Cambridge IGCSE Mathematics 0580 — 2025 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/25 · 29 questions · 80 marks · 90 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper16 pages
Mark scheme10 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write the number four hundred and sixty thousand and five in figures
1 (a) Write the number four hundred and sixty thousand and five in figures. ................................................. [1] (b) Write 52 149 correct to the nearest hundred. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 460 005 1 1(b) 52 100 cao 1
Q2 · O The diagram shows a circle, centre O
2 O The diagram shows a circle, centre O. On the diagram (a) draw a diameter [1] (b) mark a point on the circumference and label it C. [1]
Mark scheme: 2(a) Diameter drawn 1 2(b) Point marked on circumference 1
Q3 · Write down the mathematical name of this polygon
3 Write down the mathematical name of this polygon. ................................................. [1]
Mark scheme: 3 Hexagon 1
Q4 · Write down all the factors of 24
4 (a) Write down all the factors of 24. ..................................................................................................................................................... [2] 3 (b) Write down the reciprocal of . 7 ................................................. [1]
Mark scheme: 4(a) 1 2 3 4 6 8 12 24 2 B1 for 6 correct and no extras or 8 correct and one extra 4(b) 7 1 oe 3
Q5 · In triangle ABC, AB = 8 cm and BC = 6.4 cm
5 In triangle ABC, AB = 8 cm and BC = 6.4 cm. Using a ruler and compasses only, construct triangle ABC. Leave in your construction arcs. The line AC has been drawn for you. A C [2]
Mark scheme: 5 Accurate triangle with correct 2 B1 for correct triangle with incorrect or construction arcs no arcs or for two correct intersecting arcs with incorrect or no lines If 0 scored, SC1 for triangle with arcs but lines interchanged
Q6 · Shade one square so that the diagram has rotational symmetry of order 4
6 Shade one square so that the diagram has rotational symmetry of order 4. [1]
Mark scheme: 6 1
Q7 · These are the first four terms of a sequence
7 These are the first four terms of a sequence. 9 5 1 -3 (a) Find the next term. ................................................. [1] (b) Explain how you worked out your answer. ..................................................................................................................................................... [1]
Mark scheme: 7(a) –7 1 7(b) Subtracted 4 oe 1
Q8 · P = 3 q - 2r Work out the value of q when p = 50 and r = 5
8 p = 3 q - 2r Work out the value of q when p = 50 and r = 5 . q = ................................................ [2]
Mark scheme: 8 20 2 M1 for 50 = 3q – 2 × 5 or better
Q9 · Shade 3of this grid
9 (a) Shade 3of this grid. 4 [1] (b) Work out 15% of 80. ................................................. [2]
Mark scheme: 9(a) 15 rectangles shaded 1 9(b) 12 2 15 M1 for full correct method e.g. 80 100 oe
Q10 · The bar chart shows the number of books sold in a shop in each of five months
10 The bar chart shows the number of books sold in a shop in each of five months. 12 11 10 9 8 Number 7 of books 6 sold 5 4 3 2 1 0 Mar Apr May Jun Jul Aug Months (a) 4 books were sold in August. Complete the bar chart. [1] (b) Calculate the mean number of books sold in the six months. ................................................. [2]
Mark scheme: 10(a) Correct bar for August 1 10(b) 7 nfww 2 M1 for (3 + 9 + 7 + 11 + 8 + 4) ÷ 6 or better
Q11 · The temperature at midnight is - 2°C
11 The temperature at midnight is - 2°C . The temperature at noon is 5 °C. (a) Find the difference between these temperatures. ............................................ °C [1] (b) The temperature at 9 am is 8 °C higher than the temperature at midnight. Work out the temperature at 9 am. ............................................ °C [1]
Mark scheme: 11(a) 7 1 11(b) 6 1
Q12 · NOT TO SCALE 4 cm 3 cm 5 cm Complete the net of this cuboid on the 1 cm 2 grid
12 NOT TO SCALE 4 cm 3 cm 5 cm Complete the net of this cuboid on the 1 cm 2 grid. One face has been drawn for you. [3]
Mark scheme: 12 Fully correct net 3 B2 for 3 correct extra faces in correct places or B1 for 1 correct extra face in correct place
Q13 · The scale drawing shows the positions of town A and town B
13 The scale drawing shows the positions of town A and town B. The scale is 1 centimetre represents 10 kilometres. North B North A Scale: 1 cm to 10 km (a) Work out the actual distance from town A to town B. ........................................... km [2] (b) Measure the bearing of town B from town A. ................................................. [1] (c) Town C is 45 km from town A on a bearing of 310°. On the scale drawing, mark the position of town C. [2]
Mark scheme: 13(a) 80 2 B1 for 8 or M1 for their 8 × 10 13(b) 032 1 13(c) Point correctly plotted 2 B1 for distance 4.3 to 4.7 cm from A or B1 for bearing 308º to 312º from A
Q14 · These are the ages, in months, of each of 12 children
14 These are the ages, in months, of each of 12 children. 11 27 8 10 26 17 28 12 9 13 22 12 (a) Complete the stem-and-leaf diagram to show this information. 0 1 2 Key: 1 | 7 represents 17 months [2] (b) Find the number of children over 2 years old. ................................................. [1] (c) Show that the median is 12.5 . [1]
Mark scheme: 14(a) 2 B1 for a correct ordered diagram with 0 8 9 one error or omission or for a correct but unordered stem-and- 1 0 1 2 2 3 7 leaf diagram 2 2 6 7 8 14(b) 3 1 14(c) 12 + 13 1 oe leading to 12.5 nfww 2
Q15 · D NOT TO x° SCALE 140° A B C ABC is a straight line and ABD is an isosceles triangle
15 D NOT TO x° SCALE 140° A B C ABC is a straight line and ABD is an isosceles triangle. Work out the value of x. x = ................................................ [3]
Mark scheme: 15 100 3 M2 for 180 – (180 –140) × 2 oe or M1 for 180 – 140 or for 180 – (2 × their 40)
Q16 · 16 (a) Complete the table of values for y =
9 16 (a) Complete the table of values for y = . x x – 4.5 –3 –2 –1.5 –1 1 1.5 2 3 4.5 y –2 –3 – 6 –9 9 6 4.5 2 [2] 9 (b) On the grid, draw the graph of y = for - 4.5 G x G - 1 and 1 G x G 4 .5 . x y 9 8 7 6 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 [4]
Mark scheme: 16(a) –4.5 3 2 B1 for each 16(b) Correct graph drawn 4 B3FT for 9 points correctly plotted or B2FT for 7 points correctly plotted or B1FT for 5 correctly plotted
Q17 · Write down a prime number between 20 and 30
17 (a) Write down a prime number between 20 and 30. ................................................. [1] 2 (b) Simplify ` 9j . ................................................. [1]
Mark scheme: 17(a) 23 or 29 1 17(b) 9 cao 1
Q18 · 2 18 Work out -
11 2 18 Work out - . 18 9 Give your answer as a fraction in its simplest form. ................................................. [2]
Mark scheme: 18 7 2 11 4 cao M1 for – oe 18 18 18
Q19 · By writing each number in the calculation correct to 1 significant figure, find an…
19 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 5 .3 # 19 .5 . 2.49 ................................................. [2]
Mark scheme: 19 5 20 M1 2 50 cao A1 If 0 scored SC1 for 2 correct roundings or for all 3 correct but with any trailing zeros
Q20 · Some students take a test
20 Some students take a test. 75 of the students pass the test. 3 This is of the students who take the test. 5 Work out how many students take the test. ................................................. [2]
Mark scheme: 20 125 2 M1 for 75 ÷ 3 [× 5] oe
Q21 · Shapes A and B are shown on the grid
21 Shapes A and B are shown on the grid. y 5 4 3 B 2 A 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 (a) Describe fully the single transformation that maps shape A onto shape B. ..................................................................................................................................................... ..................................................................................................................................................... [3] (b) Draw the image of shape A after a reflection in the line y =-1. [2]
Mark scheme: 21(a) Rotation 3 B1 for rotation 90 anticlockwise oe (0,0) oe B2 for 90 anticlockwise and (0, 0) or for 90 clockwise and (0.5, 3.5) or B1 for 90 anticlockwise or 90 clockwise or (0, 0) or (0.5, 3.5) 21(b) Rectangle with vertices at 2 B1 for reflection in y = k or in x = –1 (1, –3) (3, –3) (3, –4) (1,–4)
Q22 · Chocolate cookies Makes 12 100 g flour 55 g butter 55 g sugar 20 g cocoa 1 egg (a) Sunita…
22 Chocolate cookies Makes 12 100 g flour 55 g butter 55 g sugar 20 g cocoa 1 egg (a) Sunita makes 24 chocolate cookies. Work out how much flour she needs. .............................................. g [1] (b) Albie has 28 g of cocoa. Does he have enough cocoa to make 18 cookies? Explain how you decide. ..................................................................................................................................................... ..................................................................................................................................................... [2]
Mark scheme: 22(a) 200 1 22(b) No and a 2 B1 for a correct statement without correct statement based on correct support e.g. reasoning or calculations 30g is needed for 18 cookies oe or 2g more [than 28g] for 18 cookies oe or 28g would only give 16 cookies oe or 8g would only give 4 more cookies oe or M1 for correct calculation 18 6 20 oe or 20 oe 12 12 28 8 or 12 oe or 12 oe 20 20 20 28 or and oe 12 18
Q23 · A 8 # a x = a 15 Find the value of x
23 (a) a 8 # a x = a 15 Find the value of x. x = ................................................ [1] (b) ( b 7 ) y = b 21 Find the value of y. y = ................................................ [1]
Mark scheme: 23(a) 7 cao 1 23(b) 3 cao 1
Q24 · % = {students in a year group} H = {students who study History} G = {students who study…
24 % = {students in a year group} H = {students who study History} G = {students who study Geography} 80 students are in the year group. 40 students study History. % H G 10 15 (a) Complete the Venn diagram. [2] (b) Find n(G). ................................................. [1] (c) A student is chosen at random. Work out the probability that the student does not study History and does not study Geography. ................................................. [1]
Mark scheme: 24(a) 2 B1 for one correct value correctly placed If 0 scored, SC1 for two positive integers such that n(G) = 55 24(b) 55 1 FT their 30 + their 25 provided their 30 + their 25 is less than 80 24(c) 15 1 oe 80
Question 25
25 Expand and simplify. ( x + 3)( x - 2) ................................................. [2]
Mark scheme: 25 x2 + x – 6 final answer 2 B1 for x2 + 3x – 2x – 6 oe with at least three terms correct
Q26 · Write .1753 # 108 as an ordinary number
26 Write .1753 # 108 as an ordinary number. ................................................. [1]
Mark scheme: 26 175 300 000 cao 1
Q27 · NOT TO SCALE 8 cm The diagram shows a semicircle
27 NOT TO SCALE 8 cm The diagram shows a semicircle. The radius of the semicircle is 8 cm. Find the perimeter of the semicircle. Give your answer in terms of r in its simplest form. ............................................ cm [3]
Mark scheme: 27 8π + 16 or 8(π + 2) 3 8 + 8 M2 for [perimeter =] × π + 8 + 8 oe 2 final answer or 8π + 16 oe seen and then spoilt 8 + 8 or M1 for [arc = ] × π oe 2
Q28 · 5 28 Work out 8 ' 1
2 5 28 Work out 8 ' 1 . 3 8 Give your answer as a mixed number in its simplest form. ................................................. [3] Question 29 is printed on the next page.
Mark scheme: 28 1 3 16 13 5 cao B2 for oe or 5 oe 3 3 39 26 8 or M2 for oe 3 their 13 their 26 8 or oe 3 13 26 13 or B1 for oe or oe 3 8
Q29 · Jim buys 15 apples and 10 pears for $42.50
29 Jim buys 15 apples and 10 pears for $42.50 . Li buys 4 apples and 5 pears for $16. Write down a pair of simultaneous equations and solve them to find the cost of one apple and the cost of one pear. Apple $ ....................................................... Pear $ ........................................................ [5]
Mark scheme: 29 15a + 10p = 42.5 oe 2 B1 for each 4a + 5p = 16 oe [apple = ] 1.5[0] cao 3 M1FT for correctly eliminating one [pear = ] 2[.00] cao variable from their equations. A1 for 1.5 A1 for 2 If M1 A0 or M0 scored, SC1 for two positive costs which satisfy one of original conditions
What was in this paper
The subtopics covered by these 29 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Area and perimeter2Classifying statistical data2Equations2Ratio and proportion2The four operations2Algebraic manipulation1Angles1Averages and range1Circles, arcs and sectors1Estimation1Fractions, decimals and percentages1Geometrical constructions1Geometrical terms1Graphs of functions1Indices I1Percentages1Scale drawings1Sequences1Standard form1Symmetry1Transformations1What you needed in this session
Cambridge’s own grade thresholds for 2025 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.