MATH40006 Practice Paper 5 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: 8dcb3c7babbb5c954534da518a26de46efff40e826185a08cdaac46a3f8fcaf1
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_5_Worked_Solutions Page 1

English passage 2 (65% down the source page) - Accessible course-material basis: the official 2021-22 marking scheme.

English passage 3 (67% down the source page) - Historical competency gap addressed: complex iteration, Boolean masks and escape-time plots, which are high-mark historical competencies absent from the 2026 paper.

English passage 4 (69% down the source page) - Equivalent 2026 difficulty unit: 2026 Q1 (20-mark array/graphics unit).

English passage 5 (72% down the source page) - Reason for equivalence: the same use of two-dimensional grids, vectorisation and graphical output; the iteration is more abstract but there are fewer figure types; estimated time: 20 minutes.

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_5_Worked_Solutions Page 2

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_5_Worked_Solutions Page 3

English passage 2 (20% down the source page) - Accessible course-material basis: the official 2021-22 marking scheme.

English passage 3 (23% down the source page) - Historical competency gap addressed: fixed points, period-2 points, derivative-based stability and boundary contours.

English passage 4 (25% down the source page) - Equivalent 2026 difficulty unit: 2026 Q2 (20-mark highly abstract method-sequence unit).

English passage 5 (27% down the source page) - Reason for equivalence: symbolic solving, lambdify, composite mapping and contours comprise 6 steps; code length is controlled; estimated time: 23-25 minutes.

Source page 4

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_5_Worked_Solutions Page 4

English passage 2 (69% down the source page) - Historical examination-question basis: 2023-24 Assessment 3 Q3(i-d to ii-e).

English passage 3 (72% down the source page) - Accessible course-material basis: the official 2023-24 marking scheme.

English passage 4 (74% down the source page) - Historical competency gap addressed: four search approaches (sequential, binary, dict and Series) and transfer of complexity analysis.

English passage 5 (76% down the source page) - Equivalent 2026 difficulty unit: 2026 Q3 (10-mark short comparison unit).

English passage 6 (79% down the source page) - Reason for equivalence: only core search and small-scale timing are required, with 4-5 steps and an estimated time of 10 minutes.

Source page 5

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_5_Worked_Solutions Page 5