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Cambridge IGCSE Mathematics (0580), Paper 1 (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_110580_s25_ms_110580/11/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
(a) Write the number 10 069 in words. …… [1] (b) Write 10 069 correct to the nearest ten. …… [1] (c) Convert 10 069 centimetres into metres. …… m [1]
Mark scheme
1(a) Ten thousand [and] sixty-nine 1 1(b) 10 070 1 1(c) 100.69 1
Question
A bag of sweets costs $0.34 . Arun buys 10 bags of sweets. Work out how much change he receives from $5. $ …… [2]
Mark scheme
2 1.6[0] 2 B1 for 3.4[0] or M1 for 5 – 10 × 0.34 oe
Question
Two numbers have a sum of -2 and a product of -15. Work out the two numbers. …… and …… [2] * 0000800000004 * DFD 4
Mark scheme
3 –5 3 2 B1 for answer of two numbers that add to –2 or multiply to –15
Question
7 27 39 49 99 112 From the list of numbers, write down (a) an even number …… [1] (b) a square number …… [1] (c) a factor of 56 …… [1] (d) a prime number. …… [1]
Mark scheme
4(a) 112 1 4(b) 49 1 4(c) 7 1 4(d) 7 1
Question
Write down the reciprocal of 5. …… [1]
Mark scheme
5 1 1 or [0].2 5
Question
Put one pair of brackets into each calculation to make it correct. (a) 7 - 5#4+8= 16 [1] (b) 7 - 5 # 4 + 8 = - 21 [1] * 0000800000005 * DFD 5
Mark scheme
6(a) (7 – 5) × 4 + 8 = 16 1 6(b) 7 – (5 × 4 + 8) = – 21 1
Question
(a) A ticket costs $18. Write down an expression, in dollars, for the cost of t tickets. $ …… [1] (b) A bag contains n red balls and 16 green balls. Write down an expression for the total number of balls in the bag. …… [1]
Mark scheme
7(a) 18t final answer 1 7(b) n + 16 final answer 1
Question
(a) Write 90% as a fraction in its simplest form. …… [1] 3 (b) Write as a decimal. 100 …… [1]
Mark scheme
8(a) 9 1 cao 10 8(b) [0].03 1
Question
(a) These are the first four terms of a sequence. 33 26 19 12 (i) Write down the term-to-term rule for this sequence. …… [1] (ii) Work out the next two terms in this sequence. …… , …… [2] (b) These are the first four terms of another sequence. 19 23 27 31 Find the nth term. …… [2] * 0000800000006 * DFD 6
Mark scheme
9(a)(i) Subtract 7 oe 1 9(a)(ii) 5 –2 2 B1 for either in this order or SC1 for second number = first number –7 9(b) 4n + 15 oe final answer 2 B1 for final answer 4n + j or kn + 15 ( k ≠ 0) or 4n + 15 seen then spoilt
Question
Ky cycles from his office to a meeting and back again. The travel graph shows his time at the meeting and his journey back. 15 14 13 12 11 10 9 Distance from 8 office (km) 7 6 5 4 3 2 1 Office 0 09 00 10 00 11 00 12 00 Time (a) How far is the meeting from his office? …… km [1] (b) How long is Ky at the meeting for? …… min [1] (c) Write down the time Ky arrives back at his office after the meeting. …… [1] (d) Ky cycles from his office to the meeting at a constant speed of 21 km/h. Complete the travel graph. [2] * 0000800000007 * DFD 7
Mark scheme
10(a) 14 1 10(b) 40 1 10(c) 11 50 1 10(d) Ruled line from 2 their (a) (9 40, 0) to (10 20, 14) M1 for oe 21 or a parallel line
Question
Calculate the volume of a cube with side length 3 cm. …… cm 3 [1]
Mark scheme
11 27 1
Question
Solve. 5x + 8 = 3x - 2 x = …… [2]
Mark scheme
12 −5 cao final answer 2 M1 for 5x – 3x = – 2 – 8 oe or better
Question
Work out. (a) - 5 # - 4 …… [1] (b) - 8 + (- 3) …… [1]
Mark scheme
13(a) 20 1 13(b) –11 1
Question
3 p # 3 4 = 3 10 Find the value of p. p = …… [1] * 0000800000008 * DFD 8
Mark scheme
14 6 final answer 1
Question
6 cm NOT TO SCALE 4 cm 3 cm Complete a net of this cuboid on the 1 cm 2 grid. One face has been drawn for you. [3] * 0000800000009 * DFD 9
Mark scheme
15 Correct net 3 B2 for 3 correct extra faces in correct places or B1 for 1 correct extra face in correct place
Question
(a) Simplify. 6a + 4b - a - 5b …… [2] (b) Factorise. (i) 6x + 15y …… [1] (ii) x 2 y - 5xy …… [2]
Mark scheme
16(a) 5a – b final answer 2 B1 for 5a or −b in final answer or for 5a – b seen then spoilt 16(b)(i) 3(2x + 5y) final answer 1 16(b)(ii) xy( x – 5) final answer 2 B1 for x( xy – 5y) or y( x2 – 5x) or xy( x – 5) seen then spoilt
Question
By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 42.8 + 17.4 . 1.97 # 5.79 …… [2] * 0000800000010 * DFD 10
Mark scheme
17 40 + 20 M1 2× 6 5 nfww A1 If 0 scored SC1 for 3 correct roundings or for all correct but with trailing zeros
Question
The diagram shows two straight lines intersecting two parallel lines. y° x° z° NOT TO 110° 50° SCALE (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] (c) Find the value of z. * 0000800000011 * DFD 11
Mark scheme
18(a) 50 2 B1 for each alternate angles 18(b) 110 2 B1 for each corresponding angles 18(c) 60 2 M1 for 180 – (180 – 110) – 50 oe or 70 marked as third angle in triangle
Question
A box contains 10 counters. The counters are either red or green. The ratio red counters : green counters = 1 : 4. Shareen picks a counter at random, notes its colour and puts it back in the box. She then picks a second counter at random. First counter Second counter …… Red Red …… Green …… Red Green …… Green (a) Complete the tree diagram. [3] (b) Find the probability that both counters are green. …… [2] * 0000800000012 * DFD 12
Mark scheme
19(a) Correct tree diagram 3 1 4 B1 for oe and seen oe 5 5 1 4 M1 for either or in the correct place 5 5 in the first branch If 0 scored, SC1 for their two probabilities adding to 1 in the first branch 19(b) 16 2 FT their (a) probabilities oe 25 4 provided 0 < each of their <1 5 4 4 M1 for their × their 5 5
Question
The scatter diagram shows the price of petrol per litre and the number of litres sold at a petrol station on each of ten days. 500 400 300 Number of litres sold 200 100 0 1.40 1.45 1.50 1.55 1.60 1.65 1.70 Price per litre ($) (a) These are the results for two more days. Price per litre ($) 1.68 1.47 Number of litres sold 90 380 Plot this information on the scatter diagram. [1] (b) What type of correlation is shown in the scatter diagram? …… [1] (c) (i) On the scatter diagram, draw a line of best fit. [1] (ii) One day the price of petrol was $1.55 per litre. Use your line of best fit to estimate the number of litres sold. …… litres [1] * 0000800000013 * DFD 13
Mark scheme
20(a) 2 points accurately plotted 1 20(b) Negative 1 20(c)(i) Correct ruled line of best fit 1 20(c)(ii) 275 1 FT their straight line of best fit with negative gradient
Question
Points A, B and C lie on the circle, centre O. NOT TO A B 39° SCALE O C Work out angle BCA. Angle BCA = …… [2]
Mark scheme
21 51 2 M1 for 90 – 39 oe or angle ABC identified as 90
Question
A = 23 # 3 B = 32 # 5 (a) Find the highest common factor (HCF) of A and B. …… [1] (b) Find the lowest common multiple (LCM) of A and B. …… [2] * 0000800000014 * DFD 14
Mark scheme
22(a) 3 1 22(b) 360 2 B1 for answer 360k, k > 1 or M1 for 23 ×32 ×5 oe or for 24, 48, 72… and 45, 90, 135… seen
Question
y 8 7 6 B 5 4 3 2 T 1 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 x –1 –2 A –3 –4 –5 –6 (a) On the grid, draw the image of triangle T after a rotation, 90° clockwise, centre (0, 0). [2] (b) Describe fully the single transformation that maps triangle T onto triangle A. …… [2] (c) Describe fully the single transformation that maps triangle T onto triangle B. …… [3] * 0000800000015 * DFD 15 1 3
Mark scheme
23(a) Correct rotation, points at 2 B1 for correct rotation 90° anti-clockwise (1, –1), (3, –1) and (1, –4) or correct rotation with incorrect centre 23(b) Translation 2 B1 for each −6 −4 23(c) Enlargement 3 B1 for each [scale factor] 2 [centre] (0, -2) Angle mentioned
Question
Work out 1 + 1 . 3 4 Give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
24 1 3 4 7 3 nfww B1 for or oe 12 3 4 1 3 or for 2 + + oe 3 4 16 21 4 9 M1 for and or and 12 12 12 12
Question
(a) Write 32 500 in standard form. …… [1] (b) Write 5.6 # 10 -3 as an ordinary number. …… [1] Question 26 is printed on the next page. * 0000800000016 * DFD 16
Mark scheme
25(a) 3.25 × 104 1 25(b) [0].0056 1
Question
Solve the simultaneous equations. 2x + 5y = 5 3x + 4y = 11 x = …… y = …… [4]
Mark scheme
26 [x =] 5 4 M1 for correctly equating one set of [y =] −1 nfww coefficients M1 for correct method to eliminate one variable A1 for x = 5 A1 for y = −1 If A0 scored, SC1 for 2 values satisfying one of the original equations.
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Mathematics 0580/11 for May/June 2025 is out of 80 marks, with 1 hour 30 minutes to answer it.
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