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Cambridge Essentials Mathematics Core 7 GM1.1 Homework 1

Original Material © Cambridge University Press 2008 1

GM1.1 Homework 1

1 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?

2 ABCD is a rectangle.

Measure these lengths to the nearest 0.1 cm.

a AB b BC c AC

3 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 millimetre.

4 Match each measurement to a number and a unit from the boxes below.

4.4 cm

1.9 cm

L

MN4.7 cm

2.8 cm

S

P Q

R

A B

C D

4

9 14

21

143

cm

m mm

height of a girl

length of a brontosaurus

height of an elephant

width of a little finger nail

length of a pen

cm



5 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 width in centimetres.

b Write down the length in metres.

c Write down the height in millimetres.

3.4 cm

1.6 cm

5.2 cm



GM1.1 Homework 2

1 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.

2 The perimeter of a square is 64 cm.

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

What is the perimeter of one rectangle?

3 The perimeter of a rectangle is one metre. Each longer side is 34 cm.

What is the length of each shorter side?

4 Work out the perimeter of each figure.

a

b

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

She draws these shapes.

a Her teacher says two of these are

really the same. Which two?

b On centimetre squared paper,

draw another rectangle with a

perimeter of 18 cm which is

different from A, B, C and D.



GM1.2 Homework 1

1 The diagram shows the shapes drawn on a centimetre square grid.

Write down the area of each shape.

2 Work out the area of each rectangle.

a

b

c

3 a Write down the area of this rectangle.

b A square has the same area as this rectangle.

Find the perimeter of the square.

4 This shaded shape is drawn on a centimetre-square grid.

a What is the area of the shape?

b Draw a rectangle that has the same area as this shaded shape.

Write down the length and width of your rectangle.



5 The diagram below shows a square.

Two straight lines cut the square into four rectangles.

The area of one of the rectangles is shown.

a i What is the length of each side of the square, in millimetres?

ii Write the side length of the square in centimetres.

b i Work out the area of the rectangle marked X in square millimetres.

ii What is the area of the rectangle marked X in square centimetres?

6 Work out the area of each shape.

a b

c

d

6 cm



GM1.2 Homework 2

1 In each of these rectangular lawns flower beds have been cut out.

Find the area of the remaining lawn.

a

b

c

2 Find the area of each triangle.

a

b c

3 Work out the area of each shape.

a

b



4 Shona cut a rectangle, a square and a triangle from a rectangular piece of card.

What area of card is left?

5 Estimate the area of this island.

Each square on the grid represents 1 km2.

6 Tariq drew the shape below on square dotty paper.

The dots are 1 cm apart.

Work out the area of the shape, explaining your method.



GM2.1 Homework 1

1 Which label belongs to each of the angles below?

a

b c

d

2 a Use a protractor to measure each angle below.

i

ii

iii

iv

v

vi

b Describe each angle in part a using the labels from question 1.

obtuse angle reflex angleright angleacute angle



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

Jack Sarah Asmat Toby Nikki Max

128° 127° 126° 52° 127° 127°

a What do you think is the real size of the angle? Give reasons for your answer.

b Toby had a very different value from all the others. Why do you think this happened?

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

A

B

C

5 This is a symmetrical shape with 12 equal sides.

a Alicia turns the pointer from zero, clockwise through 210°.

Which number will the pointer be at now?

b Ray moves the pointer clockwise from number 3 to number 8.

Through how many degrees does the pointer turn?



GM2.1 Homework 2

1 Work out the size of each lettered angle.

2 Zara measured the angles in a triangle. She said ‘The angles are 40°, 50° and 100°.’

Explain why she cannot be correct.

3 Calculate the values of angles w, x, and y.



4 This diagram is drawn on isometric dotty paper.

a The triangle has three equal sides. Each of its angles is 60°.

Explain why.

b In the other shape, find the sizes of angles a, b and c.

5 The diagram shows a square.

The square is divided into triangles.

Three of the triangles are isosceles.

Work out the size of each lettered angle.

Cambridge Essentials Mathematics Core 7 GM2.2 Homework


GM2.2 Homework

1 Look at the street plan.

a Name the roads that are parallel to i Fairways ii Park Road

b Name the roads that are perpendicular to i Bracken Way ii Sandy Lane

2 These shapes are drawn on a triangular dotty grid.

a Which of the shapes have two pairs of parallel sides?

b Which shapes have no parallel sides?

c Name all the shapes.



3 Copy and complete the diagram so that the dotted line is a line of symmetry.

4 On this square grid, some squares are shaded to make

a pattern with exactly 2 lines of symmetry.

a Draw a similar grid and shade some squares to make

a pattern with exactly 1 line of symmetry.

b Now draw another similar gird and shade some squares

to make a pattern with exactly 4 lines of symmetry.

5 Write True or False for each statement

about quadrilateral ABCD.

a The quadrilateral is a rhombus.

b The quadrilateral has exactly

one line of symmetry.

c The quadrilateral has two pairs of

parallel sides.

d The coordinates of point A are (2, 5).

e The coordinates of point C are (–3, 2).

6 Draw x- and y-axes labelled from –6 to 6.

a Plot the points A (5, 1), B (2, 4) and C (–1, 1)

b What are the coordinates of D that would make ABCD a square?

c What are the coordinates of D that would make ABCD a kite?

d What are the coordinates of D that would make ABDC a parallelogram?

x–1

–2

–3

5

4

3

2

1

y

–2 –1 1 2 3 4 5 6

A

B

C

D

0


Original material © Cambridge University Press 2008 1

GM3.1 Homework 1

1 Which label matches each item?

a

b

c

d

2 Which label matches each item?

a

b

c

d

e

3 Find items at home which have these capacities. Find as many as you can for each one.

Use a measuring jug, or look at product labels.

a 500 ml b 350 ml c 1 litre

d 750 ml e 40 ml f 2 litres

4 Find items at home which have these masses. Find as many as you can for each one.

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

a 2 kg b 20 g c 200 g

d 500 g e 1 kg f 2 g

1.5 kg

40 g

4 kg

77 kg

145 g

250 ml

500 litres

8 litres

5 ml


Original material © Cambridge University Press 2008 1

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 Copy and complete.

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 = cl f 285 cl = litres


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

6 Which of these measurements is different from the other three?

0.6 m 60 mm 0.06 m 6 cm



GM3.2 Homework 1

1 The triangles shown are drawn on square dotty paper.

List all the triangles that are

a scalene b isosceles c acute-angled

d obtuse-angled e right-angled

2 Construct the triangle shown in the diagram.

Measure XZ and angle XZY.

3 Construct triangle ABC where AB = 4.7 cm, BC = 6.3 cm and angle ABC = 46°.

Remember to sketch the triangle first.

Measure AC and angle BAC. 4 FGH is an isosceles triangle. Angle FGH = 108°.

Two of the sides of the triangle have length 8.2 cm.

a Show this information on a sketch.

b Find the size of angle GFH.

c Find the length of the third side.

AC

B

D



GM3.2 Homework 2

1 Construct the triangle shown in this sketch.

Measure RS.

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 This diagram represents a triangular plot of land.

Construct the triangle using 1 mm to represent 1 m.

Work out the perimeter of the plot.

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

b Measure these lengths on your diagrams.

i AB ii AC iii XY



GM3.3 Homework 1

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

a Copy and complete the net on a 1 cm grid.

b Which of the labelled points will meet B on the completed cuboid?

c Which of the labelled points 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 The sketch shows the net for a solid shape.

a What name is given to this solid shape?

b Use the diagram to write down these lengths.

i AB ii AC iii CD

c Work out the surface area of the solid.

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.

Calculate the perimeter of the net.

3 The diagram shows a net for a tetrahedron with flaps a, b and c.

Copy the net and use the letters a, b and c to label the edges that match the flaps.



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 1 square face.

2 Copy and complete these sketches of prisms.

3 The diagram shows 2 cubes forming a 1 by 1 by 2 cuboid.

Copy the diagram onto isometric dotty paper.

Extend it to show a 2 by 3 by 2 cuboid made from cubes.

4 Here are some 1 cm cubes drawn on an isometric grid.

a How many cubes are needed to build the shape shown?

b What is the surface area of the shape?

c Describe the shape that can be made from 8 cubes and

has a surface area of 24 cm2.



GM4.1 Homework

1 Copy the diagrams. Reflect each shape in the mirror line m.

a

c

b

d

2 The diagram shows a kite ABCD

reflected in a mirror line.

Copy the diagram.

a Point A stays in the same place.

Mark B′, the image of B after

reflection.

b Draw the mirror line on your diagram

as a dotted line.

c Write the equation of the mirror line.

d Write down the coordinates of C and those of C′, the point where C is reflected to.

What do you notice about these two pairs of coordinates?

x

8

7

6

5

4

3

2

1

y

1 2 3 4 5 6 7 8

A

B

C

D

0

m

m

m

m



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

Copy the diagram, label rectangle A′B′C′D′ and

draw the mirror line as a dotted line.

4 Copy this diagram.

a Reflect triangle PQR in the

x-axis and write down the

coordinates of the image of

point P.

b Reflect triangle PQR in the

y-axis and write down the

coordinates of the image of

point Q.

c Reflect triangle PQR in the

line y = –x and write down

the coordinates of the

image of point R.

5 a (6, –4) maps onto (–2, –4) under a reflection in which line?

b Which line is (–3, 5) reflected in to map to (–3, –7)? c (–3, –5) is reflected in y = x. What are the coordinates of the image?

6 April has reflected her name in a mirror line to make a logo.

Write your name in capitals and reflect them to make your own logo.

A B

C D



GM4.2 Homework

1 Copy the diagrams below.

Show the new position of each shape after a clockwise rotation of 90° with centre P.

a

b

c

2 Each diagram shows a rotation that maps triangle A to triangle B. Copy the diagrams.

a Mark the centre of rotation in each with a cross.

b Describe the rotation for each one.

3 Copy the diagram.

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.

5

4

3

2

1

–1

–2

–3

–4

–5

A

y

–5 –4 –3 –2 –1 1 2 3 4 50 x

B A

A

BA

B

×P ×

P

× P



GM4.3 Homework

1 Copy the diagram.

Draw the image of shape P after a translation of

4 squares to the left and 2 squares up.

2 Write down the translation that maps

triangle A onto triangle B.

3 Copy the diagram.

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

b Label your image A′B′C′D′.

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

d What translation would map A′B′C′D′ to ABCD?

–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

A

B

P



4 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′.

5 A translation maps (2, 4) to (–3, –3).

a Describe the translation.

b Find the image of (1, –2) under the same translation.

c Which point maps onto (3, –1) under this translation?

6 Interesting patterns can be made by translating a shape many times.

Draw your own translation pattern on squared paper, then colour it.

–1

–2

–3

–4

4

3

2

1

–5 –4 –3 –2 –1 1 2 3 4 50 x

y

A

B

CA′



GM5.1 Homework

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

2 Show how these shapes can be put together to make a single shape with rotational symmetry of order

a 4 b 2

3 Make two copies of this shape.

a On the first, shade 3 more squares to make a shape with rotational symmetry of order 4.

b On the second, shade 3 more squares to make a shape

with rotational symmetry of order 2.

4 This L-shape is made using 3 squares.

Two L-shapes can be used without overlap, to make a shape with exactly one line of symmetry.

a Draw a different shape with exactly one line of symmetry using two L-shapes.

b Draw a shape made from two L-shapes which has two lines of symmetry.

This shape is made from two L-shapes. It has rotational symmetry of order 2.

c Draw a different shape which has rotational symmetry of order 2 using two L-shapes.

d Draw a shape made from two L-shapes which has two lines of symmetry and rotational symmetry of order 2. It must be different from any of the shapes you have drawn so far.



5 Look at these shapes.

Copy the table and write the letter of each shape in the correct place.

The first one has been done for you.

Number of lines of symmetry 0 1 2 3 4

1

2

3 A

Order of rotational symmetry

4

6 The pattern shows part of a wallpaper border that continues in both directions.

a What translation would map the pattern onto itself?

b Describe a rotation that would map the pattern onto itself.

It might help to draw part of the pattern.

A B C

D E F



GM5.2 Homework 1

1 Lisa cut out a square. She 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 different shapes she could end up with.

(Include all the shapes with different numbers of sides or different symmetry.)

2 This is a net of six squares that can be folded to make a cube.

Draw all the nets of six squares which make a cube.

3 The large cube shown is made up from 27 smaller cubes.

Imagine that the large cube is dipped into yellow paint,

which coats just the outside faces.

If the large cube were then broken up into smaller cubes

again, how many small cubes would have 1 yellow face?

How many would have no yellow faces?

How many with 2 and how many with 3 yellow faces?

Investigate for larger cubes.



GM5.2 Homework 2

1 Here are three identical right-angled triangles PQR.

Part of each triangle has been shaded.

S is the midpoint of PR, and T is the midpoint of QR.

Which shaded part has the greatest area?

2 This pattern has rotation symmetry of order 6.

Find the size of angle w.

Show your reasoning.

3 Jason is trying to draw this triangle using just a pencil, ruler, protractor and compass.

Will he be able to draw it?

Explain your answer.

R

P

Q R

P

Q R

P

Q

S S

T

A B C

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