MATH40006 Revalidated practice comparison

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: 2f4bfcff7431831ffbf7b8243494099049a2f4687d379a9967d05b219e87bc47
Source 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 (93% down the source page) MATH40006 Replacement matrix number 1 page

English passage 2 (8% down the source page) MATH40006 Equal-difficulty replacement matrix REVALIDATED

English passage 3 (14% down the source page) Retain only replacements supported by methods in official materials and compatible with the total workload of 60 minutes and 50 marks.

English passage 4 (22% down the source page) 2026 difficulty unit / earlier candidate Verifiable replacement Shared competencies Evidence of equivalent difficulty Probability / conclusion

English passage 5 (24% down the source page) 2025-26 two-dimensional field visualisation 2021-22 escape-time matrix visualisation Array grids, vectorisation and graphical output 20 marks; 5-8 steps; moderate computation; escape time is more abstract but the plotting sequence is shorter High

English passage 6 (26% down the source page) 2025-26 two-dimensional field visualisation 2021-22 fixed-point / periodic-point stability Function iteration, numerical/symbolic assessment and graphical interpretation 20 marks; greater abstraction balanced by shorter code and direct conditions Medium

English passage 7 (28% down the source page) 2025-26 Pritchard sieve 2023-24 Eratosthenes + incremental prime generation Loops/comprehensions, testing, timing and complexity 20 marks; comparable numbers of functions and timing tasks; both integrate algorithms High

English passage 8 (30% down the source page) 2025-26 Pritchard sieve 2022-23 two integer square-root algorithms Loop invariants, bit operations, Newton and testing 20 marks; comparable computation; slightly greater abstraction, with fewer marks for explanation High

English passage 9 (32% down the source page) 2025-26 Pritchard sieve 2026 Alternative determinant by elimination Long algorithm implementation, boundary cases, tests and numerical stability 20 marks; comparable code length; greater linear-algebra abstraction Medium

English passage 10 (34% down the source page) 2025-26 short Stern-Brocot question 2021-22 LCM counts and complexity Short functions + exact counts / asymptotic assessment 10 marks; 4-5 steps; completion in 10-12 minutes High

English passage 11 (36% down the source page) 2025-26 short Stern-Brocot question 2023-24 text search / container comparison Short algorithms, testing, complexity and timing 10 marks; both combine several small functions High

English passage 12 (39% down the source page) 2025-26 short Stern-Brocot question 2023-24 integer recursion and digit representations Recursive base cases, return structures and tests At 10 marks, select only the core sequence rather than a complete examination question Medium

English passage 13 (41% down the source page) Removed: prime-number topic Sundaram sieve Same topic only; no supporting course evidence supplied Remove; scope and course methods cannot be verified Invalid

English passage 14 (43% down the source page) Removed: orthogonal-polynomial topic Chebyshev recurrence Similar form only; no supporting course evidence supplied Remove; return to Legendre, which appears in the official materials Invalid