MATH40002 Seven-year coverage analysis
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: 83506280e64636757e0be2c1df7b6bbe36ae2ad534f13fe559ad875d2a294226Source 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 (6% down the source page)
MATH40002 New seven-year effective coverage report
English passage 2 (19% down the source page)
The full matrix is 08_MATH40002_ Seven-year effective coverage matrix .csv. C is not counted. All 2025 subparts of
English passage 3 (42% down the source page)
2021-1(c)(i)
1
Construct a sequence with no convergent rearrangement
D
English passage 4 (43% down the source page)
2021-1(c)(ii)
1
Determine whether value sets are countably infinite
D
English passage 5 (45% down the source page)
2021-1(c)(iii)
1
Conditional convergence permits rearrangement to any real sum
D
English passage 6 (47% down the source page)
2021-1(d)(iii)
1
Counterexample with consecutive differences tending to zero
C
English passage 7 (48% down the source page)
2021-2(a)(ii)
3
Prove from first principles that cubing preserves a limit
C
English passage 8 (50% down the source page)
2021-2(d)
3
From dyadic Convergence of a subsequence of partial sums implies convergence of the entire series
D
English passage 9 (52% down the source page)
2021-6(a)(i)
2
Write upper and lower sums for an equally spaced partition
C
English passage 10 (53% down the source page)
2021-6(a)(ii)
2
Find the difference between upper and lower sums
D
English passage 11 (55% down the source page)
2021-6(c)(ii)
4
Prove that the limit at infinity does not exist
C
English passage 12 (57% down the source page)
2022-1(a)(i)
3
False: unboundedness does not imply that the reciprocal tends to 0
C
English passage 13 (58% down the source page)
2022-1(a)(iii)
3
A series selected by an injective indexing map remains absolutely convergent
D
English passage 14 (60% down the source page)
2022-3(a)(ii)
4
Geometric decay of consecutive differences implies convergence
C
English passage 15 (62% down the source page)
2022-3(b)(ii)
4
max(a_n,b_n) Limit
C
English passage 16 (63% down the source page)
2022-4(b)(i)
2
x=cos^3x Has a solution
D
English passage 17 (65% down the source page)
2022-4(b)(ii)
3
Alternating integer values imply infinitely many zeros
D
English passage 18 (67% down the source page)
2023-3(a)
5
Convergence of adjacent geometric means does not imply convergence of the original series
D
English passage 19 (68% down the source page)
2023-3(b)
5
Convergence of the original positive-term series implies convergence of the series of adjacent geometric means
D
English passage 20 (70% down the source page)
2023-3(d)
5
Fixed-step differences tend to 0 Does not imply convergence
C
English passage 21 (72% down the source page)
2023-5(b)(i)
3
Continuous, strictly monotone and unbounded above and below implies bijective
C
English passage 22 (73% down the source page)
2023-5(b)(ii)
4
A continuous function with finite limits at both ends is bounded
C
English passage 23 (75% down the source page)
2023-5(b)(iii)
4
Equal limits at both ends imply at least one global extremum
C
English passage 24 (77% down the source page)
2024-1(a)
5
a_n→0 and sum b_n Convergence does not imply sum a_nb_n
C
English passage 25 (79% down the source page)
2024-1(c)
5
Consecutive differences tend to 0 Does not imply Cauchy
C
English passage 26 (80% down the source page)
2024-1(d)
5
Absolute convergence implies sum(a_n)^n Convergence
D