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Binomial Expansion

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Question 232
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.

[4]
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,

[3]
c.

find the value of qqq.

[2]
Markscheme

Binomial Expansion Questions

  1. A Level
  2. /Maths
  3. /Binomial Expansion

408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.

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