Question 1 - A-Level Maths

OCR FP2 2006 June — Question 1 3 marks

Exam Board	OCR
Module	FP2 (Further Pure Mathematics 2)
Year	2006
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Taylor series
Type	Direct multiplication of series
Difficulty	Moderate -0.5 This is a straightforward application of multiplying two standard Maclaurin series (both given in formula books). It requires careful algebraic manipulation to collect terms but involves no conceptual difficulty or problem-solving—just methodical execution of a routine technique with series that students have memorized.
Spec	4.08a Maclaurin series: find series for function 4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n

1 Find the first three non-zero terms of the Maclaurin series for $$( 1 + x ) \sin x$$ simplifying the coefficients.

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Answer	Marks	Guidance
Correct expansion of $\sin x$		Multiply their expansion by $(1 + x)$
Obtain $x + x^2 - \frac{x^3}{6}$	B1

Correct expansion of $\sin x$ | | Multiply their expansion by $(1 + x)$
Obtain $x + x^2 - \frac{x^3}{6}$ | B1 |

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1 Find the first three non-zero terms of the Maclaurin series for

$$( 1 + x ) \sin x$$

simplifying the coefficients.

\hfill \mbox{\textit{OCR FP2 2006 Q1 [3]}}

This paper (9 questions)

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Q1 3 Q2 6 Q3 6 Q4 7 Q5 7 Q6 8 Q7 11 Q8 11 Q9 13

Answer	Marks	Guidance
Correct expansion of \(\sin x\)		Multiply their expansion by \((1 + x)\)
Obtain \(x + x^2 - \frac{x^3}{6}\)	B1