AQA AS Paper 1 Specimen — Question 4 8 marks

Exam BoardAQA
ModuleAS Paper 1 (AS Paper 1)
SessionSpecimen
Marks8
TopicIndices and Surds

4
0 \end{array} \right] \quad \left[ \begin{array} { c } - 4
0 \end{array} \right] \quad \left[ \begin{array} { l } 0
4 \end{array} \right] \quad \left[ \begin{array} { c } 0
- 4 \end{array} \right]$$ 2 Consider the two statements, A and B, below.
A: \(x ^ { 2 } - 6 x + 8 > 0\)
B: \(x > 4\)
Choose the most appropriate option below.
Circle your answer.
[0pt] [1 mark] $$A \Rightarrow B \quad A \Leftarrow B \quad A \Leftrightarrow B$$ There is no connection between \(A\) and B 3
  1. Write down the value of \(p\) and the value of \(q\) given that: 3
    1. \(\sqrt { 3 } = 3 ^ { p }\)
      [0pt] [1 mark] 3
  2. (ii) \(\frac { 1 } { 9 } = 3 ^ { q }\)
    [0pt] [1 mark] 3
  3. Find the value of \(x\) for which \(\sqrt { 3 } \times 3 ^ { x } = \frac { 1 } { 9 }\)
    [0pt] [2 marks]
    4 Show that \(\frac { 5 \sqrt { 2 } + 2 } { 3 \sqrt { 2 } + 4 }\) can be expressed in the form \(m + n \sqrt { 2 }\), where \(m\) and \(n\) are integers.
    [0pt] [3 marks]