Question 11 mark
Question
The temperature at 4 am is -12 °C. The temperature at 4 pm is 21 °C. Find the increase in temperature from 4 am to 4 pm. …… °C [1]
Mark scheme
1 33 1
Mathematics 0580/22 October/November 2025: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2025. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_w25_qp_220580_w25_ms_220580/22/O/N/25
- Paper
- Paper 2 (Extended)
- Total marks
- 100
- Time
- 2 hours
- Code on the paper
- 0580/22/O/N/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 21 mark
Question
Find all the common factors of 8 and 12. …… [1]
Mark scheme
2 1, 2, 4 1
Question 32 marks
Question
A cuboid has length 6 cm, width 5 cm and height 2.5 cm. Work out the volume of the cuboid. …… cm 3 [2]
Mark scheme
3 75 2 M1 for 6 × 5 × 2.5 oe
Question 42 marks
Question
A computer costs $560. In a sale, this cost is reduced by 20%. Find the cost of the computer in the sale. $ …… [2] * 0000800000004 * DFD 4
Mark scheme
4 448 2 M1 for 560 × 0.8 oe or B1 for 112
Question 55 marks
Question
The pie chart shows some information about the way 600 students travel to school. Walk 60° Bicycle (a) Work out the number of students that walk to school. …… [2] (b) 120 of the students travel to school by car. The remaining students travel by bus. Complete the pie chart. [3] * 0000800000005 * DFD 5
Mark scheme
5(a) 150 2 90 M1 for [×600] oe 360 5(b) Correctly completed pie chart including 3 B2 for 72 or 138 labels of car [72] and bus [138] 120 or M1 for × 360 oe 600 or B1FT for drawing one correct sector for their angle(s)
Question 64 marks
Question
A B NOT TO 75° SCALE 80° C E D ABCD is a quadrilateral. E lies on CD and AE is parallel to BC. EA = ED. Find (a) angle ABC Angle ABC = …… [1] (b) angle AED Angle AED = …… [1] (c) angle DAB. Angle DAB = …… [2]
Mark scheme
6(a) 105 1 6(b) 80 1 6(c) 125 2 FT (180 – their (b)) ÷ 2 + 75 B1 for EAD or EDA = 50 or B1FT for 180 − their (b) EAD or EDA = correctly 2 evaluated or M1 for (180 – their (b)) ÷ 2 + 75
Question 72 marks
Question
Represent the inequality - 4 1 x G 3 on the number line. x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 [2] * 0000800000006 * DFD 6
Mark scheme
7 2 B1 for open circle at –4 and closed circle at 3 or for a line between –4 and 3 (any circles)
Question 82 marks
Question
Kemi buys p pens that each cost 40 cents. She pays with $20. Write an expression, in terms of p, for the change, in cents, Kemi receives from the $20. …… cents [2]
Mark scheme
8 2000 – 40p final answer 2 B1 for 40p or 0.4p in final answer or 2000 – 40p seen then spoilt
Question 93 marks
Question
Rajid has a full bottle of juice. 1 He drinks of the full bottle on Monday. 3 3 He drinks of the full bottle on Tuesday. 7 Find the fraction of the bottle of juice remaining. …… [3]
Mark scheme
9 5 3 16 B2 for oe 21 21 OR 1 3 M1 for 1 − − oe 3 7 a b M1 for converting and to two 3 7 fractions with a common denominator 1 1 3 e.g. (or their 1− ) and to 3 3 7 7k 9k and 21k 21k 14k 9k or and where k is an integer 21k 21k
Question 105 marks
Question
b = dm + 2mk (a) d = 3.14 , m = 7.92 and k = 10.16 . By rounding each value correct to 1 significant figure, work out an estimate for b. …… [3] (b) Rearrange the formula to make m the subject. m = …… [2] * 0000800000007 * DFD 7
Mark scheme
10(a) 184 3 B1 for 3, 8 and 10 with 3, 8 and 10 shown M1 for 3 × 8 + 2 × 8 × 10 or for correct substitution of unrounded, truncated or incorrectly rounded values 10(b) b 2 M1 for [b =] m(d + 2k) [m =] final answer d + 2k
Question 117 marks
Question
P NOT TO S T SCALE Q R In the diagram, S lies on PQ and T lies on PR. ST is parallel to QR. (a) Explain why triangle PQR is mathematically similar to triangle PST. Give a geometrical reason for each statement you make. …… [3] (b) ST = 3 cm, QR = 9 cm and PS = 5 cm. Work out PQ. PQ = ……cm [2] (c) The area of triangle PST is 2k cm 2 . Find, in terms of k, the area of quadrilateral QRTS. …… cm 2 [2] * 0000800000008 * DFD 8
Mark scheme
11(a) Three correct pairs with correct reasons 3 B2 for two correct pairs with correct reasons PQR = PST and corresponding angles or B1 for one correct pair with correct PRQ = PTS and corresponding angles reason QPR = TPS and common angle OR Two correct pairs with correct reasons and correct similarity condition e.g. AAA 11(b) 15 2 3 5 M1 for = oe or better 9 PQ 11(c) 16k 2 1 2 M1 for 32 or oe 3
Question 126 marks
Question
A fitness club has 100 members. 60 swim (S ). 70 cycle (C ). 25 do not swim or cycle. % S C (a) Complete the Venn diagram. [3] (b) One member of the fitness club is chosen at random. For this member, find (i) P(C ) …… [1] (ii) P(S + C ) …… [1] (iii) P(S , C l ). …… [1] * 0000800000009 * DFD 9
Mark scheme
12(a) 3 If values placed: S C B2 for 55 correctly placed OR 5 55 15 B1 for 25 correctly placed M1 for total S = 60 and total C = 70 with 25 intersection not equal zero/not blank OR or Alt method if probabilities placed: B2 for 0.55 oe correctly placed S C OR 0.05 0.55 0.15 B1 for 0.25 oe correctly placed M1 for total S = 0.6 and total C = 0.7 with intersection not equal zero/not blank 0.25 12(b)(i) 70 1 oe 100 12(b)(ii) 55 1 their 55 oe FT from their Venn diagram 100 100 12(b)(iii) 85 1 their 25 + their 5 + their 55 oe FT or 100 100 their 15 1− from their Venn diagram 100
Question 134 marks
Question
M = 27 # 33 # 52 (a) Write 14M as a product of its prime factors. Give your answer in index form. …… [2] (b) R is an integer. M is a cube number. R Find the smallest possible value of R. R = …… [2]
Mark scheme
13(a) 28 × 33 × 52 × 7[1] cao 2 M1 for [14 =] 2 × 7 soi 13(b) 50 2 M1 for 23 × 33 [× 50 ] or 26 × 33 [× 50 ] oe or or 24 × 52 or 2 × 52 oe –86 400 or SC1 for answers –50, [–]400, [–]1350, [–]3200, [–]10 800, 86 400 oe
Question 144 marks
Question
Find the value of (a) 3 2 ' 3 -2 …… [2] 3 (b) 16 - 2 . …… [2] * 0000800000010 * DFD 10
Mark scheme
14(a) 81 2 B1 for 34 or 32 × 9 or 9 × 9 14(b) 1 2 1 1 [ ±] M1 for or 64–1 or 64 43 4096
Question 153 marks
Question
Factorise. (a) x 2 - 64 …… [1] (b) 5x (x - 2y) + 6 (x - 2y) 2 …… [2]
Mark scheme
15(a) (x + 8)(x – 8) final answer 1 15(b) (x – 2y)(11x – 12y) oe final answer 2 M1 for (x – 2y)(5x + 6(x – 2y)) or for (x + ay)(11x + by) where ab = 24 or 11a + b = – 34 or for correct answer seen and spoilt. If 0 scored, SC1 for 11x2 – 34xy + 24y2
Question 164 marks
Question
D NOT TO C SCALE 14° A B AB and BD are two sides of a regular 15-sided polygon. AB and BC are two sides of a regular n-sided polygon. Angle DBC = 14°. Work out the value of n. n = …… [4] * 0000800000011 * DFD 11
Mark scheme
16 36 4 360 M3 for 360 ÷ −14 oe 15 or B2 for 24 or 156 or M1 for 360 ÷ 15 or (15 − 2 ) ×180 oe 15
Question 1711 marks
Question
B is the point (-3, 1) and D is the point (-5, 9). BD is a diagonal of the kite ABCD. (a) The ratio of the lengths of the diagonals BD : AC = 2 : 3. Work out the length of AC. Give your answer as a surd in its simplest form. …… [5] (b) Find the coordinates of the midpoint of BD. ( …… , …… ) [2] (c) The diagonal AC of the kite passes through the midpoint of BD. Find an equation of AC. Give your answer in the form y = mx + c . y = …… [4] * 0000800000012 * DFD 12
Mark scheme
17(a) 3 17 cao 5 B4 for answer equivalent to 3 17 but 3 68 not in the correct form e.g. , 2 6 17 , 153 2 OR B3 for 68 or 2 17 or M2 for (9 – 1)2 + (–5 – – 3)2 oe or M1 for (9 – 1) or (–5 – – 3) oe and 3 M1 for their 68 × oe 2 17(b) (– 4, 5) 2 B1 for each coordinate 17(c) 1 4 9 −1 y= x + 6 final answer M1 for [grad BD =] oe 4 −5 − −3 −1 M1 for [ grad AC =] their grad BD M1 for their (– 4, 5) substituted into y = their mx + c oe
Question 183 marks
Question
Rationalise the denominator and simplify. 20 4+ 6 …… [3]
Mark scheme
18 2(4 – 6 ) or 8 – 2 6 3 M2 for ( 20 4 − 6 ) oe or better 16 + 4 6 − 4 6 − 6 20 4− 6 or M1 for × oe 4+ 6 4− 6
Question 193 marks
Question
7 cm NOT TO SCALE 5 cm 5 cm The diagram shows a box in the shape of a cuboid. Mala has a straight rod of length 10 cm. Show that this rod does not fit completely inside the box. [3] * 0000800000013 * DFD 13 21 1
Mark scheme
19 99 and states this is less than 10 oe 3 B2 for 99 or M2 for 52 + 52 + 72 oe or M1 for 52 + 52 or 52 + 72 oe
Question 2011 marks
Question
f (x) = , x! g(x) = 3x + 4 2x - 1 2 (a) Find (i) g(2) …… [1] (ii) gf(-1) …… [2] (iii) f -1(x) . f -1(x) = …… [3] (b) Solve f (x) = g(x) . x = …… or x = …… [5] * 0000800000014 * DFD 14
Mark scheme
20(a)(i) 10 1 20(a)(ii) –17 2 M1 for g(–7) oe 21 or 3 + 4 oe soi 2 x −1 20(a)(iii) 21 + x 21 1 3 M2 for one step from answer or + oe final answer 21 + y 21 1 2x 2x 2 e.g. x = or x = + 2y 2y 2 21 or 2 y = +1 x 21+ x or 2xy = 21 + x or 2 y = x or M1 for correct first step e.g. 21 x= or better 2 y −1 or y (2x – 1) = 21 or better 20(b) 5 5 5 B3 for 6x2 + 5x – 25 [= 0] and − oe 3 2 or M1 for 21 = (2x – 1)(3x + 4) oe B1 for 6x2 – 3x + 8x – 4 or better and M1 for correct method to solve their three-term quadratic e.g. (3x – 5)(2x + 5) [= 0] −5 ± 52 − 4 × 6 ×−25 or oe 12
Question 215 marks
Question
(a) y 1 O 180° 360° x –1 On the diagram, sketch the graph of y = cos x for 0° G x G 360° . [2] (b) Solve the equation 2 cos x + 3 = 0 for 0° G x G 360° . x = …… or x = …… [3]
Mark scheme
21(a) Correct sketch to go through (0, 1), 2 M1 for correct cos curve shape through (180, –1) and (360, 1) (0, 1) or for almost correct sketch within 1 tolerance but with an omission at either end 0 or for almost correct sketch within 360 tolerance but with incorrect curvature in one place only –1 21(b) 150 and 210 3 B2 for one correct answer 3 or M1 for cos x = − or better 2 or B1 for 30 or –30 If M1, B1 or 0 scored, award SC1 for two answers in range with a sum of 360
Question 223 marks
Question
A graph with equation y = x 2 + bx + c has a minimum point at (-5, 12). Find the value of b and the value of c. b = …… c = …… [3] * 0000800000015 * DFD 15
Mark scheme
22 [b =] 10 3 B2 for b = 10 or c = 37 [c =] 37 OR M1 for correct method for b e.g. • (x + 5)2 + 12 • 2x + b = 0 oe −b • = −5 2 [1] M1 for correct method for c e.g. • x2 + 5x + 5x + 25 [+ 12] oe • 12 = (–5)2 + their b × –5 + c oe • c− ( their b )2 = 12 oe 4 [1]
Question 237 marks
Question
A NOT TO O 12 cm SCALE B 240° The diagram shows a major sector, AOB, of a circle. The sector angle is 240° and the radius is 12 cm. (a) Show that the length of the major arc AB is 16r cm . [1] (b) OA is joined to OB to form a cone. Work out the volume of the cone. `a bj r Give your answer in the form where a is an integer and b is a prime number. 3 …… cm 3 [6] Question 24 is printed on the next page. * 0000800000016 * DFD 16
Mark scheme
23(a) 240 M1 × 2 × π ×12 oe 360 23(b) ( 256 5 ) π cao 6 B5 for answer ( 256 5 ) or ( 256 5 ) π 3 3 3 seen then spoilt or an answer equivalent to ( 256 5 ) π 3 but not in required form OR B2 for radius of cone = 8 oe or M1 for 2πr = 16π B2 for [height of cone =] 80 oe or M1 for 122 = their 82 + h2 or better 1 M1dep for × π × their 82 × their 80 oe 3 dep on attempt at Pythagoras to find height of cone
Question 242 marks
Question
27 nx = (9 x) 2 Find the value of n. n = …… [2]
Mark scheme
24 4 2 B1 for 33 n [x] or 34[x] [n =] 3
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Where can I find the 0580/22 October/November 2025 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, October/November 2025 (0580_w25_ms_22), and the question paper (0580_w25_qp_22), to read or download, with each question's marking points written out underneath.
How many marks is 0580/22 out of?
Mathematics 0580/22 for October/November 2025 is out of 100 marks, with 2 hours to answer it.
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Yes. Upload your answers to 0580/22/O/N/25 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.