4 marksThe Binomial Theorem
CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2 · Question 4(b)(ii)
Use the expansion to approximate the value of (1.0125)^8.
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Practise this questionOther parts of this question
- 4(a)Eight boys and two girls are to be seated on a bench. How many seating arrangements are possible if the girls can neither sit together nor sit at the ends?[5 marks]
- 4(b)(i)Show that the binomial expansion of
\left(1 + \frac{1}{8}x\right)^8up to and including the term inx^4is…[4 marks] - 4(c)(i)Use the intermediate value theorem to show that
f(x) = \sqrt{x} - \cos xhas a root in the interval[0, 1].[3 marks] - 4(c)(ii)Use two iterations of the interval bisection method to approximate the root of
fin the interval[0, 1].[4 marks] - 4(d)(i)Show that
x_{n+1} = \sqrt[3]{\frac{9 - 3x_n}{2}}is an appropriate iterative formula for finding the root off(x) = -2x^3 - 3x + 9.[2 marks] - 4(d)(ii)Apply the iterative formula with initial approximation
x_1 = 1, to obtain a third approximation,x_3, of the root of the equation.[3 marks]
More practice: the rest of this paper · more The Binomial Theorem questions · all CAPE Pure Mathematics Unit 2 past papers