Cambridge IGCSE Mathematics 0580 — 2025 May/June Paper 3 · Variant 1
0580/31/M/J/25 · 30 questions · 80 marks · 90 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper16 pages
Mark scheme10 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · The pictogram shows the number of goals scored by teams A, B and C
1 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: Question Answer Marks Partial Marks 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
Q2 · An angle measures 157°
2 An angle measures 157°. Write down the mathematical name for this type of angle. ................................................. [1]
Mark scheme: 2 Obtuse 1
Q3 · Find the value of .196
3 Find the value of .196 . ................................................. [1]
Mark scheme: 3 1.4 1
Q4 · Calculate the number of months in 5 years
4 Calculate the number of months in 5 years. ................................................. [1]
Mark scheme: 4 60 1
Q5 · Write down the order of rotational symmetry for this shape
5 (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
Q6 · In triangle ABC, AC = 6 .4 cm and BC = 5.3 cm
6 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 7
7 Solve. 3y = 18 y = ................................................ [1]
Mark scheme: 7 6 1
Q8 · T = 3 ( 5P - 8) + 4 Find the value of T when P = 12
8 (a) T = 3 ( 5P - 8) + 4 Find the value of T when P = 12 . T = ................................................ [2] (b) W = t4 + 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
Q9 · Represent the inequality –3 1 x G 2 on the number line
9 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]
Mark scheme: 9 2 B1 for correct line and one end correct or both ends correct and no line
Q10 · 3 0.41 17 42% 7 41 Write these numbers in order, starting with the smallest
10 3 0.41 17 42% 7 41 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% or M1 for conversion to common 41 7 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%]
Q11 · A plane leaves Seattle at 07 30 on Tuesday and arrives in Seoul 10 hours and 55 minutes…
11 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
Q12 · The equation of line L is y = 5x - 3
12 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]
Mark scheme: 12(a) 5 1 12(b) 5x + k (k ≠ −3) 1
Q13 · The scale drawing shows the position of ship A
13 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
Q14 · Tom needs 225 g of flour to make 10 cakes
14 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]
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
Q15 · A B C y y y 3 3 x xx xx NOT TO SCALE D E F y y y 3 x 3 xx 3 x 3 Write down the letter of…
15 A B C y y y 3 3 x xx xx NOT TO SCALE D E F y y y 3 x 3 xx 3 x 3 Write down the letter of the graph that shows these lines. (a) x = 3 ................................................. [1] (b) y = 3 x ................................................. [1]
Mark scheme: 15(a) E 1 15(b) B 1
Q16 · The diagram shows a shape made from a square and four congruent isosceles triangles
16 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. ......................................... cm2 [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
Q17 · The volume of a cylinder is 863.5 cm 3
17 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]
Mark scheme: 17 4.73 or 4.726 to 4.727… 3 M2 for 863.5 ÷ 12.3π oe or M1 for πr2×12.3 = 863.5 or better
Q18 · Dara changes 5700 Thai baht to dollars
18 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
Q19 · A four-sided dice is numbered 1 to 4
19 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
Q20 · A tin contains red, yellow, green and brown sweets
20 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]
Mark scheme: 20 [0].13 2 B1 for 0.87 or M1 for 1 – (0.68 + 0.05 + 0.14) oe
Q21 · The diagram shows a right-angled triangle ABC
21 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
Q22 · Anil invests $2000 and Baz invests $7500
22 (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]
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 + 100) − 4000 oe 3.5 5 or M1 for 4000 (1 + ) oe 100
Q23 · The population of an island increases from 18 400 to 19 780
23 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 18 400 780 or (19 – 1) [× 100] oe 18 400
Q24 · V B NOT TO SCALE 14 cm A C 12 cm U W 21 cm Triangle ABC is mathematically similar to…
24 V B NOT TO 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
Q25 · A bar of gold in the shape of a cuboid has dimensions 2 cm by 4 cm by 6.5 cm
25 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 = D volume .............................................. g [3]
Mark scheme: 25 1004.64 3 M1 for 2 × 4 × 6.5 oe implied by 52 mass M1 for 19.32 = or better their 52
Q26 · Li asks 28 students if they speak English (E) and if they speak Spanish (S)
26 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)
Q27 · The height, h metres, of a building is 105 m, correct to the nearest metre
27 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]
Mark scheme: 27 104.5 105.5 2 B1 for each in correct position If 0 scored SC1 for both correct but reversed
Q28 · Complete the table of values for y = x 2 - x - 5
28 (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]
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
Q29 · 10 cm NOT TO SCALE 9 cm 16 cm This shape is made from a rectangle and a semicircle
29 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.
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
Q30 · P 6 cm 8 cm NOT TO SCALE R Q The diagram shows a right-angled triangle, PQR
30 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
What was in this paper
The subtopics covered by these 30 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Surface area and volume2Time2Angles1Area and perimeter1Averages and range1Compound shapes and parts of shapes1Drawing linear graphs1Equations1Geometrical constructions1Gradient of linear graphs1Graphs of functions1Inequalities1Introduction to algebra1Introduction to probability1Limits of accuracy1Money1Ordering1Percentages1Powers and roots1Pythagoras’ theorem1Right-angled triangles1Scale drawings1Sets1Similarity1Statistical charts and diagrams1Symmetry1What you needed in this session
Cambridge’s own grade thresholds for 2025 May/June, Paper 3 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.