Chapter 6: Further Pure 1: Taylor Series

A-level Further MathsFurther Pure 1 & 23 topicsHigher

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Further Pure 1: Taylor Series: 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

FP06-1 Find the required result for Further Pure 1: Taylor Series. Given Expand

f(x) = ln(2 + x) about x = 0 up to the term in x^{3}

, then use x = 0.2. Use differentiate successively or use a transformed logarithm expansion. (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

FP06-2 Show that ln(2 + x) = ln 2 + x/2 -

x^{2}

/8 +

x^{3}

/24 + ... for Further Pure 1: Taylor Series. Start from Expand

f(x) = ln(2 + x) about x = 0 up to the term in x^{3}

, then use x = 0.2. (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

FP06-3 Determine the requested value in this structured Further Pure 1: Taylor Series problem: use the expansion to estimate ln 2.2 and state the validity range. Use the same data: Expand

f(x) = ln(2 + x) about x = 0 up to the term in x^{3}

, then use x = 0.2. (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

FP06-4 Hence use the result ln(2 + x) = ln 2 + x/2 -

x^{2}

/8 +

x^{3}

/24 + ... to complete the extension for Further Pure 1: Taylor Series: use the expansion to estimate ln 2.2 and state the validity range. (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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5. Further Pure 1: The t-formulae

7. Further Pure 1: Methods in Calculus

Key learning objectives

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