SPS SPS SM Pure 2022 November — Question 1

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2022
SessionNovember
TopicIndices and Surds

  1. Do not use a calculator for this question
    a)
Find \(a\), given that \(a ^ { 3 } = 64 x ^ { 12 } y ^ { 3 }\).
b)
  1. Express \(\frac { 81 } { \sqrt { 3 } }\) in the form \(3 ^ { k }\).
  2. Express \(\frac { 5 + \sqrt { 3 } } { 5 - \sqrt { 3 } }\) in the form \(\frac { a + b \sqrt { 3 } } { c }\), where \(a , b\) and \(c\) are integers.