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Cambridge Essentials Mathematics Support 7 GM1.1 Homework 1

Original material © Cambridge University Press 2008 1

GM1.1 Homework 1

1 Measure the length of this line.

Give your answer in a centimetres and millimetres b centimetres c millimetres

2 The diagram shows Paul’s key.

a How long is Paul’s key?

b Julie’s key is 6 mm shorter than Paul’s key. How long is Julie’s key?

3 ABCD is a rectangle.

Measure these lengths to the nearest 0.1 cm.

a AB b BC c AC

4 a Draw each diagram as accurately as you can.

Use the measurements shown.

b Measure the length of SQ in centimetres to the nearest 0.1 cm.

c Measure the length of LM in millimetres to the nearest 1 mm.

4.4 cm

1.9 cm

L

MN

cm

4.7 cm

2.8 cm

S

P Q

R

A B

CD



5 a Write each length in centimetres.

14 cm 23 mm 0.4 m 0.6 cm 83 cm 3 mm

b Put the original lengths in order of size, starting with the smallest.

6 The diagram shows a match box.

Its length is 5.2 cm.

Its width is 3.4 cm.

Its height is 1.6 cm.

I join two matchboxes in different ways.

a Write down the

length in centimetres.

b Write down the

width in centimetres.

c Write down the

height in millimetres.

3.4 cm

1.6 cm

5.2 cm



GM1.1 Homework 2

1 The perimeter of a square is 64 cm.

a What is the length of each side of the square?

The square is cut in half to make two identical rectangles.

b What is the perimeter of one rectangle?

2 What is the perimeter of each shape?

a

b

c

3 A rectangle measures 3 cm by 6 cm.

a Work out the perimeter of the rectangle.

b Silvio uses five of these rectangles to make a larger rectangle.

Work out the perimeter of this larger rectangle.



4 Two rectangles are drawn on a centimetre square grid.

Which rectangle has the larger perimeter, A or B? Explain how you know.

5 Work out the perimeter of each shape.

a

b

6 Erin is told to draw four different rectangles, each with a perimeter of 18 cm.

She draws these shapes. Each square represents one square centimetre.

a Her teacher says two of these are really the same. Which two?

b Draw another rectangle with a perimeter of 18 cm.

Make it different from A, B, C and D.

A

B

CD



GM1.2 Homework 1

1 Find the area of each shape. Each square on the grid represents 1 cm2.

2 Estimate the area of this island.

Each square on the grid represents 1 km2.

a b c

d



3 Work out the area of each shape. area of rectangle = base × height

a

b

c

4 a Write down the area of this rectangle.

b A square has the same area as this rectangle.

Work out the length of the sides.

c Find the perimeter of the square.

5 This shaded shape is drawn on a centimetre square grid.

a What is the area of the shape?

b Draw a square which has the same area as the shaded shape.

Write down the length of each side of the square.

c Now draw a rectangle which has the same area as the shaded shape.

Write down the length and width of your rectangle.

4 cm

16 cm

10 mm

15 mm

20 m

20 m

3 cm

9 cm



GM1.2 Homework 2

1 Complete this area calculation.

Area A = 9 cm × cm = cm2

Area B = cm × cm = cm2

Total area = cm2

2 Look at this shape.

a Rectangle A is 5 cm wide. Its height is missing.

Work out the missing height.

b Rectangle B is 5 cm high. Its width is missing.

Work out the missing width.

c Complete this area calculation.

Area A = 5 cm × cm = cm2

Area B = 5 cm × cm = cm2

Total area = cm2



3 Work out the area of each shape.

a

b

4 Dan has a rectangular piece of card.

It measures 20 cm by 12 cm.

a What is the area of Dan’s piece of card?

b Dan cuts a 10 cm by 8 cm

rectangle out of his card.

What area of card does Dan

cut out?

c What area of card is left?

5 The plan shows a garden.

It is 30 m by 20 m.

There is a flower bed in the garden.

It measures 15 m by 10 m.

The rest of the garden is lawn.

Find the area of the lawn.



GM2.1 Homework 1

1 Which label belongs to each of the angles below?

a

b c d

2 Describe each angle below using the labels from question 1.

a

b

c

d

e

f

obtuse angle reflex angleright angleacute angle



3 Measure each angle in question 2 using a protractor.

4 Six pupils all measured the same angle. These are their results.

Jack Sarah Asmat Toby Nikki Max

128° 127° 126° 53° 127° 127°

a What do you think is the real size of the angle? Explain your answer.

b One of the pupils had a very different value from all the others.

Why do you think this happened?

5 Which of these angles is the biggest? Explain your answer.

a

b

c

6 a Use a protractor to draw these angles.

i 30° ii 130° iii 230° iv 330° v 88° vi 302°

b Which of these angles are reflex?



GM2.1 Homework 2

1 Work out the value of each letter. Show your working.






76°

64° a b c

g

f

e d

68°



GM2.2 Homework 1

1 The dots on each circle are equally spaced.

a Join three dots to make an equilateral triangle.

b Join three dots to make an isosceles triangle.

c Join three dots to make a scalene triangle.



2 Alfie drew all these shapes using 6 squares.

A

B

C

D

E

F

G

H

I

J

a Which of Alfie’s shapes have no lines of symmetry?

b Which have just 1 line of symmetry?

c Which have 2 lines of symmetry?

3 Complete each diagram so that the dotted line is a line of symmetry.

a

b

4 Look at the street plan.

a Which roads are parallel to

i Fairways?

ii Park Road?

b Which roads are perpendicular to

i Bracken Way

ii Sandy Lane?



GM2.2 Homework 2

1 These shapes are drawn on a triangular dotty grid.

a Which shapes have two pairs of parallel sides?

b Which of the shapes have no parallel sides?

c Name all the shapes.

2 a Plot the points

(0, 4), (3, 1) and (6, 4).

b What are the coordinates

of a fourth point that

would make

i a square?

ii a parallelogram?

1 2 3 4 5 6 7 8 9

987654321

0 x

y



3 a Plot the points A(7, 2), B(–2, –7), C(–4, 1) and D(1, 6).

Join the shape ABCD.

b What shape have you drawn?

c Does it have a line of symmetry?

d Does it have a pair of parallel lines?



GM3.1 Homework 1

1 Choose the correct units from the box for each of these.

a The length of a pen is 14____.

b

The width of a little

finger nail is 9 ____.

c

The height of an elephant is 4 ____.

d

The length of a

brontosaurus is 21 ____.

e

The height of a girl is 143 ____.

2 Which label matches each item?

a

b

c d

3 Which label matches each item?

a

b

d

e

c

mm cm m

145 g1.5 kg 77 kg4 kg40 g

250 ml 5 ml500 litres8 litres



4 Make a list of items at home which have these approximate capacities.

Use a measuring jug or look at product labels.

Find as many as you can for each measurement.

a 500 ml

b 350 ml

c 1 litre

d 750 ml

e 40 ml

f 2 litres

5 Make a list of items at home which have these approximate masses.

Use kitchen scales, bathroom scales or look at product labels.

Find as many as you can for each measurement.

a 2 kg

b 20 g

c 200 g

d 500 g

e 1 kg

f 2 g

6 Sheila thinks that some of the quantities on

this shopping list don’t make sense.

Which ones are they? Explain your answers.

Shopping list 1 kg of potatoes 1.5 g of milk 200 kg of cheese 2 litres of apples 300 g of tomatoes 100 ml of toothpaste



GM3.1 Homework 2

1 What number is shown by each arrow?

a

b

c

d

2 This dial shows the speed of a motor scooter.

The speed is measured in miles per hour.

How fast is the motor scooter travelling?

3 Measure the lengths of these lines. Give your answers in centimetres.

a _________________________

b ________________

c ___________________



4 Complete these conversions.

a 14 cm = ____mm b 35 mm = ____cm c 165 cm = ____m

d 5.7 m = ____cm e 3.28 m = ____cm f 0.6 m = ____cm


a 350 ml = ____litres b 58 cl = ____ml c 593 ml = ____cl

d 5.7 litres = ____ml e 0.8 litres = ____ml f 285 cl = ____litres


a 685 g = ____kg b 5.4 kg = ____g c 70 g = ____kg

7 Write these length in order. Start with the shortest.

65 mm 1.4 m 856 cm 5.4 cm 0.62 m 265 mm 17 cm 4 mm

8 Write these times in the 24-hour clock.

a 9:44 a.m. b 9:21 p.m. c 11:15 p.m.

9 Write these times in the 12-hour clock.

a 09:45 b 19:55 c 11:20

10 It takes Lev 25 minutes to walk from his home to the railway station.

He wants to catch the 16:12 train.

What time should he leave home? Give your answer in the 12-hour clock.

11 Katja watches a film. It starts at 2:35p.m. and finishes at 4:22p.m.

Work out the length of the film in a minutes b hours and minutes



GM3.2 Homework 1

1 These triangles are drawn on square dotty paper.

List the triangles that are:

a scalene b isosceles c acute-angled

d obtuse-angled e right-angled

2 Use the information in this sketch to construct

the triangle. Use a ruler and protractor.

Measure XZ and angle XZY.

3 Construct triangle XYZ.

Use a ruler and protractor.

Measure XZ and angle XZY.

4 Construct triangle ABC where AB = 3 cm, BC = 7 cm and angle ABC = 46°.

Remember to sketch the triangle first. Measure AC and angle BAC.

AC

B

D



GM3.2 Homework 2

1 a Use the information in these sketches to construct the triangles.

b Measure these lengths on your diagrams.

i AB ii AC iii XY

2 Construct triangle LMN where LN = 5.8 cm, angle MLN = 35° and

angle MNL = 58°. Remember to sketch the triangle first.

Measure ML and MN.

3 Construct triangle FGH as shown and find its perimeter.



GM3.3 Homework 1

1 The diagram shows a partly completed net of a cuboid.

Each square represents one square centimetre.

a Complete the net.

b Which labelled point will meet B on the completed cuboid?

c Which labelled point will be furthest from A on the completed cuboid?

d What are the dimensions of the cuboid?

e Work out the surface area of the cuboid.

2 This is the net for a solid shape.

a What name is given to this solid shape?

b Use the diagram to find these distances.

i AB ii AC iii CD

c Work out the area of triangle ABC.

d Work out the surface area of the solid.

13 cm

10 cm

12 cm

5 cm A

B

C

D

F

E

D

G H

A B C



GM3.3 Homework 2

1 The cross-section of this prism is shown

shaded.

a What shape is the cross-section?

b Show that the number of faces (F),

vertices (V) and edges (E) of the prism

obey the formula V + F – E = 2.

2 This is a net for

the solid shape in

question 1.

Find the lengths

labelled a, b and c.

3 Which of the diagrams below are nets for a tetrahedron?

3 cm

6 cm

4 cmc

b

a

5 cm

Cambridge Essentials Mathematics Support 7 GM3.4 Homework


GM3.4 Homework

1 Match each object to one of the descriptions.

a It has 3 rectangular faces and 2 triangular faces.

b Each face is a square and there are 6 of them.

c Each face is a rectangle and it has 6 of them.

d Each face is a triangle and there are 4 of them.

e It has 4 triangular faces and one square face.

2 Complete these drawings of prisms.

3 Extend the diagram to show a cuboid

made from two layers of 6 cubes.

triangular prism tetrahedron cube cuboid

square-based pyramid



GM4.1 Homework 1

1 Reflect each shape in the mirror line m.

a b

c d

e

m

m

m

m

m



2 Draw in the missing mirror lines.

b a

c

3 The diagram shows a kite ABCD reflected in a mirror line.

a Draw the mirror line on your diagram as a dotted line.

b Which point in ABCD stays the same?

c Mark B′, the reflection of B, on your diagram.

Write down the coordinates of B and those of B′.

x

8

7

6

5

4

3

2

1

y

1 2 3 4 5 6 7 8

A

B

C

D

0



GM4.1 Homework 2

1 Rectangle ABCD is reflected to rectangle A′B′C′D′.

a Label rectangle A′B′C′D′.

b Draw the mirror line as a dotted line.

2 a The image of R(6, 2) after reflection in the x-axis is R′(6, –2).

Reflect P and Q in the x-axis and label the images P′ and Q′.

b Write down the coordinates of P′ and Q′.

c Complete the triangle P′Q′R′.

d The reflection of P in the line x = 2 is P″(–1, 4).

Reflect Q and R in the x = 2. Label the images Q″ and R″.

e Write down the coordinates of Q″ and R″.

f Complete the triangle P″Q″R″.

87654321

–1–2–3–4–5–6–7–8

x

y

x = 2

PQ

R

P′′ ×

–8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8

R′ ×

0

A B

CD



GM4.2 Homework

1 Here is a shape.

I turn the shape through 90° anticlockwise.

Which of these diagrams shows the shape after the turn?

2 Draw each shape after a clockwise rotation of 90° with centre P.

a

c

b

D C B

A

× P

× P

× P



3 Each diagram shows a rotation that maps triangle A to triangle B.

Mark the centre of rotation in each with a cross.

Describe the rotation for each one.

a b

c

4 a Rotate shape A through 90° anticlockwise with centre (0, 0).

Label the image B.

b Rotate shape A through 180° with centre (0, 0). Label the image C.

A

B

B A

A

B

5

4

3

2

1

–1

–2

–3

–4

–5

A

y

–5 –4 –3 –2 –1 1 2 3 4 50 x



GM4.3 Homework 1

1 Draw the image of shape P after a translation

of 4 squares to the left and 2 squares up.

Label the image Q.

2 Write down the translation that maps triangle A onto triangle B.

3 a Translate ABCD 6 squares to the right and 7 squares down.

b Label your image A′B′C′D′.

c Write the coordinates of A′, B′, C′ and D′.

P

A

B

–1

–2

–3

–4

–5

–6

6

5

4

3

2

1

–5 –4 –3 –2 –1 1 2 3 4 50 x

y

A

B

C

D



4 In the diagram, triangle PQR is mapped to triangle P′Q′R′ by a translation.

a Describe the translation that maps triangle PQR to triangle P′Q′R′.

b What translation would map triangle P′Q′R′ to triangle PQR?

5 In the diagram, triangle ABC

is mapped to triangle A′B′C′

by a translation.

a Describe the translation.

b Find the coordinates

of B′ and C′.

–8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

x

y

0

R

QP

R′

Q′P′

–1

–2

–3

4

3

2

1

–5 –4 –3 –2 –1 1 2 3 4 50 x

y

A

B

C A′



GM4.3 Homework 2

1 a Plot the points A(2, 1), B(4, –2), C(1, –4).

Join them to make triangle ABC.

b Translate triangle ABC 5 squares to the left and 6 squares up.

Label the image A′B′C′.

c Write down the coordinates of A′, B′ and C′.

d Triangle A′B′C′ is mapped to triangle A′′B′′C′′ by a translation.

The coordinates of A′′ are (–7, 7).

i Describe the translation that maps triangle A′B′C′ to A′′B′′C′′.

ii Describe the translation that maps triangle A′′B′′C′′ to ABC.



GM5.1 Homework

1 Write down the order of rotational symmetry of each shape.

a b

c d

2 Which of these shapes does not have rotational symmetry?

3 a Shade 3 more squares in this

diagram to make a shape with

rotational symmetry of order 4.

b Shade 3 more squares in this

diagram to make a shape with

rotational symmetry of order 2.



4 a Reflect the shape in the dotted line.

b Check that the dotted line is a line of

symmetry for the completed shape.

c Draw on the other line of symmetry for

the completed shape.

5 Mark on all the lines of symmetry for these shapes.

6 Match each statement to a letter in the box.

a This letter has line symmetry

but no rotational symmetry.

b This letter has rotational symmetry

but no line symmetry.

c This letter has both rotational symmetry

and line symmetry.

d This letter has neither line symmetry

nor rotational symmetry.

H

N

R

W



GM5.2 Homework 1

1 Lisa cut out a square. She then cut off the four corners.

Here are two of the shapes she could have made.

an irregular

octagon an irregular heptagon

Draw and describe all the shapes she could have ended up with.

2 This shape is made by joining the top

right-hand corner of the square to the

middle of each of the opposite sides.

This divides the square into 4 triangles, A, B, C, and D.

a What fraction of the area of the square is A?

Show how you found this answer.

b What fraction of the area of the square is B?


c What fraction of the area of the square is C?


d What fraction of the area of the square is D?




GM5.2 Homework 2

1 In this diagram, 36 square-centimetre tiles are fitted together to make a

rectangle 9 cm long and 4 cm wide.

What is the perimeter of this rectangle?

Draw different rectangles that you could make using the 36 tiles.

Find the perimeter of each one.

Which one has the smallest perimeter? What is special about it?

2 a How many degrees does the minute hand

of a clock turn through in 10 minutes?

Show your method.

b How many degrees does the hour hand

of a clock turn through in 4 hours?

c How many degrees does the hour hand of a clock turn through if the

minute hand turns through 180°?

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