Cambridge IGCSE Mathematics 0580 — 2023 Oct/Nov Paper 3 · Variant 2

1 (a) The bar chart shows the number of goals scored by a team in each of 5 months. 22 20 18 16 14 12 Frequency 10 8 6 4 2 0 Sept Oct Nov Dec Jan Feb Month (i) In February, 12 goals are scored. Complete the bar chart. [1] (ii) How many more goals were scored in January than in October? ................................................. [1] (b) Find the range of the number of goals scored. ................................................. [1] (c) (i) The team shop is open from 09 00 to 17 15 on Monday to Friday only. Work out how long the shop is open each week. Give your answer in hours and minutes. ................... h ................... min [3] (ii) Bruno buys a shirt for $36 and a scarf for $12.25 . He pays with a $50 note. Work out how much change he receives. $ ................................................ [2] (d) Ticket prices Adult $35 Child $20 Senior $25 (i) Calculate the cost of 150 adult tickets, 70 child tickets and 30 senior tickets. $ ................................................ [3] (ii) Calculate the percentage of these tickets that are senior tickets. ............................................. % [2] (e) A game starts at 15 00. The team plays for 90 minutes. There is also a break of 15 minutes. Find the time the game ends. ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Bar to 12 1 1(a)(ii) 11 1 1(b) 14 1 1(c)(i) 41 [h] 15 [min] 3 1 B2 for 41.25 or 41 or 40 hr 75 [mins] 4 1 or B1 for 8.25 or 8 or 8 h 15 [min] or 4 495 [min] or M1 for 7.25  5 oe or 9.25  5 oe OR SC2 for 57 [h] 45 [min] 1(c)(ii) 1.75 2 M1 for 50 – (36 + 12.25) oe or B1 for 48.25 1(d)(i) 7400 3 M2 for 35  150 + 20  70 + 25  30 oe or M1 for two of 35  150, 20  70 or 25  30 oe 1(d)(ii) 12 2 30 M1 for  100 oe 150 + 70 + 30 1(e) 16 45 or 4.45 pm 2 M1 for 15 00 + 90 [min] + 15 [min] oe

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2 (a) (i) Write down the mathematical name for this polygon. ................................................. [1] (ii) Write down the mathematical name for this quadrilateral. ................................................. [1] (iii) (a) Write down the mathematical name for this type of angle. ................................................. [1] (b) Measure the size of this angle. ................................................. [1] (b) Draw the lines of symmetry on this rectangle. [2] (c) A cuboid measures 6 cm by 3 cm by 2 cm. (i) Work out the volume of the cuboid. ......................................... cm3 [1] (ii) Draw a net of the cuboid on the 1 cm 2 grid. One face has been drawn for you. [3]

Mark scheme: 2(a)(i) Pentagon 1 2(a)(ii) Trapezium 1 2(a)(iii)(a) Obtuse 1 2(a)(iii)(b) 123 1 2(b) 2 correct lines 2 B1 for 1 correct and 0 extra or 2 correct and 1 extra 2(c)(i) 36 nfww 1 2(c)(ii) Fully correct net 3 B2 for 3 or 4 correct extra faces in correct place or B1 for 1 or 2 correct extra faces in correct place

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3 (a) Write the number fourteen thousand and ninety-seven in figures. ................................................. [1] (b) Write down a common multiple of 17 and 5. ................................................. [1] (c) Write 0.25 as a percentage. ............................................. % [1] (d) Find the value of (i) 75 ................................................. [1] (ii) 80. ................................................. [1] 5 (e) Ranjit buys some plants and sells of them. 11 He sells 190 plants. Work out how many plants he buys. ................................................. [2] (f) Factorise completely. 15x 3 y - 3x ................................................. [2] (g) Make n the subject of the formula V = 3n + t . n = ................................................ [2] (h) 7 15 ' 7 x = 7 9 Find the value of x. x = ................................................ [1]

Mark scheme: 3(a) 14 097 1 3(b) Any correct multiple i.e. 85k 1 3(c) 25 1 3(d)(i) 16 807 1 3(d)(ii) 1 1 3(e) 418 2 M1 for 190 ÷ 5 soi by 38 3(f) 3x(5x2y – 1) final answer 2 B1 for 3(5x3y – x) or for x(15x2y – 3) or correct answer spoilt 3(g) V − t 2 V t oe final answer M1 for V – t =3n or = n + 3 3 3 3(h) 6 1

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4 (a) Complete the table of values for y = x 2 - 4x - 2 . x -2 -1 0 1 2 3 4 5 y 3 -2 -5 -5 -2 3 [2] (b) On the grid, draw the graph of y = x 2 - 4x - 2 for - 2 G x G 5 . y 10 9 8 7 6 5 4 3 2 1 x -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 -6 [4] (c) Use your graph to solve the equation x 2 - 4x - 2 = 0 . x = ................... or x = ................... [2]

Mark scheme: 4(a) 10 –6 2 B1 for each 4(b) Correct curve 4 B3FT for 7 or 8 points correctly plotted or B2FT for 5 or 6 points correctly plotted or B1FT for 3 or 4 points correctly plotted 4(c) –0.6 to –0.3, 4.3 to 4.6 2 FT their curve B1 for each

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5 Heidi records the colour of each of 500 cars crossing a bridge. The pie chart shows some of this information. Grey Red Other (a) How many cars are red? ................................................. [1] (b) 35 cars are grey. Show, by calculation, that the sector angle for grey is 25.2°. [1] (c) 175 cars are white and 150 cars are black. Complete the pie chart to show this information. [2] (d) Find the probability that a car chosen at random is not grey. Give your answer as a fraction in its simplest form. ................................................. [2] (e) Another 320 cars cross the bridge. How many of these 320 cars are expected to be white? ................................................. [2] (f) Heidi also records the number of people in each car crossing the bridge for one hour. Number of people Frequency 1 20 2 6 3 0 4 15 5 8 6 12 Calculate the mean. ................................................. [3]

Mark scheme: 5(a) 125 1 5(b) 35 M1  360 500 5(c) Correct pie chart 2 B1 for 126º or 108º 5(d) 93 2 500 – 35 360 – 25.2 cao M1 for oe or oe 100 500 360 7 If 0 scored, then SC1 for final answer of 100 5(e) 112 2 175 126 M1 for  320 oe or  320 oe 500 360 5(f) 21 3 M1 for (1  20) + (2  6) + [3  0] + (4  15) + 3.34 or 3.344… or 3 61 (5  8) + (6  12) M1dep for their  fx  ( 20 + 6 + 0 + 15 + 8 +12 ) oe

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6 (a) Simplify. a + 4 a - 3a ................................................. [1] (b) Simplify. 8b - 4 # 7b ................................................. [1] (c) 4x + 3 x + 7 3x - 9 NOT TO SCALE 9x + 8 7x + 3 The perimeter of this shape is equal to the perimeter of a square. Find an expression for the length of one side of the square. Give your answer in its simplest form. ................................................. [4] (d) Victoria buys 5 cups of tea and 4 cakes for $15.69 . Isabella buys 3 cups of tea and 7 cakes for $17.97 . Write down a pair of simultaneous equations and solve them to find the cost of one cup of tea and the cost of one cake. You must show all your working. Tea $ ................................................ Cake $ ................................................ [6]

Mark scheme: 6(a) 2a final answer 1 6(b) – 20b final answer 1 6(c) 6x + 3 final answer 4 24 x+12 B3 for seen or 6x + 3 seen then 4 spoilt 24 x + k kx+12 or B2 for 24x + 12 or or seen 4 4 k≠0 or M2 for 3 x – 9 + 4 x + 3 + x + 7 + 9 x + 8 + 7 x + 3 oe 4 or M1 for 3x – 9 + 4x + 3 + x + 7 + 9x + 8 + 7x + 3 oe or B1 for 24x + k or kx + 12 seen k≠0 6(d) 5t + 4c = 15.69 oe B1 3t + 7c = 17.97 oe B1 correctly equating one set of M1 coefficients correct method to eliminate one M1 variable t = 1.65 A1 c = 1.86 A1 If A0 scored, SC1 for 2 values satisfying one of the original equations or if no working shown, but 2 correct answers given

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7 Elize, Lily and Marco start a business. (a) Elize invests $5000. Lily invests $8000. Marco invests $3000. After one year they make a profit of $40 000. They share this profit in the ratio of their investments. Work out how much they each receive. Elize $ ................................................ Lily $ ................................................ Marco $ ................................................ [3] (b) (i) Lily buys 20 rolls of ribbon. 8 are red, 6 are blue, 4 are yellow and 2 are pink. A roll of ribbon is chosen at random. On the probability scale, draw an arrow ( ) to show the probability that this roll is (a) yellow 0 0.5 1 [1] (b) not red 0 0.5 1 [1] (c) green. 0 0.5 1 [1] (ii) The length, l m, of a roll of ribbon is 120 m, correct to the nearest metre. Complete this statement about the value of l. ................... G l 1 ................... [2] (c) Elize buys some picture frames. The frames cost $5.80 each in New York and 4.50 euros each in Paris. The exchange rate is 1 euro = $1.37 . Calculate the difference in the cost in euros. Give your answer correct to 2 decimal places. ........................................ euros [3] (d) Elize buys a framed picture. (i) 18 cm NOT TO SCALE 18 cm The picture is a circle with diameter 18 cm. The frame is a square of side length 18 cm. Calculate the shaded area. ......................................... cm2 [3] (ii) Elize buys the framed picture for $12.50 . She sells the framed picture for $20.25 . Calculate the percentage profit. ............................................. % [2]

Mark scheme: 7(a) 12 500, 20 000, 7500 3 B2 for 12 500 or 7500 in correct place 40000 or M1 for  k where k = 1, 5, 8 or 3 5 + 8 + 3 7(b)(i)(a) Arrow at 0.2 1 7(b)(i)(b) Arrow at 0.6 1 7(b)(i)(c) Arrow at 0 1 7(b)(ii) 119.5 120.5 2 B1 for each or both correct but reversed 7(c) 0.27 3 B2 for 0.266… or 5.80 5.80 M2 for 4.50 – oe or −4.50 oe 1.37 1.37 5.80 or M1 for soi by 4.23… 1.37 If 0 or 1 scored, SC1 for correct rounding to 2dp from their more accurate answer 7(d)(i) 69.5 or 69.49 to 69.531 3 M2 for 182 – 92  π oe or M1 for 92  π oe 7(d)(ii) 62 2 20.25 − 12.50 M1 for [ 100] oe 12.50 20.25 or  100 [– 100] oe 12.50  20.25  or  –1  [ 100] oe  12.50 

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8 (a) In triangle RST, RT = 7 cm and ST = 4 cm. (i) Using a ruler and compasses only, construct triangle RST. Leave in your construction arcs. The line RS has been drawn for you. R S [2] (ii) Measure the distance from S to the midpoint of RT. Give your answer in millimetres. .......................................... mm [1] (b) Town A is 8.5 cm from town B on a map. The scale of the map is 1 : 50 000. Calculate the actual distance from town A to town B. Give your answer in kilometres. ........................................... km [2] (c) E x° NOT TO SCALE 118° A B C D The diagram shows triangle BCE and a straight line ABCD. BE = CE and angle DCE = 118°. Find the value of x. x = ................................................ [2] (d) A NOT TO 8.9 cm SCALE 4.8 cm C B The diagram shows a right-angled triangle ABC. Show that BC is 7.5 cm, correct to 2 significant figures. [3] Question 9 is printed on the next page.

Mark scheme: 8(a)(i) Correct triangle with correct arcs 2 B1 for correct triangle with incorrect or no arcs or for two correct arcs If 0 scored, SC1 for triangle with arcs but lines interchanged 8(a)(ii) 52 1 FT their complete triangle 8(b) 4.25 2 B1 for figs 425 as answer or 1 cm = 0.5 km seen or M1 for 8.5  50 000 oe 8(c) 56 2 M1 for 180 – 2  (180 – 118) oe or B1 for [angle] ECB or EBC = 62 8(d) 8.92 – 4.82 M2 M1 for 4.82 + BC2 = 8.92 2 2 A1 8.9 − 4.8 = 7.49… or 56.17 = 7.49…

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9 Triangles A, B and C are shown on the grid. y 6 5 C 4 B 3 2 1 A -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x -1 -2 -3 -4 -5 -6 -7 (a) Describe fully the single transformation that maps triangle A onto triangle B. ....................................................................................................................................................... ....................................................................................................................................................... [3] (b) Describe fully the single transformation that maps triangle A onto triangle C. ....................................................................................................................................................... ....................................................................................................................................................... [3] 6 (c) On the grid, translate triangle A by the vector [2] e- 4o. (d) On the grid, reflect triangle A in the line y =- 2 . [2]

Mark scheme: 9(a) Rotation 3 B1 for each (Centre) (0, 0) 90º clockwise 9(b) Enlargement 3 B1 for each (Scale factor) 1.5 (Centre) (–1, –7) 9(c) Correct translation 2  k  6 Vertices (2, –3), (2, –5), (5, –3) B1 for translation by   or   –4  k 9(d) Correct reflection 2 B1 for reflection in x = –2 or y = k Vertices at (–4, –3), (–4, –5), (–1, –5)

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