Chapter 1: Decision Mathematics 1: Algorithms

A-level Further MathsDecision Mathematics 1 & 26 topicsHigher

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Releases 1 August 2026

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Decision Mathematics 1: Algorithms: 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

Algorithm list

item	value	use
initial list	34, 12, 45, 18, 27, 9	sort/search
target	27	binary search

D01-1 Find the required result for Decision Mathematics 1: Algorithms. Given Apply bubble sort and binary search to the list 34, 12, 45, 18, 27, 9. Use record passes, comparisons and final ordered list. (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 marksshow thathardEdexcel

Algorithm list

item	value	use
initial list	34, 12, 45, 18, 27, 9	sort/search
target	27	binary search

D01-2 Show that after the first bubble-sort pass the largest value is in the final position for Decision Mathematics 1: Algorithms. Start from Apply bubble sort and binary search to the list 34, 12, 45, 18, 27, 9. (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

Algorithm list

item	value	use
initial list	34, 12, 45, 18, 27, 9	sort/search
target	27	binary search

D01-3 Determine the requested value in this structured Decision Mathematics 1: Algorithms problem: trace a binary search for 27 after sorting. Use the same data: Apply bubble sort and binary search to the list 34, 12, 45, 18, 27, 9. (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

Algorithm list

item	value	use
initial list	34, 12, 45, 18, 27, 9	sort/search
target	27	binary search

D01-4 Hence use the result after the first bubble-sort pass the largest value is in the final position to complete the extension for Decision Mathematics 1: Algorithms: trace a binary search for 27 after sorting. (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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Start of Decision Mathematics 1 & 2

2. Decision Mathematics 1: Graphs and Networks

Key learning objectives

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