Skip to content

Course home

Sign up

1.7.1 Binomial expansion

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697
Question 38
a.

A structural stability index SSS of a micro-beam is modeled as a function of its lateral displacement vvv by the expression S(v)=(2−14v)6S(v) = \left(2 - \frac{1}{4}v\right)^6S(v)=(2−41​v)6. Find the first four terms of the binomial expansion of S(v)S(v)S(v) in ascending powers of vvv.

[3]
b.

In a symmetric calibration test, the total response is defined as R(v)=(2−14v)6+(2+14v)6R(v) = \left(2 - \frac{1}{4}v\right)^6 + \left(2 + \frac{1}{4}v\right)^6R(v)=(2−41​v)6+(2+41​v)6. Given that vvv is sufficiently small such that terms in v4v^4v4 and higher powers of vvv may be neglected, show that

R(v)=A+Bv2 R(v) = A + Bv^2 R(v)=A+Bv2

where AAA and BBB are integers to be determined.

[3]
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