Cambridge IGCSE Mathematics 0580 — 2021 May/June Paper 3 · Variant 3

1 Ray owns an electrical shop. (a) The table shows the opening times of the shop. Sunday Closed Monday Closed Tuesday 08 00 to 12 30 and 13 30 to 17 00 Wednesday 08 00 to 12 30 and 13 30 to 17 00 Thursday 08 00 to 12 30 and 13 30 to 17 00 Friday 08 00 to 12 30 and 13 30 to 17 00 Saturday 08 00 to 13 00 and 14 00 to 19 00 Work out how many hours the shop is open in one week. ........................................ hours [3] (b) Saeed buys 2 ovens costing $440 each, 4 grills costing $184 each and 3 fridges costing $1280 each. Calculate the total cost. $ ................................................. [3] (c) Alice buys 3 batteries costing $2.85 each. Work out how much change she receives from $10. $ ................................................. [2] (d) Cherie works 32 hours one week and she is paid $8.48 per hour. In another week she works 37 hours. For each hour over 32 hours she works, she is paid 1.25 times her hourly rate. Calculate her pay for the week she works 37 hours. $ ................................................. [4] (e) Ray buys a toaster for $36. When he sells it he makes a profit of 40%. Calculate the selling price of this toaster. $ ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) 42 3 M1 for 4.5 + 3.5 or 9 – 1 M1 for 5 + 5 or 11 – 1 or M1 for 4.5 × 4 + 5 or 18 + 5 oe M1 for 3.5 × 4 + 5 or 14 + 5 oe 1(b) 5456 3 B2 for 880, 736 and 3840 or B1 for one of these or M1 for 2 × 440 or 4 × 184 or 3 × 1280 1(c) 1.45 2 M1 for 10 – 3 × 2.85 1(d) 324.36 cao 4 M1 for 32 × 8.48 M1 for 8.48 × 1.25 oe M1 for (37 – 32) × their 10.6[0] Accept alternative methods 1(e) 50.4[0] 2 M1 for 36 × 1.4 oe or B1 for 14.4[0]

More questions on The four operations

2 Mei and Jian each make a four-faced dice as shown in the diagram. The faces on each dice are numbered 1, 2, 3 and 4. (a) Mei throws her dice 90 times and records the scores. The pie chart shows the results. 1 4 76° 2 3 (i) Write down the mode. ................................................. [1] (ii) Work out how many times she scores 1. ................................................. [2] (b) Jian throws his dice 90 times and records the scores. The pie chart shows the results. 4 1 3 2 Write down the median. ................................................. [1] (c) Write down two different comparisons between the results for Mei and the results for Jian. 1. ................................................................................................................................................. ................................................................................................................................................. 2. ................................................................................................................................................. ................................................................................................................................................. [2]

Mark scheme: 2(a)(i) 3 1 2(a)(ii) 19 2 M1 for 36090 × 76 oe 2(b) 2 1 2(c) e.g. 2 B1 for each correct different comparison Mei has median of 3 and Jian has median of 2 or Mei has mode of 3 and Jian has mode of 1 e.g. Mei has larger 2 and 3 sectors than Jian or Jian has larger 1 and 4 sectors than Mei

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3 (a) The diagram shows a scale drawing of Joel’s rectangular garden. The scale is 1 centimetre represents 8 metres. Scale: 1 cm to 8 m Find the actual area of his garden. ............................................ m2 [3] (b) The diagram shows a rectangular gate, FGHJ, in Joel’s garden. F J NOT TO SCALE G H GJ = 2.1 m and FG = 0.85 m. Find FJ. FJ = ............................................ m [3] (c) 85 m NOT TO SCALE patio grass 24 m The diagram shows Brenda’s rectangular garden. There is a patio in the shape of a quarter-circle. She wants to grow grass in the shaded part of the garden. She needs 40 g of grass seed per square metre. Grass seed is sold in 1 kg bags which cost $6.80 per bag. Calculate the cost of the grass seed she needs to buy. $ ................................................. [6]

Mark scheme: 3(a) 3840 3 B1 for 5.8 to 6.2 or 9.8 to 10.2 or 4050 or 3637.76 to 4047.36 M1 for their length × their width or for use of 82 3(b) 1.92 or 1.920… 3 M2 for 2.12 − 0.852 or better or M1 for 2.12 = FJ2 + 0.852 or better 3(c) 435.2[0] cao 6 M1 for 85 × 24 M1 for π × 242 ÷ 4 oe M1 for their 2040 – their 452 M1 for their area × 100040 oe M1 for their 64 × 6.8[0]

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4 (a) Simplify. 3a - 5b + 2a + b ................................................. [2] (b) P = 3x 2 - xy Find the value of y when P = 90 and x = 5. y = ................................................ [3] (c) Factorise completely. (i) 6x - 18 ................................................. [1] (ii) 25x 2 + 10 x ................................................. [2] (d) T = 8d - 3 Make d the subject of this formula. d = ................................................ [2] (e) Solve these equations. x (i) = 12 6 x = ................................................ [1] (ii) 7x - 4 = 3x + 2 x = ................................................ [2]

Mark scheme: 4(a) 5a – 4b final answer 2 B1 for 5a or – 4b in final answer or for 5a – 4b seen then spoilt 4(b) −3 3 M1 for 90 = 3 × 52 – 5y oe or better M1FT for 90 – 3 × 52 = −5y oe or better 4(c)(i) 6(x – 3) final answer 1 4(c)(ii) 5x(5x + 2) final answer 2 B1 for 5(5x2 + 2x) or x(25x + 10) or 5x(5x + 2) seen then spoilt 4(d) T + 3 2 M1 for a correct first step d = oe final answer T 3 8 either T + 3 = 8d oe or = d − oe 8 8 4(e)(i) 72 1 4(e)(ii) 1 3 2 M1 for 7x – 3x = 2 + 4 oe or better 1.5 or 12 or 2

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5 (a) Find. (i) 320.41 ................................................. [1] (ii) 6.4 2 + 1. 2 3 ................................................. [1] (iii) the reciprocal of 2 ................................................. [1] (iv) 90 ................................................. [1] 3 (v) of $42 7 $ ................................................. [1] (vi) 12% of $62 $ ................................................. [1] (b) Insert one pair of brackets in each statement to make it correct. (i) 20 - 5 ' 5 - 3 = 0 [1] (ii) 20 - 5 ' 5 - 3 = 17.5 [1] (c) Write one of the symbols 1 , 2 or = in each statement to make it correct. 7 ............. 0.07 10 1 ............. 20% 5 3 ............. 0.38 8 [2] (d) (i) Write 90 as the product of its prime factors. ................................................. [2] (ii) Find the lowest common multiple (LCM) of 35 and 90. ................................................. [1] (iii) Find the highest common factor (HCF) of 35 and 90. ................................................. [1]

Mark scheme: 5(a)(i) 17.9 1 5(a)(ii) 42.688 cao 1 5(a)(iii) 1 2 or 0.5 1 5(a)(iv) 1 1 5(a)(v) 18 1 5(a)(vi) 7.44 1 5(b)(i) (20 – 5) ÷ 5 – 3 = 0 1 5(b)(ii) 20 – 5 ÷ (5 – 3) = 17.5 1 5(c) 7 2 B1 for 2 correct > 0.07 10 1 = 20% 5 3 < 0.38 8 5(d)(i) 2 × 3 × 3 × 5 or 2 × 32 × 5 2 B1 for 2, 3, 3, 5 or M1 for correct factor tree / diagram / table 5(d)(ii) 630 1 5(d)(iii) 5 1

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6 (a) NOT TO SCALE B O A 52° C AB is the diameter of a circle, centre O. C is a point on the circle and angle BAC = 52°. Find angle ABC. Angle ABC = ................................................ [2] (b) The diagram shows the positions of town A, town B and town C. North B NOT TO SCALE North A C The bearing of town B from town A is 042°. The bearing of town C from town A is 146°. (i) Find angle BAC. Angle BAC = ................................................ [2] (ii) Find the bearing of town A from town B. ................................................. [2] (c) A NOT TO x° SCALE 117° B C D Triangle ABC is isosceles with AB = AC. BCD is a straight line and angle ACD = 117°. Find the value of x. x = ................................................ [3]

Mark scheme: 6(a) 38 2 B1 for angle ACB marked as 90° or M1 for 90 – 52 oe 6(b)(i) 104 2 M1 for 146 – 42 oe or B1 for 42 or 146 correctly marked on diagram 6(b)(ii) 222 2 M1 for 180 + 42 oe 6(c) 54 3 M1 for 180 – 117 or 63 M1 for 180 – 2 × their 63 or 117 – 63

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7 Rita and Henry own an investment business. (a) They share the profit in the ratio Rita : Henry = 3 : 5. In one year they make a profit of $2 400 000. Calculate Rita’s share of the profit. $ ................................................. [2] (b) Henry invests $160 000 at a rate of 2.5% per year compound interest. Calculate the value of this investment at the end of 3 years. $ ................................................. [2] (c) Rita invests $12 000 at a rate of r % per year. The value of her investment at the end of one year is $12 408. Work out the value of r. r = ................................................ [2] (d) Rita and Henry decorate their office. The cost, $c, is $10 800, correct to the nearest hundred dollars. Complete this statement about the value of c. ......................... G c 1 ......................... [2]

Mark scheme: 7(a) 900 000 2 2400000 M1 for × k 3 + 5 7(b) 172 302.5[0] cao 2 M1 for 160 000 × (1 + 1002.5 ) 3 oe 7(c) 3.4 2 12408 − 12000 M1 for [× 100] oe 12000 12408 or − 1 [ × 100 ] oe 12000 12408 or × 100 [ −100 ] oe 12000 7(d) 10 750 10 850 2 B1 for each If 0 scored, SC1 for both correct but reversed

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8 (a) 15 people take a test. These are the test scores. 29 27 12 32 42 26 7 23 22 31 40 9 18 35 8 (i) Complete the frequency table. You may use the tally column to help you. Score Tally Frequency 0 to 10 11 to 20 21 to 30 31 to 40 41 to 50 [2] (ii) Use your table to complete the bar chart. 8 7 6 5 Frequency 4 3 2 1 0 0 to 10 11 to 20 21 to 30 31 to 40 41 to 50 Score [2] (b) On Monday and Tuesday, the probability that a train is late is 0.2 . Monday Tuesday Late 0.2 Late 0.2 Not late .......... Late 0.2 .......... Not late Not late .......... (i) Complete the tree diagram. [1] (ii) Use the tree diagram to find the probability that a train is (a) late on both days, ................................................. [2] (b) not late on Monday and late on Tuesday. ................................................. [2]

Mark scheme: 8(a)(i) 3 2 5 4 1 2 B1 for 3 or 4 correct or all tallies correct if no frequencies are given or for 3 2 5 4 1 in tally column 8(a)(ii) Correct bar chart 2 FT their table B1FT for correct bar chart with one height incorrect or all heights correct but with inconsistent widths or gaps 8(b)(i) [0].8 in the three correct places 1 8(b)(ii)(a) [0].04 oe 2 M1 for [0].2 × [0].2 8(b)(ii)(b) [0].16 oe 2 FT their diagram M1 for their [0].8 × [0].2

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9 The table shows some values for y = x 2 + x - 5 . x -4 -3 −2 −1 0 1 2 3 y 7 -3 -5 -5 7 (a) Complete the table. [2] (b) Draw the graph of y = x 2 + x - 5 for - 4 G x G 3 . y 8 7 6 5 4 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 [4] (c) Write down the equation of the line of symmetry of this graph. ................................................. [1] (d) Use the graph to solve the equation x 2 + x - 5 = 0 . x = ...................... or x = ...................... [2]

Mark scheme: 9(a) 1 −3 1 2 B1 for 2 correct 9(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 9(c) x = −[0].5 oe 1 9(d) −2.9 to −2.7 1.7 to 1.9 2 B1FT for each

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10 The diagram shows four triangles on a grid. y 5 4 3 2 A T C 1 0 x – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 – 1 B – 2 – 3 – 4 – 5 2 (a) On the grid, translate triangle T by the vector [2] e- 5o. (b) Describe fully the single transformation that maps (i) triangle T onto triangle A, ............................................................................................................................................. ............................................................................................................................................. [2] (ii) triangle T onto triangle B, ............................................................................................................................................. ............................................................................................................................................. [3] (iii) triangle T onto triangle C. ............................................................................................................................................. ............................................................................................................................................. [3]

Mark scheme: 10(a) Correct translation 2 2 B1 for a correct translation of  or vertices at (4, –4), (6, –4), (4, –1) k  k     −5  10(b)(i) Reflection 2 B1 for each x = 0 oe 10(b)(ii) Rotation 3 B1 for each [centre] (0, 0) oe 180° 10(b)(iii) Enlargement 3 B1 for each [centre] (0, 0) oe [sf] 12 oe

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