22 The equation of circle A is \(x^2 + y^2 = 25\)

Circle A is translated by the vector \(\begin{pmatrix} 0 \\ -2 \end{pmatrix}\) to give circle B.

Sketch circle B.
Show the coordinates of
    the centre of circle B
and the points where circle B meets the \(y\)-axis. (3)

21 Here is the graph of \(y = \mathrm{f}(x)\)

Here is a sketch of the graph of \(y = \sin x^\circ\)

The point marked \(P\) is a turning point on the graph.

The graph of \(y = \sin x^\circ\) is translated to give the graph of \(y = \sin(x + 180)^\circ + 4\)

Following the translation the point \(P\), shown on the graph above, moves to point \(R\).

21 The graph of \(y = \mathrm{g}(x)\) is shown on the grid.

On the grid, draw the graph of \(y = \mathrm{g}(-x) + 2\) (2)

20 The turning point on the graph of \(y = \text{g}(x)\) has coordinates \((-3, 6)\)

The graph of \(y = \text{f}(x)\) is shown on the grid.

21 Here is the graph of \(y = \mathrm{f}(x)\)

(a) On the grid below, draw the graph of \(y = \mathrm{f}(x) - 4\)

(1)

(b) On the grid below, draw the graph of \(y = \mathrm{f}(-x)\)

(1)

21 The graph of \(y = \mathrm{f}(x)\) is shown on the grid below.

Here is a sketch of the graph of \(y = \tan x^\circ\)

The graph of \(y = \tan x^\circ\) is translated to give the graph of \(y = \mathrm{g}(x)\)

Following the translation the point \(Q\), shown on the graph above, moves to point \(R\).
Point \(R\) has coordinates \((90, -5)\)

18 Here is a graph of \(y = \sin x^\circ\) for \(0 \leqslant x \leqslant 360\)

The graph of \(y = \sin x^\circ\) is reflected in the \(x\)-axis.

Here is a graph of \(y = \mathrm{f}(x)\)

20 The graph of \(y = \mathrm{f}(x)\) is shown on the grid.

Point \(A(-2, 1)\) lies on the graph of \(y = \mathrm{f}(x)\).

When the graph of \(y = \mathrm{f}(x)\) is transformed to the graph with equation \(y = \mathrm{f}(-x)\), point \(A\) is mapped to point \(B\).

15 The graph of the curve C with equation \(y = \mathrm{f}(x)\) is transformed to give the graph of the curve S with equation \(y = \mathrm{f}(-x) - 3\)

The point on C with coordinates \((7, 2)\) is mapped to the point \(Q\) on S.

Find the coordinates of \(Q\). (2)

18 The graph of \(y = \mathrm{f}(x)\) is shown on the grid below.

On the grid, graph A has been reflected to give graph B.

The equation of graph A is \(y = \mathrm{g}(x)\)

18 Here is the graph of  \(y = \sin x^\circ\)  for \(-180 \leqslant x \leqslant 180\)

On the grid, sketch the graph of  \(y = \sin x^\circ - 2\)  for \(-180 \leqslant x \leqslant 180\) (2)

20 The equation of a curve is \(y = a^x\)
\(A\) is the point where the curve intersects the \(y\)-axis.

The equation of circle C is \(x^2 + y^2 = 16\)

The circle C is translated by the vector \(\begin{pmatrix} 3 \\ 0 \end{pmatrix}\) to give circle B.

22

The graph of \(y = k^x\), where \(k\) is a positive constant, is shown above.

The graph of \(y = \sin x^\circ\) for values of \(x\) from \(-270\) to \(+270\) is shown above.

24

The diagram shows part of the curve with equation \(y = \mathrm{f}(x)\).
The coordinates of the maximum point of the curve are (3, 5).

The curve with equation \(y = \mathrm{f}(x)\) is transformed to give the curve with equation \(y = \mathrm{f}(x) - 4\)

25

The diagram shows part of the curve with equation \(y = \mathrm{f}(x)\).
The coordinates of the minimum point of this curve are \((3, -4)\)

Write down the coordinates of the minimum point of the curve with equation

25 \(y = \mathrm{f}(x)\)

The graph of \(y = \mathrm{f}(x)\) is shown on the grid.

The graph of \(y = \mathrm{f}(x)\) is shown on the grid.

The graph G is a translation of the graph of \(y = \mathrm{f}(x)\).

26 The graph of \(y = \mathrm{f}(x)\) is shown on each of the grids.

(a) On this grid, sketch the graph of \(y = \mathrm{f}(x - 3)\)

(2)

(b) On this grid, sketch the graph of \(y = 2\mathrm{f}(x)\)

(2)

21 The graph of \(\quad y = \mathrm{f}(x) \quad\) for \(\quad 0 \leqslant x \leqslant 3 \quad\) is shown.

(a) On the grid below, draw the graph of \(\quad y = -\mathrm{f}(x) \quad\) for \(\quad 0 \leqslant x \leqslant 3\)

The graph of \(\quad y = \mathrm{f}(x) \quad\) is shown to help you. [1 mark]

(b) On the grid below, draw the graph of \(\quad y = \mathrm{f}(x) + 1 \quad\) for \(\quad 0 \leqslant x \leqslant 3\)

The graph of \(\quad y = \mathrm{f}(x) \quad\) is shown to help you. [1 mark]

23 In each part, the graph shown is a transformation of the graph \(\quad y = x^2\)

(a) Write down the equation of the graph shown. [1 mark]

(b) Write down the equation of the graph shown. [1 mark]

(c) Write down the equation of the graph shown. [1 mark]

27

26 Here is a sketch of \(\quad y = x^2\)

26 Here is a sketch of the graph of \(\quad y = 5^x\)

In parts (a) and (b) the sketch of \(\quad y = 5^x \quad\) is shown as a dashed line.

(a) On the axes below, sketch the graph of \(\quad y = -5^x\) [1 mark]

(b) On the axes below, sketch the graph of \(\quad y = 5^x - 1\) [1 mark]

27 The grid shows the graph of \(\quad y = \mathrm{f}(x)\)

On the grid, draw the graph of \(\quad y = -\mathrm{f}(x)\) [2 marks]

28 Here is the graph of \(\quad y = \cos x \quad\) for \(\ 0° \leqslant x \leqslant 360°\)

In parts (a) and (b) the graph of \(\quad y = \cos x \quad\) is shown as a dashed line.

(a) On the grid below, draw the graph of \(\quad y = \cos(x - 90°) \quad\) for \(\ 0° \leqslant x \leqslant 360°\) [1 mark]

(b) On the grid below, draw the graph of \(\quad y = 1 + \cos x \quad\) for \(\ 0° \leqslant x \leqslant 360°\) [1 mark]

(c) Rita tries to draw the graph of \(\quad y = \cos(-x) \quad\) for \(\ 0° \leqslant x \leqslant 360°\)

Here is her graph.

Give a reason why Rita’s graph is incorrect. [1 mark]

29 The graph of \(\quad y = x^3 + 6 \quad\) is translated 4 units to the right.

The translated graph has equation \(\quad y = \mathrm{f}(x)\)

Work out \(\mathrm{f}(x)\).

Give your answer in the form \(\quad x^3 + ax^2 + bx + c \quad\) where \(a\), \(b\) and \(c\) are integers. [4 marks]

20 (7, 28) is a point on the graph \(\quad y = \mathrm{f}(x)\)

Circle the point which must be on the graph \(\quad y = \mathrm{f}(x) + 2\) [1 mark]

• (7, 26)
• (7, 30)
• (5, 28)
• (9, 28)

8 On the axes, sketch the curve \(\quad y = x^3 - 2\)

You must show the coordinates of the \(y\)-intercept. [2 marks]

24 Here is a sketch of \(\quad y = \text{f}(x)\)

The curve passes through the points

\(({-2}, {-10}) \quad ({-1}, {-3}) \quad (0, {-2}) \quad (1, {-1}) \quad (2, 6)\)

On the grid, sketch the curve \(\quad y = \text{f}(x + 2)\) [2 marks]

20 Curve P has equation \(\quad y = 2(x - 1)^2 - 5\)

Curve Q is a reflection in the \(y\)-axis of curve P.

Work out the equation of curve Q.

Give your answer in the form \(\quad y = ax^2 + bx + c \quad\) where \(a\), \(b\) and \(c\) are integers. [3 marks]

29 Here are sketches of two graphs.

The graph of \(\quad y = x^2 - 1 \quad\) is translated 3 units to the left to give graph A.

22

(a) For each graph below, select its possible equation from this list.

• \(y = \sqrt{x - 4}\)
• \(y = 4^x\)
• \(y = x^4\)
• \(y = \dfrac{4}{x}\)
• \(y = \left(\dfrac{1}{4}\right)^x\)
• \(y = -4x^2\)
• \(y = 4\cos x\)
• \(y = \sqrt{4^2 - x^2}\)

(i)

Not to scale

[1]

(ii)

Not to scale

[1]

(b) A graph is drawn on the axes below.

Not to scale

The equation of the graph is \(y = \sin(x + p)\), where \(0^\circ \leqslant x \leqslant 360^\circ\).
The \(x\)-intercepts are 130° and \(r\)°.

Write down the value of \(p\) and the value of \(r\). [2]

21 The graph of \(y = x^2\) is shown below for \(-2 \leqslant x \leqslant 2\).

13

(a) The graph of \(y = 3^x\) is sketched below.

On the same axes, sketch the graph of \(y = 2^x\). [3]

(b) Charlie sketches this graph.

Charlie says

The equation of my graph is \(y = \sin x\).

(i) Explain how you know that Charlie is not correct. [1]

(ii) Write down a possible equation for Charlie’s graph. [1]

19 Describe the single transformation that maps the graph of \(y = x^2\) onto the graph of \(y = (x + 3)^2 + 5\). [3]

18

(a) For each graph below, select its possible equation from this list.

\(y = x\)	\(y = x^2\)	\(y = \dfrac{1}{x}\)
\(y = \sin x\)	\(y = \cos x\)	\(y = \tan x\)
\(y = 3^x\)	\(y = \left(\dfrac{1}{3}\right)^x\)

(i)

[1]

(ii)

[1]

(b) Here is a sketch of \(y = x^3\).

On the axes below, sketch the graphs of

(i) \(y = -x^3\)

[1]

(ii) \(y = x^3 - 8\), showing the values of any intercepts with the axes.

[3]

15