CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

Name Date

Stage 9 End of unit 5 test

1 Show why the sum of the interior angles of any hexagon must be 720 °.

[2]

2 a Work out the sum of the interior angles of a regular octagon.

[2]

b Work out the interior angle of a regular octagon.

[1]

Calculate the size of angle a.

[2]

4 ABCD is a trapezium. CDE is a straight line.

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

Work out the size of

a angle x

b angle y [2]

The sides of this right-angled triangle are 12 cm, 13 cm and a cm.

Show that a is an integer.

[2]

6 The floor of a room is a rectangle.

The sides of the rectangle are 4.5 m and 7.5 m.

Calculate the length of the diagonal of the rectangle.

[2]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

7 Leave your construction lines in your answer to this question. You must not use
a protractor.

The sides of a triangle are 6 cm, 7.5 cm and 8.5 cm.

a Make an accurate drawing of the triangle. [2]
b Draw the perpendicular bisector of the longest side. [2]

8 Leave your construction lines in your answer to this question. You must not use a protractor.

Construct an angle of 22.5 °. [3]

[Total: 20 marks]

END OF TEST

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

Name Date

Stage 9 End of unit 7 test

1 Work out the area of these circles. Use the π button on your calculator.

Round your answers correct to three significant figures (3 s.f.)

a radius = 7 m

[2]

b diameter = 26 cm

[2]

2 The diagram shows a semicircle.

Work out, correct to one decimal place (1 d.p.):

a the area of the semicircle

[2]

b the perimeter of the semicircle.

[3]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

3 Work out the radius of a circle with area = 42 cm2.

Give your answer correct to two decimal places (2 d.p.)

[3]

4 Work out the area of these compound shapes. Give your answers correct to one
decimal place (1 d.p.)

a ______________________________________________

______________________________________________

______________________________________________

______________________________________________ [3]

b ______________________________________________

______________________________________________

______________________________________________

_______________________________________________ [3]

5 The diagram shows three circles cut out from a rectangle.

The diameter of each circle is 8 cm.

The distances shown by the arrows are 2 cm.

Work out the shaded area. Give your

answer correct to three significant figures (3 s.f.)

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________ [5]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

6 a Write these capacities in order of size, starting with the smallest.

5 centilitres

5 nanolitres

5 microlitres

5 millilitres

5 litres

5 kilolitres

smallest:

largest: [4]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

b Write each of the capacities in part a using only the correct letters for the units,
not words. For example, write 5 centilitres as 5 cL.

smallest:

largest: [1]

7 A store sells four items with different memory sizes.

A Memory: 32 GB B Memory: 256 MB C Memory: 2 TB D Memory: 512 KB

Write the items in order of memory size, from the smallest to the largest.

[2]

[Total: 30 marks]

END OF TEST

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

Stage 9 End of unit 13 test

1 Avel and Bronte stand by post P.

Avel walks on a bearing of 130 º for 40 m.

Bronte walks on a bearing of 215 º for 30 m.

a Show both of their journeys on the same scale drawing on the right.

Use a scale of ‘1 cm represents 10 m’. [2]

b On your scale drawing, measure the distance between Avel and Bronte at the end
of their walk.

At the end of their walk, how far apart are Avel and Bronte in real life?

km [2]

2 Two lighthouses are 120 km apart. Lighthouse A is west of lighthouse B.

A ship is on a bearing of 075 º from lighthouse A and 290 º from lighthouse B.

In the space, draw a scale diagram to show the position of the ship.

Use a scale of 1 : 2 000 000. [4]

3 Sadhaana cycles on a bearing of 275 ° for 24 km.

She then cycles on a bearing of 220 ° for 8 km.

a In the space, make a scale drawing of Sadhaana’s journey. [3]

Use a scale of ‘1 cm represents 4 km’.

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b How far must Sadhaana now cycle to return to her starting point?

[2]

c On what bearing must Sadhaana now cycle to return to her starting point?

[1]

4 O is the point (0, 0), M is the point (18, 21) and N is the point (35, 25).

Circle the correct answer, A, B or C.

1
a The point that lies of the way along OM is A (12, 14) B (6, 7) C (15, 18)
3

4
b The point that lies of the way along ON is A (7, 5) B (30, 20) C (28, 20) [2]
5

5 O is the point (0, 0) and D is the point (32, 48). The points A, B, C and D are equally spaced
along the line OD. Work out the coordinates of C.

[3]

2
6 F is the point (2, 7) and H is the point (11, 13). G is the point that lies of the way along
3
FH.

Work out the coordinates of G.

[3]

7 The diagram shows shape A on a coordinate grid.

On the diagram, draw the image of A after each of these combinations of transformations.

a Reflection in the line x = 1,

 3
followed by the translation   .
 5 

Label the image B.

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

b Rotation 90° anticlockwise, centre (−2, 1),

followed by a reflection in the line y = −1.
Label the image C. [4]

8 The diagram shows triangles G, H, I and J on a coordinate grid.

a Describe the reflection that transforms shape G to shape H.

[1]
b Describe the translation that transforms shape G to shape I.

[1]
c Describe the rotation that transforms shape G to shape J.

[1]
d Describe a combined transformation that transforms shape I to shape J.

[2]
e Describe a combined transformation that transforms shape J to shape H.

[2]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

9 Enlarge the shape using a scale factor of 2 and centre of enlargement shown.

[2]

10 A rectangle, R, has a perimeter of 16 cm and an area of 16 cm2.

The rectangle is enlarged by a scale factor of 3 to become rectangle T. Work out:

a the perimeter of rectangle T

[1]

b the area of rectangle T.

[2]

11 The diagram shows shapes F and G.

Complete this statement:

Shape G is an enlargement of shape F, scale factor and

centre of enlargement at ( , ). [2]

[Total: 40 marks]
END OF TEST

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Name Date

Stage 9 End of unit 14 test

1 The table shows information about three prisms. Fill in the missing values in this table.

Prism Area of cross-section Length of prism Volume of prism

A 9 cm2 12 cm ____cm3

B 12 mm2 ____mm 60 mm3

C ____m2 8m 36 m3

[3]

2 Work out the volume of this prism.

[2]

3 Work out the volume of this cylinder. Give your answer correct to 3 s.f.

[2]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

4 A cylinder has a radius of 2.5 cm and a volume of 78.54 cm2.

Work out the height of the cylinder. Give your answer to the nearest centimetre.

[3]

5 A cylinder has a height of 35 mm and a volume of 15 834 mm3.

Work out the radius of the cylinder. Give your answer to the nearest millimetre.

[3]

6 The diagram shows a cylinder and a triangular prism.

Which shape has the greater surface area? Show your working.

[8]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST

7 For each of these shapes

i write down the number of planes of symmetry

ii draw the planes of symmetry onto the shape.

a i planes of symmetry

ii

b i planes of symmetry [2]

ii

[2]

[Total: 25 marks]

END OF TEST

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