Chapter 8: Further Pure 1: Numerical Methods

A-level Further MathsFurther Pure 1 & 23 topicsHigher

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Further Pure 1: Numerical Methods: 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

FP08-1 Find the required result for Further Pure 1: Numerical Methods. Given Use Newton-Raphson on

f(x) = x^{3} - 5x - 1 starting with x0 = 2

, and compare with fixed-point iteration x =

\sqrt[3]{5x + 1}

. Use iterate with f'(x), quote values to suitable accuracy and discuss convergence numerically. (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

FP08-2 Show that x1 = 2 - (8 - 10 - 1)/(12 - 5) = 17/7 for Further Pure 1: Numerical Methods. Start from Use Newton-Raphson on

f(x) = x^{3} - 5x - 1 starting with x0 = 2

, and compare with fixed-point iteration x =

\sqrt[3]{5x + 1}

. (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

FP08-3 Determine the requested value in this structured Further Pure 1: Numerical Methods problem: perform two more iterations and identify the root to 3 decimal places. Use the same data: Use Newton-Raphson on

f(x) = x^{3} - 5x - 1 starting with x0 = 2

, and compare with fixed-point iteration x =

\sqrt[3]{5x + 1}

. (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

FP08-4 Hence use the result x1 = 2 - (8 - 10 - 1)/(12 - 5) = 17/7 to complete the extension for Further Pure 1: Numerical Methods: perform two more iterations and identify the root to 3 decimal places. (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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7. Further Pure 1: Methods in Calculus

9. Further Pure 1: Reducible Differential Equations

Key learning objectives

Understand the key principles behind Further Pure 1: Numerical Methods.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.