06 MATH40003 NEW EFFECTIVE COVERAGE MATRIX
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: d152126652eb97885fd98741fe40ab0d264dd057810bb9eb9c2defd98af05820Source 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)
8. new effective-coverage matrix across seven years
A= direct question-type coverage ;B= method coverage including transfer to unfamiliar formulations ;C= labels only ;D= not covered
English passage 2 (14% down the source page)
A
B
C
D
A+B Effective coverage
English passage 3 (21% down the source page)
summarise by year
English passage 4 (25% down the source page)
year
A
B
C
D
effective-coverage rate
English passage 5 (42% down the source page)
Acceptance check for high-mark clusters in the 2025 formal paper
English passage 6 (47% down the source page)
unit
question number
mark allocation
ability
new grade
English passage 7 (49% down the source page)
Unit | Question | Marks | Ability | Coverage
AU147 | Q1(c) | 6 | Find row-space and column-space bases by rank-1/rank-2 cases | A
AU153 | Q2(b) | 5 | Prove that the union of an increasing subspace chain is a subspace | A
AU155 | Q2(d) | 6 | Prove eventual stabilisation of an increasing subspace chain in finite dimensions | A
AU156 | Q2(e) | 5 | Construct a strictly increasing chain in F[x] | A
AU158 | Q3(b) | 6 | Transfer a vector-space structure through a bijection and prove an isomorphism | A
AU160 | Q3(d) | 4 | Find the matrix of the rotation-induced function-composition operator | A
AU161 | Q3(e) | 4 | Find the kernel, image and rank of the invertible induced operator | A
AU162 | Q4(a) | 11 | Write the matrix, find three eigenspaces and diagonalise | A
AU163 | Q4(b)(i) | 5 | Prove rank A < k if and only if every k-order minor is 0 | A
AU164 | Q4(b)(ii) | 4 | Fix a nonzero k-order minor and characterise using (k+1)-order minors containing it | B
AU165 | Q5(a)(i) | 4 | Apply Gram-Schmidt to the columns and normalise | A
AU166 | Q5(a)(ii)–(iii) | Continued in the source table.
English passage 8 (66% down the source page)
6
write the original columns in orthonormal-basis coordinates and form QR
A
English passage 9 (69% down the source page)
AU169 | Q5(b)(iii) | 4 marks | Characterise O_n(Z) as signed permutation matrices and find its order 2^n n! | A
AU171 | Q6(a)(ii) | 4 marks | Find the maximum element order in S9 | A
AU172 | Q6(b)(i)–(iii) | Continued in the source table.
English passage 10 (73% down the source page)
7 marks | Determine whether S5, the shear-matrix group and the regular-polygon rotation group are cyclic | A
English passage 11 (76% down the source page)
AU173 | Q6(c) | 7 marks | Prove that if every element has finite order, a nonempty multiplicatively closed set is automatically a subgroup | A
English passage 12 (80% down the source page)
Conclusion: every 2025 marking cluster worth at least four marks is category A or B, meeting the mandatory acceptance criterion.
English passage 13 (84% down the source page)
complete matrix
English passage 14 (88% down the source page)
The full 194×24 cell-by-cell matrix is in new_effective_coverage_matrix.csv. The PDF retains each ability unit's best grade and annual totals, avoiding compression of 24 columns into unreadable text on A4 paper.