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Haringey Sixth Form Mathematics Department 1
Shape, space and measures
Non-Calculator Exam Questions
1. Here is the plan and side elevation of a prism.
The side elevation shows the cross section of the prism.
On the grid below, draw the front elevation of the prism.
Haringey Sixth Form Mathematics Department 2
(Total 3 marks)
2. Here are the plan and front elevation of a prism.
The front elevation shows the cross section of the prism.
Plan
Front elevation
(a) On the grid below, draw a side elevation of the prism.
(3)
(b) In the space below, draw a 3-D sketch of the prism.
(2)
(Total 5 marks)
Haringey Sixth Form Mathematics Department 3
3. The diagram shows a solid object made from centimetre cubes.
Diagram accurately drawn
NOT
(a) In the space below, sketch the front elevation of the solid object from the direction marked
with an arrow.
(2)
(b) In the space below, sketch a plan of the solid object.
(2)
(Total 4 marks)
Area and Volume
4.
20 cm
Diagram accurately drawn
NOT
A semicircle has a diameter of 20 cm.
Work out the perimeter of the semicircle.
Take the value of to be 3.14
.............................. cm (Total 3 marks)
Haringey Sixth Form Mathematics Department 4
5.
20 cm
9 cm
4 cm
8 cm
Diagram accurately drawn
NOT
The diagram shows a shape.
Work out the area of the shape.
…………………………… cm2
(Total 4 marks)
6. The diagram shows a wall with a door in it.
Diagram accurately drawn
NOT
4 m
3 m
1 m
2 m
(a) Work out the shaded area.
…………………m2
(3)
Haringey Sixth Form Mathematics Department 5
Meg can cover the shaded area with 680 tiles.
She buys extra tiles in case she breaks some.
To work out the total number of tiles to buy, Meg increases 680 by 10%.
(b) (i) Increase 680 by 10%.
……………………..
The tiles Meg is going to use are sold in boxes of 50.
(ii) Work out the number of boxes of tiles Meg should buy.
…………………….. (5)
(Total 8 marks)
7. The diagram shows a 6-sided shape made from a rectangle and a right-angled triangle.
12 cm
7 cm
6 cm
2 cmDiagram accurately drawn
NOT
Work out the total area of the 6-sided shape.
...........................cm2
(Total 3 marks)
Haringey Sixth Form Mathematics Department 6
8. The diagram shows a wedge in the shape of a triangular prism.
10 cm15 cm2
Diagram accurately drawn
NOT
The cross section of the prism is shown as a shaded triangle.
The area of the triangle is 15 cm2.
The length of the prism is 10 cm.
Work out the volume of the prism.
.......................... (Total 3 marks)
9. The diagram shows a prism.
9.3 cm2 10 cm
Diagram accurately drawn
NOT
The cross section of the prism is a triangle of area 9.3 cm2.
The length of the prism is 10 cm.
Work out the volume of the prism.
State the units of your answer.
…………… ..………. (Total 3 marks)
Haringey Sixth Form Mathematics Department 7
Angles
10.
N
N
Hospital
72°
Cinema
Artgallery
Diagram accurately drawn
NOT
The diagram shows the position of each of three buildings in a town.
The bearing of the Hospital from the Art gallery is 072.
The Cinema is due East of the Hospital.
The distance from the Hospital to the Art gallery is equal to the distance from the Hospital to the
Cinema.
Work out the bearing of the Cinema from the Art gallery.
…………………… (Total 3 marks)
Haringey Sixth Form Mathematics Department 8
11.
Diagram accurately drawn
NOT
62° y°
64°
D E
F G
DE is parallel to FG.
Find the size of the angle marked y°.
..........................° (Total 1 mark)
12.
A
D
C
B
E
130º
72º
yº
xº
Diagram NOT accurately drawn
AC and BD are straight lines which cross at E.
AD is parallel to BC.
(a) (i) Find the size of the angle marked x.
……………………
(ii) Give a reason for your answer.
………………………………………………………………………………………
……………………………………………………………………………………… (2)
Haringey Sixth Form Mathematics Department 9
(b) (i) Find the size of the angle marked y.
……………………
(ii) Give a reason for your answer.
………………………………………………………………………………………
……………………………………………………………………………………… (2)
(Total 4 marks)
13.
A B
C D
P
S
R
Q
x
108º
Diagram NOT accurately drawn
AB is parallel to CD.
Explain why angle x is 72º.
................................................................................................................................................
................................................................................................................................................ (Total 2 marks)
14. (a)
S
P Q R
xº 50º
Diagram NOT accurately drawn
Haringey Sixth Form Mathematics Department 10
PQR is a straight line.
SQ = SR.
(i) Work out the size of the angle marked x°
..........................°
(ii) Give reasons for your answer.
...............................................................................................................................
............................................................................................................................... (Total 3 marks)
(b)
D
F
E
G
62º yº
64º
Diagram NOT accurately drawn
DE is parallel to FG.
(i) Find the size of the angle marked y°.
..........................°
(ii) Give a reason for your answer.
............................................................................................................................... (Total 2 marks)
15.
Diagram accurately drawn
NOT
Calculate the size of the exterior angle of a regular hexagon.
................................... (Total 2 marks)
Haringey Sixth Form Mathematics Department 11
Transformations
16.
5
4
3
2
1
–1
–2
–3
–4
–5
54321–1–2–3–4–5
A
O x
y
(a) On the grid, rotate triangle A 180° about O.
Label your new triangle B. (2)
17.
Ox
y
A
B
Haringey Sixth Form Mathematics Department 12
Describe fully the single transformation which takes shape A onto shape B.
…………………………………………………………………………………………………….
……………………………………………………………………………………………………. (Total 3 marks)
18.
–4–5 –3 –2 –1 1 2 3 4 5
4
3
2
1
–1
–2
–3
–4
Ox
y
A
B
C
Shape A is rotated 90° anticlockwise, centre (0, 1), to shape B
Shape B is rotated 90° anticlockwise, centre (0, 1), to shape C
Shape C is rotated 90° anticlockwise, centre (0, 1), to shape D
(a) Mark the position of Shape D (2)
(b) Describe the single transformation that takes shape C to shape A.
.............................................................................................................................. (2)
(Total 4 marks)
Haringey Sixth Form Mathematics Department 13
19.
7
6
5
4
3
2
1
–1
–2
–3
–4
–1–2–3–4
y
x321 7654 8
O
Enlarge the shaded triangle by a scale factor 2, centre 0. (Total 3 marks)
20.
7
6
5
4
3
2
1
–1
–2
–3
–4
–5
–6
–6 –5 –4 –3 –2 –1O
1 2 3 4 5 6x
y
P
Haringey Sixth Form Mathematics Department 14
(a) On the grid, rotate the shaded shape P one quarter turn anticlockwise about O.
Label the new shape Q. (3)
(b) On the grid, translate the shaded shape P by 2 units to the right and 3 units up.
Label the new shape R. (1)
(Total 4 marks)
21.
Triangle A and triangle B have been drawn on the grid.
(a) Reflect triangle A in the line x = 3.
Label this image C. (2)
(b) Describe fully the single transformation which will map triangle A onto triangle B.
…………………………………………………………………………………………….. (2)
(Total 4 marks)
Haringey Sixth Form Mathematics Department 15
Shape, space and measures (calculator section)
2D and 3D shapes
22. The diagram shows a solid object.
(a) In the space below, sketch the front elevation from the direction marked with an arrow.
(2)
(b) In the space below, sketch the plan of the solid object.
(2)
(Total 4 marks)
Haringey Sixth Form Mathematics Department 16
Area and Volume
23. Here is the net of a 3-D shape.
P
The net is folded to make the 3-D shape.
Two other vertices meet at P.
Mark each of these vertices with the letter P. (Total 2 marks)
24.
15 cm
Diagram accurately drawn
NOT
The diagram shows a semi-circle.
The diameter of the semi-circle is 15 cm.
Calculate the area of the semi-circle.
Give your answer correct to 3 significant figures.
............................ (Total 3 marks)
Haringey Sixth Form Mathematics Department 17
25. A can of drink is in the shape of a cylinder.
The can has a radius of 4 cm and a height of 15 cm.
Diagram accurately drawn
NOT
15 cm
4 cm
Calculate the volume of the cylinder.
Give your answer correct to 3 significant figures.
………………………… (Total 3 marks)
26. The diameter of a circle is 12 centimetres.
(a) Work out the circumference of the circle.
Give your answer, in centimetres, correct to 1 decimal place.
12 cm
Diagram drawn accurately
NOT
.............................. cm (2)
Haringey Sixth Form Mathematics Department 18
Diagram accurately drawn
NOT
The length of each diagonal of a square is 20 cm.
(b) Work out the area of the square.
.............................. cm2
(2)
(Total 4 marks)
27. The diagram shows a trapezium of height 3 m.
2 m
6 m
3 m
Diagram accurately drawn
NOT
Find the area of this trapezium
State the units with our answer.
................................ (Total 3 marks)
Haringey Sixth Form Mathematics Department 19
28.
Diagram NOT accurately drawn
The diagram shows a cylinder with a height of 10 cm and a radius of 4 cm.
(a) Calculate the volume of the cylinder.
Give your answer correct to 3 significant figures.
............................ (3)
The cylinder is solid.
(b) Calculate the total surface area of the cylinder.
Give your answer correct to 3 significant figures.
............................ (3)
(Total 6 marks)
Haringey Sixth Form Mathematics Department 20
Angles
29.
x 62°
A
B C D
Diagram accurately drawn
NOT
Triangle ABC is isosceles, with AC = BC.
Angle ACD = 62.
BCD is a straight line.
(a) Work out the size of angle x.
x = ……………… (2)
Diagram accurately drawn
NOTx
The diagram shows part of a regular octagon.
(b) Work out the size of angle x.
x = ……………… (3)
(Total 5 marks)
Haringey Sixth Form Mathematics Department 21
30.
48°
xy
A
D
B
E
F
C
G
30°
Diagram accurately drawn
NOT
BEG and CFG are straight lines.
ABC is parallel to DEF.
Angle ABE = 48°.
Angle BCF = 30°.
(a) (i) Write down the size of the angle marked x.
x = ...................
(ii) Give a reason for your answer.
........................................................................................................................... (2)
(b) (i) Write down the size of the angle marked y.
y = ...................
(ii) Give a reason for your answer.
........................................................................................................................... (2)
(Total 4 marks)
31.
Diagram NOT accurately drawn
(a) Work out the size of each interior angle of a regular octagon.
Haringey Sixth Form Mathematics Department 22
…………………………… (3)
The size of each exterior angle of a regular polygon is 30.
(b) Work out the number of sides of the polygon.
…………………………… (2)
(Total 5 marks)
32. The size of each exterior angle of a regular polygon is 40.
Work out the number of sides of the polygon.
……………………… (Total 2 marks)
Haringey Sixth Form Mathematics Department 23
33.
A
B
C
xº
43º
Diagram NOT accurately drawn
Triangle ABC is isosceles.
AB = BC
Angle C = 43°
(i) Work out the value of x.
x = .............................
(ii) Give reasons for your answer.
................................................................................................................................................
................................................................................................................................................ (Total 3 marks)
34.
D E F G
A B C
38º
xº yº
Diagram NOT accurately drawn
Haringey Sixth Form Mathematics Department 24
ABC is parallel to DEFG.
BE = EF.
Angle ABE = 38°.
(a) (i) Find the value of x.
x = .............................
(ii) Give a reason for your answer.
...................................................................................................................................... (2)
(b) Work out the value of y.
y = ............................. (2)
(Total 4 marks)
Pythagoras Theorem
35.
Diagram accurately drawn
NOT
3.2 cm
1.7 cm
X Y
Z
XYZ is a right-angled triangle.
XY = 3.2 cm.
XZ = 1.7 cm.
Calculate the length of YZ.
Give your answer correct to 3 significant figures.
…………………………. cm (Total 3 marks)
Haringey Sixth Form Mathematics Department 25
36.
Diagram NOT accurately drawn
4 cm
6 cm
P
Q R
PQR is a right-angled triangle.
PR = 6 cm.
QR = 4 cm.
Work out the length of PQ.
Give your answer correct to 3 significant figures.
.....................................cm (Total 3 marks)
37.
8 cm
11 cmB C
A
Diagram NOT accurately drawn
ABC is a right-angled triangle.
AB = 8 cm,
BC = 11 cm.
Calculate the length of AC.
Give your answer correct to 3 significant figures.
…………………………… cm (Total 3 marks)
