Cambridge IGCSE Mathematics (9-1) 0980 — 2020 Oct/Nov Paper 3 · Variant 1

1 Sean is the manager of a museum. (a) He buys a Chinese pot costing 1200 yuan. The exchange rate is $1 = 6.4 yuan. Work out the cost of this pot in dollars. $ ................................................. [1] (b) Sean records the maximum and minimum temperatures, in °C, at the museum. Some of the results for one week are shown in the table. Day Mon Tue Wed Thu Fri Sat Sun Maximum 8 12 15 14 11 7 4 temperature (°C) Minimum - 5 - 2 - 4 - 1 3 temperature (°C) (i) Find the difference between the maximum temperature and the minimum temperature on Wednesday. ............................................. °C [1] (ii) The minimum temperature on Saturday was 2 °C higher than the minimum temperature on Monday. Find the minimum temperature on Saturday. ............................................. °C [1] (iii) In this week the range of temperatures was 23 °C. Find the minimum temperature on Sunday. ............................................. °C [1] (c) These are the opening times for the museum. Monday to Friday 09 00 to 17 00 Saturday and Sunday 10 00 to 16 00 During opening hours the museum has 4 security guards working. Each guard works a maximum of 30 hours each week. Work out the smallest number of guards needed each week. ................................................. [4] (d) The entry price to the museum is $18. This price is increased by 28%. Find the increased entry price. $ ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) 187.5[0] 1 1(b)(i) 19 1 1(b)(ii) −3 1 1(b)(iii) −8 1 1(c) 7 nfww 4 M1 for 8 × 5 + 6 × 2 oe and M2 for their 52 × 4 ÷ 30 oe or M1 for their 52 × 4 oe or their 52 ÷ 30 oe 1(d) 23.04 2 28 M1 for 18 × (1 + ) oe 100 or B1 for 5.04

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2 (a) Jian has a fair spinner in the shape of a regular hexagon. The spinner is numbered 2, 2, 3, 4, 4, 5. Jian spins the spinner. Find the probability that the spinner lands on (i) an even number, ................................................. [1] (ii) a number less than 6, ................................................. [1] (iii) the number 1. ................................................. [1] (b) Mei has two fair square spinners, A and B. Spinner A is numbered 1, 2, 2, 4 and spinner B is numbered 3, 3, 4, 5. Spinner A Spinner B She spins both spinners and adds the two numbers. (i) Complete the table to show all the possible outcomes. B 3 3 4 5 A 1 4 4 2 5 5 6 7 2 5 5 6 7 4 7 7 [2] (ii) Use the table to write down the probability that the total is (a) 5, ................................................. [1] (b) more than 5. ................................................. [1] (c) Ning has a spinner numbered 1 to 6. She spins it 50 times and her results are shown in the table. Number on Frequency spinner 1 15 2 12 3 9 4 5 5 2 6 7 (i) Write down the mode. ................................................. [1] (ii) Find the median. ................................................. [1] (iii) Work out the mean. ................................................. [3]

Mark scheme: 2(a)(i) 2 1 oe 3 2(a)(ii) 1 1 2(a)(iii) 0 1 2(b)(i) 5 6 2 B1 for 2 or 3 correct, in correct places 8 9 in the correct places 2(b)(ii)(a) 5 1 FT their table oe 16 2(b)(ii)(b) 9 1 FT their table oe 16 2(c)(i) 1 1 2(c)(ii) 2 1 2(c)(iii) 2.76 3 M1 for 1 × 15 + 2 × 12 + 3 × 9 + 4 × 5 + 5 × 2 + 6 × 7 oe M1dep for their 138 ÷ 50

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3 (a) 8 15 18 33 39 41 51 57 60 81 From this list, write down (i) a factor of 54, ................................................. [1] (ii) a multiple of 19, ................................................. [1] (iii) a prime number. ................................................. [1] (b) Write down the reciprocal of 64. ................................................. [1] (c) (i) Write .481 # 10 - 3 as an ordinary number. ................................................. [1] (ii) Write 75 000 in standard form. ................................................. [1] .63 # 10 2 (iii) Calculate - 3 . 7 # 10 Write your answer in standard form. ................................................. [2] (d) (i)  = {2, 4, 8, 16, 32, 64} A = {square numbers} B = {cube numbers} Use this information to complete the Venn diagram. A B [2] (ii) On this Venn diagram, shade the region P , Q . P Q [1]

Mark scheme: 3(a)(i) 18 1 3(a)(ii) 57 1 3(a)(iii) 41 1 3(b) 1 1 64 3(c)(i) [0].00481 cao 1 3(c)(ii) 7.5 × 104 1 3(c)(iii) 9 × 104 2 B1 for figs 9 3(d)(i) 2 B1 for 4 or 5 numbers in the correct place 3(d)(ii) 1

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4 (a) Simplify. 6a - 3b + 2a - 4b ................................................. [2] (b) Expand. 5 ( x - 3) ................................................. [1] (c) Solve these equations. x (i) = 18 3 x = ................................................. [1] (ii) 5x + 18 = 8 x = ................................................. [2] (iii) 12x - 3 = 4x + 21 x = ................................................. [2] (d) 6 10 # 6 x = 6 2 Find the value of x. x = ................................................. [1] (e) The Fraser family and the Singh family go to the cinema. The Fraser family buys 6 adult tickets and 2 child tickets for $124. The Singh family buys 3 adult tickets and 5 child tickets for $100. Find the price of an adult ticket and the price of a child ticket. Adult ticket $ ................................................. Child ticket $ ................................................. [5]

Mark scheme: 4(a) 8a – 7b 2 B1 for 8a or –7b in final answer or for 8a – 7b seen then spoilt 4(b) 5x – 15 1 4(c)(i) 54 1 4(c)(ii) −2 2 M1 for 18 8 5x = 8 – 18 or x + = or better oe 5 5 4(c)(iii) 3 2 M1 for 12x – 4x = 21 + 3 or better oe 4(d) −8 cao 1 4(e) 17.5[0] 5 B1 for 6a + 2c = 124 B1 for 3a + 5c = 100 9.5[0] oe M1FT for a correct method to eliminate one variable A1 for 17.5[0] A1 for 9.5[0] If 0 scored after B0, B1 or B2, SC1 for two values that satisfy one of the/their original equations or family

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5 (a) Write one hundred and twenty thousand and twenty in figures. ................................................. [1] (b) Find the value of 3481. ................................................. [1] (c) (i) Write down the fraction of the rectangle that is shaded. ................................................. [1] (ii) Find the percentage of the rectangle that is not shaded. ..............................................% [1] (d) Write these numbers in order, starting with the smallest. 5 7 27% 0.268 17 29 .................... 1 .................... 1 .................... 1 .................... [2] smallest (e) Write 0.3728 correct to 1 decimal place. ................................................. [1] (f) Write down the value of 190. ................................................. [1] (g) The height, h metres, of a tower is 128 m, correct to the nearest metre. Complete the statement about the value of h. .................. G h 1 .................. [2] (h) Find the highest common factor (HCF) of 126 and 180. ................................................. [2] (i) Write down an irrational number with a value between 6 and 7. ................................................. [1]

Mark scheme: 5(a) 120 020 1 5(b) 59 1 5(c)(i) 5 1 8 5(c)(ii) 37.5 1 5(d) 7 5 2 B1 for 3 in the correct order 0.268 27% or M1 for .27 .29… [.268] .24… 29 17 5(e) 0.4 1 5(f) 1 1 5(g) 127.5 128.5 2 B1 for each or SC1 for both correct but reversed 5(h) 18 2 B1 for an answer of 2 or 3 or 6 or 9 or 2 × 3 × 3 or 2 × 32 as final answer or for [126 =] 2 × 3 × 3 × 7 or 2 × 32 × 7 and [180 =] 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5 or for complete correct list of factors for 126 and 180 5(i) Any irrational number between 6 and 7 1

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6 NOT TO SCALE 3 cm 6 cm 4 cm The diagram shows a right-angled triangular prism. (a) On the 1 cm2 grid, complete the net of the prism. One face has been drawn for you. [3] (b) Work out the surface area of the prism. .......................................... cm2 [3] (c) Work out the volume of the prism. .......................................... cm3 [2]

Mark scheme: 6(a) Correct net 3 B2 for 2 or 3 correct faces in the correct place or B1 for 1 correct face in the correct place 6(b) 84 3 M2 for 5 × 6 + 6 × 4 + 6 × 3 oe or better or 6 × (5 + 4 + 3) oe or better or 2( 12 × 3 × 4) oe or better or M1 for one correct area 6(c) 36 2 M1 for 12 × 3 × 4 × 6 oe

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7 (a) NOT TO w° SCALE 118° The diagram shows an isosceles triangle and a straight line. Work out the value of w. w = ................................................. [2] (b) E F NOT TO SCALE A 31° x° B y° D C ABCD is a rectangle. AE is parallel to DBF. Find the value of x and the value of y. x = ................................................. y = ................................................. [2] (c) B NOT TO SCALE a° 53° A C A, B and C are points on a circle. AC is a diameter of the circle. Find the value of a. a = ................................................. [2] (d) NOT TO SCALE P Two regular octagons and a square meet at point P. Show, by calculation, that the three interior angles at P add up to 360°. [3]

Mark scheme: 7(a) 56 2 M1 for 180 – 118 oe or 180 – 2 × their 62 oe 7(b) [x =] 31 2 B1 for each [y =] 121 or M1 for their y = 90 + their x 7(c) 37 2 B1 for the angle ABC marked as 90 or M1 for 180 – (90 + 53) oe 7(d) 360 M2 360 180 – or (8 – 2) × 180 ÷ 8 M1 for or (8 – 2) × 180 8 8 135 + 135 + 90 [= 360] A1

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8 y 6 5 4 3 D 2 C 1 0 x – 6 – 5 – 4 – 3 – 2 – 11 1 2 3 4 5 6 ––11 A ––22 – 3 – 4 B – 5 – 6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, ............................................................................................................................................. ............................................................................................................................................. [3] (ii) triangle A onto triangle C, ............................................................................................................................................. ............................................................................................................................................. [2] (iii) triangle A onto triangle D. ............................................................................................................................................. ............................................................................................................................................. [3] (b) On the grid, draw the image of triangle A after a reflection in the line x =- 2 . [2]

Mark scheme: 8(a)(i) Rotation 3 B1 for each [centre] (2, −2) 90° [anticlockwise] oe 8(a)(ii) Translation 2 B1 for each  − 4     3  8(a)(iii) Enlargement 3 B1 for each [centre] (−2, −5) [sf] 2 8(b) Correct reflection of triangle 2 B1 for correct reflection in lines x = k points at (−3, 0) (−3, −2) (−6, −2) or y = −2

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9 (a) Complete the table of values for y = . x x - 5 - 3 - 2 - 1 1 2 3 5 y - 15 15 [3] 15 (b) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 16 14 12 10 8 6 4 2 0 x – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 – 2 – 4 – 6 – 8 – 10 – 12 – 14 – 16 [4] (c) On the grid, draw the line y = 6 . [1] 15 (d) Use your graph to solve = 6 . x x = ................................................. [1]

Mark scheme: 9(a) −3 −5 −7.5 7.5 5 3 3 B2 for 4 or 5 correct or B1 for 2 or 3 correct 9(b) Correct curve 4 B3FT for 7 or 8 points plotted correctly or B2FT for 5 or 6 points plotted correctly or B1FT for 3 or 4 points plotted correctly 9(c) Correct ruled line 1 9(d) 2.5 or 2.4 to 2.6 1 FT their line (y = k) and their curve

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10 (a) These are the first four terms of a sequence. 8 15 22 29 (i) Write down the next term. ................................................. [1] (ii) Write down the term to term rule for continuing this sequence. ................................................. [1] (iii) Find an expression for the nth term. ................................................. [2] (b) Find the next term in each of these sequences. (i) 18, 21, 26, 33, 42, … ................................................. [1] (ii) 18, 20, 24, 32, 48, … ................................................. [1] (c) Find the first three terms of the sequence with nth term n 2 + 5n . ............. , ............. , ............. [2]

Mark scheme: 10(a)(i) 36 1 10(a)(ii) add 7 oe 1 10(a)(iii) 7n + 1 oe final answer 2 B1 for 7n + j or kn + 1 (k ≠ 0) as final answer, or for 7n + 1 seen then spoilt 10(b)(i) 53 1 10(b)(ii) 80 1 10(c) 6 14 24 2 B1 for 2 correct terms in the correct place If 0 scored, SC1 for 0 6 14

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