CAIE P1 2021 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionNovember
TopicBinomial Theorem (positive integer n)
TypeProduct with unknown constant to determine

8
  1. It is given that in the expansion of \(( 4 + 2 x ) ( 2 - a x ) ^ { 5 }\), the coefficient of \(x ^ { 2 }\) is - 15 .
    Find the possible values of \(a\).
  2. It is given instead that in the expansion of \(( 4 + 2 x ) ( 2 - a x ) ^ { 5 }\), the coefficient of \(x ^ { 2 }\) is \(k\). It is also given that there is only one value of \(a\) which leads to this value of \(k\). Find the values of \(k\) and \(a\).