Question 11 mark
Question
The probability of picking a green pen from a box is 0.17 . Find the probability of not picking a green pen from the box. …… [1]
Mark scheme
1 0.83 oe 1
Mathematics 0580/23 May/June 2025: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), 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_230580_s25_ms_230580/23/M/J/25
- Paper
- Paper 2 (Extended)
- Total marks
- 100
- Time
- 2 hours
- Code on the paper
- 0580/23/M/J/25
0580/23 mark scheme, question by question
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 24 marks
Question
A x° E 30° 104° y° F NOT TO SCALE D 130° B 70° C ABCD is a quadrilateral. CDE is a straight line. AFB is an isosceles triangle. Find the value of x and the value of y. x = …… y = …… [4] * 0000800000004 * DFD 4
Mark scheme
2 x = 84 4 B2 for x = 84 y = 75 or M1 for CDA = 76 or 360 – 70 – 130 – (180 – 104) oe B2 for y = 75 or M1 for (180 – 30) ÷ 2
Question 32 marks
Question
E NOT TO SCALE D C M A B The diagram shows a pyramid ABCDE with a square base. M is the centre of the square base. E is vertically above M. (a) Write down the number of planes of symmetry of this pyramid. …… [1] (b) Using two of the letters from A, B, C, D, E and M, complete the statement about the pyramid. The axis of rotational symmetry passes through the points …… and …… [1]
Mark scheme
3(a) 4 1 3(b) E and M 1
Question 41 mark
Question
The number of ice creams sold increases as the temperature rises. What type of correlation does this statement describe? …… [1] * 0000800000005 * DFD 5
Mark scheme
4 Positive 1
Question 57 marks
Question
y 9 8 7 6 B 5 4 3 A 2 1 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 x –1 –2 –3 –4 –5 –6 –7 (a) Describe fully the single transformation that maps triangle A onto triangle B. …… [3] (b) On the grid, draw the image of (i) triangle A after a reflection in the line x =-1 [2] (ii) triangle A after a rotation 90° clockwise, centre (1, -2). [2] * 0000800000006 * DFD 6
Mark scheme
5(a) Enlargement 3 B1 for each [Scale factor] 3 (1, 2) 5(b)(i) Triangle at (–6, 1), (–3, 3), (–4, 4) 2 B1 for reflection in x = k or in y = –1 5(b)(ii) Triangle at (4, –5), (6, –2), (7, –3) 2 B1 for correct 90° anticlockwise rotation about (1, –2) or correct orientation, wrong centre
Question 63 marks
Question
There are 15 giraffes in a group. The table gives information about the heights of the 15 giraffes. One giraffe has a height of 2.6 m No giraffe is shorter than 2.5 m The range of heights for the 15 giraffes is 2.3 m More than 3 giraffes have the same height The modal height for the giraffes is 3.9 m The stem-and-leaf diagram shows information about the height of 9 of these giraffes. 2 5 3 2 7 7 4 1 1 4 5 7 Key: 4|1 represents a giraffe height of 4.1 m Use the information in the table to complete the stem-and-leaf diagram for the group of 15 giraffes. [3] * 0000800000007 * DFD 7
Mark scheme
6 2 5 6 3 B1 for each correct row 3 2 7 7 9 9 9 9 4 1 1 4 5 7 8
Question 75 marks
Question
Work out. 5 7 (a) - 6 12 Give your answer as a fraction in its simplest form. …… [2] 1 8 (b) 1 ' 3 15 Give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
7(a) 1 2 M1 for correct method to find common cao 4 10 7 denominator e.g. and , 12 12 60 42 and 72 72 7(b) 1 3 4 15 2 cao M2 for × 2 3 8 20 8 or ÷ oe with common 15 15 denominator 4 their k 15 or M1 for or for × , where 3 3 8 k>3
Question 84 marks
Question
(a) Write 42 as a product of its prime factors. …… [2] (b) Find the highest common factor (HCF) of 84 and 70. …… [2] * 0000800000008 * DFD 8
Mark scheme
8(a) 2×3×7 2 B1 for 2, 3, 7 or M1 for correct factor tree/diagram/table 8(b) 14 2 B1 for answer 2 or 7 or M1 for 2 × 7 as final answer or 84 = 2 × 2 × 3 × 7 and 70 = 2 × 5 × 7 or 2 correct factor trees or tables
Question 95 marks
Question
(a) Solve. 5x 2 = 12 - 17x x = …… or x = …… [4] (b) ax 2 + a = b where a and b are integers. One solution of this equation is x = 6 . Write down the other solution. x = …… [1]
Mark scheme
9(a) 3 4 M1 for 5x2 + 17x – 12 [= 0] or 0.6 5 and –4 M2 for correct method to solve their ax2 + bx – c [= 0] e.g. factorising (5x – 3)(x + 4) [= 0], completing the square or using the formula or M1 for (5x + a)(x + b) where ab = –12 or 5b + a = 17 or correct partial factorisation e.g. 5x(x + 4) – 3(x + 4) or for 172 − 4 ( 5)( −12 ) or better −17 + d −17 − d or or 2 ( 5) 2 ( 5) 9(b) –6 1
Question 104 marks
Question
Solve the simultaneous equations. 4x - 5y = 13 3x - 2y = 8 x = …… y = …… [4] * 0000800000009 * DFD 9
Mark scheme
10 [x =] 2 4 M1 for correctly equating one set of [y =] –1 coefficients or for making x or y the subject of one equation M1 for correct method to eliminate one variable A1 for x = 2 A1 for y = –1 If M0 scored, SC1 for 2 values satisfying one of the original equations
Question 114 marks
Question
Angela picks a number at random from the numbers 1, 2 and 3. She then picks a number at random from the numbers 4, 5 and 6. She adds the two numbers to find the total. (a) Complete the table to show the possible outcomes. First number + 1 2 3 4 5 6 7 Second number 5 6 [2] (b) Given that the total is odd, find the probability that one of the numbers Angela picks is 3. …… [2] 2
Mark scheme
11(a) 2 B1 for 4 correct First number + 1 2 3 Second 4 5 6 7 number 5 6 7 8 6 7 8 9 11(b) 2 2 c oe B1 for answer where c < 5 5 5 2 or seen in working 5
Question 125 marks
Question
(a) v =e o -3 Find 5v. f p [1] (b) H is the point (-3, 8) and K is the point (-4, 0). 7 HJ = e o -2 Find JK . …… [4] * 0000800000010 * DFD 10
Mark scheme
12(a) 10 1 −15 12(b) 10 4 B3 for answer ±10 OR M3 for (–4 – 4)2 + (0 – 6)2 oe or better OR −4 4 M2 for − oe 0 6 −1 or B1 for [J =] (4, 6) soi or −8 M1 for (their –8) + (their –6)2 oe or 2 better
Question 134 marks
Question
F A 60° 35° NOT TO SCALE E D B C A, B, C and D are points on a circle. EF is a tangent to the circle at A. AB is parallel to DC. (a) Find angle DCB, giving a geometrical reason. Angle DCB = …… because …… …… [2] (b) Find angle DBC. Angle DBC = …… [2]
Mark scheme
13(a) 120 2 B1 for 120 or a fully correct reason and opposite angles of a cyclic quadrilateral sum to 180° 13(b) 25 2 M1 for (180 – 120) – 35 or B1 for ABC = 60 or ABD = 35
Question 142 marks
Question
Find the lowest common multiple (LCM) of 15xy 3 and 18x 4 y . …… [2] * 0000800000011 * DFD 11
Mark scheme
14 90x4 y3 final answer 2 B1 for two correct parts from: 90, x4 and y3 or for 3×5×x×y×y×y and 2×3×3×x×x×x×x×y or for correct answer seen then spoilt
Question 156 marks
Question
(a) Simplify. 27 + 12 …… [2] 40 8 (b) = k , where k is an integer. 5 2 Find the value of k. k = …… [2] (c) Rationalise the denominator. 1 3- 5 …… [2] o o as a fraction in its simplest form.
Mark scheme
15(a) 5 3 2 B1 for 3 3 or 2 3 15(b) 16 2 8 4 2 M1 for 40 × 2 2 , 8 ×2 2 , or 2 40 8 2 or better 5 2 2 or B1 for 8 4 or 256 15(c) 3+ 5 2 1 3+ 5 M1 for × oe 4 3− 5 3+ 5
Question 163 marks
Question
Write 0.328 …… [3] * 0000800000012 * DFD 12
Mark scheme
16 65 3 65 cao B2 for a fraction equivalent to e.g. 198 198 325 990 3 28 or M1 for 328.28 − 3.28 oe or + 10 990 k oe or 990x = 325 or 990
Question 173 marks
Question
Solid A is mathematically similar to solid B. H cm NOT TO SCALE 7 cm Solid A Solid B The height of solid A is 7 cm and its surface area is 60 cm 2 . The surface area of solid B is 540 cm 2 . Calculate the height of solid B. …… cm [3]
Mark scheme
17 21 3 540 60 M2 for 7 × oe or 7 ÷ oe 60 540 540 60 or M1 for oe or oe or 60 540 2 7 60 = oe H 540
Question 184 marks
Question
Make t the subject of the formula. m (1 - t) 2= pt t = …… [4]
Mark scheme
18 m 4 M1 for correctly clearing their fraction [t = ] final answer M1 for correct expansion 2p+m M1 for correctly collecting their terms in t on one side and other terms on the other side, not dividing by 1 – t M1 for correct factorisation and division of their two-term expression in t To a maximum of 3 marks for an incorrect answer
Question 193 marks
Question
Simplify. 7x - x 2 49 - x 2 …… [3] * 0000800000013 * DFD 13
Mark scheme
19 x 3 B1 for x(7 – x) final answer 7+ x B1 for (7 – x)(7 + x)
Question 203 marks
Question
A NOT TO 40° B SCALE O The diagram shows a sector of a circle, centre O. The radius of the circle is 6 cm. Calculate the length of the major arc AB. Give your answer in its simplest form in terms of r . ……cm [3]
Mark scheme
20 32 2 3 360 − 40 π or 10 π cao M2 for × π ×6 ×2 3 3 360 360 − 40 22 or × × 6 × 2 oe 360 7 40 or M1 for × π × 6 × 2 oe 360 or B1 for major sector angle = 320 soi or 12π
Question 216 marks
Question
(a) Differentiate x 3 - 3x 2 + 1. …… [2] (b) Find the coordinates of the turning points of the graph of y = x 3 - 3x 2 + 1. ( …… , …… ) ( …… , …… ) [4] * 0000800000014 * DFD 14
Mark scheme
21(a) 3x2 – 6x or 3x(x – 2) 2 B1 for 3x2 – kx or kx2 – 6x or correct answer spoilt or SC1 for 3x2 – 6x + 1 21(b) (0, 1) 4 B3 for one correct coordinate or for two (2, –3) correct values of x following 3x2 – 6x oe seen in (b) or M2 for [3]x(x – 2) [= 0] or −−6± ( −6)2 − 4 × 3 × 0 [= 0] oe 2×3 OR dy dy M1 for their = 0 or stating =0 dx dx M1 for correct method to solve their quadratic
Question 228 marks
Question
f (x) = 2x + 5 g (x) = x - 4 h (x) = 5 x (a) Find f (3) . …… [1] (b) Find f -1 (x) . f -1 (x) = …… [2] (c) Solve fg (x) = 25 . x = …… [3] (d) Find x when h -1 (x) = 2 . x = …… [2] * 0000800000015 * DFD 15
Mark scheme
22(a) 11 1 22(b) x −5 2 M1 for correct first step 2 y −5 x = 2y + 5 or y – 5 = 2x or =x 2 y 5 or = x+ 2 2 22(c) 14 3 M2 for x – 4 = (25 – 5) ÷ 2 oe or better or 2x – 8 = 25 – 5 oe or better or M1 for 2(x – 4) + 5 = 25 22(d) 25 2 M1 for h(2) or 52
Question 236 marks
Question
(a) Write down the value of cos 90°. …… [1] (b) x NOT TO SCALE n 30° 30° The diagram shows two different right-angled triangles joined by a common side. Find x in terms of n. x = …… [5] Question 24 is on the next page. * 0000800000016 * DFD 16
Mark scheme
23(a) 0 1 23(b) 4n 4n 3 5 B4 for correct explicit expression to find [x =] or oe x 3 3 2n 2n e.g. x = or x = oe cos30 3 2 OR M3 for correct explicit method to find x n ÷ sin 30 with 2 trig functions e.g. x = cos30 oe or a correct implicit method with one trig 2n function e.g. cos 30 = oe x OR B2 for hypotenuse of lower triangle = 2n or M2 for any correct implicit method with 2 trig functions e.g. cos 30 = n ÷ sin 30 oe x OR M1 for seeing any correct trig value from sin 30 or cos 60 = 0.5, cos 30 or 3 3 sin 60 = or tan 30 = oe 2 3 or for hypotenuse of lower triangle = n oe sin 30
Question 247 marks
Question
(a) A is the point (a, 12) and B is the point (b, 27). (i) Find the y-coordinate of the midpoint of AB. …… [1] (ii) The line AB has gradient 3. Find an expression for a in terms of b. a = …… [3] (b) D is the point (22, 34) and E is the point (23, 39). D is the point on CE such that 2CE = 5DE. Find the coordinates of C. ( …… , …… ) [3]
Mark scheme
24(a)(i) 19.5 1 24(a)(ii) [a =] b – 5 oe 3 27 −12 M1 for 3 = oe b−a M1 for 3(b – a) = 27 – 12 or better 27 −12 e.g. [a =] b – 3 24(b) 41 53 3 SC2 for answer (25.5, 51.5) or (20.5, 26.5) or ( , ) 2 2 51 103 ( , ) 2 2 OR 5 M2 for 23 − ( 23 − 22) 2 5 or 39 − ( 39 − 34 ) oe 2 or sketch 12.5 2.5 2.5 −2.5 or vector e.g. or 12.5 −12.5 or M1 for 5 1 5 5 ( 23 − 22) or ( 39 − 34 ) 2 2 1 −1 or vector e.g. or 5 −5
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On this page, free: the mark scheme for IGCSE Mathematics 0580/23, May/June 2025 (0580_s25_ms_23), and the question paper (0580_s25_qp_23), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/23 for May/June 2025 is out of 100 marks, with 2 hours to answer it.
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