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1.7.1 Binomial expansion

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Question 48

In a materials science laboratory, the expansion factor of a synthetic polymer PPP relative to temperature change ttt is modeled by the function:

P(t)=(2+kt4)5 P(t) = \left(2 + \frac{kt}{4}\right)^5 P(t)=(2+4kt​)5

where kkk is a non-zero constant.

a.

Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of P(t)P(t)P(t). Give each term in its simplest form.

[4]
b.

To account for sensor drift, a corrected expansion model R(t)R(t)R(t) is defined as:

R(t)=(5+3t)P(t) R(t) = (5 + 3t)P(t) R(t)=(5+3t)P(t)

Given that in the expansion of R(t)R(t)R(t), the coefficient of the ttt term is equal to the constant term, determine the value of kkk.

[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.

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