Chapter 5: Decision Mathematics 1: The Travelling Salesman Problem

A-level Further MathsDecision Mathematics 1 & 24 topicsHigher

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alevel · further-maths · Decision Mathematics 1 & 2 · All papers

Releases 1 August 2026

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Decision Mathematics 1: The Travelling Salesman Problem: Edexcel Further Maths Optional Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions32 marks64 min

standard / hard / synoptic

8 marksfindstandardEdexcel

D05-1 Find the required result for Decision Mathematics 1: The Travelling Salesman Problem. Given The distance matrix for A, B, C, D has AB 6, AC 9, AD 7, BC 5, BD 8, CD 4. Use use nearest-neighbour upper bounds and deletion lower bounds. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

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8 marksshow thathardEdexcel

D05-2 Show that nearest neighbour from A gives A-B-C-D-A with total 22 for Decision Mathematics 1: The Travelling Salesman Problem. Start from The distance matrix for A, B, C, D has AB 6, AC 9, AD 7, BC 5, BD 8, CD 4. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksdeterminehardEdexcel

D05-3 Determine the requested value in this structured Decision Mathematics 1: The Travelling Salesman Problem problem: find a lower bound by deleting A. Use the same data: The distance matrix for A, B, C, D has AB 6, AC 9, AD 7, BC 5, BD 8, CD 4. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 markshencesynopticEdexcel

D05-4 Hence use the result nearest neighbour from A gives A-B-C-D-A with total 22 to complete the extension for Decision Mathematics 1: The Travelling Salesman Problem: find a lower bound by deleting A. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

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4. Decision Mathematics 1: Route Inspection

6. Decision Mathematics 1: Linear Programming

Key learning objectives

Understand the key principles behind Decision Mathematics 1: The Travelling Salesman Problem.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.