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1 Unit 1: Pure Mathematics A

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Question 287

An engineering model for the structural density ρ \rho\,ρ of a composite material, relative to a depth xxx, is given by the binomial expansion of (3+kx)6(3 + kx)^6(3+kx)6 in ascending powers of xxx. The expansion is written in the form:

ρ=c0+c1x+c2x2+c3x3+… \rho = c_0 + c_1 x + c_2 x^2 + c_3 x^3 + \dots ρ=c0​+c1​x+c2​x2+c3​x3+…

where c0,c1,c2, c_0, c_1, c_2,\,c0​,c1​,c2​, and c3 c_3\,c3​ are constants.

a.

Find the value of c0c_0c0​.

[2]
b.

Given that:

  • c1=2740c3\displaystyle c_1 = \frac{27}{40} c_3c1​=4027​c3​
  • k>0 k > 0\,k>0

Find:

(i) the value of kkk

(ii) the value of c2c_2c2​

[7]
Markscheme

1 Unit 1: Pure Mathematics A Questions

  1. A Level
  2. /Maths
  3. /1 Unit 1: Pure Mathematics A

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