MATH40006 Practice Paper 2 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: d9c44fda6a29aed1d6ad1573631611081ffee44be71c7501688a513c5511a12e
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_2_Worked_Solutions Page 1

English passage 2 (64% down the source page) - Historical examination-question basis: 2026 Alternative Q1(i-a to ii-h).

English passage 3 (66% down the source page) - Accessible course-material basis: the 2026 Alternative paper (no marking scheme was supplied).

English passage 4 (69% down the source page) - Historical competency gap addressed: row operations, elimination and the general REF sequence; although these appeared in the six earlier papers, they need to be independent of the 2026 question slots.

English passage 5 (71% down the source page) - Equivalent 2026 difficulty unit: 2026 Q1 (20-mark multi-step implementation unit).

English passage 6 (73% down the source page) - Reason for equivalence: the original 25-mark Alternative sequence is reduced to 20 marks, retaining in-place row operations, column-by-column elimination, rectangular matrices and tests that the input is unchanged; 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_2_Worked_Solutions Page 2

English passage 2 (41% down the source page) - Historical examination-question basis: 2026 Alternative Q2(i-a to ii-h).

English passage 3 (44% down the source page) - Accessible course-material basis: the 2026 Alternative paper (no marking scheme was supplied).

English passage 4 (46% down the source page) - Historical competency gap addressed: determinants by elimination, partial pivoting and row-swap signs.

English passage 5 (48% down the source page) - Equivalent 2026 difficulty unit: 2026 Q2 (20-mark long-algorithm unit).

English passage 6 (51% down the source page) - Reason for equivalence: comparable long functions, boundary matrices, numerical checks and complexity explanations; a 4-mark symbolic proof is removed to keep the total time within 60 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_2_Worked_Solutions Page 3

English passage 2 (14% down the source page) - Accessible course-material basis: the 2026 Alternative paper (no marking scheme was supplied).

English passage 3 (16% down the source page) - Historical competency gap addressed: the complete data sequence of nested timing dictionaries, pickle, DataFrame and CSV.

English passage 4 (18% down the source page) - Equivalent 2026 difficulty unit: 2026 Q3 (10-mark short integrated unit).

English passage 5 (21% down the source page) - Reason for equivalence: 4 direct steps, a small number of file operations and structural checks; estimated time: 8-10 minutes.