Free until 14 Nov · 80% off for the first 100 · Pricing
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), May/June 2025. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s25_qp_310580_s25_ms_310580/31/M/J/25
Each question as it's printed, and the mark scheme's points for it, as text. Diagrams, tables and graphs are in the PDFs above.
Question
The pictogram shows the number of goals scored by teams A, B and C. Team Goals A B C D Key : represents 4 goals (a) Work out the number of goals scored by team B. …… [1] (b) Teams A, B, C and D scored a total of 43 goals. Complete the pictogram. [3]
Mark scheme
1(a) 19 1 1(b) 5 correctly shown in diagram 3 B2 for 5 OR B1 for 38 OR M1 for 43 – (13 + 19 + 6) oe B1 for a correct diagram from their 5
Question
An angle measures 157°. Write down the mathematical name for this type of angle. …… [1]
Mark scheme
2 Obtuse 1
Question
Find the value of 1.96 . …… [1]
Mark scheme
3 1.4 1
Question
Calculate the number of months in 5 years. …… [1] * 0000800000004 * DFD 4
Mark scheme
4 60 1
Question
(a) Write down the order of rotational symmetry for this shape. …… [1] (b) Draw all the lines of symmetry on this shape. [2]
Mark scheme
5(a) 2 1 5(b) Two correct lines 2 B1 for one correct line only or two correct lines and one incorrect line
Question
In triangle ABC, AC = 6.4 cm and BC = 5.3 cm . Using a ruler and compasses only, construct triangle ABC. Leave in your construction arcs. The line AB has been drawn for you. A B [2]
Mark scheme
6 Correct triangle with correct arcs 2 B1 for correct triangle with no/insufficient arcs or 2 correct arcs with no or incorrect lines If 0 scored SC1 for triangle with two arcs but lines interchanged
Question
Solve. 3y = 18 y = …… [1] * 0000800000005 * DFD 5
Mark scheme
7 6 1
Question
(a) T = 3 (5P - 8) + 4 Find the value of T when P = 12 . T = …… [2] (b) W = 4t + 8 Find the value of t when W = 369 . t = …… [2]
Mark scheme
8(a) 160 2 M1 for 3(5×12 – 8) + 4 oe or better 8(b) 90.25 2 M1 for 369 – 8 = 4t oe or better 369 8 or = t + oe or better 4 4 W −8 or [= t] oe or better 4
Question
Represent the inequality –3 1 x G 2 on the number line. x -5 -4 -3 -2 -1 0 1 2 3 4 5 [2] * 0000800000006 * DFD 6 3 17
Mark scheme
9 2 B1 for correct line and one end correct or both ends correct and no line
Question
7 0.41 41 42% Write these numbers in order, starting with the smallest. …… < …… < …… < …… [2] smallest
Mark scheme
10 17 3 2 B1 for three in the correct order 0.41 42% 41 7 or M1 for conversion to common format e.g. 0.428…or 0.429 [0.41] 0.414…or 0.415 0.42 42.8…% or 42.9% 41% 41.4…% or 41.5% [42%]
Question
A plane leaves Seattle at 07 30 on Tuesday and arrives in Seoul 10 hours and 55 minutes later. The local time in Seoul is 16 hours ahead of the local time in Seattle. Work out the day and time in Seoul when the plane arrives. Day …… Time …… [3]
Mark scheme
11 Wednesday and 10 25 3 B2 for 10 25 or B1 for one correct time calculation or M1 for 07 30 + 10 55 + 16 00
Question
The equation of line L is y = 5x - 3. (a) Write down the gradient of line L. …… [1] (b) Write down the equation of a line parallel to line L. y = …… [1] * 0000800000007 * DFD 7
Mark scheme
12(a) 5 1 12(b) 5x + k (k ≠ −3) 1
Question
The scale drawing shows the position of ship A. The scale is 1 centimetre represents 50 kilometres. North A Scale: 1 cm to 50 km Ship B is 300 km from ship A on a bearing of 105°. On the scale drawing mark the position of ship B. [2]
Mark scheme
13 Correct point marked 2 B1 for bearing of B from A 105° B1 for AB drawn length 6 cm
Question
Tom needs 225 g of flour to make 10 cakes. A shop sells flour in 500 g bags. Work out the number of bags of flour Tom needs to make 70 cakes. …… [3] * 0000800000008 * DFD 8
Mark scheme
14 4 nfww 3 B2 for 3.15 OR 70 M1 for 225 × oe 10 M1 for their 1575 ÷ 500 oe If 0 or 1 scored SC1 for their decimal rounded up to an integer
Question
A y B y C y 3 3 x x x NOT TO SCALE D y E y F y 3 3 x 3 x 3 x Write down the letter of the graph that shows these lines. (a) x = 3 …… [1] (b) y = 3x …… [1] * 0000800000009 * DFD 9
Mark scheme
15(a) E 1 15(b) B 1
Question
The diagram shows a shape made from a square and four congruent isosceles triangles. 7.8 cm NOT TO 14 cm SCALE Work out the area of this shape. …… cm 2 [3]
Mark scheme
16 109.2 3 1 M2 for 7.8 × 7.8 + 4 × × 7.8 × 2 14 − 7.8 oe 2 or M1 for 7.8 × 7.8 oe 1 14 − 7.8 or [ ×] 7.8 × oe 2 2
Question
The volume of a cylinder is 863.5 cm 3 . The height of the cylinder is 12.3 cm. Find the radius of the cylinder. …… cm [3] * 0000800000010 * DFD 10
Mark scheme
17 4.73 or 4.726 to 4.727… 3 M2 for 863.5 ÷ 12.3π oe or M1 for πr 2 ×12.3 = 863.5 or better
Question
Dara changes 5700 Thai baht to dollars. The exchange rate is $1 = 34.18 Thai baht. Calculate the amount that Dara receives. $ …… [1]
Mark scheme
18 166 or 167 or 166.7 to 166.8[0] 1
Question
A four-sided dice is numbered 1 to 4. Hrishi throws the dice 50 times. The results are shown in the table. Number Frequency 1 14 2 15 3 9 4 12 Calculate the mean. …… [2]
Mark scheme
19 2.38 2 M1 for (1 × 14 + 2 × 15 + 3 × 9 + 4 × 12) ÷ 50 oe
Question
A tin contains red, yellow, green and brown sweets. The table shows some of the probabilities of picking a sweet of each colour at random. Colour Red Yellow Green Brown Probability 0.68 0.05 0.14 Complete the table. [2] * 0000800000011 * DFD 11
Mark scheme
20 [0].13 2 B1 for 0.87 or M1 for 1 – (0.68 + 0.05 + 0.14) oe
Question
The diagram shows a right-angled triangle ABC. A NOT TO SCALE 52.5 cm 59.5 cm B C Calculate BC. BC = …… cm [3]
Mark scheme
21 28 nfww 3 M2 for 59.52 – 52.52 oe or M1 for 52.52 + […] 2 = 59.52 oe
Question
(a) Anil invests $2000 and Baz invests $7500. Write the ratio money invested by Anil : money invested by Baz in its simplest form. …… : …… [1] (b) Kamil and Lavik share some money in the ratio Kamil : Lavik = 5 : 9. Lavik receives $72 more than Kamil. Calculate the total amount of money they share. $ …… [2] (c) Vanisha invests $4000 for 5 years at a rate of 3.5% per year compound interest. Calculate the total interest earned during the 5 years. $ …… [3] * 0000800000012 * DFD 12
Mark scheme
22(a) 4 : 15 cao 1 22(b) 252 cao 2 72 M1 for × k, k = 1, 5, 9 or 14 oe 9−5 22(c) 751 or 750.7… 3 B2 for 4750 or 4751 or 4750.7… 3.5 5 or M2 for 4000 × (1 + ) − 4000 oe 100 3.5 5 or M1 for 4000 × (1 + ) oe 100
Question
The population of an island increases from 18 400 to 19 780. Calculate the percentage increase. …… % [2]
Mark scheme
23 7.5 2 19 780 − 18 400 M1 for [× 100] oe 18 400 19 780 or × 100 [– 100] oe 18 400 19 780 or ( – 1) [× 100] oe 18 400
Question
V NOT TO B SCALE 14 cm A C 12 cm U W 21 cm Triangle ABC is mathematically similar to triangle UVW. Calculate AB. AB = …… cm [2]
Mark scheme
24 8 2 12 21 M1 for = oe AB 14
Question
A bar of gold in the shape of a cuboid has dimensions 2 cm by 4 cm by 6.5 cm. The density of gold is 19.32 g/cm 3 . Calculate the mass of this bar of gold. mass :Density = volumeD …… g [3] * 0000800000013 * DFD 13
Mark scheme
25 1004.64 3 M1 for 2 × 4 × 6.5 oe implied by 52 M1 for 19.32 = [ mass ] or better their 52
Question
Li asks 28 students if they speak English (E) and if they speak Spanish (S). 15 students speak English. 12 students speak Spanish. 6 do not speak English and do not speak Spanish. % E S (a) Complete the Venn diagram. [2] (b) Write down how many students speak English but do not speak Spanish. …… [1] (c) Find n (E , S ) . …… [1]
Mark scheme
26(a) 2 B1 for one value in the correct place. 26(b) 10 1 FT their diagram (dep total = 28) 26(c) 22 1 FT their diagram (dep total = 28)
Question
The height, h metres, of a building is 105 m, correct to the nearest metre. Complete this statement about the value of h. …… G h 1 …… [2] * 0000800000014 * DFD 14
Mark scheme
27 104.5 105.5 2 B1 for each in correct position If 0 scored SC1 for both correct but reversed
Question
(a) (i) Complete the table of values for y = x 2 - x - 5 . x −3 −2 −1 0 1 2 3 4 y 1 −3 −3 1 [2] (ii) On the grid, draw the graph of y = x 2 - x - 5 for –3 G x G 4 . y 8 7 6 5 4 3 2 1 –3 –2 –1 0 1 2 3 4 x –1 –2 –3 –4 –5 –6 [4] (b) Write down the equation of the line of symmetry of the graph. …… [1] (c) Use the graph to solve the equation x 2 - x - 5 = 0 . x = …… or x = …… [2] * 0000800000015 * DFD 15
Mark scheme
28(a)(i) 7, [1], [−3], –5, –5, [−3], [1], 7 2 B1 for 2 correct 28(a)(ii) Correct graph 4 B3FT for 7 points accurately plotted or B2FT for 5 points accurately plotted or B1FT for 3 points accurately plotted 28(b) 1 1 x= oe 2 28(c) –1.9 to –1.7 2.7 to 2.9 2 FT their curve B1 for each
Question
10 cm NOT TO SCALE 9 cm 16 cm This shape is made from a rectangle and a semicircle. The diameter of the semicircle is 10 cm. Calculate the perimeter of this shape. …… cm [3] Question 30 is printed on the next page. * 0000800000016 * DFD 16
Mark scheme
29 55.7 or 55.70 to 55.71 3 M2 for 16 + 9 + 9 + (16 – 10) 1 + their( ×π×10) oe 2 1 or M1 for π × 10 [× ] 2 1 or 2× π × 5 [× ] oe 2 or 16 + 9 + 9 + (16 – 10) oe
Question
P 6 cm 8 cm NOT TO SCALE R Q The diagram shows a right-angled triangle, PQR. Calculate angle QRP. Angle QRP = …… [2]
Mark scheme
30 48.6 or 48.59… 2 6 M1 for sin […=] oe 8
Checked your answers against these? Let AI mark the whole paper, on your own working.
Mark my 0580/31Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
Done this paper? Upload your script and CIE Buddy's AI marker marks it question by question against this exact scheme, puts the ticks on your own working and says what each lost mark needed.
Question papers and mark schemes © Cambridge University Press & Assessment. CIE Buddy is independent and not connected to Cambridge.
On this page, free: the mark scheme for IGCSE Mathematics 0580/31, May/June 2025 (0580_s25_ms_31), and the question paper (0580_s25_qp_31), to read or download, with each question's marking points written out underneath.
Mathematics 0580/31 for May/June 2025 is out of 80 marks, with 1 hour 30 minutes to answer it.
Yes. Upload your answers to 0580/31/M/J/25 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.