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.