Find the value of

(i)     p ;

(ii)    q ;

(iii)   r.

The equation $y = k$ has exactly two solutions. Write down the value of k.

(i) evidence of finding the amplitude     (M1)

e.g. $\frac{{7 + 3}}{2}$ , amplitude $= 5$

$p = - 5$     A1     N2

(ii) period $= 8$     (A1)

$q = 0.785$ $\left( { = \frac{{2\pi }}{8} = \frac{\pi }{4}} \right)$     A1     N2

(iii) $r = \frac{{7 - 3}}{2}$     (A1)

$r = 2$     A1     N2

[6 marks]

$k = - 3$ (accept $y = - 3$ )     A1     N1

[1 mark]

Many candidates did not recognize that the value of p was negative. The value of q was often interpreted incorrectly as the period but most candidates could find the value of r, the vertical translation.

In part (b), candidates either could not find a solution or found too many.