Cambridge IGCSE™

* 1 0 4 3 5 8 9 5 5 9 *

MATHEMATICS 0580/31
Paper 3 (Core) October/November 2023

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 104.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Any blank pages are indicated.

DC (CJ/CB) 318217/2
© UCLES 2023 [Turn over
 2

1 (a) Write the number six and a half million in figures.

................................................. [1]

(b) Write 37 508 correct to the nearest thousand.

................................................. [1]

(c) 6 9 100 28 31 1000 32 36

From this list of numbers, write down

(i) a factor of 18

................................................. [1]

(ii) a multiple of 12

................................................. [1]

(iii) a square number

................................................. [1]

(iv) a prime number

................................................. [1]

(v) an irrational number.

................................................. [1]

(d) Put one pair of brackets in each statement to make it correct.

(i) 24 - 4 # 3 + 2 = 62 [1]

(ii) 24 - 4 # 3 + 2 = 4 [1]

3
(e) Write as a decimal.
4

................................................. [1]

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3
(f) Work out of 126.
7

................................................. [1]

(g) Write down the value of the reciprocal of 0.5 .

................................................. [1]
2 1
(h) Without using a calculator, work out 5 - 2 .
3 5
You must show all your working and give your answer as a mixed number in its simplest form.

................................................. [3]

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2 (a) The diagram shows a circle.

NOT TO
SCALE

(i) The diameter of this circle is 168 mm.

Write down the radius of this circle.

.......................................... mm [1]

(ii) On the diagram, draw a chord of this circle. [1]

(b) The scale drawing shows the position of ship A and the position of ship B.
The scale is 1 cm represents 6 km.

North

North

Scale : 1 cm to 6 km

Another ship, C, is 45 km from ship B on a bearing of 124°.

(i) On the scale drawing, mark the position of ship C. [2]

(ii) Find the actual distance of ship C from ship A.

........................................... km [2]

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(c) (i) Show that the interior angle of a regular octagon is 135°.

[1]

(ii)

NOT TO
SCALE

Show that two regular octagons and a square meet at a point without any gaps.

[1]

(d)
E
F NOT TO
49°
SCALE

The diagram shows points D, E and F on the circumference of a circle.

DF is a diameter of the circle.

Find angle EDF.

Angle EDF = ................................................. [2]

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 6

3 (a) The bar chart shows the country in which each of 80 students live.

24

20

16

Frequency 12

0
Australia Brazil China India USA
Country

(i) How many of these students live in Brazil?

................................................. [1]

(ii) In which country do the largest number of these students live?

................................................. [1]

(iii) How many more of these students live in China than live in Australia?

................................................. [1]

(iv) Find the percentage of these students who live in the USA.

.............................................. % [2]

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(b) In Hobart, the temperature at 8 am was -3 °C and the temperature at 3 pm was 7 °C.

(i) Find the difference in the temperatures between 8 am and 3 pm.

............................................ °C [1]

(ii) The temperature at 10 pm was 12 °C lower than at 3 pm.

Find the temperature at 10 pm.

............................................ °C [1]

(c) The table shows the favourite language that each of 80 students studies.

Language Frequency
French 12
Spanish 26
English 42
Total 80

Complete the pie chart to show this information.

[4]

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 8

4 (a) The diagram shows a cuboid.

NOT TO
2 cm
SCALE

3 cm
5 cm

(i) On the 1cm 2 grid, complete the net of the cuboid.

One face has been drawn for you.

[3]

(ii) Calculate the surface area of the cuboid.

......................................... cm 2 [2]

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 9

(b) The diagram shows two solids: a cube and a right-angled triangular prism.

NOT TO
SCALE

4 cm
6 cm 9 cm
x cm

Both solids have the same volume.

Calculate the value of x.

x = ................................................ [4]

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 10

5 A railway line has three stations, Town, Port and Cove.

Train A leaves Town for Cove and train B leaves Cove for Town.
Both trains stop at Port.

25
Cove B
Distance from 20
Town (km)
15
Port
10

5
A
Town 0
14 00 14 10 14 20 14 30 14 40 14 50
Time

(a) Write down the time that train B leaves Cove.

................................................. [1]

(b) Write down how long train A stops at Port.

.......................................... min [1]

(c) How many more minutes does train A take to complete the whole journey than train B?

.......................................... min [2]

(d) Write down the time that the two trains pass each other.

................................................. [1]

(e) Work out the average speed of train A between Town and Cove in kilometres per hour.

......................................... km/h [3]

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6
y

10
9
8
7
6
5
4
A
3
2
1
B
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 x
-1
C
-2
-3
-4
-5
-6

(a) Describe fully the single transformation that maps triangle A onto triangle B.

.....................................................................................................................................................

..................................................................................................................................................... [2]

(b) Describe fully the single transformation that maps triangle A onto triangle C.

.....................................................................................................................................................

..................................................................................................................................................... [3]

(c) On the grid, draw the image of triangle A after a reflection in the line y = 6 . [2]

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7 (a) Simplify.
5a + 3b + 2a - 4b

................................................. [2]

(b) P = 8x + 3y

Find the value of x when P = 21 and y =-5.

x = ................................................ [2]

(c) Make v the subject of the formula S = kv 2 .

v = ................................................ [2]

(d) Multiply out and simplify.

(x - 3) (x + 5)

................................................. [2]

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(e) Nasser has x marbles.

Selina has 15 more marbles than Nasser.
Hanif has 3 times as many marbles as Selina.
In total they have 150 marbles.

Find the value of x.

x = .................................................. [5]

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8
y
L
6
5
4
3
2
1

-3 -2 -1 0 1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
- 10

(a) Find the equation of line L in the form y = mx + c .

y = ................................................ [2]

(b) (i) On the grid, draw the line y = x . [1]

(ii) Write down the coordinates of the point where the line y = x intersects line L.

( ...................... , ...................... ) [1]

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8
(c) (i) Complete the table of values for y = .
x

x −5 −4 −3 −2 −1 1 2 3 4 5
y −1.6 −2.7 2.7 1.6
[3]
8
(ii) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5.
x

y
8

0 x
-5 -4 -3 -2 -1 1 2 3 4 5
-1

-2

-3

-4

-5

-6

-7

-8
[4]

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 16

9 (a) Pure gold costs $42 per gram.

The fraction of pure gold in an object is measured in carats.

1
One carat means of the mass of an object is pure gold.
24
Henry buys a 9-carat gold bracelet weighing 16 g.
The price of the bracelet is $204.

Is the price of the bracelet more or less than the cost of the pure gold in it?
You must show your working.

[4]

(b) A clock made of metals has a mass of 1080 g.

The mass of each metal in the clock is in the ratio
copper : zinc : other metals = 21 : 14 : 1.

Calculate the mass of copper in this clock.

.............................................. g [2]

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(c) There are 110 people in a group.

G = { people who own gold jewellery }
S = { people who own silver jewellery }

18 people own both gold jewellery and silver jewellery.

46 people own gold jewellery.
11 people own no gold jewellery and no silver jewellery.


G S

(i) Complete the Venn diagram. [2]

(ii) Write down n (G + S ) .

................................................. [1]

(iii) One of the 110 people is chosen at random.

Write down the probability that this person owns gold jewellery but not silver jewellery.

................................................. [1]

(d)

E F

Use set notation to describe the shaded region.

................................................. [1]

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 18

10 (a)

P
21.4 cm
14.4 cm
9.6 cm NOT TO
SCALE

Q 12.8 cm R V W

Triangle PQR is mathematically similar to triangle UVW.

Calculate VW.

VW = ........................................... cm [2]

(b) ABC is a right-angled triangle.

A
NOT TO
9.1 cm SCALE
3.5 cm

B C

Calculate BC.

BC = ........................................... cm [3]

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 19

(c) DEF is a right-angled triangle.

D
8.4 cm NOT TO
SCALE
35°
E F

Calculate EF.

EF = ............................................cm [2]

(d) JKL is a right-angled triangle.

J 10 cm
L
NOT TO
8 cm SCALE

Calculate angle JKL.

Angle JKL = ................................................ [2]

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BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2023 0580/31/O/N/23

 Cambridge IGCSE™
* 7 7 3 3 6 3 5 4 6 8 *

MATHEMATICS 0580/32
Paper 3 (Core) October/November 2023

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 104.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

DC (CE/SG) 318305/2
© UCLES 2023 [Turn over
 2

1 (a) The bar chart shows the number of goals scored by a team in each of 5 months.

22
20
18
16
14
12
Frequency
10
8
6
4
2
0
Sept Oct Nov Dec Jan Feb
Month

(i) In February, 12 goals are scored.

Complete the bar chart. [1]

(ii) How many more goals were scored in January than in October?

................................................. [1]

(b) Find the range of the number of goals scored.

................................................. [1]

(c) (i) The team shop is open from 09 00 to 17 15 on Monday to Friday only.

Work out how long the shop is open each week.

Give your answer in hours and minutes.

 ...................h ...................min [3]

(ii) Brunobuysashirtfor$36andascarffor$12.25.
He pays with a $50 note.

Work out how much change he receives.

$ ................................................ [2]

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 3

(d)
Ticket prices

Adult $35
Child $20
Senior $25

(i) Calculatethecostof150adulttickets,70childticketsand30seniortickets.

$ ................................................  [3]

(ii) Calculate the percentage of these tickets that are senior tickets.

............................................. % [2]

(e) A game starts at 15 00.

The team plays for 90 minutes.
There is also a break of 15 minutes.

Find the time the game ends.

................................................. [2]

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2 (a) (i)

Write down the mathematical name for this polygon.

................................................. [1]

(ii)

Write down the mathematical name for this quadrilateral.

................................................. [1]

(iii)

(a) Write down the mathematical name for this type of angle.

................................................. [1]

(b) Measure the size of this angle.

................................................. [1]

(b)

Draw the lines of symmetry on this rectangle. [2]

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 5

(c) Acuboidmeasures6cmby3cmby2cm.

(i) Work out the volume of the cuboid.

......................................... cm 3 [1]

(ii) Draw a net of the cuboid on the 1 cm 2 grid.

One face has been drawn for you.

 [3]

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3 (a) Write the number fourteen thousand and ninety-seven in figures.

................................................. [1]

(b) Write down a common multiple of 17 and 5.

................................................. [1]

(c) Write 0.25 as a percentage.

............................................. % [1]

(d) Find the value of

(i) 75

................................................. [1]

(ii) 80 .

................................................. [1]
5
(e) Ranjit buys some plants and sells of them.
11
He sells 190 plants.

Work out how many plants he buys.

................................................. [2]

(f) Factorise completely.

15x 3 y - 3x

................................................. [2]

(g) Make n the subject of the formula V = 3n + t .

n = ................................................ [2]

(h) 7 15 ' 7 x = 7 9

Find the value of x.

x = ................................................ [1]

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4 (a) Complete the table of values for y = x 2 - 4x - 2 .

x -2 -1 0 1 2 3 4 5

y 3 -2 -5 -5 -2 3
[2]

(b) On the grid, draw the graph of y = x 2 - 4x - 2 for - 2 G x G 5.

y
10

-2 -1 0 1 2 3 4 5 x
-1

-2

-3

-4

-5

-6
[4]

(c) Use your graph to solve the equation x 2 - 4x - 2 = 0 .

x = ................... or x = ................... [2]

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5 Heidi records the colour of each of 500 cars crossing a bridge.

The pie chart shows some of this information.

Grey

Red

Other

(a) How many cars are red?

................................................. [1]

(b) 35carsaregrey.

Show, by calculation, that the sector angle for grey is 25.2°.

[1]

(c) 175 cars are white and 150 cars are black.

Complete the pie chart to show this information.

[2]

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 9

(d) Find the probability that a car chosen at random is not grey.

Give your answer as a fraction in its simplest form.

................................................. [2]

(e) Another320carscrossthebridge.

Howmanyofthese320carsareexpectedtobewhite?

................................................. [2]

(f) Heidi also records the number of people in each car crossing the bridge for one hour.

Number of people Frequency

1 20
2 6
3 0
4 15
5 8
6 12

Calculate the mean.

.................................................  [3]

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6 (a) Simplify.
a + 4a - 3a

................................................. [1]

(b) Simplify.
8b - 4 # 7b

................................................. [1]

(c)

4x + 3 x+7

3x - 9 NOT TO
SCALE
9x + 8

7x + 3

The perimeter of this shape is equal to the perimeter of a square.

Findanexpressionforthelengthofonesideofthesquare.
Give your answer in its simplest form.

................................................. [4]

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 11

(d) Victoriabuys5cupsofteaand4cakesfor$15.69.
Isabellabuys3cupsofteaand7cakesfor$17.97.

Write down a pair of simultaneous equations and solve them to find the cost of one cup of tea and
the cost of one cake.
You must show all your working.

Tea $ ................................................

Cake $ ................................................  [6]

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7 Elize, Lily and Marco start a business.

(a) Elize invests $5000.

Lily invests $8000.
Marcoinvests$3000.

After one year they make a profit of $40 000.

They share this profit in the ratio of their investments.

Work out how much they each receive.

Elize $ ................................................

Lily $ ................................................

Marco $ ................................................  [3]

(b) (i) Lily buys 20 rolls of ribbon.

8arered,6areblue,4areyellowand2arepink.
A roll of ribbon is chosen at random.

On the probability scale, draw an arrow ( ) to show the probability that this roll is

(a) yellow

0 0.5 1
[1]

(b) not red

0 0.5 1
[1]

(c) green.

0 0.5 1
[1]

(ii) The length, l m, of a roll of ribbon is 120 m, correct to the nearest metre.

Complete this statement about the value of l.

................... G l 1 ................... [2]

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 13

(c) Elize buys some picture frames.

The frames cost $5.80 each in New York and 4.50 euros each in Paris.
Theexchangerateis1euro=$1.37.

Calculate the difference in the cost in euros.

Give your answer correct to 2 decimal places.

........................................euros [3]

(d) Elize buys a framed picture.

(i)
18 cm

NOT TO
18 cm SCALE

The picture is a circle with diameter 18 cm.

The frame is a square of side length 18 cm.

Calculate the shaded area.

......................................... cm 2  [3]

(ii) Elize buys the framed picture for $12.50 .

She sells the framed picture for $20.25 .

Calculate the percentage profit.

............................................. % [2]

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8 (a) In triangle RST, RT = 7 cm and ST = 4 cm.

(i) Using a ruler and compasses only, construct triangle RST.

Leave in your construction arcs.
The line RS has been drawn for you.

R S
[2]

(ii) Measure the distance from S to the midpoint of RT.

Give your answer in millimetres.

.......................................... mm [1]

(b) Town A is 8.5 cm from town B on a map.

The scale of the map is 1 : 50 000.

Calculate the actual distance from town A to town B.

Give your answer in kilometres.

........................................... km [2]

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 15

(c)
E

x° NOT TO
SCALE

118°
A B C D

The diagram shows triangle BCE and a straight line ABCD.

BE = CE and angle DCE = 118°.

Find the value of x.

x = ................................................ [2]

(d)
A

NOT TO
8.9 cm SCALE
4.8 cm

C B

The diagram shows a right-angled triangle ABC.

Show that BC is 7.5 cm, correct to 2 significant figures.

 [3]

Question 9 is printed on the next page.

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 16

9 Triangles A, B and C are shown on the grid.

y
6
5
C
4
B
3
2
1
A
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
-7

(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]
6
(c) On the grid, translate triangle A by the vector e o. [2]
-4
(d) On the grid, reflect triangle A in the line y =- 2 . [2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2023 0580/32/O/N/23

 Cambridge IGCSE™
* 7 8 4 7 5 6 2 5 2 2 *

MATHEMATICS 0580/32
Paper 3 (Core) February/March 2024

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 104.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

DC (CJ/CB) 327789/2
© UCLES 2024 [Turn over
 2

1 (a)
l

Draw a line through point P that is perpendicular to line l. [1]

(b) Write down the mathematical names for two different quadrilaterals with

• two lines of symmetry

and
• rotational symmetry of order two.

....................................... and ........................................ [2]

(c) The diagram shows a quadrilateral on a 1 cm2 grid.

Find the area of this quadrilateral.

.......................................... cm2 [1]

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 3

(d)
H
G
x°
F 143°
103°
NOT TO
SCALE

82°
E
y°
D

The diagram shows a quadrilateral DEFG and a straight line FGH.

(i) Angle DEF = 82° .

Write down the mathematical name for this type of angle.

................................................. [1]

(ii) Work out the value of x.

Give a geometrical reason for your answer.

x = .......................... because .............................................................................................

............................................................................................................................................. [2]

(iii) Work out the value of y.

Give a geometrical reason for your answer.

y = .......................... because .............................................................................................

............................................................................................................................................. [2]

© UCLES 2024 0580/32/F/M/24 [Turn over

 4

2 (a)
Fuel Fuel
Garage A Garage B
$1.41 per litre $1.50 per litre

(i) Tiya buys 55 litres of fuel from garage A.

Work out the change she receives from $100.

$ ................................................. [2]

(ii) Work out how much cheaper it is to buy 20 litres of fuel from garage A than from garage B.

$ ................................................. [2]

(iii) These are the amounts that 6 people spend on fuel at garage A.

$63 $84.50 $72.23 $46 $54.10 $80

Calculate the mean number of litres that they buy.

......................................... litres [3]

(iv) The cost of fuel at garage B increases from $1.50 to $1.53 .

Calculate the percentage increase.

.............................................. % [2]

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 5

2
(b) The fuel tank of a car is full.
5
It takes 39 more litres of fuel to fill the tank.

Work out the number of litres of fuel in a full tank.

......................................... litres [3]

(c) (i) Use 1 litre = 0.22 gallons to complete this conversion graph.

30

25

20

Gallons 15

10

0
0 10 20 30 40 50 60 70 80 90 100
Litres
[2]

(ii) Use 1 litre = 0.22 gallons to complete this statement.

1 gallon = .............................. litres. [1]

(d) A cylindrical tank for storing fuel has radius 1.5 metres and height 8 metres.

Calculate the volume of the tank in litres.

......................................... litres [3]

© UCLES 2024 0580/32/F/M/24 [Turn over

 6

3 (a) In triangle DEF, DE = 6 cm and DF = 4.8 cm .

Using a ruler and compasses only, construct triangle DEF.

Leave in your construction arcs.
The line EF has been drawn for you.

E F

[2]

(b)

A B
C
T

F G
E

(i) Write down the letter of the triangle that is congruent to triangle T.

................................................. [1]

(ii) Write down the letter of the triangle that is similar but not congruent to triangle T.

................................................. [1]

© UCLES 2024 0580/32/F/M/24

 7

(c)

NOT TO
SCALE
h

62° 62°
7 cm

The diagram shows an isosceles triangle.

(i) Show that the perpendicular height, h, is 6.58 cm, correct to 3 significant figures.

[3]

(ii) Calculate the area of the triangle.

Give the units of your answer.

........................................... ...................... [3]

(iii) Kalpit tries to arrange some of these triangles to make a regular polygon with centre O.

NOT TO
SCALE
7 cm 7 cm
62° 62°
7 cm

Show that Kalpit cannot make a regular polygon.

[3]

© UCLES 2024 0580/32/F/M/24 [Turn over

 8

4 (a) A shop sells 58 televisions in one week.

The bar chart shows the number of televisions that the shop sells on five of the days.

16
14
12
10
Number of
8
televisions
6
4
2
0
Monday Tuesday Wednesday Thursday Friday Saturday Sunday

(i) Write down the number of televisions that the shop sells on Monday.

................................................. [1]

(ii) Find the fraction of the televisions that the shop sells on Sunday.

................................................. [1]

(iii) The number of televisions that the shop sells on the other two days is in the ratio

Wednesday : Friday = 2 : 3.

Complete the bar chart.

[4]
(iv) Write down the mode.

................................................. [1]

(b) A television has a price of $550.

This price is reduced by 4%.

Calculate the new price of this television.

$ ................................................. [2]

© UCLES 2024 0580/32/F/M/24

 9

(c) The scatter diagram shows the prices of different sized televisions.

Price

Television size

Write down the type of correlation shown in the scatter diagram.

................................................. [1]

(d) Hemang buys two televisions.

The probability that a television is faulty is 0.02 .

1st television 2nd television

faulty
..............

faulty
0.02

not faulty
..............
faulty
..............
..............
not faulty

not faulty
..............

(i) Complete the tree diagram. [2]

(ii) Find the probability that Hemang buys two faulty televisions.

................................................. [2]

(iii) The shop sells 4150 televisions in one year.

Calculate the expected number of faulty televisions.

................................................. [1]

© UCLES 2024 0580/32/F/M/24 [Turn over

 10

5 (a) (i) Complete the table of values for y =- x 2 + 5x + 7 .

x -1 0 1 2 3 4 5 6
y 11 11 1

[3]

(ii) On the grid, draw the graph of y =- x 2 + 5x + 7 for - 1 G x G 6 .

14

13

12

11

10

–1 0 1 2 3 4 5 6 x
[4]

(iii) (a) Write down the equation of the line of symmetry of the graph.

................................................. [1]

(b) The points (-8, -97) and (t, -97) also lie on the graph of y =- x 2 + 5x + 7 .

Use symmetry to find the value of t.

t = ................................................. [1]
© UCLES 2024 0580/32/F/M/24
 11

(b) Write down the gradient of the line y = 9x - 4 .

................................................. [1]

(c) Write down the equation of a line parallel to y =-5x + 19 .

y = ................................................. [1]

(d)
y
7

6
L
5

–4 –3 –2 –1 0 1 2 3 4 x
–1

–2

–3

Find the equation of line L in the form y = mx + c .

y = ................................................. [2]

(e) Make x the subject of the formula y = mx + c .

x = ................................................. [2]

© UCLES 2024 0580/32/F/M/24 [Turn over

 12

6 (a) Town S is 44 km from town R on a bearing of 117°.

(i) Using a scale of 1 cm represents 8 km, mark the position of town S.

North

Scale: 1 cm to 8 km
[2]

(ii) Anvi cycles the 44 km from R to S.

She leaves R at 13 15 and cycles at a speed of 12 km/h.

Work out the time she arrives at S.

................................................. [3]

(b) A tower has a height of 16 metres.

When Jai makes a scale drawing of the tower it has a height of 20 cm.

Work out the scale Jai uses, giving your answer in the form 1 : n.

1 : ................................................. [2]

© UCLES 2024 0580/32/F/M/24

 13

(c) X, Y and Z are three towns.

North NOT TO
9.7 km SCALE
X
6 km

X is on a bearing of 288° from Y.

Z is on a bearing of 018° from Y.

(i) Show that angle XYZ is 90°.

[2]

(ii) XY = 6 km and YZ = 9.7 km .

Calculate XZ.

XZ = ............................................ km [2]

© UCLES 2024 0580/32/F/M/24 [Turn over

 14

7 (a) P = 3a + 5

Find the value of P when a = 2 .

P = ................................................. [1]

(b) Solve these equations.

(i) 7x =-42

x = ................................................. [1]

(ii) 9 (8x - 7) = 72

x = ................................................. [3]

(c) 5 8 # 5 k = 5 -24

Find the value of k.

k = ................................................. [1]

(d) Solve the simultaneous equations.

-6x - y = 13
8x + y =- 51

x = .................................................

y = ................................................. [2]

© UCLES 2024 0580/32/F/M/24

 15

(e) n is an integer where n 2- 3 and n G 1.

Write down all the possible values of n.

................................................. [2]

(f) A boy walks for 35 minutes at x metres per minute.

He then runs for t minutes at 160 metres per minute.

Write down an expression, in terms of x and t, for the total distance, in metres, the boy travels.

.............................................. m [2]

(g)

NOT TO
x–2 SCALE

x+5

Find an expression for the area of this rectangle.

Give your answer in the form x 2 + ax + b .

................................................. [3]

Question 8 is printed on the next page.

© UCLES 2024 0580/32/F/M/24 [Turn over

 16

8 (a) 120 people teach in a university mathematics department.

Some information is shown in the table.

Lecturers Professors Total

Part-time 11

Full-time

Total 120

One fifth of the people are professors.

30% of the people are part-time.

Work out the number of full-time lecturers.

................................................. [4]

(b) % = {children in a school}

F = {children who like fruit}
V = {children who like vegetables}
24 children like vegetables but do not like fruit.
8 children do not like fruit and do not like vegetables.
n (F + V ) = 9
n (F ) = 3 # n (V )


F V

........ ........ ........

........

(i) Complete the Venn diagram. [3]

(ii) Work out n (F , V ) .

................................................. [1]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2024 0580/32/F/M/24

 Cambridge IGCSE™
* 4 2 4 2 9 5 0 1 3 9 *

MATHEMATICS 0580/31
Paper 3 (Core) May/June 2024

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 104.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

DC (PQ/JG) 329290/1
© UCLES 2024 [Turn over
 2

1 (a) The cost of a cinema ticket is $6.30 .

(i) Work out the total cost of 4 tickets.

$ ................................................ [1]

(ii) The cinema sells 10 tickets for the price of 9 tickets.

A group of 10 people go to the cinema.

Work out how much each person must pay.

$ ................................................ [2]

(b) The cinema has 650 seats.

(i) There are 26 seats in each row.

Work out the number of rows.

................................................. [1]

(ii) 84% of the seats are occupied.

Work out how many seats are not occupied.

................................................. [2]

(c) Suki buys a bag of popcorn and a bottle of water.

A bag of popcorn costs twice as much as a bottle of water.
She receives $3.55 change from $10.

Work out the cost of a bag of popcorn and the cost of a bottle of water.

Bag of popcorn $ ................................................

Bottle of water $ ................................................ [3]

© UCLES 2024 0580/31/M/J/24

 3

(d) (i) A film lasts for 155 minutes.

Write 155 minutes in hours and minutes.

............. hours ............. minutes [1]

(ii) Another film starts at 14 45 and lasts for 2 hours and 20 minutes.

Work out the time that this film finishes.

................................................. [1]

(e) The table shows the hours that Trevor works in the cinema each week.

Monday No hours
Tuesday No hours
Wednesday 18 00 to 22 00
Thursday 18 00 to 22 00
Friday 12 00 to 17 30
Saturday 12 00 to 17 30
Sunday 13 00 to 18 00

Trevor is paid $11.50 per hour for the time he works before 18 00.
He is paid 30% more for the time he works after 18 00.

Work out how much Trevor is paid each week.

$ ................................................ [4]

© UCLES 2024 0580/31/M/J/24 [Turn over

 4

2 (a) Chen asks some people if they prefer a beach, cruise, lake or mountain holiday.
The pie chart shows the results.

Mountain Beach
120° 135°
75°
30°
Lake
Cruise

(i) Find the fraction of people who prefer a mountain holiday.

Give your answer in its simplest form.

................................................. [2]

(ii) Find the percentage of people who prefer a beach holiday.

.............................................. % [1]

(iii) Find the ratio of people who prefer each type of holiday in the form

beach : cruise : lake : mountain.

Give your answer in its simplest form.

.................... : .................... : .................... : .................... [2]

(iv) One person is chosen at random.

Find the probability that this person prefers a cruise or a lake holiday.

................................................. [2]

(v) 675 people prefer a beach holiday.

Show that the total number of people Chen asks is 1800.

[1]
© UCLES 2024 0580/31/M/J/24
 5

(vi) (a) Complete the table.

Type of holiday Pie chart sector angle Frequency

Beach 135° 675
Cruise 30° 150
Lake 75°
Mountain 120°
[2]

(b) Complete the bar chart, including the scale on the frequency axis.

Frequency

0
Beach Cruise Lake Mountain
[3]

(b) Mr Gibb pays $2208 for a holiday.

Mr Shah pays 2050 euros for the same holiday.
The exchange rate is 1 euro = $1.15 .

Work out how much more, in euros, Mr Shah pays for the holiday than Mr Gibb.

........................................ euros [2]

© UCLES 2024 0580/31/M/J/24 [Turn over

 6

3 (a) Here is part of the timetable for trains from Hinton to Jarmouth.
All trains take the same time to travel from Hinton to Jarmouth.

Hinton 10 47 ................

Jarmouth 11 15 12 35

(i) Complete the timetable. [2]

(ii) Marge arrives at Hinton station exactly 20 minutes before the 10 47 train leaves.

12
11 1
10 2
9 3
8 4
7 5
6

Complete the clock diagram to show the time she arrives at Hinton station. [1]

(b) Each day, a bus leaves Texford to travel to Cranbrook every 45 minutes.
The first bus leaves Texford at 07 10.
The last bus leaves Texford at 22 10.

Work out the number of buses that travel from Texford to Cranbrook each day.

................................................. [3]

(c) The cost of a bus pass increases every year.

On 1st January 2022 a bus pass costs $50.
On 1st January 2023 the cost of the bus pass increases by 10%.
On 1st January 2024 the cost of the bus pass increases by 5%.

Calculate the cost of the bus pass on 1st January 2024.

$ ................................................. [3]

© UCLES 2024 0580/31/M/J/24

 7

(d) The Venn diagram shows information about the number of workers in a hotel who travel to work
by bus (B) and train (T).


B T

31 9 85

107

(i) Work out the number of workers in the hotel.

................................................. [1]

(ii) Work out n (B , T ) .

................................................. [1]

(iii) Explain in words what the number 85 in the Venn diagram represents.

............................................................................................................................................. [1]

(iv) One of the workers is chosen at random.

Find the probability that this worker travels to work by bus and train.

................................................. [1]

(e) The hotel has single and double bedrooms in the ratio single | double = 3 | 8 .
There are 75 more double rooms than single rooms.

Work out the number of single rooms.

................................................. [2]

© UCLES 2024 0580/31/M/J/24 [Turn over

 8

4 The stem-and-leaf diagram shows the ages of the 16 workers in a shop on 1st January 2022.

2 3 5 7
3 4 6 6 6 9
4 1 1 7
5 0 7 7 8
6 1

Key: 2 5 represents 25

(a) (i) Work out the range.

................................................. [1]

(ii) Write down the mode.

................................................. [1]

(iii) Work out the median.

................................................. [1]

(iv) Work out the percentage of workers that are older than 40 but younger than 60.

.............................................. % [2]

(b) On 1st January 2023 the shop has the same 16 workers.

Write down the range, the mode and the median on 1st January 2023.

Range ................................................

Mode ................................................

Median ................................................ [2]

© UCLES 2024 0580/31/M/J/24

 9

(c) On 1st January 2024 the oldest worker leaves.

His replacement is a new worker born on 12th November 1970.
There are no other changes to the workers.

Complete the stem-and-leaf diagram for 1st January 2024.

2 5 7 9
3 6 8 8 8
4
5
6

Key: 2 5 represents 25
[2]

(d) The shop owner is x years old.

x is a prime number.
x + 2 is a square number.
x - 2 is a multiple of 9.

Find the value of x.

x = ................................................ [2]

© UCLES 2024 0580/31/M/J/24 [Turn over

 10

5 (a)
H F I
NOT TO
f°
105° SCALE

e° 52°
E G

The diagram shows a triangle EFG and a straight line HFI.

HFI is parallel to EG.

(i) Angle EFG = 105° .

Write down the mathematical name for this type of angle.

................................................. [1]

(ii) Work out the value of e.

Give a geometrical reason for your answer.

e = ......................... because ..............................................................................................

............................................................................................................................................. [2]

(iii) Find the value of f.

Give a geometrical reason for your answer.

f = ......................... because ..............................................................................................

............................................................................................................................................. [2]

(b) Calculate the interior angle of a regular 7-sided polygon.

Give your answer correct to 2 decimal places.

................................................. [3]

© UCLES 2024 0580/31/M/J/24

 11

(c) The diagram shows a regular pentagon with sides 15 cm.

(2w) cm 5(x + 7) cm
NOT TO
SCALE

15 cm (w + x + y) cm

15 cm

Work out the values of w, x and y.

w = ................................................

x = ................................................

y = ................................................ [5]

© UCLES 2024 0580/31/M/J/24 [Turn over

 12

6 The diagram shows a point, P, three triangles, A, B and C, and part of triangle D on a 1 cm 2 grid.

y
10

9
D
8

3
A
2
a
1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 x
–1
B
–2

–3
C
– 43
P
–5

–6

© UCLES 2024 0580/31/M/J/24

 13

(a) On the grid, mark the image of point P after a reflection in the line y = 0 . [1]

(b) Use trigonometry to calculate angle a.

Angle a = ................................................ [2]

(c) Describe fully the single transformation that maps

(i) triangle A onto triangle B

.............................................................................................................................................

............................................................................................................................................. [3]

(ii) triangle A onto triangle C.

.............................................................................................................................................

............................................................................................................................................. [2]

(d) Triangle A has been enlarged with centre (1, 0) to give triangle D.
The grid is only large enough to show one vertex and part of two of the sides of triangle D.

(i) Write down the scale factor of the enlargement.

................................................. [1]

(ii) Find the coordinates of the other two vertices of triangle D.

( .................... , .................... ) and ( .................... , .................... ) [2]

© UCLES 2024 0580/31/M/J/24 [Turn over

 14

7 (a) The scale drawing shows the position of a castle, C.

The scale is 1 centimetre represents 2 kilometres.

North

Scale: 1 cm to 2 km

Micah walks at 4.8 km/h for 3 hours on a bearing of 236° from C, to his house, H.

Mark the position of H on the scale drawing.

[3]

(b) A restaurant, R, is on a bearing of 083° from C.

(i) Work out the bearing of C from R.

................................................. [2]

© UCLES 2024 0580/31/M/J/24

 15

(ii) The distance, d km, from R to C is 5 km, correct to the nearest kilometre.

Complete this statement about the value of d.

.................... G d 1 .................... [2]

(c) A model of the castle is made.

On the model, the length of one of the castle walls is 5 centimetres.
The actual length of the wall is 90 metres.

Find the scale of the model in the form 1 | n .

1 | ................................................ [2]

(d) The castle has two kitchens with rectangular floors.

F G
B C
NOT TO
5.6 m 9.2 m SCALE

A 8.4 m D
E xm H

Rectangle ABCD is mathematically similar to rectangle EFGH.

Calculate the value of x.

x = ................................................ [2]

(e) The castle has a cylindrical tower.

The tower has a radius of 2.4 m and a height of 25 m.

Calculate the curved surface area of the tower.

Give the units of your answer.

........................................ .................... [3]

Question 8 is printed on the next page.

© UCLES 2024 0580/31/M/J/24 [Turn over
 16

8 The table shows some values for y = x 2 - x - 3.

x -3 -2 -1 0 1 2 3 4
y -1 -1 9

(a) Complete the table. [3]

(b) On the grid, draw the graph of y = x 2 - x - 3 for - 3 G x G 4 .
y
9

–3 –2 –1 0 1 2 3 4 x
–1

–2

–3

–4 [4]

(c) Write down the coordinates of the lowest point on the graph.

( ....................... , ...................... ) [1]

(d) Use your graph to solve the equation x 2 - x - 3 = 7 .

x = .................... or x = .................... [2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2024 0580/31/M/J/24

 Cambridge IGCSE™
* 0 2 9 9 3 1 0 0 2 0 *

MATHEMATICS 0580/32
Paper 3 (Core) May/June 2024

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 104.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

DC (CJ/SG) 329291/2
© UCLES 2024 [Turn over
 2

1 (a) 6 7 10 12 18 32 49 63

From this list of numbers, write down

(i) a factor of 21

������������������������������������������������� [1]

(ii) a square number

������������������������������������������������� [1]
(iii) a prime number�

������������������������������������������������� [1]

(b) Find the value of

(i) the cube root of 1728

������������������������������������������������� [1]

(ii) 25

������������������������������������������������� [1]

(iii) 50

������������������������������������������������� [1]
1
(iv) 36 2 �

������������������������������������������������� [1]

(c) Put one pair of brackets into this calculation to make it correct�

3#2-6-2'2= 4
[1]

(d) Find the lowest common multiple (LCM) of 30 and 68�

������������������������������������������������� [2]
© UCLES 2024 0580/32/M/J/24
 3

2 (a) Simplify�

(i) 5a - 6a + 3a

������������������������������������������������� [1]

(ii) 6x 2 - 6x - 4x 2 - x

������������������������������������������������� [2]

(b) Find the value of c 2 + d 2 when c = 7 and d =- 5�

������������������������������������������������� [2]

(c) The time, T minutes, to cook a chicken with a mass of m kg is T = 35m + 20 �

(i) Make m the subject of the formula�

m = ������������������������������������������������ [2]

(ii) Find the mass of a chicken that takes 83 minutes to cook�

�������������������������������������������� kg [2]

(d) Solve these simultaneous equations�

You must show all your working�
5x - 6y = 24
15x + 8y = 33

x = ������������������������������������������������

y = ������������������������������������������������ [3]

© UCLES 2024 0580/32/M/J/24 [Turn over

 4

3 The diagram shows four quadrilaterals, A, B, C and D, on a 1 cm 2 grid�

12

11

10

4
D
3
A
2

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x
–1

–2

–3

–4
B
–5

–6

–7

–8
C
–9

– 10

– 11

© UCLES 2024 0580/32/M/J/24

 5

(a) Write down the mathematical name of quadrilateral A�

������������������������������������������������� [1]

(b) (i) Find the area of quadrilateral A�

����������������������������������������� cm 2 [1]

(ii) Measure the perimeter of quadrilateral A�

�������������������������������������������� cm [1]

(c) Describe fully the single transformation that maps

(i) quadrilateral A onto quadrilateral B

���������������������������������������������������������������������������������������������������������������������������������������������

��������������������������������������������������������������������������������������������������������������������������������������������� [2]

(ii) quadrilateral A onto quadrilateral C

���������������������������������������������������������������������������������������������������������������������������������������������

��������������������������������������������������������������������������������������������������������������������������������������������� [2]

(iii) quadrilateral A onto quadrilateral D�

���������������������������������������������������������������������������������������������������������������������������������������������

��������������������������������������������������������������������������������������������������������������������������������������������� [3]

(d) On the grid, enlarge quadrilateral A by scale factor 2, centre (- 3, - 3) � [2]

© UCLES 2024 0580/32/M/J/24 [Turn over

 6

4 (a) Anton records the number of pets owned by each of 50 families�

The table shows some of his results�

Number of pets 0 1 2 3 4 5

Number of families 5 12 15 9

There are twice as many families with 4 pets than with 5 pets�

(i) Complete the table�

[3]

(ii) Complete the bar chart�

16

14

12

10

Number of
families 8

0
0 1 2 3 4 5
Number of pets
[2]

© UCLES 2024 0580/32/M/J/24

 7

(iii) Write down the mode�

������������������������������������������������� [1]

(iv) Calculate the mean�

������������������������������������������������� [3]

(b) 80 of the pets owned by the families are cats, rabbits or hamsters�
The table shows the number of each pet�

Type of pet Number of each pet Pie chart sector angle

Cat 38
Rabbit 28
Hamster 14

(i) Complete the table�

[2]

(ii) Complete the pie chart�

[2]

(iii) One of the pets is chosen at random�

Find the probability that a rabbit is chosen�

������������������������������������������������� [1]
© UCLES 2024 0580/32/M/J/24 [Turn over
 8

5 (a)
NOT TO
SCALE

x°
125°

The diagram shows a pair of parallel lines and a straight line�

(i) Write down the mathematical name for the type of angle marked 125°�

������������������������������������������������� [1]

(ii) Give the geometrical reason why the value of x is 125�

��������������������������������������������������������������������������������������������������������������������������������������������� [1]

(b)

y°

NOT TO
SCALE

70°

58°

The diagram shows three straight lines�

Find the value of y�

Write down the geometrical properties needed to find the value of y�

............................................................................................................................................

............................................................................................................................................

y = ������������������������������������������������ [3]

© UCLES 2024 0580/32/M/J/24

 9

(c)
NOT TO
C SCALE
D

74°
A B
O

The diagram shows a circle, centre O, with diameter AOB�

The line CDE touches the circle at D and angle DOB = 74° �

(i) Write down the mathematical name of the line CDE�

������������������������������������������������� [1]

(ii) Work out angle ODB�

Angle ODB = ������������������������������������������������ [2]

(iii) Work out angle BDE.

Give a geometrical reason for your answer�

Angle BDE = ������������������� because ������������������������������������������������������������������������������������

��������������������������������������������������������������������������������������������������������������������������������������������� [2]

(d) Find the interior angle of a regular 15-sided polygon�

������������������������������������������������� [2]

© UCLES 2024 0580/32/M/J/24 [Turn over

 10

6 (a) (i) Complete the table of values for y =- x 2 + 8x + 1�

x 0 1 2 3 4 5 6 7 8

y 13 17 13 1
[3]

(ii) On the grid, draw the graph of y =- x 2 + 8x + 1 for 0 G x G 8 �

y
18

16

14

12

10

0
0 2 4 6 8 x
[4]

© UCLES 2024 0580/32/M/J/24

 11

(iii) Write down the equation of the line of symmetry of the graph�

������������������������������������������������� [1]
1
(b) A straight line has a gradient of and passes through the point (2, 7)�
2
(i) On the grid, draw this line for 0 G x G 8 �

[2]

(ii) Write down the equation of this line in the form y = mx + c �

y = ������������������������������������������������ [2]

(iii) Write down the coordinates of the points where this line intersects the graph of
y =- x 2 + 8x + 1�

( ��������������� , ��������������� ) and ( ��������������� , ��������������� ) [2]

© UCLES 2024 0580/32/M/J/24 [Turn over

 12

7 The area of some land is in the ratio park : gardens : playground = 11 : 2 : 3�

The park has an area of 4620 m 2�

(a) Work out the area of the gardens and the area of the playground�

Gardens ������������������������������������������ m 2

Playground ������������������������������������������ m 2 [3]

(b) The park area of 4620 m 2 is made up of paths and grassland�

18% of the park area is paths�

(i) Show that the grassland area is 3788.4 m 2�

[1]

(ii) Seed for the grassland is sold in bags�

The seed in one bag covers an area of 280 m 2�
The bags cost $72 each for the first 5 bags and then $58 each for any extra bags�

Calculate the cost of the seed needed to cover the grassland�

$ ������������������������������������������������ [4]

© UCLES 2024 0580/32/M/J/24

 13

(c) The owners of the land buy new equipment for the playground�
They borrow $8500 for 4 years at a rate of 6�5% per year compound interest�

Calculate the amount they repay at the end of the 4 years�

Give your answer correct to the nearest dollar�

$ ������������������������������������������������ [3]

(d) The café in the park sells water in bottles A, B and C�

NOT TO
SCALE

Bottle A Bottle B Bottle C

330 ml 500 ml 750 ml
$1.98 $3.20 $5.10

Work out which bottle is the best value�

You must show all your working�

Bottle ������������������������������������������������ [3]

© UCLES 2024 0580/32/M/J/24 [Turn over

 14

8
B 3.6 m A

NOT TO
SCALE

4.7 m

E
F
1.7 m

C D
5.5 m

The diagram shows a plan, ABCDE, of the floor of a room in Jo’s house�
F is a point inside the room�

(a) (i) Show that EF = 1.9 m �

[1]

(ii) Work out AF�

AF = �������������������������������������������� m [1]

(b) Calculate the area of the floor�

������������������������������������������� m 2 [3]

(c) A cupboard in the room is in the shape of a cuboid�

The area of the base of the cupboard is 1�2 m 2 and the height of the cupboard is 2�3 m�

Calculate the volume of the cupboard�

Give the units of your answer�

�������������������������������� ��������������� [2]

© UCLES 2024 0580/32/M/J/24
 15

(d) Jo buys 275 floor tiles which cost $1�64 each�

Calculate the total cost of the floor tiles�

$ ������������������������������������������������ [1]

(e) Jo builds a patio in the shape of a semicircle with radius 2�3 m�

Calculate the area of the patio�

������������������������������������������� m 2 [2]

Question 9 is printed on the next page.

© UCLES 2024 0580/32/M/J/24 [Turn over

 16

9 (a) Sara rides her bicycle at a speed of 420 metres per minute�

Work out her speed in kilometres per hour�

���������������������������������������� km/h [2]

(b) Jan cycles a distance of 51 km�

She starts at 11 55�
She has a rest stop for 25 minutes�
She finishes at 14 41�

Calculate her average speed, in km/h, for the time she is cycling�

���������������������������������������� km/h [4]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2024 0580/32/M/J/24

 * 0019655331701 *

,

 
,

Cambridge IGCSE™

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MATHEMATICS 0580/33
Paper 3 (Core) May/June 2024

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 104.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Any blank pages are indicated.

DC (LK/JG) 329292/2
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2
,

 
,

1 (a) 40 football players vote on the colour of new shirts.

The results for red, yellow and green are shown in the bar chart.

12
11
10
9

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8
7
Frequency 6
5
4
3
2

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1
0
Red Yellow Green Blue Orange

(i) Twice as many football players vote blue than vote orange.

Complete the bar chart.

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[3]

(ii) Write down the mode.

................................................. [1]
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3
,

 
,

(b) 40 hockey players vote on the colour of new shirts.

The table shows the results.

Colour Frequency
White 21
Grey 12
Pink 7
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(i) Complete the pie chart.

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[4]
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(ii) Work out the percentage of hockey players who vote grey.

............................................. % [1]
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4
,

 
,

2 (a) Here is part of the timetable for buses from the station to the city centre.
All buses take the same time to travel from the station to the city centre.

Station 09 24 11 06

City centre 10 03 ...........

(i) Complete the timetable.

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[2]

(ii) Beth walks 4 km from her home to the station at a speed of 6 km/h.
She wants to travel on the 09 24 bus.

Work out the latest time she can leave her home.

................................................. [3]

(iii) 45 seats on the bus are occupied.

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3
This is of the total number of seats on the bus.
5
Work out the total number of seats on the bus.

................................................. [2]

(b) Beth buys 2.4 kg of onions costing $1.25 per kilogram and 4.5 kg of potatoes.
The total cost is $11.64 .

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Find the cost of 1 kg of potatoes.

$ ................................................ [3]
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5
,

 
,

(c) (i) One day 140 people enter a shop.

The ratio adults : children = 3 : 2.

Find the number of adults who enter the shop.

................................................. [2]
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(ii) The price of a television in this shop is $624.

37.5% of this price is profit.

Calculate the profit on this television.

$ ................................................ [1]
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(iii) The price of a phone in this shop is $420.

This price increases by 12%.

Calculate the new price.

$ ................................................ [2]
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6
,

 
,

3 (a) The grid shows a trapezium.

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On the grid, draw an enlargement of the trapezium with scale factor 3. [2]

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7
,

 
,

(b) The diagram shows four triangles, A, B, C and T, and a point P on a grid.

5
4
P
3
2
A T
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–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x
–1
C
–2
–3
B
–4
–5
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(i) Write down the coordinates of point P.

( .................... , .................... ) [1]

(ii) Describe fully the single transformation that maps

(a) triangle T onto triangle A

.....................................................................................................................................

..................................................................................................................................... [2]
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(b) triangle T onto triangle B

.....................................................................................................................................

..................................................................................................................................... [2]

(c) triangle T onto triangle C.

.....................................................................................................................................

..................................................................................................................................... [3]
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8
,

 
,

4 (a) Write down the value of the 8 in the number 39 829.

................................................. [1]

(b) Write down all the factors of 18.

............................................................................... [2]

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(c) Show that 57 is not a prime number.

[1]

(d) x = 64

Find the value of x.

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x = ................................................ [1]

(e) Find the first multiple of 40 that is greater than 620.

................................................. [1]
2
(f) Find the reciprocal of .
3

DO NOT WRITE IN THIS MARGIN

................................................. [1]
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9
,

 
,

1 1
(g) Find a fraction between and .
5 4

................................................. [1]

(h) Write down an irrational number with a value between 9 and 10.
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................................................. [1]

(i) Find the highest common factor (HCF) of 72 and 180.

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................................................. [2]
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10
,

 
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5 (a)

(i) Measure angle k.

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................................................. [1]

(ii) Write down the mathematical name for this type of angle.

................................................. [1]

(b) The diagram shows a pair of parallel lines and a straight line.
Angles a, b, c, d and x are labelled.

a NOT TO
x SCALE

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b c
d

Complete the statements.

Angle .................... is alternate to angle x.

Angle .................... is corresponding to angle x. [2]

(c) The diagram shows a parallelogram.

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y°
NOT TO
SCALE
42°

Find the value of y.

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y = ................................................ [1]

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11
,

  ,

(d)
B

C NOT TO
17° SCALE
O
A
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A, B and C lie on a circle, centre O.

Find angle ACB.

Angle ACB = ................................................ [2]

(e) The interior angle of a regular polygon is 171°.

Work out the number of sides of this polygon.

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................................................. [2]

(f)
NOT TO
18.5 cm SCALE
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7.4 cm

x°

Calculate the value of x.

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x = ................................................ [2]

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12
,

  ,

6 (a) In a sport, teams are given points using the formula

number of points = number of wins # 4 + number of draws # 2 + bonus points.

One team has 15 wins, 7 draws and 6 bonus points.

Calculate the total number of points for this team.

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................................................. [2]

(b) Solve.
x
= 18
2

x = ................................................ [1]

(c) Solve.
4x + 12 = 18

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x = ................................................ [2]

(d) Expand and simplify.

6 (3x - 4) + 5 (x - 2)

................................................. [2]

(e) T = 5r - 6

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Make r the subject of this formula.

r = ................................................ [2]
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13
,

  ,

(f) Bo has a green bag and a blue bag.

Each bag contains some marbles.

The green bag has x marbles.

There are 5 times as many marbles in the blue bag than in the green bag.

Bo now adds 6 marbles to each bag.

There are now 4 times as many marbles in the blue bag than in the green bag.

Use this information to write down an equation and solve it to find the value of x.
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x = ................................................ [5]
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14
,

  ,

7 (a) Li spins a fair 6-sided spinner numbered 1 to 6.

(i) On the probability scale, draw an arrow ( ↓) to show the probability that the spinner lands on
the number 2.

0 1 1 [1]
2
(ii) Find the probability that the spinner lands on a prime number.

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................................................. [1]

(iii) Find the probability that the spinner lands on the number 7.

................................................. [1]

(b) A bag contains 3 red balls and 12 green balls.

Li picks a ball at random.

Find the probability that it is a green ball.

Give your answer as a fraction in its simplest form.

DO NOT WRITE IN THIS MARGIN

................................................. [2]

(c) Li spins two fair 4-sided spinners, each numbered 1 to 4.

The two numbers are multiplied to give the score.

# 1 2 3 4
1 1 2 3 4

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2 2 4 6 8
3 3 6 9 12
4 4 8 12 16

Find the probability that the score is

(i) an even number

................................................. [1]

(ii) an integer
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................................................. [1]

(iii) at least 10.

................................................. [1]
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15
,

  ,

(d) A bag contains red discs and blue discs.

1
The probability that a disc picked at random is red is .
5
Li picks a disc at random, notes its colour and then replaces it in the bag.
She then picks another disc at random.

(i) Complete the tree diagram.

First disc Second disc

Red
............
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Red
1
5
............ Blue

Red
............

............ Blue
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Blue
............
[2]

(ii) Work out the probability that both of the discs she picks are blue.

................................................. [2]
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16
,

  ,

8 (a)
8.2 cm

NOT TO
5.4 cm SCALE

12.6 cm

Find the area of this trapezium.

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......................................... cm 2 [2]

(b)

NOT TO
4.5 cm SCALE

b cm

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The area of this triangle is 15.3 cm 2.

Find the value of b.

b = ................................................ [2]

(c) A circle has a circumference of 58.6 cm .

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Find the radius of this circle.

............................................ cm [2]
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17
,

  ,

(d)
28 cm NOT TO
SCALE

12 cm

The diagram shows a rectangle with two semicircles removed.

Calculate the shaded area.

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DO NOT WRITE IN THIS MARGIN

......................................... cm 2 [4]
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DO NOT WRITE IN THIS MARGIN

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18
,

   ,

9 (a) Line L has a gradient of 4 and passes through the point (0, 3).

Write down the equation of line L in the form y = mx + c .

y = ................................................ [1]

(b) Line G has the equation y = 2 - 6x .

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Line G passes through the point (a, 5).

Find the value of a.

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a = ................................................ [3]

(c) (i) Complete the table of values for y = x 2 - 6 .

x -4 -3 -2 -1 0 1 2 3 4
y 10 -2 -5 -5 -2 10
[2]

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19
,

   ,

(ii) On the grid, draw the graph of y = x 2 - 6 for - 4 G x G 4 .

10

8
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2
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–4 –3 –2 –1 0 1 2 3 4 x
–1

–2

–3

–4
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–5

–6

–7
[4]

(iii) Write down the equation of the line of symmetry of the graph.

................................................. [1]
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(iv) Use your graph to solve the equation x 2 - 6 = 0 for x 2 0 .

x = ................................................ [1]

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20
,

  
,

BLANK PAGE

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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
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 Cambridge IGCSE™
*0123456789*

MATHEMATICS0580/03
Paper 3 Calculator (Core) For examination from 2025

SPECIMEN PAPER 1 hour 30 minutes

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a scientific calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For π, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages.

© Cambridge University Press & Assessment 2022 [Turn over

 2

List of formulas

1
Area, A, of triangle, base b, height h. A = 2 bh

Area, A, of circle of radius r. A = rr 2

Circumference, C, of circle of radius r. C = 2rr

Curved surface area, A, of cylinder of radius r, height h. A = 2rrh

Curved surface area, A, of cone of radius r, sloping edge l. A = rrl

Surface area, A, of sphere of radius r. A = 4rr 2

Volume, V, of prism, cross-sectional area A, length l. V = Al

1
Volume, V, of pyramid, base area A, height h. V = 3 Ah

Volume, V, of cylinder of radius r, height h. V = rr 2 h

1
Volume, V, of cone of radius r, height h. V = 3 rr 2 h

4
Volume, V, of sphere of radius r. V = 3 rr 3

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 3

1 The pictogram shows the number of text messages sent by five students in one day.

Name of student Number of text messages

Kira

Matt

Dani

Hana

Ramos

Key: represents .................... text messages

(a) Kira sent 15 text messages.

Complete the key.  [1]

(b) Find the number of text messages sent by Hana.

................................................ [1]

2 Write down all the factors of 68.

.................................................................... [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over

 4

3 Insert one pair of brackets to make this statement correct.

4 × 6 – 2 + 1 = 17
[1]

4 Write down the reciprocal of 4.

................................................ [1]

5 Find the value of

(a) 242

................................................ [1]

(b) 2197 .
3

................................................ [1]

6 The lowest temperature recorded at Scott Base in Antarctica is –57.0 °C.

The highest temperature recorded at Scott Base is 63.8 °C more than this.

Calculate the highest temperature recorded at Scott Base.

............................................ °C [1]

7 Lee changes $450 into euros.

The exchange rate is $1 = 0.8476 euros.

Calculate the amount in euros that Lee receives.

....................................... euros [1]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 5

t
8 W= (7t – 4)
2

Find the value of W when t = 18.

W = ............................................... [2]

9 A triangle has sides 6 cm, 7 cm and 8 cm.

Using a ruler and compasses only, construct the triangle.

The 6 cm line has been drawn for you.
Show all your construction arcs.

 [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over

 6

10 Calculate.
13.7 + 14.02

− 0.31 + 3 15.625
Give your answer correct to 2 decimal places.

................................................ [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 7

11
X

NOT TO
R SCALE

(a) The line XY touches the circle at the point R.

Write down the mathematical name for the line XY.

................................................ [1]

(b) Points P and Q lie on the circle.

Write down the mathematical name for the line PQ.

................................................ [1]

(c) The area of the circle is 43.5 cm2.

Calculate the radius of the circle.

........................................... cm [2]

(d) The diameter of a different circle is 6.4 cm.

Calculate the circumference of this circle.

Give your answer in millimetres.

.......................................... mm [3]
© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over
 8

12 The stem-and-leaf diagram shows the scores of each of 27 students in a test.

2 8 8 9
3 2 5 6 6 7 8 8
4 0 1 1 2 3 4 6 7 9
5 1 3 4 5 5 7 8
6 2

Key: 2 | 8 represents a score of 28

(a) Find the range of the scores.

................................................ [1]

(b) When the score for another student is included in the diagram the new range is 38.

Find the two possible scores for this student.

 ....................... , ....................... [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 9

Question 13 is printed on the next page.

© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over

 10

13 Jason leaves Town A at 09 00 and cycles to Town C.

The travel graph shows Jason’s journey.

Town D 50

40

Town C 30
Distance from
Town A (km)

20
Town B

10

Town A 0
09 00 10 00 11 00 12 00 13 00 14 00
Time

(a) Find Jason’s average speed, in kilometres per hour, from Town A to Town B.

........................................ km/h [1]

(b) Jason leaves Town C at 12 00.

Jason continues to Town D at a constant speed of 15 kilometres per hour.

(i) Calculate the time Jason takes to travel from Town C to Town D.
Give your answer in hours and minutes.

 ....................... h ....................... min [2]

(ii) On the travel graph, complete Jason’s journey. [1]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 11

(c) Find the total time, in minutes, that Jason stopped between Town A and Town D.

......................................... min [1]

(d) Calculate Jason’s overall average speed, in kilometres per hour, from Town A to Town D.

........................................ km/h [3]

(e) Lisa leaves Town C at 11 00 and arrives at Town A at 13 42.

Lisa cycles at a constant speed on the same road as Jason, without stopping.

(i) Draw a line on the travel graph to show Lisa’s journey. [2]

(ii) Find the distance from Town A when Lisa and Jason pass each other.

........................................... km [1]

© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over

 12

14 (a)
6 cm

4 cm

NOT TO
SCALE
5 cm

The diagram shows the net of a cuboid.

(i) Find the volume of the cuboid.

.......................................... cm3 [2]

(ii) Show that the total surface area of the cuboid is 148 cm2.

 [2]

(iii) Calculate the total length of the edges of the cuboid.

........................................... cm [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 13

(b) In this part, all measurements are in centimetres.

y
NOT TO
SCALE

(x – 1)

This is the net of a cuboid with edges of length x, y and (x – 1).

Find an expression, in terms of x and y, for the perimeter of the net.

Give your answer in its simplest form.

................................................ [3]

© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over

 14

15 A sphere has a surface area of 177 cm2.

(a) Calculate the radius of the sphere.

........................................... cm [2]

(b) Calculate the volume of the sphere.

......................................... cm3 [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 15

16 Jo and Mira buy a shop.

(a) They pay for the shop in the ratio Jo : Mira = 7 : 15.
Mira pays $84 000 more than Jo.

Work out how much they each pay.

Jo $......................................................

Mira $......................................................
 [3]

(b) The shop makes a profit of $56 000.

Jo receives 12% of the profit.
Mira receives $14 000 of the profit.
The rest of the profit is put into a bank account.

(i) Calculate how much money Jo receives.

$................................................ [1]

(ii) Calculate the amount put into the bank account as a percentage of the profit.

............................................. % [2]

(iii) Mira invests $14 000 at a rate of 2.4% per year compound interest.

Calculate the value of this investment at the end of 4 years.

$................................................ [2]
© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over
 16

17 The number, N, is written as a product of its prime factors.

N = 24 × 32

(a) Work out the value of N.

................................................ [1]

(b) Find the highest common factor (HCF) of 120 and N.

................................................ [2]

(c) Find the lowest common multiple (LCM) of 120 and N.

................................................ [1]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 17

18 (a) These are the first five terms of a sequence.

7 a b c 31

In the sequence, the same number is added each time to obtain the next term.

Find the value of each of the terms a, b and c.

a = .....................................................

b = .....................................................

c = .....................................................
 [2]

(b) These are the first five terms of another sequence.

4 11 18 25 32

(i) Find the nth term of the sequence.

................................................ [2]

(ii) Show that 361 is a term in the sequence.

 [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over

 18

19 In a quiz, the mean score of each of 12 adults is 43.25 .

In the same quiz, the mean score of each of 16 children is 39.75 .

Calculate the mean score of the 28 people.

................................................ [3]

20 Luca walks at a speed of 5.4 kilometres per hour.

Write this speed in metres per second.

.......................................... m/s [2]

© Cambridge University Press & Assessment 2022 0580/03/SP/25

 19

21

NOT TO
P
SCALE
32° 6.2 cm

The diagram shows a circle, centre O, with diameter PQ.

R is a point on the circumference.

(a) Give a geometrical reason why angle PRQ is 90°.

....................................................................................................................................................... [1]

(b) Calculate the length of PQ.

PQ =........................................... cm [3]

© Cambridge University Press & Assessment 2022 0580/03/SP/25 [Turn over

 20

22

NOT TO
SCALE
5.6 m

1.5 m

A ladder of length 5.6 m rests against a vertical wall.

The bottom of the ladder is 1.5 m from the bottom of the wall, on horizontal ground.

Calculate the distance from the top of the ladder to the base of the wall.

............................................. m [3]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (Cambridge University Press & Assessment) to trace copyright holders, but if any items requiring clearance
have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.

Cambridge Assessment International Education is part of Cambridge University Press & Assessment. Cambridge University Press & Assessment is a department
of the University of Cambridge.

© Cambridge University Press & Assessment 2022 0580/03/SP/25