1
1 Shape A is shown on the grid.
On the grid, enlarge shape A by scale factor 3. [2]
[Total: 2]
2 (a) Explain why these rectangles are mathematically similar.
..........................................................................................................................................................
.......................................................................................................................................................... [1]
(b) How many times bigger is the area of the large rectangle than the area of the small rectangle?
................................................... [2]
[Total: 3]
3 The grid shows triangles A, B and C.
2
y
8
7
6
5
4
3
B
2
A
1
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x
–1
C
–2
–3
–4
–5
–6
–7
–8
(a) Describe fully the single transformation that maps triangle A onto triangle B.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
(b) Describe fully the single transformation that maps triangle A onto triangle C.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
(c) Draw the image of
(i) triangle A after a translation by the vector , [2]
(ii) triangle A after a reflection in the line y = −2. [2]
[Total: 10]
3
Draw the enlargement of the triangle by scale factor 3, centre X. [2]
[Total: 2]
5 Enlarge the rectangle using a scale factor of 3 and centre of enlargement O.
[2]
[Total: 2]
4
y
3
2
A
1
x
–4 –3 –2 –1 0 1 2 3 4 5
–1
–2
–3
6 Draw the image of the shape A after a translation by the vector . [2]
[Total: 2]
y
3
2
A
1
x
–4 –3 –2 –1 0 1 2 3 4 5
–1
–2
–3
7 Draw the image of shape A after a translation by the vector . [2]
[Total: 2]
5
8
y
6
5
4
3
A
2
1
B
–5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 x
–1
–2
–3
–4
–5
Describe fully the single transformation that maps triangle A onto triangle B.
....................................................................................................................................................................
.................................................................................................................................................................... [3]
[Total: 3]
9
y
6
3
S
2
T
1
x
0
1 2 2 4 5 6 7 8 9
Describe fully the single transformation that maps triangle S onto triangle T.
Answer......................................................................................................................................................
.................................................................................................................................................................. [3]
6
[Total: 3]
10
NOT TO
y°
SCALE
x° 68°
The diagram shows two parallel lines and a straight line crossing them.
Find the value of x and the value of y.
x = ...................................................
y = ................................................... [2]
[Total: 2]
7
11
NOT TO
59° 37° SCALE
a°
c°
b°
The diagram shows two parallel lines intersected by two straight lines.
Find the values of a, b and c.
a = ..................................
b = ..................................
c = .................................. [3]
[Total: 3]
12
NOT TO
SCALE
100°
y°
y°
Find the value of y.
y = .................................. [2]
[Total: 2]
8
13
x NOT TO
SCALE
40°
The diagram shows a pair of parallel lines and a straight line.
Complete the statement with the correct geometrical reason.
x = 40° because the angles are ................................................. [1]
[Total: 1]
14
a°
NOT TO
126° SCALE
c°
b° 63°
The diagram shows two straight lines intersecting two parallel lines.
Find the values of a, b and c.
a = ...................................................
b = ...................................................
c = ................................................... [3]
[Total: 3]
9
15
In the triangle ABC, AB = AC and angle BAC = 38°.
BCD is a straight line.
Work out angle ACD.
Angle ACD = ................................................... [3]
[Total: 3]
16
In the diagram, AB is parallel to CD.
10
(a) Find the value of x.
Give a geometrical reason for your answer.
x = .............................. because ....................................................................................................... [2]
(b) Work out the value of y.
Give a geometrical reason for your answer.
y = .............................. because ....................................................................................................... [2]
[Total: 4]
17
AB = BC and ABD is a straight line.
Find the value of x.
x = ................................................... [2]
[Total: 2]
11
18
The diagram shows two pairs of parallel lines.
Find the value of a, the value of b and the value of c.
a = ...................................................
b = ...................................................
c = ................................................... [3]
[Total: 3]
19 Show that the interior angle of a regular pentagon is 108°.
[2]
[Total: 2]
20 (a) Show that the exterior angle of a regular octagon is 45°.
[1]
12
20 (b) Find the interior angle of a regular octagon.
................................................... [1]
[Total: 2]
21 The diagrams show the angles in a triangle and two angles on a straight line.
(a) The triangle is used to write down an equation in terms of x and y.
Give the geometrical reason why this equation is correct.
Reason ...................................................................................................................................... [1]
(b) Use the diagram with two angles on a straight line to write down another equation in terms of x and y.
................................................... [1]
13
(c) Solve these simultaneous equations.
You must show all your working.
x = ...................................................
y = ................................................... [3]
[Total: 5]
22 Calculate the interior angle of a regular pentagon.
................................................... [2]
[Total: 2]
23 Calculate the size of one interior angle of a regular octagon.
......................................................... [2]
[Total: 2]
14
24 Work out the interior angle of a regular 18-sided polygon.
........................................ [2]
[Total: 2]
25 The exterior angle of a regular polygon is 36°.
Find how many sides this polygon has.
........................................ [1]
[Total: 1]
26 The exterior angle of a regular polygon is 24°.
Work out the number of sides of this polygon.
................................................... [1]
[Total: 1]
27 Work out the size of one interior angle of a regular 9-sided polygon.
................................................... [2]
[Total: 2]
15
28 Find the total surface area of a cuboid with length 8 cm, width 6 cm and height 3 cm.
................................................... cm2 [3]
[Total: 3]
29
NOT TO
SCALE
5 cm
4 cm
7 cm
Calculate the total surface area of this cuboid.
................................................... cm2 [3]
[Total: 3]
16
30
The diagram shows a cuboid.
Calculate the volume of the cuboid.
................................................... cm3 [1]
[Total: 1]
31
The diagram shows a cuboid measuring 15 cm by 12 cm by 4 cm.
Calculate the surface area of the cuboid.
................................................... cm2 [3]
[Total: 3]
17
32 The length of the edge of a cube is 8 cm.
Calculate the surface area of this cube.
................................................... cm2 [2]
[Total: 2]
33
Calculate the total surface area of the cuboid.
................................................... cm2 [3]
[Total: 3]
34
NOT TO
SCALE
4 cm
7 cm
3 cm
The diagram shows a right-angled triangular prism.
18
(a) On the 1 cm2 grid, complete a net of this prism.
One face has been drawn for you.
[4]
(b) Work out the volume of this prism.
................................................... cm3 [2]
[Total: 6]
19
35 A cylinder has a radius of 8 cm and a height of 12 cm.
Calculate, in terms of , the volume of the cylinder.
................................................... cm3 [2]
[Total: 2]
36
The diagram shows a right-angled triangular prism.
Work out the volume of the prism.
................................................... cm3 [3]
[Total: 3]
20
37 A cylinder has a radius of 6 cm and a height of 17 cm.
Show that the volume of this cylinder is 1923 cm3, correct to 4 significant figures.
[2]
[Total: 2]
38 Find the volume of a cylinder of radius 5 cm and height 8 cm.
Give the units of your answer.
.............................. .................... [3]
[Total: 3]
39 A cylinder has diameter 12 cm and length 18 cm.
NOT TO
SCALE
12 cm
18 cm
Calculate the volume of the cylinder.
Answer ................................................... cm3 [2]
21
[Total: 2]
40 Calculate the area of a circle with radius 12 cm.
................................................... cm2 [2]
[Total: 2]
