Cambridge IGCSE™

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MATHEMATICS 0580/04
Paper 4 Calculator (Extended) For examination from 2025

SPECIMEN PAPER 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 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 100.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

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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

-b ! b 2 - 4ac
For the equation ax2 + bx + c = 0, where a ≠ 0, x= 2a

For the triangle shown,

A a b c
= =
sin A sin B sin C

a 2 = b 2 + c 2 - 2bc cos A
c b
1
Area = 2 ab sin C

B a C

© Cambridge University Press & Assessment 2022 0580/04/SP/25

 3

1 Write down the integer values of x that satisfy the inequality –2 ⩽ x < 2.

2 1,0 13
............................................... [2]

2
P

In triangle PQR, QR = 10 cm and PR = 11 cm.

Using a ruler and compasses only, construct triangle PQR.

The line PQ has been drawn for you. [2]

3 Simplify.
(x8y7) (x–1y3)

t 44
............................................... [2]

4 f(x) = 3x – 5
The domain of f(x) is {–3, 0, 2}.

Find the range of f(x).

3 3 5 14
at 3
3 0 5 5
0 1
14 5,1
{ ........................................... } [2]

312 5

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 4

5
North

North

1cm 3km
11cm B

Two towns, A and B, are shown on a map.

The scale of the map is 1 cm to 3 km.

(a) Find the actual distance between A and B.

11 3 33
.......................................... km [1]

(b) Measure the bearing of B from A.

120
............................................... [1]

(c) Calculate the bearing of A from B.

You must show all your working.

120 180

300
............................................... [2]

© Cambridge University Press & Assessment 2022 0580/04/SP/25

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6 A solid metal cuboid has a volume of 600 cm3.

(a) The base of the cuboid is 10 cm by 12 cm.

Calculate the height of the cuboid.

600 10 12 4
5
.......................................... cm [2]

(b) The solid metal cuboid is melted and made into 1120 spheres, each with radius 0.45 cm.

Find the volume of metal not used in making these spheres.

sphere
10453 0 3817 cm 1120
427 508
600 427 508 172 49

172 5
......................................... cm3 [2]

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1
7 On any day the probability that it rains is .
3
3
When it rains the probability that Amira goes fishing is 5 .
3
When it does not rain the probability that Amira goes fishing is .
4

(a) In a period of 60 days on how many days is it expected to rain?

60 20
............................................... [1]

(b) Complete the tree diagram.

Rain Fishing

3 Yes
5

Yes
1
3

................ No

Yes
................

................ No

................ No
[2]

(c) Find the probability that on any day Amira goes fishing.

1 35 3 7 70

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

© Cambridge University Press & Assessment 2022 0580/04/SP/25

 7

8
y
8

R
4

0 1 2 3 4 5 6 7 8 x

(a) On the grid, draw the lines y = x and x + y = 7 . [3]

(b) Region R satisfies the three inequalities y ⩾ 0 , y ⩽ x and x + y ⩾ 7 .

On the grid, label the region R. [1]
bx axis
9

8 10 8
NOT TO
Speed SCALE
(m/s)

0 113,0
0 Time (seconds) 10 13

The diagram shows the speed–time graph of part of a car journey.

(a) Find the deceleration of the car between 10 and 13 seconds.

........................................ m/s2 [1]

9 0 5
(b) Calculate the total distance travelled during the 13 seconds.

8
1011 92
............................................ m [2]
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10 Factorise.
2x + 6 – 3xy – 9y

3
21 3
3y
2 3 [2]
3
...............................................

11

A B

20 3 17
4 6 7
10 13 23
23 17 6
3

0
n( ) = 20, n(A B) = 3, n(A) = 10 and n(B) = 13.
The Venn diagram shows some of this information. 0
Find

(a) n(A B)

6
............................................... [2]

(b) n(A B) .

7
............................................... [1]

12 The height, h cm, of each of 100 students is measured.

The table shows the results.
1250 1550 162.50 1750
Height (h cm) 100 < h ⩽ 150 150 < h ⩽ 160 160 < h ⩽ 165 165 < h ⩽ 185
Frequency 7 30 41 22

Calculate an estimate of the mean.

125 7 22
15511162.544171175
160.375
.......................................... cm [4]

© Cambridge University Press & Assessment 2022 0580/04/SP/25

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13
D

NOT TO
15 cm
SCALE

A C
62°

14 4
12 cm
14 cm

The diagram shows a quadrilateral, ABCD, formed from two triangles, ABC and ACD.
ABC is a right-angled triangle.

(a) Calculate angle BAC.

tanx 1
x tañ 49.398
49.4
Angle BAC = .............................................. [2]

(b) Calculate BD.

Levered
BD 12415221121415 11.45
22.36
22.4
22.4
BD = ......................................... cm [4]

(c) Calculate the shortest distance from D to AC.

sin 62
2 15 29
13.2
.......................................... cm [3]

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14 (a) Hong has $4000 to invest.

She invests $2000 at a rate of 2.5% per year simple interest.
She also invests $2000 at a rate of 2% per year compound interest.

(i) Find the value of each investment at the end of 8 years.

Simple
I P ftp
1 18
2qf5x8 20oo 1
I 400 fA A 2343 32

A 2400
2400
Simple interest investment $ ....................................................

2343.32 [5]
Compound interest investment $ ....................................................

(ii) Find the overall percentage increase in the $4000 investment at the end of 8 years.

4743.32
4000 100

1
47432,3 118.583
18.6
............................................ % [2]

© Cambridge University Press & Assessment 2022 0580/04/SP/25

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(iii) Find the number of complete years it takes for the compound interest investment of $2000 to
become greater than $2500.

2500 2000 1 F
using
trial improvement

n 11 2486.7
12 2536 5

12
............................................... [3]
years
(b) Alain invests $5000 at a rate of r% per year compound interest.
At the end of 15 years, the value of the investment is $7566.

Find the value of r.

15
5 oct fat

100
FF 1 r
2.799 2.80
r = .............................................. [3]

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15 y= u2x

(a) Find the value of y when u = 7 and x = 25.

Fx25 35
y = .............................................. [2]

(b) Rearrange the formula to write x in terms of u and y.

U x
y
x
5
x = .............................................. [2]

16 A is the point (7, 2) and B is the point (−5, 8).

(a) Calculate the length of AB.

51412 85 13.42
13 4

13 4 units
............................................... [3]

(b) Find the equation of the line that is perpendicular to AB and that passes through the point (−1, 3).
Give your answer in the form y = mx + c .

2
8
m
MAB

Y m x C

3 2 1 C
3 2 C
C 5

2 5
y = .............................................. [4]

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17
18 cm
x° NOT TO
SCALE

13 cm

The area of the triangle is 50 cm2.

Calculate the value of sin x.

50 21 18 13 sinx

50 117 sinx
5
sinx

57
sin x = .............................................. [2]

18 Solve.
3y 3
=
2y 1 4

3
12g 6y
3
6y y y = .............................................. [3]

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19 The cross-section of a prism is an equilateral triangle of side 6 cm.

The length of the prism is 20 cm.

Calculate the total surface area of the prism.

63sin60
As
953
Anect 20 6 120
6 6
20
6 2 95 3 120
360
3188
391.2
......................................... cm2 [4]

dy
20 y = 2xk + ux7 and = 18xk–1 + 21x6
dx
Find the value of k and the value of u.

74 21
2k 18
4 3
k 9
9
k = ....................................................

3
u = ....................................................
[2]

21 Simplify.
5p 2 20p

EE
2p 2 32

2 IFIaFa
© Cambridge University Press & Assessment 2022 0580/04/SP/25
............................................... [3]
 15

22 The diagram shows triangle OPT.

T
ᵗ
K NOT TO
t
2 s
L
SCALE

O P

Ip
p
m
In the diagram OT = t and OP = p.
OK : KT = 2 : 1 and TL : LP = 2 : 1.

(a) Find, in terms of t and p, in its simplest form

(i) PL
TL LP TP
2
ti t p
LP t p
(ii) KL. It SP
............................................... [2]

OK KT OT TL 3 ttp
2
3 38
12
ᵗ3P
............................................... [2]

(b) KL is extended to the point M.

KM =
2 4
t + p.
KLI.IE Ep
3 3

Show that M lies on OP extended.

KM 3t P 0m Ip
one p
3
OT OT
[2]

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7900
23 Serge walks 7.9 km, correct to the nearest 100 metres.
The walk takes 133 minutes, correct to the nearest minute.
50
Calculate the maximum possible average speed of Serge’s walk.
Give your answer in kilometres/hour.

7850 distance 7950

132.5 time 4133.5

speed distance 3 6 timth

7,1
3.6
....................................... km/h [3]

24 The straight line y = 2x + 1 intersects the curve y = x2 + 3x – 4 at the points A and B.

Find the coordinates of A and B.

Give your answers correct to 2 decimal places.

2x 1 43 4
4 x 5 0

f
biz
É
2.79 1 79
A ( .................... , .................... )
12.99
48
B ( .................... , .................... )
[6]
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