Skip to content

Course home

Sign up

Binomial Expansion

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114
Question 98

In a high-frequency signal filter design, the gain GGG relative to a frequency shift ω\omegaω is modelled by the function G(ω)=(25+2ω)−12G(\omega) = (25 + 2\omega)^{-\frac{1}{2}}G(ω)=(25+2ω)−21​. The first three terms, in ascending powers of ω\omegaω, of the binomial expansion of G(ω)G(\omega)G(ω) are given by

(25+2ω)−12≈a−1125ω+36250ω2(25 + 2\omega)^{-\frac{1}{2}} \approx a - \frac{1}{125}\omega + \frac{3}{6250}\omega^2(25+2ω)−21​≈a−1251​ω+62503​ω2

where aaa is a constant.

a.

State the range of values of ω\omegaω for which this expansion is valid.

Choose from the options below:

∣ω∣<225∣ω∣<252∣ω∣<5∣ω∣<25|\omega| < \frac{2}{25} \quad |\omega| < \frac{25}{2} \quad |\omega| < 5 \quad |\omega| < 25∣ω∣<252​∣ω∣<225​∣ω∣<5∣ω∣<25
[1]
b.

Find the value of aaa.

Choose from the options below:

12515525\frac{1}{25} \quad \frac{1}{5} \quad 5 \quad 25251​51​525
[1]
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.

Question bank