Cambridge IGCSE Mathematics 0580 — 2024 May/June Paper 3 · Variant 3

1 (a) 40 football players vote on the colour of new shirts. The results for red, yellow and green are shown in the bar chart. 12 11 10 9 8 7 Frequency 6 5 4 3 2 1 0 Red Yellow Green Blue Orange (i) Twice as many football players vote blue than vote orange. Complete the bar chart. [3] (ii) Write down the mode. ................................................. [1] (b) 40 hockey players vote on the colour of new shirts. The table shows the results. Colour Frequency White 21 Grey 12 Pink 7 (i) Complete the pie chart. [4] (ii) Work out the percentage of hockey players who vote grey. ............................................. % [1]

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Correct bars at [blue] 10 and [orange] 5 3 M1 for 40 – their(11 + 6 + 8) oe M1 for their 15 ÷ (1 + 2) oe 1(a)(ii) Red 1 1(b)(i) Correct pie chart 4 B2 for correct angles 189, 108, 63 soi or B1 for 1 correct angle soi 360 or M1 for k where k is 1, 21, 12 or 40 7 AND B2FT for two correct FT sectors drawn provided the sum of their 3 stated angles is 360 or B1FT for one correct sector drawn or one correct FT sector drawn 1(b)(ii) 30 1

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2 (a) Here is part of the timetable for buses from the station to the city centre. All buses take the same time to travel from the station to the city centre. Station 09 24 11 06 City centre 10 03 ........... (i) Complete the timetable. [2] (ii) Beth walks 4 km from her home to the station at a speed of 6 km/h. She wants to travel on the 09 24 bus. Work out the latest time she can leave her home. ................................................. [3] (iii) 45 seats on the bus are occupied. 3 This is of the total number of seats on the bus. 5 Work out the total number of seats on the bus. ................................................. [2] (b) Beth buys 2.4 kg of onions costing $1.25 per kilogram and 4.5 kg of potatoes. The total cost is $11.64 . Find the cost of 1 kg of potatoes. $ ................................................ [3] (c) (i) One day 140 people enter a shop. The ratio adults : children = 3 : 2. Find the number of adults who enter the shop. ................................................. [2] (ii) The price of a television in this shop is $624. 37.5% of this price is profit. Calculate the profit on this television. $ ................................................ [1] (iii) The price of a phone in this shop is $420. This price increases by 12%. Calculate the new price. $ ................................................ [2]

Mark scheme: 2(a)(i) 11 45 2 B1 for 39 [m] or 1 [h] 42 [m] or 102 [m] 2(a)(ii) 08 44 3 B2 for 40 [m] or M1 for 4 ÷ 6 [×60] oe 2(a)(iii) 75 2 45 M1 for [×5] oe 3 2(b) 1.92 3 M2 for (11.64 – 2.4 × 1.25) ÷ 4.5 oe or M1 for 2.4 × 1.25 oe 2(c)(i) 84 2 140 M1 for [× k] oe where k = 1, 2 or 3 2  3 2(c)(ii) 234 1 2(c)(iii) 470.40 cao 2  12  M1 for 420   1   oe  100  or B1 for 50.40

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3 (a) The grid shows a trapezium. On the grid, draw an enlargement of the trapezium with scale factor 3. [2] (b) The diagram shows four triangles, A, B, C and T, and a point P on a grid. y 5 4 P 3 2 A T 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 C – 2 – 3 B – 4 – 5 (i) Write down the coordinates of point P. ( .................... , .................... ) [1] (ii) Describe fully the single transformation that maps (a) triangle T onto triangle A ..................................................................................................................................... ..................................................................................................................................... [2] (b) triangle T onto triangle B ..................................................................................................................................... ..................................................................................................................................... [2] (c) triangle T onto triangle C. ..................................................................................................................................... ..................................................................................................................................... [3]

Mark scheme: 3(a) Correct enlargement 2 B1 for 2 sides correct length 3(b)(i) 4,3 1 3(b)(ii)(a) Reflection 2 B1 for each x = −1 oe 3(b)(ii)(b) Translation 2 B1 for each  3      5  3(b)(ii)(c) Rotation 3 B1 for each (0,0) 180°

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4 (a) Write down the value of the 8 in the number 39 829. ................................................. [1] (b) Write down all the factors of 18. ............................................................................... [2] (c) Show that 57 is not a prime number. [1] (d) x = 64 Find the value of x. x = ................................................ [1] (e) Find the first multiple of 40 that is greater than 620. ................................................. [1] (f) Find the reciprocal of 2. 3 ................................................. [1] 1(g) Find a fraction between and 1. 5 4 ................................................. [1] (h) Write down an irrational number with a value between 9 and 10. ................................................. [1] (i) Find the highest common factor (HCF) of 72 and 180. ................................................. [2]

Mark scheme: 4(a) 800 1 4(b) 1 2 3 6 9 18 2 B1 for 4 or 5 correct no extras or 6 correct and 1 extra or for 1×18 and 2×9 and 3×6 4(c) [57 =] 3× 19 oe 1 4(d) 4096 1 4(e) 640 1 4(f) 1 12 or 1.5 1 4(g) Any correct fraction 1 4(h) Any correct irrational number 1 4(i) 36 2 B1 for any of 2, 3, 4, 6, 9, 12, 18 as answer or M1 for 2×2×3×3 oe as answer or [72 = ] 2×2×2 ×3×3 and [180 = ] 2×2 ×5× 3×3 or a complete list of factors of 72 and 180 or 2 correct factor trees or tables or Venn diagram

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5 (a) k (i) Measure angle k. ................................................. [1] (ii) Write down the mathematical name for this type of angle. ................................................. [1] (b) The diagram shows a pair of parallel lines and a straight line. Angles a, b, c, d and x are labelled. a NOT TO x SCALE b c d Complete the statements. Angle .................... is alternate to angle x. Angle .................... is corresponding to angle x. [2] (c) The diagram shows a parallelogram. y° NOT TO SCALE 42° Find the value of y. y = ................................................ [1] (d) B C NOT TO 17° SCALE O A A, B and C lie on a circle, centre O. Find angle ACB. Angle ACB = ................................................ [2] (e) The interior angle of a regular polygon is 171°. Work out the number of sides of this polygon. ................................................. [2] (f) NOT TO 18.5 cm SCALE 7.4 cm x° Calculate the value of x. x = ................................................ [2]

Mark scheme: 5(a)(i) 326 1 5(a)(ii) reflex 1 5(b) c 2 B1 for each d 5(c) 138 1 5(d) 73° 2 M1 for 180 – 90 – 17 oe or 90 – 17 or angle B marked as 90° 5(e) 40 2 M1 for 360 ÷ (180 – 171) oe 180  n  2  or  171 oe n 5(f) 23.6 or 23.57 to 23.58 2 7.4 M1 for sin […. = ] oe 18.5

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6 (a) In a sport, teams are given points using the formula number of points = number of wins # 4 + number of draws # 2 + bonus points. One team has 15 wins, 7 draws and 6 bonus points. Calculate the total number of points for this team. ................................................. [2] (b) Solve. x = 18 2 x = ................................................ [1] (c) Solve. 4x + 12 = 18 x = ................................................ [2] (d) Expand and simplify. 6 ( 3x - 4) + 5 ( x - 2) ................................................. [2] (e) T = 5r - 6 Make r the subject of this formula. r = ................................................ [2] (f) Bo has a green bag and a blue bag. Each bag contains some marbles. The green bag has x marbles. There are 5 times as many marbles in the blue bag than in the green bag. Bo now adds 6 marbles to each bag. There are now 4 times as many marbles in the blue bag than in the green bag. Use this information to write down an equation and solve it to find the value of x. x = ................................................ [5]

Mark scheme: 6(a) 80 2 M1 for 15×4 + 7×2 + 6 oe 6(b) 36 1 6(c) 1 12 or 1.5 2 M1 for 4x = 18 – 12 or x  12  18 oe 4 4 6(d) 23x – 34 final answer 2 M1 for 23x or – 34 in the final answer or for 18x – 24 or 5x – 10 or 23x – 34 seen then spoilt 6(e) T  6 2 T 6 [r = ] oe final answer M1 for 5r = T + 6 or  r  5 5 5 6(f) 5x + 6 = 4(x + 6) oe B2 B1 for 5x or 5x + 6 or x + 6

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7 (a) Li spins a fair 6-sided spinner numbered 1 to 6. (i) On the probability scale, draw an arrow (↓) to show the probability that the spinner lands on the number 2. 1 0 1 [1] 2 (ii) Find the probability that the spinner lands on a prime number. ................................................. [1] (iii) Find the probability that the spinner lands on the number 7. ................................................. [1] (b) A bag contains 3 red balls and 12 green balls. Li picks a ball at random. Find the probability that it is a green ball. Give your answer as a fraction in its simplest form. ................................................. [2] (c) Li spins two fair 4-sided spinners, each numbered 1 to 4. The two numbers are multiplied to give the score. # 1 2 3 4 1 1 2 3 4 2 2 4 6 8 3 3 6 9 12 4 4 8 12 16 Find the probability that the score is (i) an even number ................................................. [1] (ii) an integer ................................................. [1] (iii) at least 10. ................................................. [1] (d) A bag contains red discs and blue discs. The probability that a disc picked at random is red is 1. 5 Li picks a disc at random, notes its colour and then replaces it in the bag. She then picks another disc at random. (i) Complete the tree diagram. First disc Second disc Red ............ Red 1 5 Blue ............ Red ............ ............ Blue Blue ............ [2] (ii) Work out the probability that both of the discs she picks are blue. ................................................. [2]

Mark scheme: 7(a)(i) Arrow at 16 1 7(a)(ii) 1 2 oe 1 7(a)(iii) 0 1 7(b) 4 2 12 cao B1 for oe 5 15 7(c)(i) 3 4 oe 1 7(c)(ii) 1 1 7(c)(iii) 3 oe 1 16 7(d)(i) 2 4 B1 for on the first branch 5 1 or in both correct places in second 5 branches 7(d)(ii) 16 2 FT for 2 marks or 1 mark for 2 fractions oe less than 1 25 4 4 M1FT for  5 5

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8 (a) 8.2 cm NOT TO 5.4 cm SCALE 12.6 cm Find the area of this trapezium. ......................................... cm2 [2] (b) NOT TO SCALE 4.5 cm b cm The area of this triangle is 15.3 cm 2. Find the value of b. b = ................................................ [2] (c) A circle has a circumference of 58.6 cm . Find the radius of this circle. ............................................ cm [2] (d) 28 cm NOT TO SCALE 12 cm The diagram shows a rectangle with two semicircles removed. Calculate the shaded area. ......................................... cm2 [4]

Mark scheme: 8(a) 56.2 or 56.16 2 8.2  12.6 M1 for  5.4 oe 2 8(b) 6.8 2 M1 for 12 × 4.5 × b = 15.3 or better 8(c) 9.33 or 9.325 to 9.327 2 M1 for 58.6 ÷ [2]π 8(d) 223 or 222.8 to 222.91 4 M1 for 28 × 12 or 336 M1 for π × 62 oe M1 for their 336 − their 113

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9 (a) Line L has a gradient of 4 and passes through the point (0, 3). Write down the equation of line L in the form y = mx + c . y = ................................................ [1] (b) Line G has the equation y = 2 - 6x . Line G passes through the point (a, 5). Find the value of a. a = ................................................ [3] (c) (i) Complete the table of values for y = x 2 - 6 . x -4 -3 -2 -1 0 1 2 3 4 y 10 -2 -5 -5 -2 10 [2] (ii) On the grid, draw the graph of y = x 2 - 6 for - 4 G x G 4 . y 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 – 6 – 7 [4] (iii) Write down the equation of the line of symmetry of the graph. ................................................. [1] (iv) Use your graph to solve the equation x 2 - 6 = 0 for x 2 0 . x = ................................................ [1]

Mark scheme: 9(a) [y =] 4x + 3 1 9(b) – 12 oe 3 B1 for 5 = 2 – 6a M1 for rearranging their linear equation to ra = s 9(c)(i) 3 –6 3 2 B1 for 2 correct 9(c)(ii) correct curve 4 B3FT for 8 or 9 points plotted accurately or B2FT for 6 or 7 points plotted accurately or B1FT for 4 or 5 points plotted accurately 9(c)(iii) x = 0 1 9(c)(iv) 2.3 to 2.6 1 FT their point of intersection

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