MATH40006 Practice Paper 3 Solutions

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: 639a021ef28e7872cf9dc439ee518138f13d5a6f0c8f1d550b795a09f517e0f1
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 (95% down the source page) MATH40006_Practice_Paper_3_Worked_Solutions Page 1

English passage 2 (71% down the source page) - Accessible course-material basis: the official 2023-24 marking scheme.

English passage 3 (74% down the source page) - Historical competency gap addressed: Eratosthenes, conditional appending, construction by trial division and timing comparisons.

English passage 4 (76% down the source page) - Equivalent 2026 difficulty unit: 2026 Q2 (20-mark integrated-algorithm unit).

English passage 5 (79% down the source page) - Reason for equivalence: two algorithms, testing and timing comprise 5 stages; reducing the explanation at the million-element scale keeps code length and the estimated 22 minutes comparable.

Source page 2

Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.

English passage 1 (95% down the source page) MATH40006_Practice_Paper_3_Worked_Solutions Page 2

English passage 2 (47% down the source page) - Accessible course-material basis: the official 2023-24 marking scheme.

English passage 3 (49% down the source page) - Historical competency gap addressed: recursive branches, base representations, run-length compression and transfer of methods.

English passage 4 (51% down the source page) - Equivalent 2026 difficulty unit: 2026 Q1 (20-mark multi-step integrated unit).

English passage 5 (54% down the source page) - Reason for equivalence: greater abstraction but less plotting work; base cases, recursion, inverse-function tests, list compression and complexity take approximately 20 minutes in total.

Source page 3

Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.

English passage 1 (95% down the source page) MATH40006_Practice_Paper_3_Worked_Solutions Page 3

English passage 2 (68% down the source page) - Historical examination-question basis: 2023-24 Assessment 3 Q3(i-a to ii-e).

English passage 3 (71% down the source page) - Accessible course-material basis: the official 2023-24 marking scheme.

English passage 4 (73% down the source page) - Historical competency gap addressed: file reading, sequential search, dictionaries and Series; the complete 35-mark examination question is reduced to a short bridging exercise.

English passage 5 (75% down the source page) - Equivalent 2026 difficulty unit: 2026 Q3 (10-mark short data unit).

English passage 6 (78% down the source page) - Reason for equivalence: only the core reading step, two container types and successful/unsuccessful search tests are selected; estimated time: 9-10 minutes.