Cambridge IGCSE Mathematics 0580 — 2025 May/June Paper 3 · Variant 3
0580/33/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 paper20 pages
Mark scheme10 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · 2 6 16 18 24 26 27 33 From this list, write down the number that is (a) a multiple of 12…
1 2 6 16 18 24 26 27 33 From this list, write down the number that is (a) a multiple of 12 ................................................. [1] (b) a square number ................................................. [1] (c) a cube number. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 24 1 1(b) 16 1 1(c) 27 1
Q2 · Shade one square so that the diagram has 1 line of symmetry
2 Shade one square so that the diagram has 1 line of symmetry. [1]
Mark scheme: 2 1
Q3 · Put one pair of brackets into this calculation to make it correct
3 Put one pair of brackets into this calculation to make it correct. 80 ' 8 + 2 # 3 = 24 [1]
Mark scheme: 3 80 ÷ (8 + 2) × 3 = 24 1
Q4 · Tim drives home from work
4 Tim drives home from work. The travel graph shows his journey. Work 36 30 Distance 24 from home (km) 18 12 6 Home 0 14 00 14 30 15 00 15 30 Time (a) Write down the time Tim leaves work. ................................................. [1] (b) Tim stops on the way home. (i) Find how far Tim travels before he stops. ............................................ km [1] (ii) Find how long Tim stops for. ........................................... min [1]
Mark scheme: 4(a) 14 10 1 4(b)(i) 24 1 4(b)(ii) 20 1
Question 5
5 Calculate. 2 .8 5 - 0 .3 2 5 Give your answer correct to 2 decimal places. ................................................. [2]
Mark scheme: 5 76.93 cao 2 B1 for 76.9 or 76.92…. or for their decimal seen and rounded to 2 decimal places
Q6 · In a bag of counters, 6 of the counters are blue
6 In a bag of counters, 6 of the counters are blue. The arrow (↓) on the probability scale shows the probability of picking a blue counter at random. 0 0.5 1 Work out the total number of counters in the bag. ................................................. [1]
Mark scheme: 6 30 1
Q7 · 7 The local time in Japan is 3 hours ahead of the local time in India
1 7 The local time in Japan is 3 hours ahead of the local time in India. 2 Find the time in Japan when it is 21 45 in India. ................................................. [1]
Mark scheme: 7 01 15 1
Q8 · Mia changes $350 into euros
8 Mia changes $350 into euros. The exchange rate is $1 = 0.92 euros. Calculate the amount Mia receives. ........................................ euros [1]
Mark scheme: 8 322 cao 1
Q9 · C NOT TO SCALE 53° B D 32° y° x° A E ABC is a straight line
9 C NOT TO SCALE 53° B D 32° y° x° A E ABC is a straight line. BD is parallel to AE. (a) Find the value of x. Give a geometrical reason for your answer. x = .................... because ............................................................................................................ [2] (b) Find the value of y. Give a geometrical reason for your answer. y = .................... because ............................................................................................................ [2]
Mark scheme: 9(a) 32 2 B1 for 32 alternate angles 9(b) 53 2 B1 for 53 corresponding angles
Question 10
10 Solve. 4p + 11 = 25 p = ................................................. [2]
Mark scheme: 10 1 7 2 11 25 3 or 3.5 or M1 for 4p = 25 – 11 oe or p + = 2 2 4 4 oe
Question 11
11 (a) Expand and simplify. 5 ( x - 2) + 3 ( x - 7) ................................................. [2] (b) Factorise. 4a 2 + 16a ................................................. [2]
Mark scheme: 11(a) 8x – 31 final answer 2 B1 for 5x – 10 or 3x – 21 or for 8x – 31 seen then spoilt or for 8x or –31 in the final answer 11(b) 4a(a + 4) final answer 2 B1 for 4(a2 + 4a) or a(4a + 16) or 2a(2a + 8) as answers or for 4a(a + 4) seen and spoilt
Q12 · Kai opens his restaurant from Tuesday to Saturday each week
12 Kai opens his restaurant from Tuesday to Saturday each week. He counts the number of customers each day for two weeks. The bar chart shows some of the results. 70 60 50 Number of 40 customers 30 20 10 0 Tue Wed Thur Fri Sat Day Key: = Week 1 = Week 2 (a) In week 1 there were 200 customers in total. Complete the bar chart. [2] (b) Write down the mode for week 2. ................................................. [1] (c) Find the mean number of customers for the 5 days in week 2. ................................................. [2]
Mark scheme: 12(a) Bar drawn in correct position with height 2 M1 for 200 – (20 + 30 + 50 + 60) soi 40 12(b) 40 1 12(c) 48 2 30 + 40 + 40 + 70 + 60 M1 for oe 5
Q13 · In May a shop makes a profit of $542
13 In May a shop makes a profit of $542. In June the shop makes a profit of $600. (a) Calculate the percentage increase in the profit from May to June. .............................................. % [2] 2 (b) The shop gives of the profit from May to a charity. 5 Find the amount the shop gives to the charity. $ ................................................. [1] (c) The shop spends 38% of the profit from June on a fridge. Find the amount the shop spends on the fridge. $ ................................................. [1]
Mark scheme: 13(a) 10.7 or 10.70… 2 600 − 542 M1 for 100 oe 542 600 or 100 −100 oe 542 600 or − 1 100 oe 542 13(b) 216.8[0] 1 13(c) 228 1
Q14 · Meg invests $2500 at a rate of 4.6% per year simple interest
14 Meg invests $2500 at a rate of 4.6% per year simple interest. Calculate the total amount of her investment at the end of 3 years. $ ................................................. [3]
Mark scheme: 14 2845 3 B2 for 345 2500 4.6 3 or M2 for 2500 + oe 100 2500 4.6[3] or M1 for oe 100
Q15 · The table gives information about the costs of hiring bikes
15 The table gives information about the costs of hiring bikes. Type of bike Cost for first day Cost for each extra day Road $25 $20 Mountain $40 $35 Electric $70 $50 (a) Work out the cost of hiring 2 road bikes for 3 days. $ ................................................. [2] (b) The cost, M, of hiring a mountain bike for d days can be written as M = 35d + 5 . (i) Write a formula for the cost, E, of hiring an electric bike for d days. E = ................................................. [2] (ii) The cost of hiring an electric bike for 6 days is the same as the cost of hiring a mountain bike for d days. Find the value of d. d = ................................................. [3]
Mark scheme: 15(a) 130 2 B1 for 65 or M1 for 2 × (25 + 2 × 20) oe 15(b)(i) 50d + 20 oe final answer 2 B1 for 50d + j or kd + 20 k ≠ 0, or 50d + 20 seen then spoilt 15(b)(ii) 9 nfww 3 320 − 5 M2 for 35d = 320 – 5 oe or for 35 oe or M2FT for 35d = correct evaluation of 6 in their(b)(i) – 5 oe or B1 for 320 soi or M1 for 70 + 50 × 5 = 35d + 5 oe or 50 × 6 + 20 = 35d + 5 oe or M1FT for substitution of 6 into their (b)(i) = 35d + 5 If 0 scored, SC1 for correct evaluation of 6 substituted into their (b)(i)
Q16 · The scale drawing shows a path from S to P
16 The scale drawing shows a path from S to P. The scale is 1 cm represents 2.5 km. North P North S Scale: 1 cm to 2.5 km (a) Work out the actual distance between S and P. ............................................ km [2] (b) Measure the bearing of S from P. ................................................. [1] (c) E is 20 km from P on a bearing of 070°. On the scale drawing, mark the position of E. [2]
Mark scheme: 16(a) 16.25 2 B1 for 6.5 or M1 for their 6.5 × 2.5 16(b) 142 1 16(c) E correctly placed 2 B1 for E on a bearing of 070 from P or for E 8 cm from P If 0 scored, SC1 for fully correct but from S not P
Q17 · Y 8 7 6 5 4 A 3 B 2 1 C – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 x – 1 – 2 – 3 – 4 (a) Sue…
17 y 8 7 6 5 4 A 3 B 2 1 C – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 x – 1 – 2 – 3 – 4 (a) Sue describes the single transformation that maps shape A onto shape B as a translation by the 7 vector e o. 1 Explain why Sue is incorrect. ............................................................................................................................................................ ..................................................................................................................................................... [1] (b) On the grid, draw the image of shape A after a rotation of 90° anticlockwise about (0, 0). [2] (c) Describe fully the single transformation that maps shape A onto shape C. ............................................................................................................................................................ ..................................................................................................................................................... [3]
Mark scheme: 17(a) She counted 1 up instead of 1 down oe 1 17(b) Correct shape drawn at 2 B1 for correct shape drawn 90 clockwise (–4,–1), (–2,–1), (–5,–2), (–2,–2) about the origin or for correct orientation, wrong centre 17(c) Enlargement 3 B1 for each [scale factor] 2 [centre] (–5, 7)
Q18 · D C Points C and D lie on the circle
18 (a) D C Points C and D lie on the circle. Write down the mathematical name for the line CD. ................................................. [1] (b) The diagram shows a circle with centre O. O Points K, L and M lie on the circumference of the circle. Draw triangle KLM so that angle KLM = 90° . [1]
Mark scheme: 18(a) Chord 1 18(b) Correct triangle drawn 1
Q19 · 19 (a) Complete the table of values for y =
20 19 (a) Complete the table of values for y = . x x 1 2 3 4 5 y 20 10 4 [2] 20 (b) On the grid, draw the graph of y = for 1 G x G 5 . x y 25 20 15 10 5 0 x 0 1 2 3 4 5 6 [3] 20 (c) Use your graph to solve the equation = 8 . x x = ................................................. [1]
Mark scheme: 19(a) [20], [10], 6.67, 5, [4] 2 B1 for each 19(b) Correct graph 3 B2FT for 4 points correctly plotted or B1FT for 2 points correctly plotted 19(c) 2.45 to 2.55 1 FT their curve
Q20 · A spinner is numbered 1, 2, 3, 4 and 5
20 A spinner is numbered 1, 2, 3, 4 and 5. Rinesh spins the spinner many times. He works out the relative frequency that the spinner lands on each number. Number 1 2 3 4 5 Relative frequency 0.15 0.22 0.26 0.25 (a) Complete the table. [2] (b) Rinesh spins the spinner another 1500 times. Calculate the expected number of times the spinner lands on 2. ................................................. [1]
Mark scheme: 20(a) 0.12 oe 2 B1 for 0.88 oe or M1 for 1 – (0.15 + 0.22 + 0.26 + 0.25) oe 20(b) 330 1
Q21 · These are the distances above the surface of the Earth of five satellites, A, B, C, D and…
21 (a) These are the distances above the surface of the Earth of five satellites, A, B, C, D and E. Each distance is in kilometres. A B C D E 35 800 .78 # 102 .15 # 106 535 2 # 104 (i) Write these distances in order, starting with the shortest. .................... , .................... , .................... , .................... , .................... [2] shortest (ii) The radius of Earth is 6370 km. Satellite A is k times further from the centre of Earth than satellite D. Show that k = 6.11 correct to 2 decimal places. [2] (b) A satellite travels at a speed of 27 000 km/h. Find the distance the satellite travels in 95 minutes. ............................................ km [2] (c) A different satellite travels at a speed of 25 200 km/h. Convert this speed into m / s. .......................................... m / s [2]
Mark scheme: 21(a)(i) 535, 7.8×102, 2×104, 35 800, 1.5×106 2 B1 for 4 in correct order or M1 for (B)780, (C)1 500 000 and (E)20 000 seen or for 3.58 × 104 and 5.35 × 102 seen 21(a)(ii) (35800 + 6370) ÷ (535 + 6370) M1 6.107…. A1 21(b) 42750 2 M1 for 27000 × their time 21(c) 7000 2 25200 1000 M1 for oe 60 60 or B1 for final answer figs 7
Q22 · The diagram shows a solid cylinder with height 10 cm
22 The diagram shows a solid cylinder with height 10 cm. NOT TO SCALE 10 cm The volume of the cylinder is 478 cm3. (a) Find the radius of the cylinder. ............................................ cm [3] (b) The cylinder is made from gold. The density of the gold is 19.3 g/cm3. Calculate the mass of the cylinder. mass :Density = D volume ............................................... g [1]
Mark scheme: 22(a) 3.9[0] or 3.900 to 3.901 3 2 478 M2 for r = oe 10π or M1 for π × r2 × 10 = 478 22(b) 9225.4 1
Q23 · The diagram shows a right-angled triangle
23 The diagram shows a right-angled triangle. 35 cm NOT TO SCALE 22 cm h cm Calculate the value of h. h = ................................................. [2]
Mark scheme: 23 41.3 or 41.34… 2 M1 for 352 + 222 oe or better
Q24 · The diagram shows a right-angled triangle
24 The diagram shows a right-angled triangle. 52° NOT TO SCALE 18.4 cm y cm Calculate the value of y. y = ................................................. [2]
Mark scheme: 24 23.6 or 23.55… 2 y M1 for tan52 = oe or better 18.4
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.
2Rates2Algebraic manipulation1Angles1Averages and range1Circles, arcs and sectors1Equations1Geometrical terms1Graphs of functions1Interpreting statistical data1Introduction to probability1Ordering1Percentages1Pythagoras’ theorem1Ratio and proportion1Right-angled triangles1Symmetry1The four operations1Time1Transformations1Types of number1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2025 May/June, Paper 3 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.