1. 1
   Triangle T has vertices at (1, 1), (3, 1) and (1, 4). Triangle T is reflected in the line y = -1 to give triangle T'.

   (a)

   What are the coordinates of the image of vertex (3, 1) under this reflection?

   [1 mark]

   • A(3, -3)
   • B(3, 3)
   • C(-3, 1)
   • D(3, -2)

   (b)

   Triangle T has area 3 square units. What is the area of triangle T'?

   [1 mark]

   • A6
   • B3
   • C1.5
   • D9

   (c)

   Which single transformation maps triangle T' back onto triangle T?

   [1 mark]

   • AReflection in the line y = 1
   • BRotation of 180 degrees about (0, -1)
   • CReflection in the line y = -1
   • DTranslation by column vector (0, -2)

   Total for question 1: 3 marks

2. 2
   Point C has coordinates (-4, 6). It is translated by the column vector $\begin{pmatrix} 5 \\ -9 \end{pmatrix}$ to give point C'.

   (a)

   Find the coordinates of C'.

   [2 marks]

   (b)

   Point C' is then translated by the column vector $\begin{pmatrix} -2 \\ 4 \end{pmatrix}$ to give point C''. Find the single column vector that translates C directly to C''.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Shape D has an area of 8 square units. Shape D is enlarged by scale factor -2, centre the origin, to give shape D'.

   (a)

   State the ratio of side lengths of D' to D, and hence find the area of D'.

   [3 marks]

   (b)

   A vertex of D' lies at (-6, 10). Given that the enlargement has centre the origin, find the coordinates of the corresponding vertex of D.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In triangle OXY, $\vec{OX} = \vec{x}$ and $\vec{OY} = \vec{y}$. Point K lies on XY such that XK:KY = 3:2.

   (a)

   Find $\vec{XY}$ in terms of $\vec{x}$ and $\vec{y}$, and hence find $\vec{XK}$ in terms of $\vec{x}$ and $\vec{y}$.

   [4 marks]

   (b)

   Hence find $\vec{OK}$ in terms of $\vec{x}$ and $\vec{y}$, simplifying your answer.

   [4 marks]

   (c)

   Point L lies on OY such that OL:LY = 2:3. By expressing $\vec{OL}$ in terms of $\vec{y}$, determine whether K lies on the line OL. Justify your answer.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   $\vec{p} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}$ and $\vec{q} = \begin{pmatrix} 2 \\ -6 \end{pmatrix}$.

   (a)

   What is $2\vec{p} + \vec{q}$?

   [1 mark]

   • A$\begin{pmatrix} -8 \\ 16 \end{pmatrix}$
   • B$\begin{pmatrix} 1 \\ -7 \end{pmatrix}$
   • C$\begin{pmatrix} -2 \\ -2 \end{pmatrix}$
   • D$\begin{pmatrix} -4 \\ 4 \end{pmatrix}$

   (b)

   What is the magnitude of $\vec{q}$, in surd form where appropriate?

   [1 mark]

   • A$2\sqrt{10}$
   • B$2\sqrt{14}$
   • C8
   • D40

   (c)

   Which vector is parallel to $\vec{p}$?

   [1 mark]

   • A$\begin{pmatrix} 5 \\ -3 \end{pmatrix}$
   • B$\begin{pmatrix} -6 \\ 10 \end{pmatrix}$
   • C$\begin{pmatrix} -3 \\ -5 \end{pmatrix}$
   • D$\begin{pmatrix} 6 \\ 10 \end{pmatrix}$

   Total for question 5: 3 marks

6. 6
   Rectangle E has vertices at (2, 1), (6, 1), (6, 3) and (2, 3). Rectangle E is rotated 90 degrees anti-clockwise about the point (2, 1) to give rectangle E'.

   (a)

   Find the coordinates of the image of the vertex (6, 1) under this rotation.

   [2 marks]

   (b)

   State the length of the image of the side from (2, 1) to (6, 1) after the rotation.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   $\vec{u} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}$ and $\vec{v} = \begin{pmatrix} -3 \\ 6 \end{pmatrix}$.

   (a)

   Find $3\vec{u} - 2\vec{v}$ as a column vector, and hence find its magnitude to 3 significant figures.

   [3 marks]

   (b)

   Find the value of $k$ such that $\vec{u} + k\vec{v}$ is parallel to the vector $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   Shape F is mapped to shape G by a rotation of 180 degrees about the point (1, -2). Shape G is then mapped to shape H by the translation with column vector $\begin{pmatrix} 6 \\ -4 \end{pmatrix}$.

   (a)

   A vertex of F is at (5, 0). Find the coordinates of the corresponding vertex of G.

   [4 marks]

   (b)

   Find the coordinates of the corresponding vertex of H, and state the single column vector that would map the vertex of F directly to the vertex of H.

   [4 marks]

   (c)

   Show that the combined transformation mapping F to H is equivalent to a single rotation of 180 degrees, and find the coordinates of its centre.

   [5 marks]

   Total for question 8: 13 marks

End of questions