AQA Paper 1 Specimen — Question 16 10 marks

Exam BoardAQA
ModulePaper 1 (Paper 1)
SessionSpecimen
Marks10
TopicDifferentiation Applications

16 A student argues that when a rational number is multiplied by an irrational number the result will always be an irrational number. 16
  1. Identify the rational number for which the student's argument is not true. 16
  2. Prove that the student is right for all rational numbers other than the one you have identified in part (a).
    [0pt] [4 marks]
    \(17 \quad \mathrm { f } ( x ) = \sin x\)
    Using differentiation from first principles find the exact value of \(f ^ { \prime } \left( \frac { \pi } { 6 } \right)\)
    Fully justify your answer.
    [0pt] [6 marks] \section*{DO NOT WRITE ON THIS PAGE} ANSWER IN THE SPACES PROVIDED