Cambridge IGCSE Mathematics 0580 — 2017 Oct/Nov Paper 3 · Variant 1

1 (a) Write down the temperature shown by each arrow. (i) Temperature (°C) 0 10 20 ............................................°C [1] (ii) Temperature (°C) –20 0 20 ............................................°C [1] (b) The table shows the daily temperature in Hayville for one week in January. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Temperature –4 2 –1 0 1 –6 –2 (°C) (i) Which was the coldest day? ................................................. [1] (ii) Find the difference between the temperature on Sunday and the temperature on Monday. ............................................°C [1] (c) In Grassington, the temperature recorded at 07 35 was −3 °C. (i) The temperature was recorded again 8 12 hours later. At what time was this temperature recorded? ................................................. [1] (ii) By this time, the temperature had risen by 7 °C. Find this temperature. ............................................°C [1]

Mark scheme: Question Answer Marks Partial marks 1(a)(i) 16 1 1(a)(ii) –15 1 1(b)(i) Friday 1 1(b)(ii) 6 1 1(c)(i) 16 05 or 4 05 pm 1 1(c)(ii) 4 1

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2 Jeff owns a clothes shop. (a) Shirt Tie Coat $24 $12.50 $46 A customer buys 3 shirts, 5 ties and 1 coat. Calculate the total cost. $ ................................................ [3] (b) A jacket has a price of $64. Jeff increases this price by 8%. Calculate the new price. $ ................................................ [2] (c) Jeff also increases the price of a dress from $250 to $280. Calculate the percentage increase in the price of the dress. .............................................% [3] (d) The shop has a rectangular floor measuring 5.5 m by 8.5 m. The floor covering costs $12 per square metre. Calculate the cost of the floor covering. $ ................................................ [3] (e) Jeff invests $3600 for 3 years at a rate of 6% per year compound interest. Work out the value of the investment at the end of the 3 years. $ ................................................ [3]

Mark scheme: 2(a) 180.5[0] 3 M2 for 3 × 24 + 5 × 12.50 + 46 oe or M1 for 3 × 24 or 5 × 12.50 or better, soi by 72 or 62.5 2(b) 69.12 2 M1 for 64 × 1.08 oe 2(c) 12 3 M2 for ( 280250 – 1) × 100 or 280250− 250 × 100 oe or M1 for 280250 – 1 or 280250 × 100 or 280250− 250 oe 2(d) 561 3 M1 for 5.5 × 8.5 soi by 46.75 M1 for their 46.75 × 12 2(e) 4287.66 3 M2 for 3600 × (1 + 1006 )3 oe or M1 for 3600 × (1 + 1006 )2 oe soi by 4044.96 If zero scored, SC2 for 687.6576, 687.658, 687.66, 687.65, 687.7, 688 or 690

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3 (a) The scatter diagram shows the scores for each student in class A for the written test and the speaking test in French. A line of best fit has been drawn. 60 55 50 45 40 35 Score in written test 30 25 20 15 10 5 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Score in speaking test (i) Each test is marked out of 60. In which test did the class perform better? Give a reason for your answer. .............................................. because ......................................................................................... ...................................................................................................................................................... [1] (ii) What type of correlation is shown in the scatter diagram? ................................................. [1] (iii) One student is much better at speaking French than writing French. Put a ring around the cross that represents this student. [1] (iv) One student scored 39 in the speaking test but was absent for the written test. Use the line of best fit to estimate a score for this student in the written test. ................................................. [1] (b) Here are the scores in the written test for class B. 21 14 48 32 8 29 41 39 30 23 17 Find (i) the median, ................................................. [2] (ii) the mean. ................................................. [2]

Mark scheme: 3(a)(i) Written test and a valid reason 1 3(a)(ii) Positive 1 3(a)(iii) (45,10) indicated 1 3(a)(iv) 42 1 3(b)(i) 29 2 M1 for 6 in the correct order, 8 14 17 21 23 29… or … 29 30 32 39 41 48 3(b)(ii) 27.5 or 27.45 to 27.46 2 M1 for all 11 numbers added, allowing one error or omission, and divided by 11

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4 (a) y 4 3 2 B 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 A –3 –4 (i) Plot point C at (–4, 2). [1] (ii) Write down the mathematical name of the triangle formed by joining the points A, B and C. ................................................. [1] (iii) Write down the vector AB. AB = [1] f p (iv) (a) Find the gradient of the line AB. ................................................. [2] (b) Write down the equation of the line AB. y = ................................................ [1] (b) (i) Complete the table of values for y = x 2 + x - 5 . x –4 –3 –2 –1 0 1 2 3 4 y 7 –3 –3 7 [3] (ii) On the grid below, draw the graph of y = x 2 + x - 5 for - 4 G x G 4 . y 16 14 12 10 8 6 4 2 x –4 –3 –2 –1 0 1 2 3 4 –2 –4 –6 [4] (iii) Use your graph to solve the equation x 2 + x - 5 = 0 . x = .................... or x = .................... [2]

Mark scheme: 4(a)(i) Correct point plotted 1 4(a)(ii) Right-angled or scalene 1 4(a)(iii) 8 1 4 4(a)(iv)(a) 0.5 oe 2 M1 for attempt at rise ÷ run 4(a)(iv)(b) [y =] 0.5x oe 1FT Correct or FT their (iv)(a) 4(b)(i) …1 …–5 –5…1 15 3 B2 for 3 or 4 correct or B1 for 1 or 2 correct 4(b)(ii) Correct curve 4 B3FT for 8 or 9 points correctly plotted or B2FT for 6 or 7 points correctly plotted or B1FT for 4 or 5 points correctly plotted 4(b)(iii) –2.8 1.8 2FT B1FT for each

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5 The scale drawing shows the positions of three towns A, B and C. The scale is 1 centimetre represents 12 kilometres. North North B North C A Scale: 1 cm to 12 km (a) Find the actual distance between town A and town B. ........................................... km [2] (b) Measure the bearing of town B from town A. ................................................. [1] (c) Measure the bearing of town B from town C. ................................................. [1] (d) Town D is 84 km from town A and 42 km from town C. (i) In this part, use a ruler and compasses only and show your construction arcs. On the diagram, construct a possible position for town D. [3] (ii) A plane takes 10 minutes to fly the 84 km from town A to town D. Work out the average speed of the plane in kilometres per hour. ........................................km/h [2] (e) The bearing of town E from town A is 118°. Work out the bearing of town A from town E. ................................................. [2]

Mark scheme: 5(a) 51.6 2 B1 for 4.3[cm] 5(b) [0]47 1 5(c) 292 1 5(d)(i) Arc centre A radius 7 cm 1 Arc centre C radius 3.5 cm 1 One point marked at intersection 1 If zero scored, SC1 for any arc centred on A or C, of correct arcs or correct point marked with no arcs 5(d)(ii) 504 2 M1 for 84 ÷ their time or 84 × 6 5(e) 298 2 M1 for 118 + 180 oe

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6 (a) Find (i) all the factors of 18, ................................................. [2] (ii) a multiple of 30, ................................................. [1] (iii) 2134.44, ................................................. [1] (iv) 2.53, ................................................. [1] (v) (0.2) −1. ................................................. [1] (b) Write 72 as a product of its prime factors. ................................................. [2] (c) Find the lowest common multiple (LCM) of 16 and 30. ................................................. [2] (d) Clock A chimes every 6 hours. Clock B chimes every 9 hours. Both clocks chime at 2 am. At what time will the two clocks next chime together? ................................................. [3]

Mark scheme: 6(a)(i) 1, 2, 3, 6, 9, 18 only 2 B1 for 4 or 5 correct factors and no extras or 6 correct with one extra 6(a)(ii) Any multiple of 30 1 6(a)(iii) 46.2 1 6(a)(iv) 15.625 1 6(a)(v) 5 1 6(b) 23 × 32 2 M1 for a complete factor tree or 2, 2, 2, 3, 3 clearly identified as factors 6(c) 240 2 M1 for [16=] 24 or 2 × 2 × 2 × 2(×1) or [30=] 2 × 3 × 5(×1) or lists of multiples of both at least up to 240, or any product that equals 240 or B1 for 240n 6(d) 20 00 or 8 pm 3 M1 for [LCM of 6 and 9 =] 18(00) or M1 for lists of multiples B1FT for “2 am” + their 18 correctly worked out soi OR B2 for [clock A = 2] 8, 14, 20… and [clock B = 2] 11, 20…. or B1 for [clock A = 2] 8, 14, 20…or [clock B = 2] 11, 20…

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7 (a) Bag A contains 20 counters. 6 are red, 9 are blue and the rest are white. Jared takes one counter at random. Write down the probability that the counter is (i) red, ................................................. [1] (ii) white, ................................................. [1] (iii) yellow. ................................................. [1] (b) Bag B contains green counters, black counters, purple counters and brown counters. Louise takes one counter at random. Colour Green Black Purple Brown Probability 0.3 0.24 0.18 Complete the table. [2] (c) Bag C contains 8 red counters and 12 blue counters only. Bag D contains 6 red counters and 9 blue counters only. A counter is taken at random from each bag. Show that the probability of taking a red counter from bag C is equal to the probability of taking a red counter from bag D. [3]

Mark scheme: 7(a)(i) 6 1 oe 20 7(a)(ii) 5 1 oe 20 7(a)(iii) 0 1 7(b) [0].28 oe 2 M1 for 1 – 0.3 – 0.24 – 0.18 oe or 1 – 0.72 oe 7(c) 8 1 Accept 8 ÷ 20 20 6 1 Accept 6 ÷ 15 15 Comparing the two fractions 1 8 24 6 24 e.g. = and = with equal denominators or as 20 60 15 60 decimals 2 or both shown equal to or [0] .4 or 40% 5

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8 (a) Multiply out the brackets and simplify. 5 2x + 3 - 2 x + 4 ^ h ^ h ................................................. [2] (b) (i) An equilateral triangle has side length 2x. Write down an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest form. ................................................. [1] (ii) A square has a perimeter of 20a. Write down an expression, in terms of a, for the length of one side of the square. Give your answer in its simplest form. ................................................. [1] (c) The diagram shows a rectangle. 3y + 1 NOT TO SCALE 2y + 5 Find an expression, in terms of y, for the perimeter of the rectangle. Give your answer in its simplest form. ................................................. [3] (d) One mint costs m cents. One toffee costs 6 cents more than one mint. The cost of 3 mints and 7 toffees is 182 cents. Write an equation, in terms of m, and solve it to find the cost of one mint. Cost of one mint = .............................. cents [5]

Mark scheme: 8(a) 8x + 7 final answer 2 B1 for 10x + 15 or –2x – 8 or 8x + j or kx + 7 as final answer 8(b)(i) 6x final answer 1 8(b)(ii) 5a final answer 1 8(c) 10y + 12 or 2(5y + 6) 3 M1 for 2(3y + 1) + 2(2y + 5) oe final answer B1 for 10y + j or ky + 12 (k≠0) 8(d) 7(m + 6) + 3m = 182 or 2 B1 for m + 6 7m + 42 + 3m = 182 or 7t + 3m = 182 14 3 M1 for 7m + 42 [+ 3m = 182] M1 for 7m + 3m = 182 − 42 or better OR M2 for [m=] (182 – (6 × 7)) / (7 + 3) or better or M1 for 182 – (6 × 7) or better

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9 (a) The diagram shows a triangle, A, on a 1 cm2 grid. A (i) Find the area of triangle A. ..........................................cm2 [2] (ii) On the grid, draw an enlargement of triangle A with scale factor 2. [2] (b) y 7 6 5 4 3 B 2 1 x 0 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 C –3 –4 –5 –6 –7 (i) Describe fully the single transformation that maps triangle B onto triangle C. ...................................................................................................................................................... ...................................................................................................................................................... [3] (ii) Reflect triangle B in the line y = –1. [2] 5 (iii) Translate triangle B by the vector [2] f 1 p. Question 10 is printed on the next page.

Mark scheme: 9(a)(i) 7.5 2 M1 for 12 × 5 × 3 or evidence of counting squares 9(a)(ii) Correct enlargement 2 B1 for one line correctly scaled 9(b)(i) Rotation 3 B1 for each [centre] (0,0) oe 180° 9(b)(ii) Correct reflection with points 2 B1 for reflection in y = k or x = –1 (–3,–3), (–1,–5) and (–6,–6) 9(b)(iii) Correct translation with points 2 B1 for a correct horizontal translation (5 to the right) (4,4), (2,2) and (–1,5) or a correct vertical translation (1 up)

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10 (a) These are the first four terms of a sequence. –2 6 14 22 (i) Write down the next term. ................................................. [1] (ii) Write down the rule for continuing the sequence. .............................................................................................................. [1] (iii) Find an expression for the nth term. ................................................. [2] (b) The nth term of another sequence is 5 n + 1 - 6 . ^ h Write down the second term of this sequence. ................................................. [1] (c) These are the first four terms of a different sequence. –2 1 8 19 Write down the next term of this sequence. ................................................. [1]

Mark scheme: 10(a)(i) 30 1 10(a)(ii) add 8 oe 1 10(a)(iii) 8n – 10 oe final answer 2 B1 for 8n + j or kn – 10 (k ≠ 0) 10(b) 9 1 10(c) 34 1

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