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1.7.1 Binomial expansion

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Question 35
a.

Use the binomial expansion to expand

(16+2v)−12∣v∣<8 (16 + 2v)^{-\frac{1}{2}} \quad |v| < 8 (16+2v)−21​∣v∣<8

in ascending powers of vvv, up to and including the term in v2v^2v2, giving each coefficient as a fully simplified fraction.

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b.

The pressure PPP in a pneumatic cylinder is modeled by the function

P(v)=12+kv16+2vwhere k is a constant and ∣v∣<8 P(v) = \frac{12 + kv}{\sqrt{16 + 2v}} \quad \text{where } k \text{ is a constant and } |v| < 8 P(v)=16+2v​12+kv​where k is a constant and ∣v∣<8

Given that the series expansion of P(v)P(v)P(v), in ascending powers of vvv, is

3+916v+qv2+…where q is a constant 3 + \frac{9}{16}v + qv^2 + \dots \quad \text{where } q \text{ is a constant} 3+169​v+qv2+…where q is a constant

find the value of kkk,

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c.

find the value of qqq.

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Markscheme

1.7.1 Binomial expansion Questions

  1. A Level
  2. /Maths
  3. /1.7.1 Binomial expansion

144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.

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