CAIE P1 2023 November — Question 4

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2023
SessionNovember
TopicBinomial Theorem (positive integer n)
TypeProduct with unknown constant to determine

4
  1. Expand the following in ascending powers of \(x\) up to and including the term in \(x ^ { 2 }\).
    1. \(( 1 + 2 x ) ^ { 5 }\).
    2. \(( 1 - a x ) ^ { 6 }\), where \(a\) is a constant.
      In the expansion of \(( 1 + 2 x ) ^ { 5 } ( 1 - a x ) ^ { 6 }\), the coefficient of \(x ^ { 2 }\) is - 5 .
  2. Find the possible values of \(a\).