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MATH40004 DIFFICULTY CALIBRATION REVISED 2

English review edition prepared on 4 October 2026 from a preserved source copy. It is a later presentation, not the historical study interface. Source checks and difficulty judgements describe the original material author's own process; they do not indicate Imperial College London endorsement.

Source SHA-256: 11171b0309b8783b0f80dd820649c4ce57e96baef966ab3abc3fecb640c1dde3
Source date: 2026-08-06

Source page 1

Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.

Mathematical content of source page 1 with translated prose supplied below
English passage 1 (6% down the source page) AUDITED_REVISED_2 revision statement
English passage 2 (11% down the source page) The body of this report comes from the previous revised version. Codex's independent review found that the previous main ZIP omitted the 2020 original question booklet and official solutions/marking materials, affecting the 2020 question-level evidence.
English passage 3 (12% down the source page) These question-level claims could not be independently verified within the package.
English passage 4 (15% down the source page) This version includes the original file “MATH40004MATH40011_Calculus and Applications_Q&S;_May_2020(3).pdf” unchanged under 06_SOURCE
English passage 5 (16% down the source page) _EVIDENCE/2020, registered in the original-evidence index and SHA256SUMS. This PDF has 22 pages. Its SHA-256 is:
English passage 6 (19% down the source page) 143a8d4fdaaf7f49f781e464c0794cc7a29cd1f96d25440bc26dafa79164520b Question-level conclusions for 2020–2026 must therefore be read with the original PDFs. Reports cannot replace original materials. Apart from evidence-chain completion and workbook
English passage 7 (22% down the source page) mechanical-format repairs, the report's conclusions have not been recalculated or altered. Version date: 2026-08-06.

Source page 2

Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.

Mathematical content of source page 2 with translated prose supplied below
English passage 1 (5% down the source page) Difficulty calibration report for six papers

Source page 3

Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.

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English passage 1 (5% down the source page) 2026 mandatory benchmark
English passage 2 (9% down the source page) The 2026 formal paper has four questions, 80 marks and 120 minutes, with 20 marks per question. The official marking review allocates A24, B15, C9 and D12, plus Mastery 20, totalling 80. This structure is used as a whole-paper difficulty budget, not a fixed set of knowledge points or question-position method sequences.
English passage 3 (13% down the source page) Paper | Questions | Marks | Minutes | Difficulty budget | Calibration 2026 official | 4 | 80 | 120 | A24/B15/C9/D12/M20 | Benchmark Revised P1 | 4 | 80 | 120 | A24/B15/C9/D12/M20 | 2026 structural reinforcement; calibrated steps and integration Revised P2 | 4 | 80 | 120 | A24/B15/C9/D12/M20 | 2025 bridge; calibrated Jordan/Euler-Cauchy calculation volume Revised P3 | 4 | 80 | 120 | A24/B15/C9/D12/M20 | 2023–24 historical combination; calibrated proof/transform workload Revised P4 | 4 | 80 | 120 | A24/B15/C9/D12/M20 | 2020–22 historical combination; balanced definitions/curves/improper integrals Revised P5 | 4 | 80 | 120 | A24/B15/C9/D12/M20 | Gap paper; does not use 2026 question positions as a template Revised P6 | 4 | 80 | 120 | A24/B15/C9/D12/M20 | Mixed transfer; unfamiliar entry points without exceeding the benchmark workload
English passage 4 (35% down the source page) normal completion-time budget for each paper
English passage 5 (39% down the source page) Q1 Q2 Q3 Q4 total
English passage 6 (52% down the source page) calibration dimension
English passage 7 (56% down the source page) • Step count: normally 3–5 explicit marking stages per question. Difficult marks do not rely on excessively long mechanical calculations.
English passage 8 (58% down the source page) • Calculation volume: balance calculation-heavy Jordan/Euler-Cauchy/Hessian questions with shorter definitions, convergence values or self-check subparts.
English passage 9 (60% down the source page) • Proof length: uniqueness, convergence, error and bifurcation classification require explanation, but no advanced theory beyond the style of official solutions.
English passage 10 (62% down the source page) • Modelling/figures: at most one major modelling or figure-heavy task per paper, to avoid distorting total time.
English passage 11 (64% down the source page) • Abstraction and integration: P6 has less familiar entry points but a correspondingly reduced algebraic burden per question, so its overall difficulty remains comparable to 2026.
English passage 12 (68% down the source page) being in the same module does not by itself establish equal difficulty
English passage 13 (72% down the source page) Each question's historical basis, entry point, first step, method sequence and estimated time are listed in the workbook's “Six revised papers: design mapping” and “Seven-year ability-unit inventory”. The acceptance conclusion here concerns only the total burden of the whole paper.