Cambridge IGCSE™
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MATHEMATICS0580/01
Paper 1 Non-calculator (Core) For examination from 2025
SPECIMEN PAPER B 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.
● Calculators must not be used in this paper.
● You may use tracing paper.
● You must show all necessary working clearly.
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 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
© Cambridge University Press & Assessment 2023 0580/01B/SP/25
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Calculators must not be used in this paper.
1
3 4 10 23 25 27 37 120 130
From this list, write down
(a) a multiple of 30
................................................ [1]
(b) a factor of 50 that is a square number
................................................ [1]
(c) a common factor of 12 and 20
................................................ [1]
(d) a prime number between 20 and 30.
................................................ [1]
2 Find the reciprocal of 0.5 .
................................................ [2]
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3 Sam has some money.
He spends 36% of the money and gives 22% of the money to his friend.
Find the percentage of the money that Sam has left.
............................................. % [2]
4 The grid shows a trapezium and a line L.
On the grid, draw the image of the trapezium after a reflection in line L.
[1]
© Cambridge University Press & Assessment 2023 0580/01B/SP/25
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5 Here is some information about five positive integers.
• The median is 7.
• The mode is 13.
• The range is 10.
• They add up to 40.
Find the five integers.
.................... , .................... , .................... , .................... , .................... [3]
6 (a) Write down the value of the 5 in the number 1 252 800.
................................................ [1]
(b) Write 72.5796 correct to 3 decimal places.
................................................ [1]
(c) 0.28 × 9.6 = 2.688
Use this information to find the value of 28 × 9.6 .
................................................ [1]
7 T = 2a – 3b
Find the value of T when a = 12 and b = 5 .
T = ............................................... [2]
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8 Lee sells books and magazines.
(a) He records the number of books he sells to each of 16 people.
1 2 0 4 2 2 3 0
0 3 4 0 5 2 0 3
(i) Complete the table.
The first row has been completed for you.
Number of books Tally Frequency
0 5
5
[3]
(ii) Use your table to complete the bar chart.
Frequency 4
0
0 1 2 3 4 5
Number of books
[2]
© Cambridge University Press & Assessment 2023 0580/01B/SP/25
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(b) Lee records the number of magazines he sells to each of 20 people.
The results are shown in the table.
Number of magazines Frequency
1 8
2 2
3 4
4 2
5 4
(i) Work out the mean.
................................................ [3]
(ii) Lee says ‘The mode is 8.’
Explain why Lee is wrong.
............................................................................................................................................... [1]
............................................................................................................................................... [1]
9 (a) Convert 600 m into km.
........................................... km [1]
(b) Convert 3 m2 into cm2.
.......................................... cm2 [1]
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10 Represent the inequality x > –2 on the number line.
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 x
[1]
11 Shirts cost $28.40 each.
Scarves cost $5.25 each.
Anna buys 6 shirts and 4 scarves.
By writing the cost of each item correct to 1 significant figure, work out an estimate for the amount
Anna pays.
$................................................ [2]
12 Work out.
–8 × 2 + 3
................................................ [1]
13 Find the value of
(a) 5–1
................................................ [1]
(b) ` 16j .
3
................................................ [2]
© Cambridge University Press & Assessment 2023 0580/01B/SP/25
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14
C
NOT TO
SCALE
x° y° z°
B
2y°
100°
A
The diagram shows a parallelogram and a trapezium.
The parallelogram and the trapezium are joined along a common side.
ABC is a straight line.
(a) Find the value of x.
Give a geometrical reason for your answer.
x = .................... because .............................................................................................................. [2]
....................................................................................................................................................... [2]
(b) Find the value of y.
Give a geometrical reason for your answer.
y = .................... because .............................................................................................................. [2]
....................................................................................................................................................... [2]
(c) Find the value of z.
z = ............................................... [2]
© Cambridge University Press & Assessment 2023 0580/01B/SP/25 [Turn over
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30
15 (a) Complete the table of values for y = x .
x –4 –3 –2 –1 1 2 3 4
y –7.5 7.5
[3]
30
(b) On the grid, draw the graph of y = x for –4 ⩽ x ⩽ –1 and 1 ⩽ x ⩽ 4 .
y
30
20
10
–4 –3 –2 –1 0 1 2 3 4 x
– 10
– 20
– 30
[4]
© Cambridge University Press & Assessment 2023 0580/01B/SP/25
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(c) Write down the order of rotational symmetry of the graph.
................................................ [1]
(d) (i) On the grid, draw the line y = 25 . [1]
30
(ii) Use your graph to solve x = 25 .
x = ............................................... [1]
16 The diagram shows a trapezium.
8 cm
h cm NOT TO
SCALE
B
12 cm
The area of the trapezium is 60 cm2.
Find the value of h.
h = ............................................... [2]
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17 (a) The diagram shows a triangular prism.
NOT TO
SCALE
On the 1 cm2 grid, complete a net of the triangular prism.
Two faces have been drawn for you.
[3]
(b) Work out the volume of this triangular prism.
Give the units of your answer.
............................... ............... [4]
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2 4
18 (a) Find the fraction that lies exactly halfway between 5 and 7 .
................................................ [2]
(b) Work out.
2 2
33 − 15
Give your answer as a mixed number in its simplest form.
................................................ [3]
19 Work out.
4000 × 70
Give your answer in standard form.
................................................ [2]
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20
NOT TO
SCALE
l
4 cm
The diagram shows a solid cone with a radius of 4 cm.
The total surface area of the cone is 56π cm2.
Work out the length, l, of the sloping edge of the cone.
l = .......................................... cm [3]
21 Expand and simplify.
(y – 6)(y + 5)
................................................ [2]
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22 (a) 83 × 8b = 812
Find the value of b.
b = ............................................... [1]
(b) Simplify.
8x5y4 ÷ 2x–7y3
................................................ [2]
23
G
B NOT TO
12 cm SCALE
3 cm
A C F H
x cm 8 cm
Triangle ABC is mathematically similar to triangle FGH.
Work out the value of x.
x = ............................................... [2]
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24 In this question, all measurements are in centimetres.
The diagram shows a quadrilateral.
3x
NOT TO
(x + 6) SCALE
(2x – 1)
(2x + 1)
The perimeter of the quadrilateral is 26 cm.
Write down an equation and solve it to find the value of x.
x = ............................................... [3]
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