Cambridge IGCSE Mathematics 0580 — 2017 Oct/Nov Paper 2 · Variant 1

1 NOT TO 72° 83° SCALE 104° x° The diagram shows a quadrilateral. Find the value of x. x = .................................................. [1]

Mark scheme: Question Answer Mark Partial marks 1 101 1

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2 Work out. 2 -4 # 2 5 ................................................... [1]

Mark scheme: 2 2 1

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5 .04 - 33 (a) Use a calculator to work out . 0.13 - 0. 015 Write down all the digits in your calculator display. ................................................... [1] (b) Write your answer to part (a) correct to 2 significant figures. ................................................... [1]

Mark scheme: 3(a) 1.49220…. 1 3(b) 1.5 1FT FT their answer to (a) rounded correctly to 2 significant figures

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4 Amber’s mean mark on five tests is 80. Her marks on four of these tests are 68, 81, 74 and 89. Work out her mark on the fifth test. ................................................... [2]

Mark scheme: 4 88 2 68 + 81 + 74 + 89 + x M1 for = 80 oe 5 or B1 for 400

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5 Factorise completely. 12x 2 + 15xy - 9x ................................................... [2]

Mark scheme: 5 3x(4x + 5y − 3) final answer 2 B1 for 3(4x2 + 5xy – 3x) or x(12x + 15y – 9) allow in working or correct answer spoiled If zero scored, SC1 for 3x(4x + 5y – 3) with only 2 correct elements in the brackets, allow in working

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6 y 5 4 A 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 B –2 C –3 –4 –5 The diagram shows two sides of a rhombus ABCD. (a) Write down the co-ordinates of A. ( ..................... , ..................... ) [1] (b) Complete the rhombus ABCD on the grid. [1]

Mark scheme: 6(a) (−2, 3) 1 6(b) Correct rhombus with 4th point at 1 (2,2)

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7 Petra begins a journey in her car. She accelerates from rest at a constant rate of 0.4 m/s2 for 30 seconds. She then travels at a constant speed for 40 seconds. On the grid, draw the speed-time graph for the first 70 seconds of Petra’s journey. 16 14 12 10 Speed 8 (m/s) 6 4 2 0 0 10 20 30 40 50 60 70 Time (s) [2]

Mark scheme: 7 Diagonal line from 1 (0, 0) to (30, 12) and 1FT FT for horizontal line from (30, k) to (70, k) where k is their 12 Horizontal line from (30, 12) to (70, 12)

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8 NOT TO SCALE The diagram shows three identical cuboids in a tower. The height of one cuboid is 6.5 cm, correct to the nearest millimetre. Work out the upper bound of the height of the tower. ............................................. cm [2]

Mark scheme: 8 19.65 cao 2 B1 for 6.55 seen (must be evaluated, not 6.5 + 0.05) or M1 for 3 × (6.5 + 0.05)

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9 The value of a motorbike is $12 400. Each year, the value of the motorbike decreases exponentially by 15%. Calculate the value of the motorbike after 3 years. $ ................................................... [2]

Mark scheme: 9 7615.15 2 3  15  M1 for 12 400 ×  1 −  oe  100 

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2 1110 Without using a calculator, work out 1 - . 3 15 Write down all the steps of your working and give your answer as a fraction in its lowest terms. ................................................... [3]

Mark scheme: 10 5 2 4 B1 5 k + Allow 3 3 15 3k 25 11 10 4 M1 Correct method to find common denominator [and ] [and ] 15 15 15 15 75 33 e.g. and 45 45 5 Follow through their for the M1 mark 3 14 14 A1 cao cao 15 15

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11 The diagram shows a regular pentagon. A AB is a line of symmetry. d ° Work out the value of d. NOT TO SCALE B d = .................................................. [3]

Mark scheme: 11 54 3 180 × ( 5 − 2 ) 360 M2 for or 180 − 5 5 360 or M1 for 180 × (5 − 2) or 5

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112 5 -7 343 -11 0.4 2.5 3 From this list of numbers, write down (a) a cube number, ................................................... [1] (b) the smallest number, ................................................... [1] (c) a natural number. ................................................... [1]

Mark scheme: 12(a) 343 1 12(b) –11 1 12(c) 343 1

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13 Simplify. (a) m5 2 ^ h ................................................... [1] (b) 4x 3 y # 5 x 2 y ................................................... [2]

Mark scheme: 13(a) m10 final answer 1 13(b) 20x5y2 final answer 2 B1 for 2 out of 3 elements correct in final answer or correct answer spoiled

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7 14 (a) D is the point (2, ‒5) and DE = c 1 m. Find the co-ordinates of the point E. ( ..................... , ..................... ) [1] t (b) v = and v = 13 . c12m Work out the value of t, where t is negative. t = .................................................. [2]

Mark scheme: 14(a) (9, −4) 1 14(b) −5 2 M1 for t2 + 122 = 132 oe or SC1 for answer 5 or ± 5

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15 (a) Q = {1, 2, 3, 4, 5, 6} Write down a set P where P 1 Q . P = .................................................. [1] (b) Shade these regions in the Venn diagrams. M N' (A B) C' M N A B C [2]

Mark scheme: 15(a) Fewer than 6 elements from 1 {1, 2, 3, 4, 5, 6} or ∅ 15(b) 1 M N 1 A B C

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16 y 11 10 9 8 7 A 6 5 4 3 B 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 Describe fully the single transformation that maps triangle A onto triangle B. ...................................................................................................................................................................... ...................................................................................................................................................................... [3]

Mark scheme: 16 Enlargement 1 1 1 3 (2, 1) 1

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17 y is inversely proportional to (x + 1) 2 . y = 50 when x = 0.2 . (a) Write y in terms of x. y = .................................................. [2] (b) Find the value of y when x = 0.5 . y = .................................................. [1]

Mark scheme: 17(a) 72 2 k (y =) oe M1 for y = ( x + 1) 2 ( x+ 1) 2 17(b) 32 1FT FT correct evaluation from their equation in (a) using 0.5

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18 The diagram shows a scale drawing of Tariq’s garden. The scale is 1 centimetre represents 2 metres. Tree Bird bath Tree Scale: 1 cm to 2 m Tariq puts a statue in the garden. The statue is equidistant from the two trees and 10 m from the bird bath. Find, by construction, the point where Tariq puts the statue. Label the point S. [4]

Mark scheme: 18 Correct position of S with 2 pairs of 4 B3 for correct position of S with correct construction arcs for line missing/incorrect construction arcs but correct line or B2 for correct ruled line equidistant from the two trees with correct arcs or B1 for correct line with no/wrong arcs or correct arcs with no line and B1 for arc centre bird bath, radius 5 cm or S in correct position with no/incorrect working

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19 Write as a single fraction in its simplest form. 5 3 1 + + x - 3 x + 7 2 ................................................... [4]

Mark scheme: 19 x 2 + 20 x + 31 4 B1 for a common denominator of final answer [2](x ‒ 3)(x + 7) seen isw 2 ( x − 3 )( x + 7 ) M1 for 2×5×(x + 7) + 2×3×(x ‒ 3) + (x ‒ 3)(x + 7) oe and must have attempted to expand all the brackets in the numerator M1 for 10x + 70 + 6x ‒ 18 or x2 − 3x + 7x ‒ 21 or [2](5x + 35 + 3x −9) or better

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20 (a) 20 cm NOT TO SCALE A cylinder has height 20 cm. The area of the circular cross section is 74 cm2. Work out the volume of this cylinder. ............................................cm3 [1] (b) Cylinder A is mathematically similar to cylinder B. NOT TO 10 cm A B SCALE The height of cylinder A is 10 cm and its surface area is 440 cm2. The surface area of cylinder B is 3960 cm2. Calculate the height of cylinder B. ............................................ cm [3]

Mark scheme: 20(a) 1480 1 20(b) 30 3 3960 440 M2 for 10 × or 10 ÷ 440 3960 3960 440 or M1 for or or 440 3960  h 2 3960 oe  =  10  440

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21 E NOT TO SCALE 9 cm D C 12 cm M A 12 cm B The diagram shows a square-based pyramid ABCDE. The diagonals of the square meet at M. E is vertically above M. AB = BC = 12 cm and EM = 9 cm. Calculate the angle between the edge EC and the base, ABCD, of the pyramid. ................................................... [4]

Mark scheme: 21 46.7 or 46.68 to 46.69 4 9 M3 for tan […=] oe 1 2 2 12 + 12 2 or  1  2 2 12 2 M1 for × 12 + 12 oe e.g.    2  2 and M1 for identifying angle MCE

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22 Simon records the heights, h cm, of 200 sunflowers in his garden. The cumulative frequency diagram shows this information. 200 180 160 140 120 Cumulative frequency 100 80 60 40 20 0 h 100 120 140 160 180 200 220 Height (cm) (a) Find the number of these sunflowers that have a height of more than 160 cm. ................................................... [2] (b) Sue records the heights, h cm, of 200 sunflowers in her garden. The cumulative frequency table shows this information. Height (h cm) Cumulative frequency h G 100 0 h G 110 20 h G 120 48 h G 130 100 h G 140 140 h G 150 172 h G 160 188 h G 170 200 On the grid above, draw another cumulative frequency diagram to show this information. [3] (c) Work out the difference between the median heights of Simon’s sunflowers and Sue’s sunflowers. ............................................. cm [2] Question 23 is printed on the next page.

Mark scheme: 22(a) 80 to 84 2 M1 for 116 to 120 22(b) Correct curve or ruled lines 3 B2 for 7 or 8 correct points B1 for 5 or 6 correct points 22(c) 26 2 B1 for 156 or 130 or for their 130 from their increasing curve (or lines)

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23 In one week, Neha spends x hours cooking and y hours cleaning. The time she spends cleaning is at least equal to the time she spends cooking. This can be written as y H x. She spends no more than 16 hours in total cooking and cleaning. She spends at least 4 hours cooking. (a) Write down two more inequalities in x and/or y to show this information. ................................................... ................................................... [2] (b) Complete the diagram to show the three inequalities. Shade the unwanted regions. y y = x 18 16 14 12 Hours 10 cleaning 8 6 4 2 x 0 2 4 6 8 10 12 14 16 18 Hours cooking [3] (c) Neha receives $10 for each hour she spends cooking and $8 for each hour she spends cleaning. Work out the largest amount she could receive. $ ................................................... [2]

Mark scheme: 23(a) x + y ⩽ 16 oe 2 B1 for each mark final answers x ⩾ 4 oe If zero scored, SC1 for x + y < 16 and x > 4 23(b) Correct shading 3 M2 for lines at x = 4 and x + y = 16 or for correct shading of x < 4 or x + y > 16 or M1 for line at x = 4 or their x = 4 or for line at x + y = 16 or their x + y = 16 23(c) 144 2 M1 for (8, 8) selected or for 10 × x + 8 × y for any numerical point which is inside or on the boundary of their unshaded region

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