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Mathematics 0580/21 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_210580_w25_ms_210580/21/O/N/25

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Paper
Paper 2 (Extended)
Total marks
100
Time
2 hours
Code on the paper
0580/21/O/N/25
0580_w25_ms_21.pdf

0580/21 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 12 marks

Question

Divide $90 in the ratio 2 : 3. $ …… , $ …… [2]

Mark scheme

1 36, 54 2 90 M1 for × k where k = 1, 2 or 3 2+3

Question 23 marks

Question

148° NOT TO 82° B SCALE C A In the diagram, AC = BC. Work out angle CAB. Angle CAB = …… [3]

Mark scheme

2 25 3 M1 for 360 – 148 – 82 M1 for (180 – their 130) ÷ 2

Question 32 marks

Question

Find the interior angle of a regular 20-sided polygon. …… [2] * 0000800000004 * DFD 4

Mark scheme

3 162 2 360 180 ( 20 − 2 ) M1 for 180 – or for 20 20

Question 42 marks

Question

The area of a triangle is 12 cm 2 . The length of the base of the triangle is 8 cm. Work out the height of the triangle. …… cm [2]

Mark scheme

4 3 2 1 M1 for × 8 × h = 12 oe 2

Question 54 marks

Question

y 4 3 P 2 T 1 –4 –3 –2 –1 0 1 2 3 4 x –1 –2 (a) Describe fully the single transformation that maps triangle T onto triangle P. …… [2] (b) Draw the image of triangle T after an enlargement of scale factor 2, centre (3, 3). [2]

Mark scheme

5(a) Translation 2 B1 for each −3 1 5(b) Triangle at (3, 1) , (3, –1) (–1, –1) 2 B1 for correct size and orientation but wrong position

Question 63 marks

Question

Find the value of (a) 5 -5 # 5 5 …… [1] 2 (b) 125 3 . …… [2] * 0000800000005 * DFD 5

Mark scheme

6(a) 1 cao 1 6(b) 25 cao 2 2 ( 125 ) or 125 or ( 5 ) 2 3 3 2 3 3 M1 for or B1 for 3 125 = 5

Question 74 marks

Question

Simplify. p 2 (a) ' t t …… [2] 3x x - 1 (b) - 4 2 …… [2]

Mark scheme

7(a) p 2 p t final answer M1 for × or for cross cancelling of t 2 t 2 7(b) x+2 x 1 2 3x − 2 ( x − 1) or + final answer M1 for oe 4 4 2 4 x−2 If 0 scored, SC1 for final answer 4 oe

Question 85 marks

Question

The cost of one orange is t cents. The cost of one apple is w cents. The total cost of 3 oranges and 1 apple is 51 cents. The total cost of 6 oranges and 5 apples is 129 cents. Use simultaneous equations to find the value of t and the value of w. You must show all your working. t = …… w = …… [5] * 0000800000006 * DFD 6

Mark scheme

8 3t + w = 51 2 B1 for each 6t + 5w = 129 Correctly eliminating one variable from M1 e.g. 6t + 2w = 102 and 6t + 5w = 129 their equations leading to 3w = 27 or w = 51 − 3t and 6t + 5(51 − 3t ) = 129 [t =] 14 A2 A1 for [t =] 14 [w =] 9 A1 for [w =] 9 If M1A0A0 scored, M1 SC1 for two values satisfying one of their original equations or if M0 scored, SC1 for 2 correct answers

Question 94 marks

Question

Nina walks at an average speed of 5 km/h, correct to the nearest km/h. She walks for exactly 2 hours. Work out the lower bound for the distance Nina walks. …… km [2] 10 % = {n: n is an integer and 1 G n G 8 } A = {factors of 12} B = {odd numbers} Find (a) A + B A + B = {……} [1] (b) n (Al , B) . …… [1]

Mark scheme

9 9 2 B1 for 4.5 seen

Question 10

Question

In the question paper above.

Mark scheme

10(a) 1, 3 1 10(b) 5 1

Question 112 marks

Question

o o as a fraction in its simplest form. Write 0.24 …… [2] * 0000800000007 * DFD 7

Mark scheme

11 8 2 24 cao B1 for oe 33 99 or M1 for 24.24… – 0.24… oe

Question 124 marks

Question

The diagram shows a sector of a circle with centre O and radius 9 cm. 9 cm NOT TO SCALE O 9 cm The perimeter of the sector is (18 + 2r) cm. Find the area of the sector. Give your answer in terms of r . …… cm 2 [4]

Mark scheme

12 9π 4 M3 for a fully correct method 2π e.g. × π × 92 oe 2π × 9 OR 1 B2 for 40 or oe 9 or M1 for 18 + k × 2 × π × 9 = 18 + 2π oe M1 for (their k ) × π × 92 oe OR SC2 for answer 81 + 9π oe

Question 134 marks

Question

These are Rahul’s 10 test scores. 9 8 9 10 7 x 9 9 x 7 The mean of these scores is 8. Find the interquartile range. You must show all your working. …… [4] * 0000800000008 * DFD 8

Mark scheme

13 68 + 2 x M1 = 8 or better 10 x=6 A1 Lower quartile = 6.5 or 6.75 or 7 B1 or upper quartile = 9 2 or 2.25 or 2.5 nfww A1

Question 149 marks

Question

C 55° NOT TO B SCALE X 88° A D E A, B, C, D and E lie on the circle. AC and BD intersect at X. Angle ACD = 55° and angle CXD = 88°. (a) Complete the statements, giving a geometrical reason in each part. Angle CDB = …… because …… Angle ABD = …… because …… Angle AED = …… because …… [6] * 0000800000009 * DFD 9 (b) Triangle CXD is mathematically similar to triangle BXA. DX = 8.0 cm, BX = 2.7 cm and AX = 4.0 cm. (i) Work out the length of CX. CX = …… cm [2] (ii) Complete the statement. Area of triangle CXD : area of triangle BXA = …… : …… [1]

Mark scheme

14(a) 37 2 B1 for each Angle sum of triangle = 180 55 2 B1 for each Angles in the same segment are equal 125 2 B1 for each Opposite angles of cyclic quadrilateral sum to 180 14(b)(i) 5.4 2 4 2.7 M1 for = oe 8 CX 14(b)(ii) 4 : 1 oe 1

Question 153 marks

Question

(a) Write 66 000 in standard form. …… [1] (b) Work out `3.7 # 10 8j + `3.7 # 10 7j. Give your answer in standard form. …… [2] * 0000800000010 * DFD 10

Mark scheme

15(a) 6.6 × 104 1 15(b) 4.07 × 108 2 M1 for figs 407 or for 0.37 × 10 8 or 37 × 107 or 107 (3.7 × 10 + 3.7) or 108 (3.7+ 3.7 ÷ 10) oe

Question 164 marks

Question

y 6 5 4 R 3 2 1 0 1 2 3 4 x Write down all the inequalities that define the region R. [4]

Mark scheme

16 x ⩽ 2.5 4 B3 for answer y>3 x < 2.5 y ⩾ 3 y<4 y < 2x y⩽4 y ⩽ 2x OR B1 for each If 0 or 1 scored, instead award SC2 for recognition of x = 2.5, y = 3, y = 4, y = 2x If 0 scored, SC1 for recognition of y = 2x

Question 175 marks

Question

I = M ( k 2 + c 2) (a) Find the value of I when M = 7, k = 3 and c = 2. I = …… [2] k = …… [3] * 0000800000011 * DFD 11

Mark scheme

17(a) 91 2 M1 for 7(32 + 22 ) oe 17(b) I I − Mc2 3 M1 for correctly dividing by M [±] − c 2 or [ ±] M1 for correctly isolating term in k2 M M M1 for correctly taking square root final answer Maximum M2 if answer is incorrect

Question 184 marks

Question

f (x) = 2x + 5 f (x) f (x) - ff (x) = ax 2 + bc + c Find the value of a, the value of b and the value of c. a = …… b = …… c = …… [4]

Mark scheme

18 [a =] 4 4 B3 for two correct nfww [b =] 16 [c =] 10 OR B2 for 4 x 2 + 20 x + 25 or B1 for three terms correct from 4 x 2 + 10 x + 10 x + 25 M1 for 2(2x + 5) + 5 soi

Question 193 marks

Question

Solve. x 1 e o = 9x+4 3 x = …… [3] * 0000800000012 * DFD 12

Mark scheme

19 8 2 3 M2 for –x = 2(x + 4) oe − or −2 oe or M1 for (3–1 )x, 3− x , (32 )x+4 , 3 ( ) or 2 x+4 3 3 −2( x + 4 ) 1 oe 3

Question 209 marks

Question

Bag A Bag B Bag A contains 5 white balls and 3 black balls. Bag B contains 3 white balls and 1 black ball. (a) Two balls are picked at random from bag B without replacement. Find the probability that both balls are black. …… [1] (b) The balls are replaced into bag B. Kyle picks a ball at random from each bag. (i) Complete the tree diagram. Bag A Bag B white white 5 8 …… black white …… black …… black [2] (ii) Find the probability that the two balls are the same colour. …… [3] * 0000800000013 * DFD 13 (c) The balls are replaced into their bags. Jo picks a ball at random from bag A and places it into bag B. She then picks a ball at random from bag B. Find the probability that she picks a black ball from bag B. …… [3] * 0000800000014 * DFD 14

Mark scheme

20(a) 0 1 20(b)(i) 2 3 B1 for 8 3 1 or for and correctly placed on the 4 4 same pair of branches 20(b)(ii) 18 3 5 3 3 1 oe M2 for × their + their × their oe 32 8 4 8 4 or M1 for one correct branch e.g. 5 3 3 1 × their or their × their oe 8 4 8 4 20(c) 11 3 5 1 3 2 oe M2 for × + × oe 40 8 5 8 5 or M1 for one product of the form 5 k 3 k × or × oe (k = 1, 2, 3 or 4) 8 5 8 5

Question 214 marks

Question

(a) `3 - 5j`2 + 3 5j = a + b 5 Find the value of a and the value of b. a = …… b = …… [2] (b) Rationalise the denominator. Write your answer in its simplest form. 6 2 …… [2]

Mark scheme

21(a) [a =] –9 2 B1 for each [b =] 7 or for three correct terms from 6 + 9 5 − 2 5 − 3 5 5 oe 21(b) 3 2 final answer 2 2 M1 for × oe 2

Question 225 marks

Question

Solve. 2 x = x-1 x+2 x = …… or x = …… [5] * 0000800000015 * DFD 15

Mark scheme

22 –1 and 4 5 B2 for x2 – 3x – 4 [= 0] or M1 for 2(x + 2) = x(x – 1) or better M2 for a correct method to solve their three-term quadratic in the numerator or M1 for (x + a)(x + b) where ab = –4 or a + b = –3 or x( x − 4) + [1]( x − 4) or x( x + 1) − 4( x + 1) or M1 for (−3)2 − 4 × [1] × −4 or better p+ q p− q or if in the form or then r r M1 for p = −(−3) and r = 2(1) or better

Question 234 marks

Question

Find the coordinates of the turning point on the graph of y = 7 - 2x - x 2 . ( …… , …… ) [4]

Mark scheme

23 (–1, 8) 4 B3 for x = –1 OR M1 for –2 – 2x M1 for their derivative = 0 OR − ( −2 ) M2 for [x =] or better 2 ( −1) −b or B1 for 2a OR M2 for – ((x + 1)2 – 8) [= 0] oe or M1 for [±](x + 1)2 + k

Question 244 marks

Question

A NOT TO a SCALE C M O b B D In the diagram, OBD and ACD are straight lines. O is the origin, the position vector of A is a and the position vector of B is b. 1 BC = OA 3 M is the midpoint of CD. Find the position vector of M. Give your answer in terms of a and b, in its simplest form. …… [4] Questions 25 and 26 are printed on the next page. * 0000800000016 * DFD 16

Mark scheme

24 1 5 4 1 1 a + b final answer B3 for DM or MC = − b + a 6 4 4 6 1 1 or MD or CM = b – a 4 6 1 3 or B2 for BD = b or OD = b 2 2 or M1 for a correct route for OM

Question 254 marks

Question

Simplify. 10ax + 6bx - 25a - 15b 4x 2 - 25 …… [4] 1

Mark scheme

25 5a + 3b 4 B2 for (5a + 3b)(2 x − 5) final answer 2x + 5 or B1 for 5a(2 x − 5) + 3b(2 x − 5) or for 2 x(5a + 3b) − 5(5a + 3b) B1 for (2 x + 5)(2 x − 5)

Question 263 marks

Question

Solve tan x =- for 0° G x G 360° . 3 x = …… , x = …… [3]

Mark scheme

26 150 and 330 3 B2 for one correct answer or B1 for [tan–1 …] = 30 or –30 If 0 scored, SC1 for two answers in range with a difference of 180

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Where can I find the 0580/21 October/November 2025 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/21, October/November 2025 (0580_w25_ms_21), and the question paper (0580_w25_qp_21), to read or download, with each question's marking points written out underneath.

How many marks is 0580/21 out of?

Mathematics 0580/21 for October/November 2025 is out of 100 marks, with 2 hours to answer it.

Can I get my 0580/21 answers marked?

Yes. Upload your answers to 0580/21/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.