MATH40006 Practice Paper 6 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: 99d90f8ae12963ec22ca2f8b8009124af473bf92fc4579a9c58db9e14d639b09
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_6_Worked_Solutions Page 1

English passage 2 (69% down the source page) - Accessible course-material basis: the official 2021-22 marking scheme.

English passage 3 (71% down the source page) - Historical competency gap addressed: the complete historical sequence of copying, shuffling, pairing, bidirectional mapping, and recursive binary-search encoding/decoding.

English passage 4 (73% down the source page) - Equivalent 2026 difficulty unit: 2026 Q1 (20-mark integrated multi-function unit).

English passage 5 (76% down the source page) - Reason for equivalence: several short functions and a round-trip self-check, with the information presented in a different order; approximately 20 minutes for all code and tests.

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_6_Worked_Solutions Page 2

English passage 2 (40% down the source page) - Accessible course-material basis: the official 2022-23 marking scheme and the Alternative paper.

English passage 3 (42% down the source page) - Historical competency gap addressed: a combination across years of Newton iteration counts, performance data, pickle, DataFrame and CSV.

English passage 4 (44% down the source page) - Equivalent 2026 difficulty unit: 2026 Q2 (20-mark long-algorithm and data unit).

English passage 5 (47% down the source page) - Reason for equivalence: approximately 12 marks for the main Newton algorithm and 8 marks for the data pipeline; greater integration but short individual functions; estimated time: 24 minutes.

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_6_Worked_Solutions Page 3

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

English passage 3 (27% down the source page) - Historical competency gap addressed: practise recognition of binary runs and transfer of run lengths and run heads through an unfamiliar formulation.

English passage 4 (29% down the source page) - Equivalent 2026 difficulty unit: 2026 Q3 (10-mark short recursion/list unit).

English passage 5 (31% down the source page) - Reason for equivalence: base cases, traversal, two outputs and example self-checks comprise 4 steps; approximately 10 minutes.