Chapter 7: Further Pure 1: Methods in Calculus

A-level Further MathsFurther Pure 1 & 23 topicsHigher

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Further Pure 1: Methods in Calculus: 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

FP07-1 Find the required result for Further Pure 1: Methods in Calculus. Given Evaluate the improper integral integral from 1 to infinity of 4/

x^{3}

dx and derive a reduction formula for I_n = integral

x^{n}

e^{x}

dx. Use use limiting notation and integration by parts. (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

FP07-2 Show that the improper integral converges to 2 for Further Pure 1: Methods in Calculus. Start from Evaluate the improper integral integral from 1 to infinity of 4/

x^{3}

dx and derive a reduction formula for I_n = integral

x^{n}

e^{x}

dx. (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

FP07-3 Determine the requested value in this structured Further Pure 1: Methods in Calculus problem: apply the reduction formula to find I_2 between 0 and 1. Use the same data: Evaluate the improper integral integral from 1 to infinity of 4/

x^{3}

dx and derive a reduction formula for I_n = integral

x^{n}

e^{x}

dx. (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

FP07-4 Hence use the result the improper integral converges to 2 to complete the extension for Further Pure 1: Methods in Calculus: apply the reduction formula to find I_2 between 0 and 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.

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6. Further Pure 1: Taylor Series

8. Further Pure 1: Numerical Methods

Key learning objectives

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