Chapter 13: Further Pure 2: Recurrence Relations

A-level Further MathsFurther Pure 1 & 24 topicsHigher

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alevel · further-maths · Further Pure 1 & 2 · All papers

Releases 1 August 2026

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Further Pure 2: Recurrence Relations: 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

FP13-1 Find the required result for Further Pure 2: Recurrence Relations. Given Solve u_{n+2} - 5u_{n+1} + 6u_n = 4 with u_0 = 1 and u_1 = 3. Use find complementary and particular solutions, then use initial conditions. (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

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8 marksshow thathardEdexcel

FP13-2 Show that u_n =

A2^{n}

B3^{n}

+ 2 for Further Pure 2: Recurrence Relations. Start from Solve u_{n+2} - 5u_{n+1} + 6u_n = 4 with u_0 = 1 and u_1 = 3. (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

FP13-3 Determine the requested value in this structured Further Pure 2: Recurrence Relations problem: determine A and B exactly. Use the same data: Solve u_{n+2} - 5u_{n+1} + 6u_n = 4 with u_0 = 1 and u_1 = 3. (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

FP13-4 Hence use the result u_n =

A2^{n}

B3^{n}

+ 2 to complete the extension for Further Pure 2: Recurrence Relations: determine A and B exactly. (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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12. Further Pure 2: Complex Numbers

14. Further Pure 2: Matrix Algebra

Key learning objectives

Understand the key principles behind Further Pure 2: Recurrence Relations.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.