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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_130580_s25_ms_130580/13/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 70 000 000 in words. …… [1] (b) (i) Write down the value of the 5 in the number 0.25 . Give your answer as a fraction. …… [1] (ii) Find the value of the reciprocal of 0.25 . …… [2]
Mark scheme
1(a) Seventy million(s) cao 1 1(b)(i) 5 1 1 or 100 20 1(b)(ii) 4 2 1 4 M1 for oe or 0.25 1
Question
(a) Write down the mathematical name for an angle between 90° and 180°. …… [1] (b) Write down the mathematical term that describes two polygons that are the same shape and size. …… [1] * 0000800000004 * DFD 4
Mark scheme
2(a) Obtuse 1 2(b) Congruent 1
Question
(a) Write down 169 . …… [1] (b) Work out the value of 2 4 . …… [1] (c) Work out the value of 10 -2 . …… [1] (d) Work out -18 ' -4 . …… [1] (e) Work out 1.6 # 0.02 . …… [1] * 0000800000005 * DFD 5
Mark scheme
3(a) 13 1 3(b) 16 1 3(c) 1 1 or 0.01 100 3(d) 9 1 1 or 4.5 or 4 2 2 3(e) 0.032 1
Question
The diagram shows a quadrilateral with sides of equal length. NOT TO SCALE a° 2a° (a) Write down the mathematical name for this quadrilateral. …… [1] (b) Work out the value of a. a = …… [2]
Mark scheme
4(a) Rhombus 1 4(b) 60 2 M1 for a + 2a = 180 oe or better
Question
Find the next term in each sequence. (a) 1, 5, 10, 16, 23, … …… [1] (b) 1, 2, 4, 8, 16, … …… [1] * 0000800000006 * DFD 6
Mark scheme
5(a) 31 1 5(b) 32 1
Question
These are the lengths of time, in minutes, of seven phone calls. 10 22 5 7 35 8 75 (a) (i) Find the median. …… min [2] (ii) Find the range. …… min [1] (b) The longest phone call is 75 minutes. Write 75 minutes in hours. …… h [1]
Mark scheme
6(a)(i) 10 2 M1 for at least the first four or last four correctly ordered 6(a)(ii) 70 1 6(b) 1 1 1.25 or 1 4
Question
70 students study one of French, Spanish and German. The ratio number who study French : number who study Spanish = 3 : 7. 15 students study French. Find the number of students who study German. …… [3] * 0000800000007 * DFD 7
Mark scheme
7 20 3 15 × 7 M2 for 70 − 15 + oe 3 15 or M1 for × k , k = 1, 7 or 10 3
Question
The diagram shows two faces of a net of a cuboid on a 1 cm 2 grid. (a) Complete the statement. The dimensions of the cuboid are …… cm by …… cm by …… cm. [1] (b) On the grid, complete a net of the cuboid. [3] (c) Work out the volume of the cuboid. …… cm 3 [2] * 0000800000008 * DFD 8
Mark scheme
8(a) 3, 3, 5 1 8(b) Fully correct net 3 B2 for 2 correct extra faces in correct places or B1 for 1 correct extra face in correct place 8(c) 45 2 FT their dimensions from (a) M1 for 3 × 3 × 5 oe
Question
The diagram shows the net of a square-based pyramid. 4 cm NOT TO SCALE 5 cm The perpendicular height of each triangle is 4 cm. The base has side length 5 cm. (a) Calculate the surface area of the pyramid. …… cm 2 [2] (b) Write down the number of edges of the square-based pyramid. …… [1] * 0000800000009 * DFD 9
Mark scheme
9(a) 65 2 1 M1 for 4 × × 5 × 4 + 5 × 5 oe 2 9(b) 8 1
Question
(a) Line A has equation y = 3x + 1. Line B has equation y = 3x - 1. Draw a ring around the description that is correct. Line A intersects Line A has a Line A is line B steeper gradient perpendicular to than line B line B Line A is parallel Line A and Line B to line B intersect the y-axis at the same point [1] (b) y 5 4 3 2 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 x –1 –2 –3 –4 –5 On the grid, draw the graph of y = 2x - 1. [2] * 0000800000010 * DFD 10
Mark scheme
10(a) Circle around the statement 1 Line A is parallel to line B 10(b) Correct graph of y = 2x – 1 2 B1 for short or unruled line or for two correct coordinates plotted or for line with positive gradient passing through (0, –1) or for line with gradient 2
Question
Jo asks 90 people whether they prefer pop, rock, classical, jazz or folk music. The pie chart shows some of the results. Pop 120° 100° Rock (a) Work out the number of people who prefer pop. …… [2] (b) The sector angle for classical is 80°. Draw this sector on the pie chart. [1] (c) 9 people prefer jazz and the rest prefer folk. (i) Work out the size of the sector angle for jazz. …… [2] (ii) Complete the pie chart. [1] * 0000800000011 * DFD 11
Mark scheme
11(a) 30 nfww 2 120 M1 for ×90 oe 360 11(b) Sector 80° drawn on pie chart 1 11(c)(i) 36 2 9 M1 for × 360 oe 90 11(c)(ii) Completed pie chart 1 FT their (c)(i) dependent on their (c)(i) < 60°
Question
A music group has 30 members. 7 members play a flute (F ) and play a clarinet (C ). 12 members play a flute. 1 member does not play a flute and does not play a clarinet. (a) Use this information to complete the Venn diagram. % F C [2] (b) Find n(C ). …… [1]
Mark scheme
12(a) E 2 B1 for two correct values in the correct F C position 5 7 17 1 12(b) 24 1 FT their diagram provided a value in both sections of C
Question
By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 62.5 . 9.7 # 0.52 …… [2] * 0000800000012 * DFD 12
Mark scheme
13 60 M1 10 × 0.5 12 A1 If 0 scored, SC1 for 2 correct roundings or for all correct but with any trailing zeros
Question
4 cm NOT TO SCALE h cm 10 cm The diagram shows a trapezium. The area of the trapezium is 42 cm 2 . Work out the value of h. h = …… [2]
Mark scheme
14 6 nfww 2 1 M1 for (4 + 10)h = 42 oe or better 2
Question
(a) Write down the inequality represented on the number line. x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 1 (b) Write down the smallest integer that satisfies the inequality d 2-3 . 4 …… [1] * 0000800000013 * DFD 13
Mark scheme
15(a) –4 ⩽ x < 3 2 B1 for –4 ⩽ x or x < 3 15(b) –3 cao 1
Question
On Monday the cost of a concert ticket is $x. On Tuesday the cost of a ticket for the same concert is 20% more than the cost on Monday. Jack buys 4 tickets on Monday and 5 tickets on Tuesday. Jack pays $270 in total. Work out the value of x. x = …… [3]
Mark scheme
16 27 3 B2 for 10 or 10x 20 or M1 for [5 ×] x + x oe 100
Question
Simplify. (a) y 4 # y 6 …… [1] p5 (b) p8 …… [1] 3 (c) `w 4j …… [1] * 0000800000014 * DFD 14
Mark scheme
17(a) y10 1 17(b) 1 1 p–3 or p3 17(c) w12 1
Question
NOT TO SCALE P 25° O x° y° Q R S T The diagram shows a circle, centre O. P and S are points on the circle. POR is a straight line. QRST is a tangent to the circle at S. (a) Find the value of x. Give a geometrical reason for your answer. x = …… because …… [2] (b) Find the value of y. y = …… [3] * 0000800000015 * DFD 15
Mark scheme
18(a) 25 2 B1 for either base angles of an isosceles triangle are equal 18(b) 140 3 M2 for [ORS = ]180 – (90 + their 25 + 25) oe or B1 for OSR= 90 or ROS = 50
Question
60° NOT TO 3 cm SCALE The diagram shows a sector of a circle with radius 3 cm and sector angle 60°. Calculate the area of the sector. Give your answer in terms of r in its simplest form. …… cm 2 [2]
Mark scheme
19 3 1 2 60 π , 1 π , or 1.5π M1 for × π × 32 oe 2 2 360
Question
Find the highest common factor (HCF) of 36 and 54. …… [2] * 0000800000016 * DFD 16
Mark scheme
20 18 2 B1 for answer 2 or 3 or 6 or 9 or M1 for 2 × 3 × 3 oe as final answer or 36 = 2 × 2 × 3 × 3 and 54 = 2 × 3 × 3 × 3 or 2 correct factor trees or tables
Question
In this question, all lengths are in centimetres. 2x − 1 2x + 1 9 NOT TO x SCALE x+3 The perimeter of the triangle is equal to the perimeter of the rectangle. Form an equation and solve it to find the value of x. x = …… [4] h
Mark scheme
21 3x = 15 M3 M2 for 2x + 1 + x + 3 + 9 = 2(x + 2x – 1) or better or M1 for rearranging their equation to give ax = b or B1 for 3x + 13 or 6x – 2 5 A1 dep on at least M2 If 0 scored, SC1 for answer 5 with no algebra
Question
g= -8 3 Rearrange the formula to make h the subject. h = …… [2] * 0000800000017 * DFD 17
Mark scheme
22 3(g + 8) or 3g + 24 2 h M1 for g + 8 = or 3g = h – 24 3
Question
8 cm NOT TO SCALE 2 cm x cm 1.5 cm Rectangle A Rectangle B Rectangle A is mathematically similar to rectangle B. Work out the value of x. x = …… [2] 1 4
Mark scheme
23 6 nfww 2 1.5 2 M1 for = oe or better x 8
Question
Work out 3 - 1 . 2 7 Give your answer as a mixed number in its simplest form. …… [3] * 0000800000018 * DFD 18
Mark scheme
24 13 3 27 1 cao nfww B2 for 14 14 7k 11k or B1 for or 2k 7k 49 22 M1 for and 14 14 7 8 or 3 and 1 14 14 their 7 × 7 their 11× 2 or and 2×7 7×2 21 8 or [1] and 14 14 35 8 or and 14 14 7 8 or [ 2] and 14 14
Question
Solve the simultaneous equations. 8x + 5y = 4 2x - y = 10 x = …… y = …… [3] DFD 19 * 0000800000020 * DFD 20
Mark scheme
25 [x = ] 3 final answer nfww 3 M1 for correctly eliminating one variable [y = ] –4 OR M1 for correct substitution of x or y into the other equation A1 for x = 3 A1 for y = –4 If A0 scored, SC1 for 2 values satisfying one of the original equations.
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Mark my 0580/13Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
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Mathematics 0580/13 for May/June 2025 is out of 80 marks, with 1 hour 30 minutes to answer it.
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