05 MATH40003 SIX PAPER DIFFICULTY CALIBRATION
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: e3043bf9e5d8c749ea805abc36b56576b018ad9a0d258c07e79c6e8c8fb9370dSource 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.
English passage 1 (5% down the source page)
7. Difficulty calibration report for six papers
2026 is an overall workload benchmark, not a fixed question-type template.
English passage 2 (12% down the source page)
Mandatory constraints: each paper lasts two hours, carries 80 marks and contains four questions worth 20 marks each, with approximately 30 minutes per question. The 2026 official solutions allocate approximately A 34, B 18, C 14 and D 14, with rounding and overlapping classifications in the official summary. The revised papers retain approximately 30–32 basic marks, 18–20 medium marks, 12–16 medium-high marks and 16 difficult marks.
English passage 3 (18% down the source page)
paper
role
A/B/C/D plan
calibration rationale
English passage 4 (21% down the source page)
Paper | Role | A/B/C/D marks | Calibration
1 | 2026 structural reinforcement | 30/20/14/16 | Current kernel/image, operator, spectral and conjugacy progression; only this paper closely follows the 2026 structure.
2 | 2025 historical bridge | 32/20/12/16 | REF/RREF, ascending chains, function spaces, rank and minors; compresses the abilities of six 2025 questions into four questions worth 80 marks.
3 | 2023–2024 abilities | 30/20/14/16 | Rings and centres, map constructions, alternating forms, dihedral groups and automorphisms; proof workload comparable with the latter half of 2026.
4 | 2020–2022 abilities | 32/18/14/16 | Systems over different fields, idempotents/nilpotents, recurrences/spectral norms and homomorphisms of cyclic groups.
5 | Seven-year gaps | 30/20/14/16 | Determinants/minors, tridiagonal recurrence, QR/integer orthogonal groups and finite-group counting.
6 | Mixed-transfer challenge | 28/20/16/16 | Mixes ability families from at least three years and changes information order and formulation while keeping the calculation workload within 120 minutes.
English passage 5 (37% down the source page)
question-by-question calibration rules
English passage 6 (41% down the source page)
1. Entry section, 2–4 marks: definitions, matrix transcription and basic calculations; normally 4–7 minutes.
English passage 7 (44% down the source page)
2. Middle section, 5–8 marks: a complete algorithm or standard proof; normally 8–13 minutes.
English passage 8 (46% down the source page)
3. Later section, 6–8 marks: two-way proofs, constructions or transfer to unfamiliar formulations; normally 10–15 minutes.
English passage 9 (48% down the source page)
4. Each question usually has 8–12 meaningful marking steps. Calculations should fit within one and a half pages and structural proofs within two pages.
English passage 10 (51% down the source page)
5. Every question can be completed using basic methods found in official solutions. Advanced methods are optional supplements, not the sole required solution route in this package.
English passage 11 (55% down the source page)
Main combinations distinguishing the six papers from 2026
English passage 12 (59% down the source page)
Apart from Paper 1, Papers 2–6 draw their main ability combinations from 2025, 2023–2024, 2020–2022, seven-year gaps and cross-year transfer respectively. At least five papers do not copy the four-question 2026 combination.