Find the coordinates of A.

Write down the coordinates of

(i)     the image of B after reflection in the y-axis;

(ii)    the image of B after translation by the vector $\left( {\begin{array}{*{20}{c}} { - 2}\\ 5 \end{array}} \right)$ ;

(iii)   the image of B after reflection in the x-axis followed by a horizontal stretch with scale factor $\frac{1}{2}$ .

$f(x) = {x^2} - 2x - 3$     A1A1A1

evidence of solving $f'(x) = 0$     (M1)

e.g. ${x^2} - 2x - 3 = 0$

evidence of correct working     A1

e.g. $(x + 1)(x - 3)$ ,  $\frac{{2 \pm \sqrt {16} }}{2}$

$x =  - 1$ (ignore $x = 3$ )     (A1)

evidence of substituting their negative x-value into $f(x)$     (M1)

e.g. $\frac{1}{3}{( - 1)^3} - {( - 1)^2} - 3( - 1)$ , $- \frac{1}{3} - 1 + 3$

$y = \frac{5}{3}$     A1

coordinates are $\left( { - 1,\frac{5}{3}} \right)$     N3

[8 marks]

(i) $( - 3{\text{, }} - 9)$     A1     N1

(ii) $(1{\text{, }} - 4)$     A1A1    N2

(iii) reflection gives $(3{\text{, }}9)$     (A1)

stretch gives $\left( {\frac{3}{2}{\text{, }}9} \right)$     A1A1     N3

[6 marks]

A majority of candidates answered part (a) completely.

Candidates were generally successful in finding images after single transformations in part (b). Common incorrect answers for (biii) included $\left( {\frac{3}{2},\frac{9}{2}} \right)$ , (6, 9) and (6, 18) , demonstrating difficulty with images from horizontal stretches.