Cambridge IGCSE Mathematics 0580 — 2024 Oct/Nov Paper 3 · Variant 3

1 (a) (i) Li has $20. A box of cereal costs $2.29 . Work out the maximum number of boxes of cereal that Li can buy. ................................................. [2] (ii) Each box of cereal has mass 615 g. Work out the total mass of 5 boxes of cereal. Give your answer in kilograms. ............................................. kg [2] (iii) The box of cereal is a cuboid. The cuboid measures 25 cm by 20 cm by 5 cm. Work out the volume of the cuboid. .......................................... cm3 [1] (b) A cereal bar is in a box. The box is a cuboid measuring 6 cm by 3 cm by 1 cm. NOT TO 6 cm SCALE 1 cm 3 cm On the 1 cm2 grid, complete a net of the cuboid. One face has been drawn for you. [3] (c) The cereal contains fat, protein, carbohydrate and fibre. The pie chart shows the information about the masses of fat and protein. Fat 36° Protein (i) Work out the percentage of the mass of the cereal that is fat. ..............................................% [1] (ii) 60% of the mass of the cereal is carbohydrate. Complete the pie chart. [2] (iii) Work out the mass of protein in 30 g of the cereal. ............................................... g [2]

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 8 2 M1 for 20 ÷ 2.29 1(a)(ii) 3.075 2 M1 for 615 × 5 1(a)(iii) 2500 1 1(b) Fully correct net 3 B2 for 3 or 4 correct extra faces in correct place B1 for 1 or 2 correct extra faces in correct place 1(c)(i) 10 1 1(c)(ii) Correct pie chart 2 B1 for 216º soi 1(c)(iii) 5.67 5.666 to 5.67 2 B1 for 68 OR k M1 FT for  30 oe 360

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2 (a) Write the number 845 024 in words. ..................................................................................................................................................... [1] (b) Write these numbers in order, starting with the smallest. 7 15 39% 0.388 18 40 .................... 1 .................... 1 .................... 1 .................... [2] smallest (c) Find the value of (i) 45 ................................................. [1] (ii) 60 ................................................. [1] (iii) 16 # 49 . ................................................. [1] (d) Solve. 6x + 5 = 29 x = ................................................ [2] (e) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 2.7 # 42.4 . 8.6 - 4.3 You must show all your working. ................................................. [2] (f) 3 5 # 3 x = 3 20 Find the value of x. x = ................................................ [1] (g) Simplify ( x4 ) 3. ................................................. [1] (h) A boat to town A leaves a port every 16 minutes. A boat to town B leaves the same port every 34 minutes. Both boats leave the port at 07 30. Work out the next time both boats leave the port together. ................................................. [3]

Mark scheme: 2(a) Eight hundred and forty five thousand 1 and twenty four 2(b) 15 7 2 0.388 39% 40 18 B1 for 3 in the correct order Or M1 for 0.389 or 0.3888 or 0.3889 and 0.39 and 0.375 2(c)(i) 1024 1 2(c)(ii) 1 1 2(c)(iii) 28 1 2(d) 4 2 5 29 M1 for 6x = 29 – 5 or x + = oe 6 6 2(e) 3  40 M1 9 – 4 24 A1 If 0 scored SC1 for 3 correct from 3, 40, 9 and 4 or for all correct but with trailing zeros 2(f) 15 1 2(g) x12 1 2(h) 12 02 3 B2 for 272 or 4 h 32 mins or M1 for 272k or 2  2  2  2  17 oe or [16 = ] 2  2  2  2 and [34 = ] 2  17 or 2 correct factor trees/tables of both 16 and 34 OR M2 for listing times/multiples of both 16 and 34 to at least 1202 or 272 or M1 for listing at least the next 2 of each or 1 full list

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3 (a) A wedding invitation is in the shape of a rectangle. Draw the lines of symmetry on this rectangle. [2] (b) There are 98 adults and 56 children at the wedding. Find the fraction of people who are children. Give your fraction in its simplest form. ................................................. [2] (c) The wedding meal starts at 13 15 and lasts for 2 hours 50 minutes. Find the time the meal ends. ................................................. [1] (d) The probability that it will rain at the wedding is 0.12 . Find the probability that it will not rain. ................................................. [1] (e) (i) These are the ages of the staff at the wedding. 16 24 39 28 17 48 31 33 17 29 40 25 Complete the stem-and-leaf diagram. 1 2 3 4 Key: 1|6 represents 16 [2] (ii) Find the range. ................................................. [1]

Mark scheme: 3(a) 2 correct lines only 2 B1 for one correct line with no extras or 2 correct and 1 extra 3(b) 4 2 M1 for 98 + 56 cao 11 3(c) 16 05 1 3(d) 0.88 1 3(e)(i) 1 6 7 7 2 B1 for two or three rows correct or a fully 2 4 5 8 9 correct unordered stem-and-leaf diagram 3 1 3 9 4 0 8 3(e)(ii) 32 1 FT their (e)(i) dep. on an ordered table

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4 (a) n = 15 r + 20c Find the value of r when n = 180 and c = 3 . r = ................................................ [2] (b) Factorise completely. 20p 2 q - 5p ................................................. [2] (c) Apples cost 35 cents each and bananas cost 14 cents each. Write down an expression for the total cost, in cents, of x apples and y bananas. ........................................ cents [2] (d) Solve the simultaneous equations. You must show all your working. 8x + 3y = 59 5x + 7y = 83 x = ................................................ y = ................................................ [4]

Mark scheme: 4(a) 8 2 M1 for 180 = 15r + 20 × 3 or better 4(b) 5p (4pq – 1) 2 B1 for 5 (4p2q – p) or p (20pq – 5) or 5p (4pq – 1) seen then spoilt 4(c) 35x + 14y 2 B1 for 35x or 14y in final answer or for 35x + 14y seen then spoilt 4(d) correctly equating one set of coefficients M1 correct method to eliminate one variable M1 x = 4 A1 y = 9 A1 If A0 scored SC1 for 2 values satisfying one of the original equations

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5 (a) Kurt owns some toy cars of different colours. The pictogram shows the number of each colour. Colour Number of toy cars Red Yellow Green Blue White Other Key: = 8 cars (i) Write down the colour of toy car that Kurt owns most of. ................................................. [1] (ii) Find the number of yellow toy cars that Kurt owns. ................................................. [1] (iii) Find how many more red toy cars than white toy cars Kurt owns. ................................................. [1] (b) A toy car costs $12.40 in the USA and 11.50 euros in Spain. The exchange rate is 1 euro = $1.12 . Calculate the difference in the cost of the toy car in euros. Give your answer correct to 2 decimal places. ........................................ euros [3] (c) Leo owns some toy vehicles. He owns 57 cars, 12 bicycles and 42 trucks. Find the ratio of the number of cars : bicycles : trucks in its simplest form. .................. : .................. : .................. [2] (d) Leo keeps his toy vehicles on a shelf. (i) The shelf is in the shape of a right-angled triangle. NOT TO SCALE 0.75 m y m The area of the shelf is 0.3 m2. Calculate the value of y. y = ................................................ [2] (ii) The shelf is 1.35 metres from the floor. Change 1.35 metres into centimetres. ............................................ cm [1]

Mark scheme: 5(a)(i) Blue 1 5(a)(ii) 18 1 5(a)(iii) 20 1 5(b) 0.43 cao 3 B2 for 0.429 or 0.428[5…] Or 12.4 M2 for 11.50 – oe 1.12 11.50 1.12 − 12.4 or oe 1.12 12.4 or M1 for soi by 11.07… 1.12 If 0 or M1 scored SC1 for correct rounding to 2dp from their more accurate answer 5(c) 19 : 4 : 14 cao 2 M1 for correct ratio not in its simplest form 5(d)(i) 0.8 2 1 M1 for y 0.75 = 0.3 or better 2 5(d)(ii) 135 1

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6 (a) 8 m NOT TO SCALE 11 m 6 m 15 m The diagram shows a plan of Zak’s garden. Find the perimeter of the garden. .............................................. m [2] (b) Zak records the temperature in his garden each night for one week. Sunday Monday Tuesday Wednesday Thursday Friday Saturday 4 °C 1 °C -2 °C 2 °C -5 °C 3 °C -4 °C (i) Which night was coldest? ................................................. [1] (ii) Find the difference in temperature between Friday night and Saturday night. ............................................. °C [1] (c) Zak buys pea plants, bean plants and sunflower plants in the ratio peas : beans : sunflowers = 7 : 5 : 2. He buys 45 bean plants. Show that the total number of plants he buys is 126. [2] (d) Zak has a water barrel. On Monday the barrel contains 120 litres of water. On Friday the barrel contains 43.2 litres of water. Calculate the percentage decrease of the water in the barrel. ..............................................% [2] (e) Zak drives to a shop. 1 The journey takes 1 hours. 4 He drives at an average speed of 57 km/h. Calculate the distance he drives. ............................................ km [2] (f) Machine hire charges 1st day $22.60 Each additional day $11.80 Zak pays $69.80 to hire a machine. Calculate the number of days he hires it for. ......................................... days [3]

Mark scheme: 6(a) 52 2 M1 for 15 – 8 and 11 – 6 or 2 × 11 + 2 × 15 oe or 11 + 8 + (11 − 6 ) + (15 − 8 ) + 6 + 15 oe 6(b)(i) Thursday 1 6(b)(ii) 7 1 6(c) 45 ÷ 5 × (7 + 5 + 2) [=126] M2 M1 for 45 ÷ 5 6(d) 64 2 120 − 43.2 M1 for [×100] 120 43.2 or [100−] ×100 120  43.2  or  1 −  [×100]  120  6(e) 71.25 2 M1 for their time × 57 oe 6(f) 5 nfww 3 69.80 – 22.60 M2 for oe 11.80 or M1 for 69.80 – 22.60 or 22.60 + 11.80 + 11.80 +. or better

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7 (a) Write down the mathematical name for this solid. ................................................. [1] (b) x (i) Measure the size of angle x. ................................................. [1] (ii) Write down the mathematical name for this type of angle. ................................................. [1] (c) A NOT TO SCALE O C B Points A, B and C lie on the circle, centre O. AB = 11 cm and BC = 5 cm . (i) Give a geometrical reason why angle ACB is 90°. ............................................................................................................................................. [1] (ii) Calculate the circumference of the circle. ............................................ cm [2] (iii) Show that AC is 9.8 cm, correct to 2 significant figures. [3] (d) The surface area of a sphere is 250 cm2. Calculate the radius of the sphere. [The surface area, A, of a sphere with radius r is A = 4 r r 2 .] ............................................ cm [3]

Mark scheme: 7(a) Cylinder 1 7(b)(i) 137 1 7(b)(ii) Obtuse 1 7(c)(i) Angle in a semicircle is 90º 1 7(c)(ii) 34. 6 or 34.55 to 34.562 2 M1 for 11 × π 7(c)(iii) 112 – 52 = AC2 M2 M1 for 52 +(…)2 = 112 96 = 9.79…or 9.80 A1 7(d) 4.46 or 4.460 … 3 250 M2 for 4 250 or M1 for 4

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8 (a) (i) Complete the table of values for y = 4x - x 2 . x -1 0 1 2 3 4 5 6 y -5 0 3 4 3 -5 [2] (ii) On the grid, draw the graph of y = 4x - x 2 for -1 G x G 6 . y 5 4 3 2 1 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – 10 – 11 – 12 – 13 [4] (iii) Use your graph to solve the equation 4x - x 2 = 1. x = .................. or x = .................. [2] (b) The line L is shown on the grid. y 5 L 4 3 2 1 – 2 – 1 0 1 2 3 4 x – 1 – 2 – 3 – 4 Find the equation of line L. ................................................. [3] Question 9 is printed on the next page.

Mark scheme: 8(a)(i) 0 –12 2 B1 for each 8(a)(ii) Correct curve 4 B3FT for 7 or 8 points correctly plotted or B2FT for 5 or 6 points correctly plotted or B1 FT for 3 or 4 points correctly plotted 8(a)(iii) 0.2 to 0.4 , 3.6 to 3.8 2 FT their curve B1 for each 8(b) y = 1.5x – 1 oe final answer 3 B2 for 1.5x – 1 oe or y = 1.5x + c oe or y = mx – 1 oe m is their gradient m ≠0 or B1 for 1.5x + c or mx – 1 where m is their gradient m ≠0

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9 Shapes A, B and C are shown on the grid. y 5 4 A 3 B 2 1 x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 1 C – 2 – 3 – 4 – 5 (a) Write down the mathematical name of shape A. ................................................. [1] (b) Describe fully the single transformation that maps shape A onto shape B. ..................................................................................................................................................... ..................................................................................................................................................... [3] (c) Describe fully the single transformation that maps shape A onto shape C. ..................................................................................................................................................... ..................................................................................................................................................... [2] (d) Draw the image of shape A after a rotation, 90° clockwise, centre (0, 0). [2] (e) Draw the image of shape A after a reflection in the line x = 1. [2]

Mark scheme: 9(a) Trapezium 1 9(b) Enlargement 3 B1 for each [SF] 0.5 [Centre] ( 2,1) 9(c) Translation 2 B1 for each  –7     –5  9(d) Correct rotation, vertices at 2 B1 for correct 90 anticlockwise rotation (3, – 3) ( 3, –5) (4, –3)(4, –4) about the origin or correct orientation, wrong centre 9(e) Correct reflection, Vertices at 2 B1 for reflection in x = k, or y = 1 (–3, 3) (–2, 4)(–1, 4) (–1, 3)

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