submit "extrapolation so unreliable" alone. Source: codex-formula-and-method-bank.md §2.4

FC-084 — Front: What does the real Jun 2022 Q2(e) marking note explicitly zero-credit, and what does it require instead? Back: It explicitly zero-credits "extrapolation so unreliable" alone (B0), and separately zero-credits "reference to [a value being] out of range" when no range was ever supplied — only a comment naming the actual value and reference point earns the mark. Source: codex-formula-and-method-bank.md §2.4; codex-deep-dive-mathematical-modelling-in-probability-and-statistics.md §2.3

FC-085 — Front: For a PMCC "show that" step, what precision must the standardisation/S-formula working show? Back: One extra decimal place beyond the printed target — a confirmed real failure loses the final accuracy mark purely on insufficient shown precision, not a wrong method (Jun 2024 Q4(c)). Source: codex-formula-and-method-bank.md §2.4

FC-086 — Front: State the two credited methods for a reverse-gradient solve (e.g. "find the change in x for a stated change of 0.1 in y"), and prove they are the same calculation. Back: Method 1: equate the stated Δy directly with b×Δx. Method 2: substitute two y-values differing by Δy into ŷ=a+bx separately, solve each for x, then subtract. Subtracting the two equations of Method 2 gives y₂−y₁ = b(x₂−x₁), i.e. Δy = bΔx — Method 1's equation exactly, with the intercept a cancelling out. Source: codex-deep-dive-regression-gradient-interpretation-extrapolation.md §4

FC-087 — Front: Under linear coding, how does the gradient b transform, and why is this different from how r transforms? Back: b_xy = (t/q)·b_uv (for u=(x−p)/q, v=(y−s)/t) — the q and t do not cancel, because b compares a y-shaped quantity (S_uv) against an x-shaped one (S_uu) alone. r, by contrast, divides by √(S_uu·S_vv), so every factor of q and t cancels — which is why b has units and r does not. Source: codex-deep-dive-regression-gradient-interpretation-extrapolation.md §2

Section 4.3 — The product moment correlation coefficient (PMCC)

FC-088 — Front: PMCC formula, and its formula-booklet status. Back: r = S_xy/√(Sₓₓ·S_yy) — GIVEN, printed in the booklet. Source: codex-formula-and-method-bank.md §1.3

FC-089 — Front: What are the bounds on r, and what does a value outside those bounds signal? Back: −1 ≤ r ≤ 1 always; |r| > 1 from a calculation signals an arithmetic error, not an unusual dataset. Source: codex-formula-and-method-bank.md §1.3

FC-090 — Front: How does the sign of r relate to the sign of b, and why? Back: The sign of r always matches the sign of b — both share the same numerator, S_xy. Source: codex-formula-and-method-bank.md §1.3

FC-091 — Front: Is r affected by a linear coding of the data, and what confirmed mark-scheme wording states this? Back: No — confirmed verbatim in mark-scheme use: "r not affected by (linear) coding" (Jan 2024 MS Q2(d)). Recomputing r from original units after already finding it on coded data is wasted work, not extra rigour. Source: codex-formula-and-method-bank.md §1.3

FC-092 — Front: Are derivations of a, b, or r, or a significance test of r, required on this paper? Back: Explicitly NOT required — spec guidance states plainly that derivations are not required for 4.2, and "derivations and tests of significance will not be required" for 4.3. Source: codex-formula-and-method-bank.md §1.3

FC-093 — Front: Prove that −1 ≤ r ≤ 1 always holds, rather than just asserting it. Back: For any real λ, Σ(x'−λy')² ≥ 0 (a sum of squares), where x'=x−x̄, y'=y−ȳ. Expanding gives a quadratic in λ that's never negative, so its discriminant must be ≤ 0: (−2S_xy)² − 4S_yy·Sₓₓ ≤ 0, which rearranges to S_xy² ≤ Sₓₓ·S_yy, i.e. |r| ≤ 1. Equality holds exactly when every point lies exactly on a straight line through (x̄,ȳ). Source: codex-deep-dive-correlation-coefficient-and-regression-calculation.md §2.3

FC-094 — Front: What real error omits the square root in the PMCC denominator, and what danger does it share with other traps? Back: Jun 2024 Q4(b): dividing by Sₓₓ·S_yy directly instead of √(Sₓₓ·S_yy) — produces a small, in-range wrong number, not an out-of-range red flag, so it trips no "|r|>1 means a mistake" self-check. Source: codex-deep-dive-correlation-coefficient-and-regression-calculation.md §4

FC-095 — Front: What real error substitutes a mean-squared term for the computational correction term inside an S-formula feeding a PMCC calculation, and which series? Back: Oct 2021 Q2(b): the examiner report's own words, "the most common error made was using (273/12)² in the calculation of S_pp" — substituting p̄² for (Σp)²/n directly, a genuinely different number (over fifteen times larger in the disclosed reconstruction), not a rounding-scale difference. Source: codex-deep-dive-correlation-coefficient-and-regression-calculation.md §2.1, §3.3

FC-096 — Front: Can r be exactly 0 even for a perfect, entirely deterministic relationship? Give the mechanism. Back: Yes — for x = −2,−1,0,1,2 and y = x² (a perfect parabola), S_xy = 0 exactly, so r = 0, because the relationship is symmetric about x=0 and curved rather than straight. The strongest possible relationship can produce the weakest possible PMCC reading when it isn't linear. Source: codex-deep-dive-correlation-coefficient-and-regression-calculation.md §3.4

Section 5.1/5.2 — Discrete random variables and the probability function

FC-097 — Front: What makes a random variable "discrete"? Back: It can take only a finite, or countably infinite, list of separate values — never a value lying strictly between two of them — which is what makes it sensible to attach one specific probability to each individual value, rather than to a whole interval. Source: codex-deep-dive-discrete-random-variables-probability-function.md §1

FC-098 — Front: State the two conditions every valid probability function p(x) = P(X=x) must satisfy. Back: (1) 0 ≤ p(x) ≤ 1 for every value x in the domain. (2) Σp(x) = 1, summed across the entire domain. Source: codex-deep-dive-discrete-random-variables-probability-function.md §2

FC-099 — Front: What real error leaves a genuinely possible domain value out of the sum entirely, and which series? Back: Oct 2021 Q4(d): "the most common error was to miss out the value x = 0" — a probability function whose stated values summed short of 1 because a valid value of x was never written down. Source: codex-formula-and-method-bank.md §1.4; codex-deep-dive-discrete-random-variables-probability-function.md §7.1

FC-100 — Front: What real error omits the Σp(x)=1 equation itself when solving for an unknown constant, and which series? Back: Jun 2022 Q5(d): candidates "failed to write down the equation for the sum of probabilities" even while going on to earn a later method mark — the equation itself is a mark-earning line, separate from the algebra that solves it. Source: codex-formula-and-method-bank.md §1.4; codex-deep-dive-discrete-random-variables-probability-function.md §7.2

FC-101 — Front: CDF definition, and its formula-booklet status. Back: F(x₀) = P(X ≤ x₀) = Σp(x) for x ≤ x₀ — MEMORISE, explicitly on the spec's "will not appear in the booklet" list (unlike the base E(X), Var(X), E(g(X)) definitions, which are printed). Source: codex-formula-and-method-bank.md §1.4; codex-deep-dive-discrete-random-variables-probability-function.md §3

FC-102 — Front: Name the two conventions in the CDF definition that are easy to get backwards under pressure. Back: The inequality is ≤, not < (a boundary value belongs to F(x₀)). The sum always runs from the smallest domain value upward, never from the largest value downward. Source: codex-deep-dive-discrete-random-variables-probability-function.md §3

FC-103 — Front: How do you recover an individual p(xₖ) from a CDF table, given F(xₖ) and F(x_{k−1})? Back: p(xₖ) = F(xₖ) − F(x_{k−1}), where x_{k−1} is the next smaller value actually present in the domain (not necessarily xₖ−1 as a plain number). Source: codex-deep-dive-discrete-random-variables-probability-function.md §3.1

Section 5.3 — Expectation and variance of linear transformations

FC-104 — Front: State E(aX+b) and Var(aX+b), and their formula-booklet status. Back: E(aX+b) = aE(X)+b; Var(aX+b) = a²Var(X) — both MEMORISE (the shortcut forms, distinct from the base E(X)/Var(X) definitions, which are printed in the booklet). Source: codex-formula-and-method-bank.md §1.4

FC-105 — Front: What is the single most repeatedly-confirmed numeric error on this paper, and how many series confirm it? Back: Forgetting to square the constant a in Var(aX+b) — independently confirmed across a three-year span, three separate series (Jan 2021 Q4, Jun 2024 Q2(c), Jun 2024 Q3(d)) — the identical mechanism each time. Source: codex-formula-and-method-bank.md §1.4

FC-106 — Front: Does any b term survive into Var(aX+b)? Back: No — whatever sign b has, a pure translation changes no variance; the deviation of aX+b from its own mean is a(X−E(X)), with b already cancelled before any squaring happens. Source: codex-formula-and-method-bank.md §1.4; codex-deep-dive-expectation-and-variance-of-linear-transformations.md §1.3

FC-107 — Front: Given Var(Y)=18 where Y=aX+b and a=3, find Var(X). What is the direction rule? Back: Var(X) = Var(Y)/a² = 18÷9 = 2 — divide by a², never multiply, when decoding backwards. Source: codex-deep-dive-expectation-and-variance-of-linear-transformations.md §1.4

FC-108 — Front: Is E(X²) the same thing as Var(X)? What real error conflates them, and which series? Back: No — E(X²) ≠ [E(X)]² in general, and Var(X) = E(X²) − [E(X)]². Jan 2021 Q4 examiner commentary records some candidates believing E(X²) = Var(X), collapsing a raw second moment with that moment minus [E(X)]². Source: codex-deep-dive-expectation-and-variance-of-linear-transformations.md §1.5

FC-109 — Front: In a two-unknown backward solve for W=aX+b given E(W), Var(W), E(X), Var(X), which equation must be solved first, and why? Back: The variance equation first — a²Var(X) = Var(W) determines a alone; only once a is known can the mean equation aE(X)+b = E(W) be solved for b. Confirmed in two real anchors three years apart (Jun 2024 Q2(c); Jan 2021 Q4(d)) with the identical forced order. Source: codex-deep-dive-expectation-and-variance-of-linear-transformations.md §4

FC-110 — Front: Jan 2021 Q4(d): a>0, E(X)=13, Var(X)=5, E(Y)=3, Var(Y)=1.8, E(W)=E(Y), Var(W)=Var(Y), W=aX+b. Find a and b. Back: Variance first: a²(5)=1.8 ⟹ a²=0.36 ⟹ a=0.6 (positive root). Mean second: 3=0.6(13)+b ⟹ 3=7.8+b ⟹ b=−4.8. Source: codex-deep-dive-expectation-and-variance-of-linear-transformations.md §4

Section 5.4 — The discrete uniform distribution

FC-111 — Front: Definition of a discrete uniform distribution. Back: p(x) = 1/n for n equally likely values — "uniform" means equally likely, not evenly sized or evenly spaced; the values need not be consecutive integers. Source: codex-formula-and-method-bank.md §1.4; codex-deep-dive-discrete-random-variables-probability-function.md §4

FC-112 — Front: For a symmetric, evenly-spaced discrete uniform variable, what shortcut exists for E(X)? Is there an equivalent for the variance? Back: E(X) = ½(min+max) is a genuine shortcut by symmetry. No equivalent variance shortcut is confirmed anywhere in the reviewed record — every real variance calculation on a discrete uniform variable sums xᵢ²p(xᵢ) term by term. Source: codex-formula-and-method-bank.md §1.4; codex-deep-dive-discrete-random-variables-probability-function.md §4

FC-113 — Front: Should a remembered (n²−1)/12-style closed form ever be used for the variance of a discrete uniform variable on this paper? Back: No — it is not confirmed as examined content on this paper; the one clean worked example in the archive explicitly asks for the variance "showing your working," which a memorised closed form would not demonstrate. Source: codex-formula-and-method-bank.md §1.4

Section 6.1 — The Normal distribution

FC-114 — Front: Standardisation formula, and its formula-booklet status. Back: Z = (X−μ)/σ — MEMORISE, explicitly on the spec's memorise list. Standardise first, always, before any table lookup. Source: codex-formula-and-method-bank.md §1.5

FC-115 — Front: Derive why E(Z)=0 and Var(Z)=1, using the spec 5.3 linear-transformation rules. Back: Write Z = aX+b with a=1/σ, b=−μ/σ. Then E(Z) = aE(X)+b = μ/σ − μ/σ = 0, and Var(Z) = a²Var(X) = (1/σ²)·σ² = 1 — following purely from the general linear-transformation rules, nothing Normal-specific used yet. Source: codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md §1.2

FC-116 — Front: What is the single most repeated Normal-distribution error, and how many series confirm it, in which direction(s)? Back: Deciding when to subtract Φ(z) from 1 — confirmed independently in both directions across three series (under-subtracting: Jan 2021 Q3(a), Jan 2023 Q5(a); over-subtracting: Jun 2024 Q5(a)). Source: codex-formula-and-method-bank.md §1.5

FC-117 — Front: What is Pearson's own stated fix for the subtract-from-1 and sign-of-z errors? Back: Draw a diagram first — Pearson's own examiner-report advice, stated after both an under-subtraction and a sign-reversal error, in each case attributing the mistake to skipping the sketch. Source: codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md §1.4; codex-formula-and-method-bank.md §2.6

FC-118 — Front: What confirmed real accuracy trap involves rounding a percentage-points z-value, and how many series confirm it? Back: A rounded 2–3 d.p. table value substituted for the required 4 d.p. one — confirmed across three independent series (1.64 for 1.6449, Oct 2021 Q6(b); 1.03/1.04 for 1.0364, Jan 2021 Q3(b); a less-precise equivalent, Jun 2024 Q5(b)). Source: codex-formula-and-method-bank.md §1.5

FC-119 — Front: Derive the symmetry identity Φ(−z) = 1 − Φ(z), and explain why it is structurally necessary, not just convenient. Back: The area to the left of z is Φ(z); the area to the right is 1−Φ(z). By symmetry about z=0, reflecting "left of z" produces "right of −z" with identical area, giving Φ(−z) = 1−Φ(z). Because the printed Φ(z) table's own domain runs only from z=0.00 to 4.00, this identity is the only route from a negative z back into the table's domain. Source: codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md §1.3

FC-120 — Front: Four-way taxonomy: given a target event A and conditioning event B, each a threshold on the same Normal variable, what are the four possible structural relationships? Back: (1) A⊂B (target nested inside conditioning): P(A|B)=P(A)/P(B). (2) B⊂A (conditioning nested inside target): P(A|B)=1 trivially. (3) Overlap (opposite directions, cutoffs interleaved): P(A∩B) found by subtracting two Φ-values, a genuine interval. (4) Disjoint (opposite directions, no overlap): P(A|B)=0 trivially. Source: codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md §2

FC-121 — Front: Real anchor Jan 2021 Q3: W~N(18, 5.4²), P(W>j)=0.15 gives j≈23.6. Find P(W>18 | W<23.6). Back: P(W<23.6)=0.85; P(W>18)=0.5 by symmetry of the mean. P(W>18|W<23.6) = (0.85−0.5)/0.85 = 0.35/0.85 = 7/17 ≈ 0.412 — the credited real mark-scheme route. Source: codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md §2.2; codex-complete-worked-paper.md Q3(c)

FC-122 — Front: What is described as the single most consistently "most discriminating" sub-skill on the whole paper, and what real citations confirm it? Back: Recognising that a conditional probability is even required at all under a Normal model, before computing one — confirmed across Jan 2021 Q3(c), Oct 2021 Q6(c), Jan 2023 Q5(e), and named by Pearson as the final, most discriminating part of the Jun 2022 Q6(c) paper. Source: codex-formula-and-method-bank.md §1.5, §2.6; codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md §4

FC-123 — Front: For an inverse-Normal problem with only one unknown parameter, what real citation confirms it as the hardest single skill type on this paper? Back: Jun 2024 Q5(c): a multi-step inverse-Normal problem where "only the more able candidates scored full marks," and abandoning the problem partway through was common — by the facts bank's own framing, the single hardest Normal-distribution skill type in the reviewed archive, by a clear margin. Source: codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md §3.1

Cross-cutting — "Show that" answer discipline

FC-124 — Front: What is the M/A mark dependency rule, and why does a "show that" question make it bite harder? Back: An M mark requires a method to be visible on the page to be awarded at all; an A mark can only be awarded if the preceding M mark has been earned. On an ordinary question a correct final value is itself indirect evidence a correct method was used; a "show that" question destroys that evidence on purpose, by printing the target in the stem, so the mark scheme's only defence is to refuse the accuracy mark unless the method is independently visible. Source: codex-deep-dive-show-that-answer-discipline.md §1

FC-125 — Front: What does the mark code cso mean? Back: "Correct solution only" — there must be no errors in that part of the question to obtain this mark, verified as a real, recurring mark-scheme code, not editorial description. Source: codex-deep-dive-show-that-answer-discipline.md §1

FC-126 — Front: What real error reverse-engineers two plausible values with the target gap between them instead of genuinely interpolating, and which series? Back: Oct 2021 Q3(b): some candidates invented two values with the target IQR gap between them, rather than interpolating either quartile from the actual data. Source: codex-deep-dive-show-that-answer-discipline.md §2.1; codex-deep-dive-measures-of-location-and-dispersion.md §3

FC-127 — Front: Is a bare final answer with no working ever allowed to score full marks on this paper — and how conditional is that allowance? Back: Yes, but only on an ordinary (non-"show that") part, and only when precision-conditional: the real Jan 2021 Q3(a) mark scheme awards "Ans only 3/3" for a bare correct answer in range. But Q3(b) shows this is precision-conditional — a bare "23.6" earns only M1B0A1 (2/3), while a bare "awrt 23.60" earns the full 3/3, because the extra trailing zero proves 4-d.p. table accuracy rather than 3-s.f. rounding. Source: codex-deep-dive-show-that-answer-discipline.md §2.4

From the complete worked paper (Jan 2021, WST01/01) — content new to this course

FC-128 — Front: On a scatter-diagram question, does describing the association as "positive skew" earn the mark, and why not? Back: No — B0. "Skew" describes a distribution's shape; a scatter diagram's association between two variables is described as positive/negative correlation, not skew — a genuine, checkable category error. Source: codex-complete-worked-paper.md Q5(a)

FC-129 — Front: X ~ B(4, 0.15). Find P(X=2), and name the confirmed real error in the binomial coefficient. Back: P(X=2) = C(4,2)×0.15²×0.85² = 6×0.0225×0.7225 ≈ 0.0975. The confirmed real error: candidates multiplied by k=4 instead of k=6 — confusing the number of packages (4) with the number of ways to choose which 2 of 4 (C(4,2)=6). Source: codex-complete-worked-paper.md Q3(d)

FC-130 — Front: On a regression scatter plot, how is the "underperforming" point identified — by its raw x-value, its raw y-value, or something else? Back: By its residual, not its raw score or raw pay alone — the point (25, 48) is underperforming because the fitted line predicts a salary of only ≈32.6 for a performance score of 25, so this manager is paid far more than their performance score alone would justify. Source: codex-complete-worked-paper.md Q5(h)

FC-131 — Front: In a combining-two-groups standard-deviation question, what alternate mark scheme exists for a documented misread, and what does it substitute? Back: Pearson's own alternate mark scheme substitutes n=300 (20 rolls × 15 students) for the first group and n=240 for the second, for candidates who "misread the question... and counted the number of rolls rather than the number of students" — a full, separately-marked column for that specific misread. Source: codex-complete-worked-paper.md Q6(c)

FC-132 — Front: In a geometric-probability "show that P(prize)=1/5" question, what real wrong route divides the disc's own area by the rectangle's area? Back: Some candidates computed the disc's own area, π(1)²=π, and divided it by the rectangle's area, 15 — this answers a different question (what fraction of the rectangle the disc itself covers) and has no bearing on where the disc's centre can land, which is the actual winning condition. Source: codex-complete-worked-paper.md Q6(a)

Closing provenance note

132 flashcards, organised across every spec section this facts-bank-grounded CODEX layer covers (1.1; 2.1–2.4; 3.1–3.4; 4.1–4.3; 5.1–5.4; 6.1) plus the cross-cutting "show that" discipline and five cards drawn from real, previously-unworked question parts in the complete worked paper. No card invents a likelihood, percentage, or grade-boundary figure — every frequency claim above is copied through exactly as its source CODEX file states it ("N of 6," "confirmed on one series only," "not found in the reviewed archive"), never rounded up or converted into a new statistic. Where a source document itself flags a fact as a derivation rather than a confirmed exam angle (e.g. FC-031, FC-032, FC-087's r-vs-b coding contrast, FC-119's symmetry identity), or as a genuine, currently-unevidenced gap (e.g. FC-042 on skewness, FC-016 on even-n quartile interpolation), this document repeats that flag rather than upgrading it. This is a reformatting layer only — every card traces to a real sentence, formula, table row, or worked value in one of the fifteen CODEX files named in the provenance line at the top of this document, cited individually after each card.