Question 12 marks
Question
NOT TO x° SCALE 25° The diagram shows an isosceles triangle. Find the value of x. x = …… [2]
Mark scheme
1 130 2 M1 for 180 – 2 × 25
Mathematics 0580/23 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_230580_w25_ms_230580/23/O/N/25
- Paper
- Paper 2 (Extended)
- Total marks
- 100
- Time
- 2 hours
- Code on the paper
- 0580/23/O/N/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 21 mark
Question
Find the largest odd number that is a common factor of 90 and 120. …… [1]
Mark scheme
2 15 1
Question 31 mark
Question
The diagram shows a net for a dice. The dice has six faces numbered 1 to 6. The sum of each pair of opposite faces on the dice is 7. Write the missing numbers on the net. 1 4 5 [1] * 0000800000004 * DFD 4
Mark scheme
3 1 2 1 4 5 6 3
Question 42 marks
Question
A rectangle measures 5 cm by 19 cm. 19 cm NOT TO 5 cm SCALE Two of these rectangles are joined to make a shape. NOT TO SCALE Work out the perimeter of the shape. …… cm [2]
Mark scheme
4 86 2 M1 for 5 × 3 + 19 × 3 + 19 – 5 oe
Question 52 marks
Question
B F C 12º xº E NOT TO SCALE yº A G D The diagram shows a rectangle ABCD. EFG is an equilateral triangle that touches the rectangle at F and G. Find the value of x and the value of y. x = …… y = …… [2] * 0000800000005 * DFD 5
Mark scheme
5 x = 108 2 B1 for x = 108 or y = 72 y = 72 or their x + their y = 180
Question 64 marks
Question
The scatter diagram shows the value, in thousands of dollars, of ten paintings in 2005 and the value of the same paintings in 2025. 200 180 160 140 120 Value in 2025 ($ thousands) 100 80 60 40 20 0 0 10 20 30 40 50 60 70 80 90 100 Value in 2005 ($ thousands) (a) The value of one of the paintings in 2025 is less than expected. Draw a circle around the point that represents this painting. [1] (b) Another painting had a value of $75 000 in 2005 and $140 000 in 2025. On the scatter diagram, plot this point. [1] (c) Write down the number of paintings with a value of less than $53 000 in 2005. …… [1] (d) What type of correlation is shown on the scatter diagram? …… [1] * 0000800000006 * DFD 6
Mark scheme
6(a) A ring around the point (70, 60) 1 6(b) Point correctly plotted at (75, 140) 1 6(c) 5 1 6(d) Positive 1
Question 73 marks
Question
(a) The sum of all the prime numbers less than 10 is equal to 17. Find the sum of all the prime numbers less than 16. …… [2] (b) x is an integer. The sum of the prime numbers greater than 6 and less than x is equal to 18. Find a possible value for x. x = …… [1] 3 DE = e o
Mark scheme
7(a) 41 2 B1 for 11 or 13 seen with no more than one incorrect value 7(b) 12 or 13 1
Question 85 marks
Question
-4 (a) Find 5 DE . f p [1] (b) Find DE . …… [2] (c) D is the point (‒2, ‒3). Find the coordinates of the point E. ( …… , …… ) [2] * 0000800000007 * DFD 7
Mark scheme
8(a) 15 1 −20 8(b) 5 2 M1 for 32 + (–4)2 or better 8(c) (1, ‒ 7) 2 1 B1 for each or for −7
Question 91 mark
Question
n 15 ' n x = n 5 Find the value of x. x = …… [1]
Mark scheme
9 10 1
Question 104 marks
Question
C 11 cm NOT TO SCALE x° B A 8 cm The diagram shows a right-angled triangle ABC. (a) Work out the exact length of AC. …… cm [3] (b) cos x = k Write down the value of k. k = …… [1] * 0000800000008 * DFD 8
Mark scheme
10(a) 57 3 M2 for 112 – 82 or M1 for 112 = AC2 + 82 10(b) 8 1 11
Question 112 marks
Question
Sarah rolls a fair 6-sided dice twice. Find the probability she rolls a number greater than 4 both times. …… [2]
Mark scheme
11 1 2 2 2 oe M1 for × oe 9 6 6
Question 125 marks
Question
(a) Write down the value of 730. …… [1] 7 (b) Find the value of . 3 -2 …… [2] (c) Write 27 # 81 2 in the form 3n. …… [2] * 0000800000009 * DFD 9
Mark scheme
12(a) 1 1 12(b) 63 2 1 M1 for 3–2 = soi 9 12(c) 311 2 M1 for 33 or (34 )2 or better
Question 134 marks
Question
D A NOT TO SCALE 44° O C E x° B A, B, C and D are points on the circumference of a circle with centre O. ED and EB are tangents to the circle. AC is parallel to EB. Angle AOD = 44°. Find the value of x. x = …… [4]
Mark scheme
13 23 4 M3 for x + x + 44 + 90 = 180 oe OR B1 for ODE or OBE or BOA = 90° B1 for AOE = x or OED = x
Question 142 marks
Question
The minimum point on a quadratic curve is (–3, –5). (a) Find the equation of the line of symmetry of the curve. …… [1] (b) Write the equation of the curve in the form y = (x + a) 2 + b . y = …… [1] * 0000800000010 * DFD 10
Mark scheme
14(a) x = –3 1 14(b) [y =] (x + 3)2 – 5 1
Question 154 marks
Question
Factorise. (a) x 2 - 7x + 12 …… [2] (b) 5x + 10y + 6ny + 3nx …… [2]
Mark scheme
15(a) (x – 3)(x – 4) final answer 2 B1 for (x + a)(x + b) where ab = 12 or a + b = –7 or x(x – 4) –3(x – 4) or x(x – 3) –4(x – 3) 15(b) (5 + 3n)(x + 2y) final answer 2 B1 for 5(x + 2y) + 3n(x + 2y) or x(5 + 3n) + 2y(5 + 3n)
Question 165 marks
Question
The table shows three sequences. 1st 2nd 3rd 4th 5th nth term term term term term term Sequence 8 13 18 23 28 A Sequence 3 4 5 6 7 B 2 3 4 5 6 Sequence 1 1 1 2 4 C 4 2 Complete the table to show the nth term of each sequence. [5] * 0000800000011 * DFD 11
Mark scheme
16 5n + 3 oe final answer 2 B1 for answer 5n + j or kn + 3, k ≠ 0 or 5n + 3 seen then spoilt n+2 1 oe final answer n +1 2n – 3 oe final answer 2 B1 for answer 2an+b , a ≠ 0 oe or a correct answer seen then spoilt
Question 174 marks
Question
(a) Sketch the graph of y = cos x for 0° G x G 360° . y 1 0 x 180° 360° –1 [2] 1 (b) cos x° = and x is a reflex angle. 2 Find the value of x. x = …… [2] * 0000800000012 * DFD 12
Mark scheme
17(a) Correct sketch to go through (0, 1), 2 M1 for correct cos curve shape through (180, –1) and (360, 1) (0, 1) 1 or for almost correct sketch within 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 17(b) 315 2 B1 for 45
Question 182 marks
Question
Shade the region in each Venn diagram. (a) (A + B)l % A B [1] (b) (C , D) + E l % C D E [1] * 0000800000013 * DFD 13
Mark scheme
18 (a) E 1 A B 18 (b) E 1 C D E
Question 195 marks
Question
A NOT TO SCALE 60° B O The diagram shows a circle, centre O, radius 12 cm. (a) Work out the area of the minor sector AOB. Give your answer in terms of r in its simplest form. …… cm 2 [2] (b) Calculate the length of the major arc AB. Give your answer in terms of r in its simplest form. …… cm [3] * 0000800000014 * DFD 14 o o + 0.2 .
Mark scheme
19(a) 24π cao 2 60 M1 for × π ×122 oe 360 19(b) 20π cao 3 360 − 60 M2 for × π ×12 × 2 oe 360 k or M1 for × π ×12 × 2 oe 360 where k < 360
Question 203 marks
Question
Work out 0.114 Give your answer as a fraction. …… [3]
Mark scheme
20 311 3 M2 for 314.14 − 3.14 oe oe fraction 990 113 198 or + 990 990 or M1 for 114.14 −1.14 oe or 113 or 0.314 990
Question 214 marks
Question
y° NOT TO SCALE m° p° `m + 10j°c The diagram shows a cyclic quadrilateral. The ratio p | m = 2 | 3. Find the value of y. y = …… [4] * 0000800000015 * DFD 15 1
Mark scheme
21 62 4 B3 for [m + 10 =] 118 or B2 for m = 108 or p = 72 180 or M2 for ×3 3+ 2 or M1 for recognising opposite angles in a cyclic quadrilateral add up to 180° soi
Question 223 marks
Question
The equation of line L is y =- x + 7 . 2 Find an equation of the line perpendicular to line L that passes through the point (3, 5). Give your answer in the form y = mx + c . y = …… [3]
Mark scheme
22 [y =] 2x – 1 3 −1 M1 for oe −0.5 M1 for (3, 5) correctly substituted into y = (their 2)x + c
Question 233 marks
Question
B NOT TO 6 cm SCALE 30° A 10 cm C Work out the area of triangle ABC. …… cm 2 [3] * 0000800000016 * DFD 16
Mark scheme
23 15 3 1 M1 for × 6 ×10 × sin 30 oe 2 1 B1 for sin 30 = soi 2
Question 246 marks
Question
(a) Simplify. 125 - 20 …… [2] (b) 2 2 cm NOT TO SCALE 3 8 cm The area of this rectangle is k cm 2 . Work out the value of k. k = …… [2] (c) Rationalise the denominator. 1 7 +2 …… [2] * 0000800000017 * DFD 17
Mark scheme
24(a) 3 5 2 B1 for 5 5 or 2 5 24(b) 24 2 M1 for 6 16 oe or 6 2 × 2 2 or 3 8 × 8 24(c) 7 −2 1 2 2 1 7 −2 or 7 ‒ M1 for × oe 3 3 3 7 +2 7 −2
Question 253 marks
Question
Mahir picks one number at random from the numbers 5, 10 and 15. He then picks one number at random from the numbers 4, 5 and 6. He adds the two numbers. The sample space diagram shows some of the possible outcomes. First number + 5 10 15 4 14 19 Second 5 15 20 number 6 16 21 (a) Complete the sample space diagram. [1] (b) Given that the total of the two numbers is odd, find the probability that one of the numbers added is 15. …… [2]
Mark scheme
25(a) 1 9 10 11 25(b) 2 2 their 2 oe FT for 5 their 5 their 2 B1FT for where their 2 ⩽ k ⩽ 9 k c or for where 0 < c ⩽ their 5 their 5
Question 265 marks
Question
Write as a single fraction in its simplest form. mp 15 (a) # 25y m …… [2] 3 4 (b) + 2x - 5 x - 3 …… [3] * 0000800000018 * DFD 18
Mark scheme
26(a) 3p 2 15 p 3mp final answer cao B1 for or final answer 5y 25 y 5my or for correct answer spoilt 26(b) 11x − 29 3 B1 for 3( x − 3) + 4(2 x − 5) or better final answer (2 x − 5)( x − 3) seen or B1 for common denominator of (2 x − 5)( x − 3) oe isw 11x − 29 final answer 2 x 2 − 11x + 15
Question 276 marks
Question
Solve the simultaneous equations. y = x 2 - 8x + 22 y + 2 = 3x x = …… , y = …… x = …… , y = …… [6]
Mark scheme
27 [x =] 3, [y =] 7 6 M2 for x² – 11x + 24 [= 0] oe simplified [x =] 8, [y =] 22 or M1 for x² – 8x + 22 = 3x – 2 oe or better M2 for correct method to solve their three- term quadratic e.g. (x – 8)(x – 3) [= 0] or M1 for x(x – 3) – 8(x – 3) or x(x – 8) – 3(x – 8) or (x + a)(x + b) where ab = 24 or a + b = –11 B1 for x = 3 and x = 8 or y = 7 and y = 22 or one correct pair If B0 scored and at least two method marks scored SC1 for correct substitution of both of their x-values into y + 2 = 3x or y = x2 – 8x + 22
Question 284 marks
Question
Simplify. 2x 2 - 11x - 21 x 2 - 49 …… [4] * 0000800000019 * DFD 19
Mark scheme
28 2x + 3 4 B2 for (2x + 3)(x – 7) final answer or B1 for 2x(x – 7) + 3(x – 7) x+7 or x(2x + 3) – 7(2x + 3) or (2x + a)(x + b) where ab = – 21 or a + 2b = – 11 B1 for (x + 7)(x – 7)
Question 295 marks
Question
In this question all measurements are in centimetres. R 2R NOT TO SCALE 5R x Solid A Solid B Solid A is made from a cylinder and a hemisphere, both of radius 2R. The cylinder has height 5R. Solid B is a cone of radius R and sloping edge x. The total surface area of solid A is equal to the total surface area of solid B. Find R in terms of x. R = …… [5] * 0000800000020 * DFD 20
Mark scheme
29 x 5 M1 for π (2R)2 oe [R =] M1 for 2 × π × 2R × 5R oe 31 4π ( 2R ) 2 M1 for oe 2 M1 for π × R × x + π × R 2 oe
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Where can I find the 0580/23 October/November 2025 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/23, October/November 2025 (0580_w25_ms_23), and the question paper (0580_w25_qp_23), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/23 for October/November 2025 is out of 100 marks, with 2 hours to answer it.
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