Cambridge IGCSE Mathematics 0580 — 2025 Feb/March Paper 3 · Variant 2
0580/32/F/M/25 · 21 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 · 1 Taj is 3 years old
1 1 Taj is 3 years old. 4 Work out her age in months. ..................................... months [1]
Mark scheme: Question Answer Marks Partial Marks 1 39 1
Q2 · Div has $25 to buy some cups which cost $4.25 each
2 Div has $25 to buy some cups which cost $4.25 each. Calculate the maximum number of cups he can buy and the change he receives. Number of cups ................................................ Change $ ................................................. [3]
Mark scheme: 2 5 3.75 3 B2 for 5 in answer space 25 or M1 for soi 4.25
Q3 · A (a) Measure angle A
3 A (a) Measure angle A. ................................................. [1] (b) Write down the mathematical name of this type of angle. ................................................. [1]
Mark scheme: 3(a) 33 1 3(b) acute 1
Q4 · 30 31 32 33 34 35 36 37 38 39 From this list, write down the number that is (a) a…
4 30 31 32 33 34 35 36 37 38 39 From this list, write down the number that is (a) a multiple of 13 ................................................. [1] (b) a factor of 140 ................................................. [1] (c) the largest prime number ................................................. [1] (d) divisible by an even cube number ................................................. [1] (e) 20% of 190. ................................................. [1]
Mark scheme: 4(a) 39 1 4(b) 35 1 4(c) 37 1 4(d) 32 1 4(e) 38 1
Q5 · A farmer plants t trees each day
5 (a) A farmer plants t trees each day. Write an expression for the number of trees he plants in d days. ................................................. [1] (b) A train has p passengers. x passengers get off the train and y passengers get on the train. Write an expression for the number of passengers on the train now. ................................................. [1]
Mark scheme: 5(a) dt oe final answer 1 5(b) p − x + y oe final answer 1
Q6 · Raj thinks of a negative number, n
6 Raj thinks of a negative number, n. He adds 10 to n and then multiplies by 5. The answer is 30. Work out the value of n. n = ................................................. [2]
Mark scheme: 6 –4 2 B1 for 6 seen or M1 for ( n + 10 ) 5 = 30 or better
Q7 · The diagram shows a straight line crossing a pair of parallel lines
7 The diagram shows a straight line crossing a pair of parallel lines. c b d A e h f g Complete these statements. (a) Angle A and angle ................. are corresponding angles. [1] (b) Angle A and angle e are ........................................................ angles. [1]
Mark scheme: 7(a) g 1 7(b) alternate 1
Q8 · These are the first four terms of a sequence
8 These are the first four terms of a sequence. 31 24 17 10 (a) Write down the term-to-term rule for continuing this sequence. ................................................. [1] (b) Find the next two terms in this sequence. ........................ , ........................ [2] (c) Find the nth term. ................................................. [2]
Mark scheme: 8(a) subtract 7 oe 1 8(b) 3 −4 2 B1 for each If 0 scored SC1 for two answers with a difference of −7 8(c) 38 −n7 oe final answer 2 B1 for j − 7 n or 38−kn , k 0 or 38 −n7 seen then spoilt
Q9 · A cuboid measures 3 cm by 7 cm by 11 cm
9 A cuboid measures 3 cm by 7 cm by 11 cm. Calculate the surface area of the cuboid. ......................................... cm2 [3]
Mark scheme: 9 262 3 M2 for [2] ( 3 7 + 3 11 + 7 11) oe or M1 for 3 7 or 3 11 or 7 11 oe
Q10 · The table shows an ordered stem-and-leaf diagram
10 The table shows an ordered stem-and-leaf diagram. A, B and C are missing numbers. 0 2 A 1 1 3 B 7 2 0 4 6 C Key : 1 | 3 represents 13 For the ten numbers • the range is 27 • the median is 16 • the mean is 16.5 . (a) Work out the values of A, B and C. A = ....................................................... B = ....................................................... C = ....................................................... [5] (b) Complete this statement. There is no mode because ................................................................................................................. ..................................................................................................................................................... [1]
Mark scheme: 10(a) 8 5 9 5 B1 for [B=] 5 B1 for [C=] 9 If B0,B0 scored SC1 for B = 15 and C = 29 B3 for 8 , 15 , 29 or 8 , 5 , 29 or 8 , 15 , 9 or M2 for ( 2 + A + 11 + 13 + (10 + theirB) + 17 + 20 + 24 + 26 ++ (20 + theirC))10[=16.5] oe soi or better or M1 for 16.5×10 oe or better 10(b) All the numbers are different oe 1
Q11 · The scale drawing shows the positions of two lighthouses, P and Q
11 The scale drawing shows the positions of two lighthouses, P and Q. The scale is 1 centimetre represents 0.8 kilometres. North North P Q Scale: 1 cm to 0.8 km (a) (i) Find the actual distance between P and Q. ........................................... km [2] (ii) Measure the bearing of Q from P. ................................................. [1] (b) A boat, B, is on a bearing of 127° from P. Calculate the bearing of P from B. ................................................. [2]
Mark scheme: 11(a)(i) 7.6 2 B1 for 9.5 [cm] or M1 for 0.8×k , 9 k 10 11(a)(ii) 102 1 11(b) 307 2 M1 for 180 + 127 or 360 − (180 − 127 ) or the correct angle is indicated on a sketch
Q12 · Mo asks some people if they prefer sun, rain or wind
12 Mo asks some people if they prefer sun, rain or wind. The pie chart shows the results. Wind 95° Sun 80° Rain 45 more people prefer wind than rain. Work out how many people prefer sun. ................................................. [4]
Mark scheme: 12 555 4 360 − 95 − 80 M3 for 45 oe 95 − 80 95 − 80 45 or M2 for or oe 45 95 − 80 or M1 for 360 − 95 − 80 or 95 − 80 45 oe
Q13 · Xie changes 2000 dollars into krona
13 Xie changes 2000 dollars into krona. 1 dollar = 0.615 euros 1 krona = 0.087 euros Use the exchange rates to calculate how many krona she receives. Give your answer correct to the nearest krona. ....................................... krona [3]
Mark scheme: 13 14 138 cao 3 2000 0.615 M2 for oe 0.087 or M1 for 2000 0.615 oe If 0 or M1 scored SC1 for a decimal answer seen, correctly rounded to the nearest integer
Question 14
14 (a) Factorise. 8x 2 - 2x ................................................. [2] (b) Expand the brackets and simplify. 5 ( 2m - 1) + 3 ( m + 7) ................................................. [2]
Mark scheme: 4 x 2 − x or x ( 8 x − 2 )14(a) 2 x ( 4 x − 1) final answer 2 B1 for 2 ( ) or 2 x ( 4 x − 1) seen then spoilt 14(b) 13m + 16 final answer 2 M1 for 10m − 5 or 3 m + 21 or for 13m or +16 in the final answer or for 13m + 16 seen then spoilt
Q15 · A car travels 95 km in 2 hours and 15 minutes
15 (a) A car travels 95 km in 2 hours and 15 minutes. Calculate the average speed of the car in km/h. ......................................... km/h [1] (b) Convert 8 m/s into km/h. ......................................... km/h [2]
Mark scheme: 15(a) 42.2 or 42.22… 1 15(b) 28.8 2 8 60 60 M1 for oe 1000 or B1 for answer figs 288
Q16 · Chi shares $480 in the ratio 2 : 3 : 7
16 (a) Chi shares $480 in the ratio 2 : 3 : 7. Calculate the value of the largest share. $ ................................................ [2] (b) Simplify these ratios. (i) 98 : 147 ....................... : ....................... [1] (ii) 2 450 : 2 452 ....................... : ....................... [1]
Mark scheme: 16(a) 280 2 480 M1 for k , k = 1,2,3 or 7 2 + 3 + 7 16(b)(i) 2:3 cao 1 16(b)(ii) 1:4 cao 1
Question 17
17 (a) Solve. x = 18 3 x = ................................................ [1] 6 9 11 (b) y = 6 6 Find the value of y. y = ................................................ [1] (c) Simplify. a 6 b -2 a 4 b 3 ................................................. [2]
Mark scheme: 17(a) 54 1 17(b) −2 1 17(c) a 2 2 −5 2 B1 for a 2 b k or a k b − 5 as final answer 5 or a b final answer or for correct answer spoilt b
Q18 · Clare invests $12 000 for 3 years at a rate of 8% per year compound interest
18 (a) Clare invests $12 000 for 3 years at a rate of 8% per year compound interest. Calculate the value of her investment at the end of the 3 years. Give your answer correct to the nearest $10. $ ................................................. [3] (b) Zak invests $560 for one year. After one year his investment is worth $630. Calculate the percentage increase. ..............................................% [2]
Mark scheme: 18(a) 15 120 3 B2 for 15100, 15110 or 15116 to 15117 OR 8 3 M1 for 12000 1 + oe 100 B1 for rounding their seen answer correct to the nearest 10 18(b) 12.5 2 630 − 560 M1 for 100 oe 560 630 or 100 −100 oe 560 630 100 oe or − 1 560
Q19 · Write 2025 as the product of its prime factors
19 (a) Write 2025 as the product of its prime factors. ................................................. [2] (b) Write 2025 as a product of two square numbers that are both greater than one. ................................................. [1]
Mark scheme: 19(a) 4 2 2 B1 for 3,3,3,3,5,5 3 5 or M1 for correct factor tree/diagram/list/table 19(b) 25×81 or 225×9 1
Q20 · The diagram shows three shapes, A, B and C, on a 1 cm 2 grid
20 The diagram shows three shapes, A, B and C, on a 1 cm 2 grid. y 7 6 5 4 C A 3 B 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x (a) On the grid, draw the image of shape A after a rotation, 90° clockwise, centre (0, 3). [2] (b) Describe fully the single transformation that maps (i) shape A onto shape B .................................................................................................................................................... ............................................................................................................................................. [2] (ii) shape A onto shape C. .................................................................................................................................................... ............................................................................................................................................. [3] (c) Calculate the size of the smallest angle in triangle C. ................................................. [2]
Mark scheme: 20(a) triangle with coordinates 2 B1 for correct 90˚ anticlockwise rotation ( 0,1)( 0,3 )(1,1) about (0,3) or correct orientation, wrong centre 20(b)(i) 2 2 B1 for each translation −1 20(b)(ii) enlargement 3 B1 for each centre (5,3) scale factor 2 20(c) 26.6 or 26.56 to 26.57 2 M1 for tan x = 2 oe 4
Q21 · Show that the sum of the interior angles of a pentagon is 540°
21 (a) Show that the sum of the interior angles of a pentagon is 540° . [1] (b) In this part, all angles are in degrees. 3x - 25 3x - 5 x + 35 NOT TO SCALE x + 40 2x The diagram shows the five interior angles of a pentagon, written in terms of x. (i) Write down an expression, in terms of x, for the sum of the interior angles of the pentagon. Give your answer in its simplest form. ................................................. [2] (ii) Work out the value of x. x = ................................................ [2]
Mark scheme: 21(a) 360 1 180 − 5 ( 5 − 2 ) 180 or 5 21(b)(i) 10 x + 45 or 5 ( 2 x + 9 ) final answer 2 B1 for 10 x + c or kx + 45 or correct answer seen then spoilt 21(b)(ii) 49.5 nfww 2 M1 for their (b)(i) = 540 and a first correct step to solve their equation provided in the form ax + b = 540 or c ( dx + e ) = 540
What was in this paper
The subtopics covered by these 21 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
What you needed in this session
Cambridge’s own grade thresholds for 2025 Feb/March, Paper 3 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.