Chapter 15: Further Pure 2: Integration Techniques

A-level Further MathsFurther Pure 1 & 23 topicsHigher

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Further Pure 2: Integration Techniques: 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

FP15-1 Find the required result for Further Pure 2: Integration Techniques. Given Find the arc length of y =

x^{3/2}

from x = 0 to x = 4, and decompose 1/((x+1)(

x^{2}

+4)). Use use the arc length formula and partial fractions with an irreducible quadratic. (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

FP15-2 Show that

\dfrac{ds}{dx}

\sqrt{1 + 9x/4}

for Further Pure 2: Integration Techniques. Start from Find the arc length of y =

x^{3/2}

from x = 0 to x = 4, and decompose 1/((x+1)(

x^{2}

+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

FP15-3 Determine the requested value in this structured Further Pure 2: Integration Techniques problem: evaluate the definite integral exactly. Use the same data: Find the arc length of y =

x^{3/2}

from x = 0 to x = 4, and decompose 1/((x+1)(

x^{2}

+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

FP15-4 Hence use the result

\dfrac{ds}{dx}

\sqrt{1 + 9x/4}

to complete the extension for Further Pure 2: Integration Techniques: evaluate the definite integral 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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14. Further Pure 2: Matrix Algebra

End of Further Pure 1 & 2

Key learning objectives

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