10 MATH40003 GRAPHICS AND FILE QA
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: 9c593d7af41a7685a63cf6048f017510483efd6c32f82fda1a581f9b6f259537Source 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.
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10. figure and file quality inspection report
six revised papers and course-method solutions
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acceptance conclusion
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Overall result: PASS. Each of the six papers lasts 120 minutes and carries 80 marks across four 20-mark questions. The six solution sets correspond question by question to the question booklets. All PDFs are A4, unencrypted and parsable/renderable. Preflight returned no warning or error; the final LaTeX log had no overfull/underfull, missing-character or undefined-reference warning.
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format consistency for each paper
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papers
Page count
question count
marks per question
total marks
Result
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solution structure
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Each of the six separate solution files has five pages and four Question sections. Every question includes a historical basis, recognition signal, first key step, complete course method, marking points, common errors and final self-check. Main solutions use methods actually found in seven years of official solutions; advanced methods are not the only route to marks.
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figures and layout
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• Render verification checked 142 PNG pages. No corrupted or nearly blank renderings were found, and the PDFs have no structural blank pages.
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• The combined question booklet has 30 pages and the combined solution booklet has 30 pages. Covers, Q1–Q4 and solution Q1–Q4 are in matching order for each paper.
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• None of the six revised papers in this course requires a diagram to determine its structure or refers to a missing figure. The required figure count is therefore 0; this is not an omission.
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• Margins, page numbers, headings, matrices, fractions, superscripts/subscripts and Chinese fonts were checked. No clipping, overlap, black squares or garbled text was found.
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coverage and mandatory acceptance criteria
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revised version
131
43
20
0
174/194=89.7%
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Category C is knowledge-label coverage only and is excluded from the effective-coverage rate. Every marking cluster worth at least four marks in the 2025 formal paper is A or B. Of the six papers, only Paper 1 closely follows the current 2026 structure. Papers 2–6 respectively provide a 2025 bridge, 2023–2024 abilities, 2020–2022 abilities, seven-year gaps and mixed transfer, avoiding repetition of one combination across all six.
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mathematical verification summary
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• Linear algebra: parameter-dependent row reduction, kernels/images and direct sums, finite-field exceptions, eigenspaces, orthogonal diagonalisation, matrix square roots, QR, determinant recurrences, rank and minors were independently checked by substitution or symbolic calculation.
Source page 2
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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• Group theory: cycle decomposition, sign, element orders, conjugation, dihedral normal forms, commutator normality, finite-group counting and Cayley/subgroup tests were all reviewed.
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• Two layout overflows were rewritten in the final version. Two proof formulations—idempotent intersections and distinctness of dihedral elements—were replaced by complete direct arguments.
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material scope
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No separate lecture notes, problem sheets, tutorial or assignment files were found in this session. The evidence scope of “COURSE METHOD AUDITED” is therefore the main methods in 2020–2026 official solutions, official A/B/C/D classifications, seen/similar/unseen labels and examiner comments. The report does not invent lecture-note page numbers or claim to have checked unavailable materials.
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detailed file hashes and per-file checks are in verification_log.txt.