Cambridge IGCSE Mathematics 0580 — 2025 May/June Paper 1 · Variant 1
0580/11/M/J/25 · 26 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 the number 10 069 in words
1 (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: Question Answer Marks Partial Marks 1(a) Ten thousand [and] sixty-nine 1 1(b) 10 070 1 1(c) 100.69 1
Q2 · A bag of sweets costs $0.34
2 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
Q3 · Two numbers have a sum of -2 and a product of -15
3 Two numbers have a sum of -2 and a product of -15. Work out the two numbers. ........................ and ........................ [2]
Mark scheme: 3 –5 3 2 B1 for answer of two numbers that add to –2 or multiply to –15
Q4 · 7 27 39 49 99 112 From the list of numbers, write down (a) an even number…
4 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
Q5 · Write down the reciprocal of 5
5 Write down the reciprocal of 5. ................................................. [1]
Mark scheme: 5 1 1 or [0].2 5
Q6 · Put one pair of brackets into each calculation to make it correct
6 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]
Mark scheme: 6(a) (7 – 5) × 4 + 8 = 16 1 6(b) 7 – (5 × 4 + 8) = – 21 1
Q7 · A ticket costs $18
7 (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
Q8 · Write 90% as a fraction in its simplest form
8 (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
Q9 · These are the first four terms of a sequence
9 (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]
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
Q10 · Ky cycles from his office to a meeting and back again
10 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 009 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]
Mark scheme: 10(a) 14 1 10(b) 40 1 10(c) 11 50 1 10(d) Ruled line from 2 their(a) M1 for oe (9 40, 0) to (10 20, 14) 21 or a parallel line
Q11 · Calculate the volume of a cube with side length 3 cm
11 Calculate the volume of a cube with side length 3 cm. .......................................... cm3 [1]
Mark scheme: 11 27 1
Question 12
12 Solve. 5x + 8 = 3 x - 2 x = ................................................ [2]
Mark scheme: 12 −5 cao final answer 2 M1 for 5x – 3x = – 2 – 8 oe or better
Question 13
13 Work out. (a) - 5 # - 4 ................................................. [1] (b) - 8 + ( - 3 ) ................................................. [1]
Mark scheme: 13(a) 20 1 13(b) –11 1
Q14 · 3 p # 3 4 = 3 10 Find the value of p
14 3 p # 3 4 = 3 10 Find the value of p. p = ................................................ [1]
Mark scheme: 14 6 final answer 1
Q15 · 6 cm NOT TO SCALE 4 cm 3 cm Complete a net of this cuboid on the 1 cm2 grid
15 6 cm NOT TO SCALE 4 cm 3 cm Complete a net of this cuboid on the 1 cm2 grid. One face has been drawn for you. [3]
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 16
16 (a) Simplify. 6a + 4b - a - 5 b ................................................. [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
Q17 · By writing each number in the calculation correct to 1 significant figure, find an…
17 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]
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
Q18 · The diagram shows two straight lines intersecting two parallel lines
18 The diagram shows two straight lines intersecting two parallel lines. y° x° z° NOT TO 110° SCALE 50° (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. z = ................................................ [2]
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
Q19 · A box contains 10 counters
19 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]
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 4 25 provided 0 < each of their < 1 5 4 4 M1 for their × their 5 5
Q20 · The scatter diagram shows the price of petrol per litre and the number of litres sold at…
20 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]
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
Q21 · Points A, B and C lie on the circle, centre O
21 Points A, B and C lie on the circle, centre O. NOT TO A B SCALE 39° 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
Q22 · A = 2 3 # 3 B = 3 2 # 5 (a) Find the highest common factor (HCF) of A and B
22 A = 2 3 # 3 B = 3 2 # 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]
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
Q23 · 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…
23 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]
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
Q24 · 3 24 Work out 1 + 1
1 3 24 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
Q25 · Write 32 500 in standard form
25 (a) Write 32 500 in standard form. ................................................. [1] (b) Write .56 # 10 -3 as an ordinary number. ................................................. [1] Question 26 is printed on the next page.
Mark scheme: 25(a) 3.25 × 104 1 25(b) [0].0056 1
Q26 · Solve the simultaneous equations
26 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.
What was in this paper
The subtopics covered by these 26 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Surface area and volume2The four operations2Types of number2Algebraic manipulation1Angles1Circle theorems I1Estimation1Fractions, decimals and percentages1Graphs in practical situations1Indices I1Introduction to algebra1Limits of accuracy1Money1Powers and roots1Probability of combined events1Scatter diagrams1Sequences1Standard form1The four operations1Transformations1What you needed in this session
Cambridge’s own grade thresholds for 2025 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.