Cambridge IGCSE Mathematics 0580 — 2025 May/June Paper 3 · Variant 2
0580/32/M/J/25 · 24 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 · Write 3.45 pm using the 24-hour clock
1 Write 3.45 pm using the 24-hour clock. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 15 45 1
Q2 · The diagram shows a square-based pyramid
2 The diagram shows a square-based pyramid. Complete this statement. The pyramid has .............................. edges and .............................. vertices. [2]
Mark scheme: 2 8 5 2 B1 for each in correct position
Q3 · Convert 3 m into mm
3 Convert 3 m into mm. .......................................... mm [1]
Mark scheme: 3 3000 1
Q4 · Apples cost $1.20 per kilogram and one banana costs 35 cents
4 Apples cost $1.20 per kilogram and one banana costs 35 cents. (a) Work out the total cost, in dollars, of 3 kg of apples and 7 bananas. $ ................................................. [3] (b) Work out the change from $20. $ ................................................. [1]
Mark scheme: 4(a) 6.05 cao 3 M2 for 3 1.2 0 + 7 0.35 oe or B2 for 605 or 6.05 seen then spoilt or B1 for 3.6[0] or 360 or 2.45 or 245 or M1 for 3 × 120 + 7 × 35 4(b) 13.95 1 FT 20 − their (a)
Q5 · A student scores 58 out of 80 in a test
5 A student scores 58 out of 80 in a test. Calculate their percentage score. ..............................................% [1]
Mark scheme: 5 72.5 1
Q6 · Calculate 57% of 45
6 Calculate 57% of 45. ................................................. [2]
Mark scheme: 6 25.65 2 57 M1 for 45 oe 100
Q7 · A train leaves station A at 13 44
7 A train leaves station A at 13 44. The train arrives at station B after 3 hours and 30 minutes. (a) Work out the time the train arrives at station B. ................................................. [1] (b) The distance between station A and station B is 210 km. Calculate the average speed of the train in km/h. ........................................ km/h [1]
Mark scheme: 7(a) 17 14 1 7(b) 60 1
Q8 · The exchange rate is $1 = 0.923 euros
8 The exchange rate is $1 = 0.923 euros. Calculate the difference between 750 euros and $846. Give your answer in euros correct to 2 decimal places. ........................................ euros [3]
Mark scheme: 8 30.86 cao 3 B2 for 30.858 or M1 for 846 0.923 750 or 846 − 0.923 0.923 B1 for rounding their answer correct to 2 decimal places
Q9 · Flo has a bag of counters
9 Flo has a bag of counters. She picks a counter at random from the bag. The probability that she picks a green counter is 0.52 . (a) Work out the probability that she does not pick a green counter. ................................................. [1] (b) The bag contains three colours of counters, green, pink and red. Colour of counter Green Pink Red Probability 0.52 There are three times as many pink counters as red counters. Complete the table. [2] (c) Flo picks one counter from the bag at random, records the colour and replaces it in the bag. She does this 200 times. Calculate the expected number of times she picks a green counter. ................................................. [1]
Mark scheme: 9(a) 0.48 1 9(b) 0.36 0.12 2 B1 for each in correct position their(a) 1 − 0.52 or M1 for or oe 4 4 9(c) 104 1
Q10 · A NOT TO 65° SCALE O y° x° C B A, B and C are points on a circle, centre O, diameter AC
10 A NOT TO 65° SCALE O y° x° C B A, B and C are points on a circle, centre O, diameter AC. Complete these statements, giving geometrical reasons. (a) The value of x is .......................... because ................................................................................. ..................................................................................................................................................... [2] (b) Angle ABC = 90° because ......................................................................................................... ..................................................................................................................................................... [1] (c) The value of y is .......................... because ................................................................................. ..................................................................................................................................................... [2]
Mark scheme: 10(a) 65 2 B1 for 65 base angles of an isosceles triangle are equal 10(b) Angle in a semicircle equals 90 1 10(c) 25 2 B1 for each Angle sum of a triangle equals 180
Q11 · The scale drawing shows the position of a hospital, H
11 The scale drawing shows the position of a hospital, H. The scale is 1 centimetre represents 6 kilometres. North H Scale: 1 cm to 6 km A school, S, is 33 km from H on a bearing of 155°. Mark the position of S on the scale drawing. [2]
Mark scheme: 11 S marked correctly 2 B1 for HS drawn length 5.5cm B1 for bearing of S from H 155˚
Q12 · Kim and Tom ask some students if they prefer Chemistry, Biology or Physics
12 (a) Kim and Tom ask some students if they prefer Chemistry, Biology or Physics. Kim draws the bars for Biology and Physics on a bar chart. 10 9 8 7 6 Number of 5 students 4 3 2 1 0 Chemistry Biology Physics Tom draws the sector for Chemistry on a pie chart. Chemistry 120° Use the information from both diagrams to complete (i) the bar chart [2] (ii) the pie chart. [4] (b) Give one advantage of reading results from a bar chart compared to from a pie chart. ..................................................................................................................................................... [1]
Mark scheme: 12(a)(i) Bar for Chemistry drawn height 8 2 M1 7 + 9 [students] = 2 [× 360˚] or better 3 12(a)(ii) Pie chart correctly drawn 4 B3 for 105 or 135 120 or M2 for k their 8 240 or k 7 + 9 360 or k 7 + 9 + their 8 where k = 1, 7 or 9 or B1 for 240 and 7 and 9 seen or 24 or 7 + 9 +their8 correctly evaluated 12(b) [Bar chart] gives the frequencies 1 [whereas pie chart only gives proportions] oe
Q13 · 2, e, f, 20, … A linear sequence has a first term of 2 and a fourth term of 20
13 (a) 2, e, f, 20, … A linear sequence has a first term of 2 and a fourth term of 20. The term-to-term rule for this sequence is add k. Work out the values of e, f and k. e = ....................................................... f = ....................................................... k = ....................................................... [3] (b) These are the first four terms of another sequence. 9 7 5 3 Find the nth term. ................................................. [2]
Mark scheme: 13(a) 8 14 6 3 B1 for each correctly assigned 20 − 2 or M1 for oe 3 13(b) 11 −n2 oe final answer 2 B1 for answer j −n2 or 11−kn , k 0 or 11 −n2 seen then spoilt
Q14 · P = 6 a + 5b Find the value of b when P = 25 and a = 3
14 (a) P = 6 a + 5b Find the value of b when P = 25 and a = 3 . b = ................................................ [2] (b) Make T the subject of the formula W = kT + y . T = ................................................ [2]
Mark scheme: 14(a) 1.4 2 M1 for 25 = 6 +3 5b or better 14(b) W − y W y 2 W y T = or T = − M1 for W − y = kT or = T + k k k k k final answer
Q15 · The equation of a line is y =- 5x + 7
15 The equation of a line is y =- 5x + 7 . (a) Write down the gradient of this line. ................................................. [1] (b) Find the coordinates of the point where this line crosses the y-axis. ( ...................... , ...................... ) [1]
Mark scheme: 15(a) −5 1 15(b) 0 , 7 1
Q16 · Sam spends $187 on electricity and gas
16 (a) Sam spends $187 on electricity and gas. The ratio electricity : gas = 8 : 3 . Work out how much Sam spends on electricity. $ ................................................. [2] (b) Jai spends $180 on electricity and $150 on gas. Write down the ratio electricity : gas in its simplest form. ........................ : ....................... [1] (c) Kat spends money on electricity and gas in the ratio electricity : gas = E : G. Write down an expression, in terms of E and G, for the fraction she spends on gas. ................................................. [1]
Mark scheme: 16(a) 136 2 187 M1 for k , where k = 1, 3 or 8 oe 3 + 8 16(b) 6 : 5 cao 1 16(c) G 1 E + G
Q17 · Rick invests $6000 for 5 years at a rate of 9% per year compound interest
17 Rick invests $6000 for 5 years at a rate of 9% per year compound interest. Calculate the total interest earned during the 5 years. $ ................................................. [3]
Mark scheme: 17 3 230 or 3231 or 3232 or 3231.7… 3 B2 for 9230 or 9231 or 9232 or 9231.7… OR 9 5 M2 for 6000 1 + − 6000 oe 100 9 5 or M1 for 6000 1 + oe 100
Q18 · A factory produces brass at a rate of 172 kilograms per hour
18 A factory produces brass at a rate of 172 kilograms per hour. (a) Convert this rate into grams per second. .............................................g/s [2] (b) The rate is increased to 176 kilograms per hour. Calculate the percentage increase in the rate. ..............................................% [2]
Mark scheme: 18(a) 47.8 or 47.77 to 47.78 2 172 1000 M1 for oe 60 60 or B1 for figs 478 or 4777 to 4778 18(b) 2.33 or 2.325 to 2.326 2 176 − 172 M1 for 100 oe 172 176 or 100 −100 oe 172 176 or − 1 100 oe 172
Q19 · Write 0.000 000 0347 in standard form
19 (a) Write 0.000 000 0347 in standard form. ................................................. [1] (b) Calculate 3 # 10 4 # 5 # 10 6 . Give your answer in standard form. ................................................. [1]
Mark scheme: 19(a) 3.47 10−8 1 19(b) 1.5 1011 1
Question 20
20 Solve. (a) x + 3 = 3 x = ................................................ [1] 5y (b) = 8 3 y = ................................................ [2]
Mark scheme: 20(a) 0 1 20(b) 4 2 y 8 4.8 or 4 M1 for 5 y = 3 8 or = or better 5 3 5
Question 21
21 Simplify. (a) ( w3 ) 10 ................................................. [1] (b) t 6 v 7 # t 3 v - 2 ................................................. [2]
Mark scheme: 21(a) w30 final answer 1 21(b) t 9 v 5 final answer 2 B1 for t 9 v k or kt v 5 , final answer or correct answer seen then spoilt
Q22 · In this question, all lengths are in centimetres
22 In this question, all lengths are in centimetres. NOT TO 4x - 9 SCALE 2x - 5 2x + 2 The diagram shows a right-angled triangle. (a) Write down an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest form. ................................................. [2] (b) The perimeter of the triangle is 40 cm. Work out the value of x. x = ................................................ [2] (c) Work out the area of the triangle. .......................................... cm2 [3]
Mark scheme: 22(a) 8x − 12 final answer 2 M1 for 2 x −+5 2 x + 2 + 4 x − 9 soi or better or B1 for 8x or −12 , in final expression or correct expression seen then spoilt 22(b) 6.5 2 12 40 M1 for 8x = 40 + 12 or x − = 8 8 or a correct first step in rearranging their kx + j = 40 k ≠ 0, j ≠ 0 22(c) 60 3 FT their (b) for 3 marks if their (b) > 2.5 M2 for 1 ( 2 their (b) − 5 ) ( 2 their (b) + 2 ) oe or 2 better or M1 for substituting their (b) into 2 x − 5 and 2 x + 2 1 or M1 for (2 x − 5) (2 x + 2) 2
Q23 · A sphere has radius 8 cm
23 A sphere has radius 8 cm. A cone has radius 8 cm and height h. The sphere and the cone have the same volume. Work out the height, h, of the cone. h = ............................................cm [4] Question 24 is printed on the next page.
Mark scheme: 23 32 4 4 3 π 8 3 M3 for [h =] oe 1 2 π 8 3 4 3 1 2 or M2 for π 8 = π 8 h oe 3 3 4 3 1 2 or M1 for π 8 oe or π 8 h oe 3 3
Q24 · The diagram shows two right-angled triangles
24 The diagram shows two right-angled triangles. B d m C NOT TO SCALE 14.7 m 52° A D 10.8 m Calculate the value of d. d = ................................................ [5]
Mark scheme: 24 12.8 or 12.76… 5 d M4 for tan 52 = oe 14.7 2 − 10.8 2 or B3 for 9.97[…] or M2 for 14.7 2 − 10.8 2 oe 2 2 2 or M1 for 10.8 + ( BD ) = 14.7 oe if M2 or M1 or M0 scored, d SC1 for tan52 = oe their BD
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Percentages2Time2Area and perimeter1Circle theorems I1Exponential growth and decay1Geometrical terms1Gradient of linear graphs1Indices I1Introduction to probability1Money1Money1Rates1Ratio and proportion1Right-angled triangles1Scale drawings1Sequences1Standard form1Statistical charts and diagrams1Surface area and volume1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2025 May/June, Paper 3 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.