Skip to content

Course home

Sign up

1.7.1 Binomial expansion

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697
Question 93
a.

Determine the first two terms, in ascending powers of uuu, of the binomial expansion of

(1+34u)−13 \left(1 + \frac{3}{4}u\right)^{-\frac{1}{3}} (1+43​u)−31​
[2]
b.

A signal processing engineer models the gain G G\,G of a circuit at frequency offset x x\,x using the formula:

G(x)=cos⁡(5x)+(1+6x2)−13 G(x) = \cos(5x) + \left(1 + 6x^2\right)^{-\frac{1}{3}} G(x)=cos(5x)+(1+6x2)−31​

Hence, for small values of xxx, show that the gain can be approximated by

G(x)≈A+Bx+Cx2 G(x) \approx A + Bx + Cx^2 G(x)≈A+Bx+Cx2

where AAA, B B\,B and C C\,C are constants to be found.

[4]
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.

Question bank