Cambridge IGCSE Mathematics 0580 — 2025 Oct/Nov Paper 3 · Variant 3
0580/33/O/N/25 · 27 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 down all the factors of 26
1 Write down all the factors of 26. ................................................. [2]
Mark scheme: Question Answer Marks Partial Marks 1 1 2 13 26 2 B1 for 3 correct and no extra or 4 correct and 1 extra
Q2 · B O A A and B lie on a circle, centre O
2 B O A A and B lie on a circle, centre O. (a) Write down the mathematical name of the line AB. ................................................. [1] (b) On the diagram, draw a radius. [1]
Mark scheme: 2(a) Chord 1 2(b) Radius drawn 1
Q3 · Write 0.25 as a fraction
3 (a) Write 0.25 as a fraction. ................................................. [1] 1 (b) Write as a percentage. 2 ..............................................% [1] (c) Write 7% as a decimal. ................................................. [1]
Mark scheme: 3(a) 1 1 or equivalent fraction 4 3(b) 50 1 3(c) 0.07 cao 1
Q4 · Write down the mathematical name of this solid
4 (a) Write down the mathematical name of this solid. ................................................. [1] (b) 60° 60° 60° Write down the mathematical name of this type of triangle. ................................................. [1]
Mark scheme: 4(a) Cylinder 1 4(b) Equilateral 1
Q5 · Red white white blue red The diagram shows a fair 5-sided spinner
5 red white white blue red The diagram shows a fair 5-sided spinner. The spinner is spun once. (a) Write down the colour the spinner is least likely to land on. ................................................. [1] (b) Find the probability that the spinner lands on white. ................................................. [1] (c) Find the probability that the spinner does not land on red. ................................................. [1]
Mark scheme: 5(a) Blue 1 5(b) 2 1 oe 5 5(c) 3 1 oe 5
Q6 · Write down the reciprocal of 8
6 (a) Write down the reciprocal of 8. ................................................. [1] (b) Work out 193. ................................................. [1]
Mark scheme: 6(a) 1 1 or 0.125 8 6(b) 6859 1
Q7 · 200 175 150 125 100 90 Number of 80 cars sold 70 60 50 40 30 20 10 0 Mar Apr May Months A…
7 200 175 150 125 100 90 Number of 80 cars sold 70 60 50 40 30 20 10 0 Mar Apr May Months A newspaper prints this bar chart to show the number of cars sold by a garage in March, April and May. Give two reasons why the bar chart is incorrect. 1 .......................................................................................................................................................... ............................................................................................................................................................. 2 .......................................................................................................................................................... ............................................................................................................................................................. [2]
Mark scheme: 7 Bar width not equal oe 2 B1 for each Scale not linear oe
Q8 · Work out the number of seconds in six and a half hours
8 Work out the number of seconds in six and a half hours. .................................... seconds [1]
Mark scheme: 8 23 400 1
Q9 · 8 cm 7 cm NOT TO 15 cm 12 cm SCALE 5 cm 23 cm Find the area of the shape
9 8 cm 7 cm NOT TO 15 cm 12 cm SCALE 5 cm 23 cm Find the area of the shape. ........................................... cm2 [2]
Mark scheme: 9 171 2 M1 for 12 × 8 + 5 × 15 oe or 23 × 5 + 8 × 7 oe or 15 × 5 + 8 × 7 + 8 × 5 oe or 23 × 12 – 15 × 7 oe
Q10 · Jason records his score in each of 10 games of cricket
10 (a) Jason records his score in each of 10 games of cricket. 16 7 21 8 20 9 11 7 14 3 (i) Find the mode. ................................................. [1] (ii) Work out the range. ................................................. [1] (b) Ed plays 5 games. His mean score is 28. After one more game his mean score is now 26. Work out his score in the sixth game. ................................................. [2]
Mark scheme: 10(a)(i) 7 1 10(a)(ii) 18 1 10(b) 16 2 M1 for (26 × 6) and (28 × 5) oe
Q11 · Calculate 19% of $46.25
11 Calculate 19% of $46.25 . Give your answer correct to the nearest cent. $ ................................................. [2]
Mark scheme: 11 8.79 cao 2 19 M1 for × 46.25 oe 100 or B1 for correctly rounding their more accurate answer
Question 12
12 (a) Simplify. 5b - 8c + 2 b - 3 c ................................................. [2] (b) q = 3r + 5t Find the value of t when q = 37 and r = 4 . t = ................................................ [2]
Mark scheme: 12(a) 7b – 11c final answer 2 B1 for 7b or – 11c in final answer or for 7b – 11c seen then spoilt 12 (b) 5 2 M1 for 37 = 3 × 4 + 5t oe
Q13 · Divide $136 in the ratio 3 : 5
13 Divide $136 in the ratio 3 : 5. $...................... , $...................... [2]
Mark scheme: 13 51 85 2 M1 for 136 ÷ (3 + 5) × k where k is 1, 3 or 5
Q14 · Carl packs pens into boxes
14 Carl packs pens into boxes. Each box holds 68 pens. Carl has 980 pens and 14 boxes. Does Carl have enough boxes to pack all the pens? Show how you decide. .................... because .......................................................................................................................... ............................................................................................................................................................. [2]
Mark scheme: 14 Correct working shown leading to 2 B1 for 980 ÷ 68 answer No with a correct statement. e.g. or No, he would need 15 boxes oe 980 ÷ 68 [= 14.4…] or 14 × 68 No, he would need 15 boxes oe or No, he can only pack 952 or or he has 28 remaining oe 14 × 68 [= 952] or 980 14 No, he can only pack 952 or he has 28 remaining oe or No, each box would need to hold 70 pens oe or 980 14 [ = 70] No, each box would need to hold 70 pens oe
Q15 · NOT TO SCALE x° 68° 43° 135° Find the value of x
15 NOT TO SCALE x° 68° 43° 135° Find the value of x. x = ................................................ [1]
Mark scheme: 15 114 1
Q16 · NOT TO x cm SCALE 5 cm 4 cm The diagram shows an isosceles triangle
16 NOT TO x cm SCALE 5 cm 4 cm The diagram shows an isosceles triangle. (a) Calculate the value of x. x = ................................................ [2] (b) The triangle is one face of a square-based pyramid. Each triangular face of the pyramid is the same. On the 1 cm2 grid, draw a net of this pyramid. [3]
Mark scheme: 16(a) 5.39 or 5.385… 2 M1 for 52 + 22 oe 16(b) Correct net of the pyramid 3 B2 for a 4 by 4 square and 4 identical isosceles triangles correctly placed on the square or 3 correct faces e.g. a 4 by 4 square and at least two correct triangles correctly placed on the square or B1 for one correct face on a net or 4 isosceles triangles with height 5 on the sides of a square
Q17 · Write 46.179 correct to 4 significant figures
17 Write 46.179 correct to 4 significant figures. ................................................. [1]
Mark scheme: 17 46.18 cao 1
Question 18
18 Calculate. 8 .4 2 + 9 .3 (a) 26.5 ................................................. [1] (b) 4 -3 ................................................. [1]
Mark scheme: 18(a) 1.74 or 1.735 to 1.736 1 18(b) 1 1 0.015625 or 64
Question 19
19 Expand and simplify. 3 ( 5x + 2) - 4 ( x + 1) ................................................. [2]
Mark scheme: 19 11x + 2 final answer 2 B1 for 15x + 6 or – 4x – 4 or for 11x + 2 seen then spoilt or for 11x or 2 in the final answer
Q21 · The diagram shows shapes A and B
21 The diagram shows shapes A and B. y 5 4 3 A B 2 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) On the grid, draw the image of shape A after a reflection in the line y = 0 . [2]
Mark scheme: 21(a) Rotation 3 B1 for rotation [centre] (0,0) 90 clockwise B2 90 clockwise and centre (0,0) or 90 [anticlockwise] and centre (0,5) OR B1 for 90 clockwise or 90 [anticlockwise] or centre (0,0) or centre (0,5) 21(b) Points plotted at 2 B1 for reflection in y = k or in x = 0 (–4, 2) (–2, –2) (–3,–3) (–1, –3)
Q22 · Complete the table of values for y = x 2 - 4
22 (a) Complete the table of values for y = x 2 - 4 . x –4 –3 –2 –1 0 1 2 3 4 y 12 0 –3 –3 0 12 [2] (b) On the grid, draw the graph of y = x 2 - 4 for - 4 G x G 4 . y 12 11 10 9 8 7 6 5 4 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 – 3 – 4 – 5 [4]
Mark scheme: 22(a) 5 – 4 5 2 B1 for 2 correct 22(b) Correct curve 4 B3FT for 8 points correctly plotted B2FT for 6 points correctly plotted B1FT for 4 points correctly plotted
Q23 · Jo buys a candle for $3.20
23 (a) Jo buys a candle for $3.20 . She sells the candle for $4.64 . Find the percentage profit on the candle. ..............................................% [2] (b) The candle is in the shape of a cone. The volume of the candle is 900 cm3. The height of the candle is 8 cm. Calculate the radius of the candle. ............................................ cm [3]
Mark scheme: 23(a) 45 2 4.64 −3.2 M1 for [×100] oe 3.2 4.64 or ×100[–100] oe 3.20 4.64 or – 1 [×100] oe 3.20 23(b) 10.4 or 10.36… 3 900 3 M2 for oe 8π or 900 3 M1 for [r2 =] oe 8π 1 2 or for 900 = πr 8 oe and a correct first 3 step
Q24 · Make p the subject of the formula m = 9p + 32
24 Make p the subject of the formula m = 9p + 32 . p = ................................................ [2]
Mark scheme: 24 m − 32 2 m 32 p = final answer oe M1 for m – 32 = 9p or = p + oe 9 9 9
Q25 · Find the lowest common multiple (LCM) of 20 and 36
25 Find the lowest common multiple (LCM) of 20 and 36. ................................................. [2]
Mark scheme: 25 180 2 B1 for 180k as final answer or M1 for [20 =] 2 × 2 × 5 and [36 =] 2 × 2 × 3 × 3 or 2 correct factor trees or tables or lists or a list of multiples of both 20 and 36 with at least 3 of each or 2 × 2 × 3 × 3 × 5 oe
Q26 · Line L is drawn on the grid
26 Line L is drawn on the grid. y 22 L 20 18 16 14 12 10 8 6 4 2 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 2 – 4 – 6 Find the equation of line L in the form y = mx + c . y = ................................................ [3]
Mark scheme: 26 [y=] 3x + 9 cao final answer 3 B2 for 3x + c or for a correct unsimplified answer or M1 for a correct rise/run or for a right-angled triangle with run = 1 and rise = 3 marked on graph oe or B1 for mx + 9 where m is their gradient
Q28 · The travel graph shows Chi’s journey from home to the station
28 The travel graph shows Chi’s journey from home to the station. 6 Station 5 4 Distance 3 (km) 2 1 Home 0 08 00 08 05 08 10 08 15 08 20 08 25 08 30 08 35 08 40 Time Calculate Chi’s average speed for the whole journey. Give your answer in kilometres per hour. ......................................... km/h [3] Question 29 is printed on the next page.
Mark scheme: 28 9 3 5.4 M2 for × 60 oe 36 their distance or M1 for their time
Q29 · NOT TO SCALE 20.8 cm A x cm B 9.1 cm 1.4 cm The diagram shows two similar triangles, A…
29 (a) NOT TO SCALE 20.8 cm A x cm B 9.1 cm 1.4 cm The diagram shows two similar triangles, A and B. Calculate the value of x. x = ................................................ [2] (b) 5.4 cm 38° y cm The diagram shows a right-angled triangle. Calculate the value of y. y = ................................................ [2]
Mark scheme: 29(a) 3.2 2 20.8 9.1 M1 for = oe x 1.4 29(b) 4.26 or 4.255.. 2 y M1 for cos38 = or better 5.4 y or sin 52 = or better 5.4
What was in this paper
The subtopics covered by these 27 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Algebraic manipulation2Geometrical terms2Angles1Averages and range1Circles, arcs and sectors1Compound shapes and parts of shapes1Equations1Equations of linear graphs1Fractions, decimals and percentages1Graphs of functions1Introduction to probability1Limits of accuracy1Percentages1Rates1Ratio and proportion1Similarity1Statistical charts and diagrams1Surface area and volume1The four operations1Time1Transformations1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2025 Oct/Nov, Paper 3 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.