Cambridge IGCSE Mathematics 0580 — 2025 Oct/Nov Paper 3 · Variant 1
0580/31/O/N/25 · 24 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 · A B (a) Measure the length of line AB in centimetres
1 A B (a) Measure the length of line AB in centimetres. ............................................ cm [1] (b) Draw a line that is perpendicular to the line AB. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 4.7 1 1(b) Perpendicular line drawn 1
Q2 · Complete this shopping bill
2 Complete this shopping bill. 3.4 kg of flour at $4.60 per kg = $ ...................... 2.75 kg of sugar at $ ...................... per kg = $ 9. 90 Total = $ ...................... [3]
Mark scheme: 2 15.64 3 B1 for each 3.6[0] 25.54 FT their 15.64
Q3 · Total cost of a journey = number of litres of fuel used # cost of fuel per litre
3 Total cost of a journey = number of litres of fuel used # cost of fuel per litre. A journey uses 128 litres of fuel. The cost of fuel is $1.52 per litre. Calculate the total cost of this journey. $ ................................................ [1]
Mark scheme: 3 194.56 cao 1
Q4 · 1 16 10 5 4 15 10 80 25 2 2 Draw a ring around the fractions which are not equivalent to 5
6 1 16 10 5 4 15 10 80 25 2 2 Draw a ring around the fractions which are not equivalent to 5. [2]
Mark scheme: 4 1 16 5 2 B1 for 2 correct and no incorrect or all 3 correct and 1 incorrect 10 80 2
Q5 · Find the value of (a) (i) .196 ................................................
5 Find the value of (a) (i) .196 ................................................. [1] (ii) 173 ................................................. [1] (iii) -0.8 # - 1 .2 . ................................................. [1] (b) Write these numbers in order, starting with the smallest. 11 27 58% 0.574 19 47 ..................... 1 ..................... 1 ..................... 1 ..................... [2] smallest
Mark scheme: 5(a)(i) 1.4 1 5(a)(ii) 4913 1 5(a)(iii) 0.96 1 5(b) 27 11 2 B1 for 3 in correct order 0.574 58[%] or M1 for all decimal or % equivalents to 47 19 enable comparison. 0.578… or 0.579 , 0.58 , 0.5744… or 0.5745 , [0.574]
Q6 · 17 4 25 18 14 6 3 18 12 Find (a) the mode ................................................
6 17 4 25 18 14 6 3 18 12 Find (a) the mode ................................................. [1] (b) the range. ................................................. [1]
Mark scheme: 6(a) 18 1 6(b) 22 1
Q7 · A bag contains 6 red balls, 4 green balls and 2 blue balls
7 A bag contains 6 red balls, 4 green balls and 2 blue balls. Zia takes a ball from the bag at random. The diagram shows a probability scale. A B C D E F G 0 1 Which arrow shows the probability that, (a) Zia takes a green ball ................................................. [1] (b) Zia takes a yellow ball ................................................. [1] (c) Zia does not take a blue ball. ................................................. [1]
Mark scheme: 7(a) C 1 7(b) A 1 7(c) F 1
Question 8
8 Solve. (a) 8x = 32 x = ................................................ [1] (b) 6x - 3 = 12 x = ................................................ [2] (c) Represent the inequality -4 G x 1 2 on the number line. x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 [2]
Mark scheme: 8(a) 4 1 8(b) 2.5 oe 2 3 12 M1 for 6x = 12 + 3 oe or x – = oe 6 6 8(c) 2 B1 for correct line with circles at both ends or for correct circles but line missing –5 –4 –3 –2 –1 0 1 2 3 4
Q9 · Write down the mathematical name for this type of angle
9 (a) Write down the mathematical name for this type of angle. ................................................. [1] (b) ABC is a triangle. C 102° NOT TO SCALE 54° x° A B Lily says x is 34. Give a geometrical reason why Lily is not correct. ..................................................................................................................................................... ..................................................................................................................................................... [1] (c) D 126° C A 48° x° NOT TO E SCALE 75° B ABCD is a quadrilateral. DCE is a straight line. Calculate the value of x. x = ................................................ [2]
Mark scheme: 9(a) reflex 1 9(b) Angles in a triangle add to 180, 1 accept angles in a triangle should add up to 180 angles in the/this/Lily’s triangle do not add up to 180 9(c) 69 2 M1 for 360 – (126 + 48 + 75) oe
Q10 · Anna and Bruno share some money in the ratio Anna : Bruno = 3 : 7
10 Anna and Bruno share some money in the ratio Anna : Bruno = 3 : 7. Bruno receives $36 more than Anna. Calculate the total amount of money they share. $ ................................................ [2]
Mark scheme: 10 90 2 36 M1 for [ × k , where k = 1, 3, 7 or 10] oe 4
Q11 · Naz pays $76.25 per day to hire a car
11 (a) Naz pays $76.25 per day to hire a car. He hires this car for 7 days. He also pays $146 for fuel. Calculate the total amount Naz pays. $ ................................................ [2] (b) Li pays $1400 to hire a car. $364 of this is insurance. Calculate the insurance as a percentage of the $1400. ............................................. % [1]
Mark scheme: 11(a) 679.75 cao 2 M1 for 76.25 × 7 + 146 oe or B1 for 533.75 11(b) 26 1
Q12 · 300 students choose where to go on a trip
12 300 students choose where to go on a trip. The students choose either a zoo, a museum, an art gallery or a sports stadium. Zoo Museum (a) Show that 75 students choose the museum. [1] (b) 45 students choose the art gallery and 120 students choose the sports stadium. Complete the pie chart to show this information. [2]
Mark scheme: 12(a) 90 1 × 300 360 12(b) Correct pie chart 2 360 M1 for × k oe where k is 1 or 45 or 120 300
Q13 · The surface area of a solid cube is 121.5 cm 2
13 (a) The surface area of a solid cube is 121.5 cm 2 . Calculate the length of the side of the cube. ............................................ cm [3] (b) 10 cm NOT TO h SCALE 15 cm The area of the trapezium is 106.25 cm 2. (i) Calculate the height of the trapezium. ............................................ cm [2] (ii) Convert 106.25 cm 2 into m2. ............................................ m2 [1]
Mark scheme: 13(a) 4.5 nfww 3 121.5 M2 for oe 6 121.5 or M1 for oe 6 13(b)(i) 8.5 2 1 M1 for (10 + 15)h = 106.25 oe or better 2 13(b)(ii) 0.010625 cao 1
Q14 · A bag contains red, yellow, blue and green cards
14 A bag contains red, yellow, blue and green cards. The table shows the probability of taking a red card and a yellow card. The probability of taking a blue card or a green card is in the ratio blue : green = 5 : 2 . Complete the table. Colour red yellow blue green Probability 0.53 0.19 [3]
Mark scheme: 14 0.2[0] 0.08 oe 3 1 − ( 0.53 + 0.19 ) M2 for oe 7 or M1 for 1 – (0.53 + 0.19) oe
Q15 · Shapes A and B are shown on the grid
15 Shapes A and B are shown on the grid. y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 B – 3 A – 4 – 5 – 6 (a) Describe fully the single transformation that maps shape A onto shape B. ..................................................................................................................................................... ..................................................................................................................................................... [3] 6 (b) On the grid, draw the image of shape A after a translation by the vector e o. [2] 7
Mark scheme: 15(a) Enlargement 3 B1 for each [centre] (0,0) [scale factor] 0.5 15(b) Triangle at (2,2) (4,2) (2,5) 2 k 6 B1 for translation by or 7 k
Q16 · Bob travels from town A to town B
16 Bob travels from town A to town B. The travel graph shows his journey. 600 500 400 Distance from town A (km) 300 200 100 0 08 00 09 00 10 00 11 00 12 00 13 00 14 00 15 00 Time (a) Between which two times did Bob stop for a rest? Explain how you know. ................ and ................ because ..................................................................................................... ..................................................................................................................................................... [2] (b) Calculate Bob’s average speed, in km/h, for the whole journey. ........................................ km/h [3]
Mark scheme: 16(a) 10 30 and 11 15 1 line is horizontal oe 1 distance remains the same oe 16(b) 100 nfww 3 M2 for 625 ÷ 6.25 or M1 for 625 ÷ their time
Question 17
17 Factorise. 21x - 7xy ................................................. [2]
Mark scheme: 17 7x(3 – y) 2 B1 for 7(3x – xy) or x(21 – 7y) or for 7x(3 – y) seen then spoilt
Q18 · The nth term of a sequence is n 2 - 4
18 (a) The nth term of a sequence is n 2 - 4 . Find the first 3 terms of this sequence. ............... , ............... , ............... [2] (b) These are the first four terms of a different sequence. 5 2 -1 -4 Find the nth term. ................................................. [2]
Mark scheme: 18(a) –3 0 5 2 B1 for 2 in correct position in final answer 18(b) –3n + 8 oe final answer 2 B1 for final answer of –3n + j or kn + 8 where k ≠ 0 , or –3n + 8 seen then spoilt
Q19 · Jo invests $500 at a rate of 2% per year compound interest
19 Jo invests $500 at a rate of 2% per year compound interest. Calculate the amount of interest earned at the end of 7 years. $ ................................................ [3]
Mark scheme: 19 74.3 or 74.34… 3 B2 for 574 or 574.3… 2 7 or M2 for 500 1 + - 500 oe 100 2 7 or M1 for 500 1 + oe 100
Q20 · Work out the size of one interior angle of a regular 8-sided polygon
20 (a) Work out the size of one interior angle of a regular 8-sided polygon. ................................................. [2] (b) D NOT TO C SCALE x° B 71° O E A A, B and C lie on the circumference of the circle, centre O. AB is a diameter. DBE is a tangent to the circle at B. Find the value of x. Give a geometrical reason for your answer. ................ because ...................................................................................................................... ..................................................................................................................................................... [2]
Mark scheme: 20(a) 135 2 ( 8 − 2 )180 M1 for 180 – 360 ÷ 8 or oe 8 20(b) 19 2 B1 for each Angle between tangent and radius = 90
Q21 · The line L is shown on the grid
21 The line L is shown on the grid. y 18 L 16 14 12 10 8 6 4 2 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 2 – 4 Find the equation of the line L. Give your answer in the form y = mx + c . y = ................................................ [3]
Mark scheme: 21 3x + 5 3 B2 for 3x + c or (2.7 to 3.3)x + (4.8 to 5.2) or for a correct unsimplified answer or M1 for a correct rise/run or for a right-angled triangle with run = a and rise = b marked on graph oe where b ÷ a = 2.7 to 3.3 or B1 for mx + 5 or mx + (4.8 to 5.2) where m is their gradient
Q22 · A train to town P leaves a station every 20 minutes
22 (a) A train to town P leaves a station every 20 minutes. A train to town Q leaves the same station every 35 minutes. Both trains leave at 09 30. Find the next time both trains leave together. ................................................. [3] (b) The distance, d km, between town P and town Q is 97 km, correct to the nearest kilometre. Complete the statement about the value of d. ................... G d 1 ................... [2]
Mark scheme: 22(a) 11 50 3 B2 for 140 or 2 hr 20 mins or M1 for 140k or 2 2 5 7 or [20 =] 2 2 5 and [35 =] 5 7 or two correct factor trees/tables of both 20 and 35 OR M2 for listing correct times/multiples of both 20 and 35 to at least 1150 or 140 or M1 for listing at least 3 correct of each or one full list 22(b) 96.5 97.5 2 B1 for each in correct position If 0 scored SC1 for both correct but reversed
Q23 · 6 # 10 3 23 Calculate
4.6 # 10 3 23 Calculate . 1 .84 # 10 5 Give your answer in standard form. ................................................. [2] Question 24 is printed on the next page
Mark scheme: 23 2.5 × 10–2 cao 2 B1 for 0.025 or correct answer not in standard form e.g. 25 × 10–3 , 0.25 × 10–1
Q24 · 32 cm A C NOT TO SCALE 27° B ABC is a right-angled triangle
24 32 cm A C NOT TO SCALE 27° B ABC is a right-angled triangle. Calculate BC. BC = ĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭ cm [3]
Mark scheme: 24 70.5 or 70.48 to 70.49 3 32 32 M2 for [ BC = ]sin27 or cos63 oe 32 32 or M1 for sin 27 = or cos 63 = oe BC BC
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Rates2Algebraic manipulation1Angles1Averages and range1Equations1Equations of linear graphs1Fractions, decimals and percentages1Money1Percentages1Powers and roots1Ratio and proportion1Right-angled triangles1Sequences1Standard form1Statistical charts and diagrams1Surface area and volume1The four operations1Time1Transformations1Types of number1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2025 Oct/Nov, Paper 3 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.