Question 12 marks
Question
(a) Shade one more small square so that the diagram has one line of symmetry. [1] (b) Shade one more small square so that the diagram has rotational symmetry of order 2. [1]
Mark scheme
1(a) or 1 1(b) 1
Mathematics 0580/22 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_220580_s25_ms_220580/22/M/J/25
- Paper
- Paper 2 (Extended)
- Total marks
- 100
- Time
- 2 hours
- Code on the paper
- 0580/22/M/J/25
0580/22 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 23 marks
Question
The scale drawing shows the positions of two villages, P and Q. The scale is 1 cm represents 0.5 km. North P North Q (a) Find the actual distance between village P and village Q. …… km [2] (b) Measure the bearing of village Q from village P. …… [1] * 0000800000004 * DFD 4
Mark scheme
2(a) 4.4 to 4.6 2 B1 for 8.8 [cm] to 9.2 [cm] or M1 for 0.5 × their written measurement where their measurement is in the range 8 to 10 2(b) 108 to 112 1
Question 33 marks
Question
45° 65° NOT TO SCALE x° y° The diagram shows two straight lines intersecting two parallel lines. Find the value of x and the value of y. x = …… y = …… [3]
Mark scheme
3 [x =] 70 3 B2 for either correct and or B1 for 45 and 65 correctly placed on [y =] 65 diagram or M1 for 180 – 45 – 65 oe
Question 42 marks
Question
1 2 3 4 5 6 7 Samira picks one of these cards at random and replaces it. (a) Find the probability that she picks an odd number. …… [1] (b) Samira repeats this 35 times. Calculate the number of times Samira is expected to pick an odd number. …… [1] * 0000800000005 * DFD 5
Mark scheme
4(a) 4 1 oe 7 4(b) 20 1 FT their (a) × 35 provided 0 < their (a) < 1
Question 54 marks
Question
y 4 3 2 T 1 –4 –3 –2 –1 0 1 2 3 4 x –1 U –2 –3 –4 0 (a) Translate triangle T by the vector e o. [1] -2 (b) Describe fully the single transformation that maps triangle T onto triangle U. …… [3]
Mark scheme
5(a) Triangle at (–1, –1), (–1, 1), (–2, –1) 1 5(b) Rotation 3 B1 for each 90 anticlockwise oe (2, 2)
Question 65 marks
Question
Solve. (a) 8x + 7 = 39 x = …… [2] (b) 2 (5y - 1) = 24 y = …… [3] * 0000800000006 * DFD 6
Mark scheme
6(a) 4 2 M1 for 8x = 39 – 7 or better 6(b) 13 3 M1 for correct first step e.g. 2.6 or oe 5 24 5y – 1 = or 10y – 2 = 24 or better 2 M1 for correctly isolating terms in y FT their first step e.g. 5y = 12 + 1 or 10y = 24 + 2
Question 73 marks
Question
These are the first 4 terms of a sequence. 11 8 5 2 (a) Find the next term of this sequence. …… [1] (b) Find the nth term of this sequence. …… [2]
Mark scheme
7(a) –1 1 7(b) 14 – 3n oe final answer 2 B1 for c – 3n or 14 – kn (k ≠ 0) or 14 – 3n seen then spoilt
Question 82 marks
Question
Find the highest common factor (HCF) of 36 and 54. …… [2] * 0000800000007 * DFD 7
Mark scheme
8 18 2 B1 for answer 2, 3, 6 or 9 or M1 for answer 2 × 32 oe or for 2 × 2 × 3 × 3 and 2 × 3 × 3 × 3 or 2 correct factor trees or tables
Question 96 marks
Question
A is the point (3, - 1) . 2 AB = e o -4 (a) AC = 2 AB Find the coordinates of the point C. ( …… , …… ) [2] (b) The length of AB is k 5. Find the value of k. k = …… [2] (c) P is a point on AB. AP | PB = 1 | 3 Find the position vector of P. f p [2] * 0000800000008 * DFD 8
Mark scheme
9(a) (7, –9) 2 7 B1 for (7, k) or (k, –9) or −9 4 or for seen −8 3 2 or M1 for + 2 −1 −4 9(b) 2 2 M1 for 22 + ([–]4)2 oe or better 9(c) 3.5 2 3.5 k oe B1 for answer or −2 k −2 1 0.5 or for or 2 seen −1 −1 3 1 2 or M1 for + oe −1 4 −4
Question 102 marks
Question
18 cm NOT TO SCALE O 45° The diagram shows a sector of a circle, centre O. The length of the arc is nr cm . Find the value of n. n = …… [2]
Mark scheme
10 9 2 45 oe M1 for × 2 × [ π] ×18 oe 2 360
Question 113 marks
Question
(a) Write 0.007 08 in standard form. …… [1] (b) Work out (3.8 # 10 22) + (3.8 # 10 23) . Give your answer in standard form. …… [2] * 0000800000009 * DFD 9
Mark scheme
11(a) 7.08 × 10–3 cao 1 11(b) 4.18 × 1023 cao 2 B1 for figs 418 or M1 for 0.38 × 1023 or 38 × 1022 or 1022 (3.8 + 3.8 × 10) or 1023 (3.8 ÷ 10 + 3.8) oe
Question 122 marks
Question
R NOT TO SCALE P 74° Q P, Q and R lie on a circle. QR is a diameter. Find angle PRQ. Give geometrical reasons for your answer. Angle PRQ = …… because …… …… [2] * 0000800000010 * DFD 10
Mark scheme
12 16 2 B1 for 16 or angle in a semicircle = 90 and angle in a semicircle = 90 and angle sum of a triangle = 180
Question 1311 marks
Question
(a) 100 students solve a puzzle. The table shows information about the time taken by each student to solve the puzzle. Time (t seconds) 20 1 t G 40 40 1 t G 60 60 1 t G 100 Frequency 30 40 30 (i) Work out an estimate of the mean. ……s [4] (ii) Complete the histogram to show the information in the table. 4 3 Frequency density 2 1 0 100 t 20 30 40 50 60 70 80 90 Time (seconds) [2] * 0000800000011 * DFD 11 (b) 80 adults solve the same puzzle as the students. The cumulative frequency table shows information about the time taken by each adult to solve the puzzle. Time (t seconds) t G 20 t G 40 t G 60 t G 80 t G 100 t G 120 Cumulative frequency 0 12 36 60 74 80 (i) On the grid, draw a cumulative frequency diagram. 80 70 60 50 Cumulative frequency 40 30 20 10 0 20 30 40 50 60 70 80 90 100 110 120 t Time (seconds) [3] (ii) Use your cumulative frequency diagram to find an estimate for (a) the median …… s [1] (b) the lower quartile. …… s [1] * 0000800000012 * DFD 12
Mark scheme
13(a)(i) 53 4 M1 for correct midpoints soi M1 for Σfx where x is in correct interval including boundaries M1 for Σfx ÷ 100 dep on second M1 13(a)(ii) Two correct bars with correct widths 2 B1 for one correct bar and heights 2 and 0.75 or M1 for 40/20 oe and 30/40 oe soi 13(b)(i) Correct diagram 3 B1 for correct horizontal placement for 6 plots B1 for correct vertical placement for 6 plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 6 points If 0 scored, SC1 for 5 out of 6 points correctly plotted 13(b)(ii)(a) 62 to 64 1 FT their increasing curve or polygon reading at 40 13(b)(ii)(b) 46 to 48 1 FT their increasing curve or polygon reading at 20
Question 142 marks
Question
Write 0.25o as a fraction. …… [2] * 0000800000013 * DFD 13
Mark scheme
14 23 2 M1 for 25.55… – 2.55… oe oe fraction 90 or for 90x = 23 oe 2 5 or for + oe 10 90
Question 156 marks
Question
y 5 4 3 2 1 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x –1 –2 –3 –4 –5 2 The diagram shows the graph of y = - 1. x (a) Write down the coordinates of the point where the graph crosses the x-axis. ( …… , …… ) [1] (b) Write down the equation of each asymptote. [2] 2 (c) By drawing a suitable straight line on the grid, solve - x - 1 = 0. x x = …… or x = …… [3] * 0000800000014 * DFD 14
Mark scheme
15(a) (2, 0) 1 15(b) x = 0, y = –1 2 B1 for each 15(c) y = x ruled B1 x = –2 and x = 1 B2 B1 for one correct or for two correct answers FT from their line
Question 164 marks
Question
NOT TO SCALE 6 cm 5 cm The diagram shows a solid made by joining a hemisphere to a cylinder. The radius of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 5 cm. Find the total surface area of the solid. Give your answer in terms of r. …… cm 2 [4]
Mark scheme
16 168 π 4 B3 for answer 168 OR M3 for 1 π × 62 + × 4π × 62 + 2π × 6 × 5 oe 2 OR To a maximum of 2 marks ignoring extra areas added or subtracted M1 for π × 62 1 M1 for × 4 × π × 62 oe 2 M1 for 2 × π × 6 × 5
Question 174 marks
Question
Find the value of 2 (a) 125 3 …… [2] 5 (b) 4 - 2 . …… [2] * 0000800000015 * DFD 15 9
Mark scheme
17(a) 25 2 2 ( 125 ) or 125 or ( 5 ) 2 3 3 2 3 3 M1 for or B1 for 3 125 = 5 17(b) 1 2 1 1 [±] M1 for or 32–1 or 32 25 1024
Question 184 marks
Question
(a) 3 Rationalise the denominator. Give your answer in its simplest form. …… [2] (b) (5 - 2) (1 + 3 2) = c + k 2 Find the value of c and the value of k. c = …… k = …… [2]
Mark scheme
18(a) 3 3 cao 2 9 3 M1 for × oe 3 3 18(b) [c =] –1 2 B1 for each [k =] 14 or for 3 correct terms from 5 + 15 2 − 2 − 3 2 2 oe
Question 197 marks
Question
Write as a single fraction in its simplest form. 5a 3b (a) # 6 a …… [2] p 3t (b) + 2 4 …… [2] 2 3 (c) - x-2 x+1 …… [3] * 0000800000016 * DFD 16 1
Mark scheme
19(a) 5b 2 15ab cao final answer B1 for or better seen 2 6a 19(b) 2 p + 3t 2 M1 for adding two correct fractions with a cao final answer 4 p 6t 4 common denominator e.g. + 8 8 19(c) 8− x 8− x 3 B1 for 2(x + 1) – 3(x – 2) or better isw or 2 ( x − 2 )( x +1) x − x−2 B1 for common denominator (x – 2)(x + 1) oe isw cao final answer
Question 204 marks
Question
y\ x (a) When x = 9, y = 2 . Find the value of y when x = 36 . y = …… [3] (b) When x is increased by a factor of 4, the value of y changes by a factor of p. Find the value of p. p = …… [1] * 0000800000017 * DFD 17
Mark scheme
20(a) [±] 1 3 k M1 for 2 = oe 9 their k M1 for 36 OR M2 for 2 × 9 = y × 36 20(b) 1 1 oe 2
Question 219 marks
Question
y Q NOT TO A O B x SCALE P The diagram shows the graph of y = 3x - x 3 . The graph crosses the x-axis at A, at O and at B. The turning points of the graph are at P and at Q. (a) Find the x-coordinate of A and the x-coordinate of B. Give your answers as exact values. x-coordinate of A …… x-coordinate of B …… [3] (b) (i) Differentiate 3x - x 3 . …… [2] (ii) Find the coordinates of P and Q. P ( …… , …… ) Q ( …… , …… ) [4] * 0000800000018 * DFD 18
Mark scheme
21(a) [A =] − 3 oe 3 B2 for – 3 oe or 3 oe [B =] 3 oe ( ) or M1 for [ x ] 3 − x 2 [ = 0] or better 0 ± 02 − 4 × −1 × 3 or oe 2 × −1 21(b)(i) 3 – 3x2 final answer 2 B1 for 3 or – 3x2 correct in an expression or for correct answer spoilt 21(b)(ii) [P =] (–1, –2) 4 B3 for (–1, –2) or (1, 2) and or for two correct values of x [Q =] (1, 2) or M2 for x2 = 1 or for [3](1 – x)(1 + x) [= 0] oe factorised 0 ± 0 2 − 4 × −3 × 3 or oe 2 × −3 OR M1 for [3](1 – x2 ) [= 0] or their (b)(i) = 0 dy or for stating =0 dx M1 for correct method to solve their quadratic
Question 224 marks
Question
(a) Write down the exact value of tan 60°. …… [1] (b) Solve 2 sin x - 1 = 0 for 0° G x G 360° . x = …… or x = …… [3]
Mark scheme
22(a) 3 1 22(b) 30, 150 3 B2 for 30 or 150 1 or M1 for sin x = 2 If 0 or M1 scored, SC1 for one acute angle and one obtuse angle with a sum of 180
Question 233 marks
Question
B C NOT TO SCALE b M O a A In the diagram, OA is parallel to BC. BC = 3OA M is the midpoint of AC. The position vector of A is a and the position vector of B is b. Find the position vector of M. Give your answer in terms of a and b, in its simplest form. …… [3] * 0000800000019 * DFD 19
Mark scheme
23 1 3 B2 for a correct route in terms of a and b 2a + b final answer not in its simplest form 2 1 1 or for AM (or AC ) = a + b oe 2 2 or B1 for AC = –a + b + 3a oe or M1 for correct route for OM using the lines of the diagram
Question 245 marks
Question
The line y = 7x + 3 intersects the curve y = x 2 + 5x - 12 at the points A and B. Find the coordinates of A and B. A ( …… , …… ) B ( …… , …… ) [5] * 0000800000020 * DFD 20
Mark scheme
24 (5, 38) and (–3, –18) 5 B4 for one correct coordinate or for x = 5 and x = –3 OR M2 for x2 – 2x – 15 [= 0] or y2 – 20y – 684 [= 0] or M1 for 7x + 3 = x2 + 5x – 12 oe 2 y −3 y −3 or y = + 5 − 12 7 7 M1 for correct method to solve their three- term quadratic (x – 5)(x + 3) − ( −2 ) ± ( −2)2 − 4 ×1× −15 oe 2 ×1 If B0 scored and at least 2 method marks scored, SC1 for correct substitution of both of their x values or their y values into y = 7x + 3 or y = x2 + 5x – 12
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Where can I find the 0580/22 May/June 2025 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, May/June 2025 (0580_s25_ms_22), and the question paper (0580_s25_qp_22), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/22 for May/June 2025 is out of 100 marks, with 2 hours to answer it.
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