MATH40006 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: 79623d30d392564c1ff4d31ce5303436a732bd262dff33703c0ea1735ce39851Source date: 2026-08-06
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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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MATH40006 Difficulty calibration
number 1 page
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MATH40006 Difficulty calibration report for six revised papers
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Primary constraint: each paper's overall difficulty must be comparable to the 2025-26 main examination.
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The calibration benchmark is 2025-26 Assessment 2: 60 minutes, 50 marks, 3 questions, allocated 20+20+10. Because the official materials have no uniform A/B/C/D difficulty labels, the following distribution is calibrated using marks,
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code length, derivation steps, abstraction, testing workload and official solution length.
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Paper
Role
Duration
Total marks
Question count
Mark allocation
Basic
Intermediate
High difficulty
Estimated completion
Calibration notes
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1
2025-26 structural consolidation
60
50
3
20+20+10
18
24
8
58
Same type of workload as the main examination; the only permitted paper with a closely similar structure
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2
Alternative bridging
60
50
3
20+20+10
15
24
11
60
Longer matrix code balanced by marks for direct tests and data export
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3
2023-24 historical competencies
60
50
3
20+20+10
17
24
9
58
Intermediate recursion and search; prime timing requires only a short explanation
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4
2021-23 earlier competencies
60
50
3
20+20+10
14
25
11
60
Legendre and two isqrt methods are more abstract; a short LCM question controls the overall workload
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5
Addressing 2021-22 gaps
60
50
3
20+20+10
13
25
12
60
Dynamical systems are highly abstract, but the search question is short and direct
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6
Mixed transfer challenge
60
50
3
20+20+10
16
24
10
59
Unfamiliar combinations increase recognition difficulty, but the size of each independent function is controlled
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Paper 1: 2025-26 structural consolidation
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Historical basis: 2025-26 Q1/Q2/Q3. Course-method basis: the corresponding official marking scheme. Purpose: familiarity with the current structure only, not coverage of the historical scope.
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Equivalent difficulty: the same grid construction, complete sieve and short-sequence structures, with marks allocated 20+20+10.
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Paper 2: Alternative bridging
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Historical basis: 2026 Alternative Q1-Q3. Course-method basis: the paper's algorithm requirements (no official marking scheme). Gaps addressed: row-echelon form,
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determinants by elimination and data export. Equivalent difficulty: balance longer matrix code with short direct tests and a 10-mark data question.
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Paper 3: 2023-24 historical competencies
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Historical basis: 2023-24 Q1-Q3. Course-method basis: the official 2023-24 marking scheme. Gaps addressed: prime-algorithm comparison, integer recursion and text search.
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Equivalent difficulty: reduce the function count and explanation length of each main question to match the 2026 total workload.
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Paper 4: 2021-23 earlier competencies
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Historical basis: 2021-22 Q1, 2022-23 Q3/Q4 and the 2023-24 Legendre question. Course-method basis: the corresponding official marking schemes. Gaps addressed: earlier recursion,
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complexity and numerical algorithms. Equivalent difficulty: two more abstract 20-mark questions paired with a short 10-mark LCM question.
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Paper 5: Addressing 2021-22 gaps
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Historical basis: 2021-22 escape time and dynamical systems, and 2023-24 search questions. Course-method basis: the corresponding official marking schemes. Gaps addressed: competencies absent from 2026, namely
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dynamical-system and Boolean-mask sequences. Equivalent difficulty: control code size for highly abstract content and use a direct search question.
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Paper 6: Mixed transfer challenge
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Historical basis: 2021-22 codebook, 2022-23 isqrt, 2023-24 digit recursion and Alternative serialisation. Course-method basis: the corresponding official solutions.
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Gaps addressed: combinations across years and unfamiliar approaches. Equivalent difficulty: harder recognition but shorter independent functions; estimated total time: 59 minutes.