Calculate the value of \(p\) when \(x = 45^\circ \), \(y = 8192\) and \(z = 64\). Write down your full calculator display.

Write down your answer to part (a)

(i)     correct to two decimal places;

(ii)     correct to four significant figures;

(iii)     in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).

\(\frac{{2\cos 45^\circ  - \tan 45^\circ }}{{\sqrt {8192}  - 64}}\)     (M1)

\( = 0.015625\)     (A1)     (C2)

Notes:     Accept \(\frac{1}{{64}}\) and also \(1.5625 \times {10^{ - 2}}\).

[2 marks]

(i)     0.02     (A1)(ft)

(ii)     0.01563     (A1)(ft)

Notes:     For parts (i) and (ii), accept equivalent standard form representations.

(iii)     \(1.5625 \times {10^{ - 2}}\)     (A2)(ft)     (C4)

Notes:     Award (A1)(A0) for correct mantissa, between 1 and 10, with incorrect index.

     Follow through from their answer to part (a).

     Where the candidate has correctly rounded their mantissa from part (a) and has the correct exponent, award (A0)(A1)

     Award (A0)(A0) for answers of the type: \(15.625 \times {10^{ - 3}}\).

[4 marks]