Cambridge IGCSE Mathematics 0580 — 2016 May/June Paper 3 · Variant 1

1 Joel spins a fair five-sided spinner numbered 2, 3, 4, 5 and 6. (a) Write down the probability that the spinner lands on (i) an odd number, .................................................. [1] (ii) a prime number, .................................................. [1] (iii) the number 7. .................................................. [1] (b) Here are the results of his first 20 spins. Number 2 3 4 5 6 Frequency 3 2 6 4 5 (i) Write down the mode. .................................................. [1] (ii) Calculate the mean. .................................................. [3] (iii) Joel wants to draw a pie chart to show the results in the table. (a) Show that the sector angle for the number 2 is 54°. [1] (b) Find the sector angle for the number 6. .................................................. [2] (c) Joel asks 30 students to guess the number that the spinner will next land on. The results are shown in this pie chart. 2 3 6 4 5 (i) The sector angle for the number 6 is 168°. How many students guessed the number 6? .................................................. [2] (ii) Find the percentage of the students who guessed a number less than 5. ...............................................% [3] (iii) Joel spins the spinner. 10% of the 30 students guessed correctly. Which number did the spinner land on? .................................................. [2]

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 2 oe 1 Allow 0.4 , 40% 5 (ii) 3 oe 1 Allow 0.6 , 60% 5 (iii) 0 1 (b) (i) 4 1 (ii) 4.3 3 M1 for 2×3 + 3×2 + 4×6 + 5×4 + 6×5 or 86 M1dep for their 86 ÷ 20 If M0M0 SC1 for 57.5 3 (iii) (a) × 360 1 20 5 360 (b) 90 2 M1 for oe or oe implied by 18 seen 20 20 168 360 (c) (i) 14 2 M1 for oe or oe implied by 12 seen 360 30 (ii) 43.3 3 B1 for [total angle=] 156° their angle M1 for [× 100] oe 360 If B0M0 SC1 for 53.3 10 (iii) 5 2 M1 for × 360 oe or 36 100

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2 (a) 3 6 19 20 24 27 30 32 35 36 48 49 51 From this list of numbers write down (i) a factor of 15, .................................................. [1] (ii) a multiple of 18, .................................................. [1] (iii) an odd square number, .................................................. [1] (iv) a cube number. .................................................. [1] (b) Write as a percentage. (i) 0.43 ...............................................% [1] 1 (ii) 2 ...............................................% [1] 28 (c) Write in its lowest terms. 42 .................................................. [1] (d) (i) Write 45 as a product of its prime factors. .................................................. [2] (ii) Find the highest common factor (HCF) of 45 and 105. .................................................. [2]

Mark scheme: 2 (a) (i) 3 1 (ii) 36 1 (iii) 49 1 (iv) 27 1 (b) (i) 43 1 (ii) 50 1

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3 Paul and Mary go on a 14 night cruise in the Mediterranean. (a) The price of the cruise is $237 per person per night. A tax of 6% is added to this price. Find the total amount Paul and Mary pay for this cruise. $ .................................................. [3] (b) At a port Mary buys 2 bottles of sun cream. Each bottle costs $7.89 . Work out the change she receives from $20. $ .................................................. [2] (c) Paul and Mary leave the ship at 09 23 to tour Pisa. 3 The tour lasts for 6 hours. 4 Find the time when the tour finishes. .................................................. [2] (d) The ship leaves at 18 40 to sail to the next port. It sails 270 km at an average speed of 32.4 km/h. Find the time when the ship arrives. .................................................. [3] (e) There are 1800 passengers on the ship. They are in the ratio males : females = 5 : 4. Work out the number of male passengers. .................................................. [2]

Mark scheme: 3 (a) 7034.16 3 M2 for 14 × 237 × 2 × 1.06 oe or M1 for 14 × 237 × 2 oe or 237 × 1.06 oe or 237 × 2 × 1.06 oe or 237 × 1.06 × 14 oe (b) 4.22 2 M1 for 20 – 2 × 7.89 (c) 16 08 or 4 08 pm 2 B1 for 45 min soi (d) 03 00 or 3 am 3 M1 for 270 ÷ 32.4 or 8.33[…] or 8 (h) 20 (min) M1dep for 18 40 + their 8.33 (e) 1000 2 M1 for 18004 + 5 [×5] oe

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4 (a) The table shows the temperature at noon each day for one week in a city. Monday Tuesday Wednesday Thursday Friday Saturday Sunday 5 °C 2 °C −3 °C −1°C 0 °C 1°C −2 °C (i) Which day had the lowest noon temperature? .................................................. [1] (ii) Find the difference between the noon temperatures on Tuesday and Wednesday. ..............................................°C [1] (iii) Write these seven temperatures in order, starting with the lowest. ..............., ..............., ..............., ..............., ..............., ..............., ............... [1] lowest (iv) On Sunday the noon temperature was −2 °C. The next day the noon temperature fell by 4 °C. Find the noon temperature on the next day. ..............................................°C [1] (b) The number of houses in the city is 1 935 364. Write this number correct to the nearest million. .................................................. [1] (c) The height, h metres, of a tower in the city is 120 m, correct to the nearest 10 m. Complete this statement about the value of h. .................... G h < .................... [2] (d) The diagram shows the cross section of a circular tunnel in the city. NOT TO SCALE 8 m 1 m Calculate the shaded area. ............................................. m2 [4]

Mark scheme: 4 (a) (i) Wednesday 1 (ii) 5 1 accept –5 (iii) –3 –2 –1 0 1 2 5 1 (iv) –6 1 (b) 2 million or 2 000 000 1 (c) 115 125 2 B1 for either correct or both correct but reversed (d) 28.3 or 28.27 to 28.28 4 B1 for radius of 5 cm or 4 cm soi M2 for π × 52 – π × 42 soi or M1 for π × 52 or π × 42 soi If 0 scored SC2 for π × 102 – π × 82 or SC1 for π × k2

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5 (a) The scale drawing shows port A and port B. The scale is 1 centimetre represents 15 kilometres. North North B A Scale: 1 cm to 15 km A ship sails from port A to port B. (i) Measure the bearing of port B from port A. .................................................. [1] (ii) Find the actual distance from port A to port B. .............................................km [2] (iii) The ship then sails from port B to port C. Port C is 90 km from port B on a bearing of 146°. On the scale drawing mark the position of port C. [2] (b) Another ship sails from port P to port Q. It then sails from port Q to port R before returning to port P. North NOT TO Q North SCALE 84° North 67° R 43° P (i) Find angle RPQ. Angle RPQ = ................................................. [1] (ii) Find the bearing of port P from port R. .................................................. [2] (c) North T NOT TO 356 km SCALE S 267 km Port T is 267 km east and 356 km north of port S. Calculate the distance ST. ST = ............................................km [2]

Mark scheme: 5 (a) (i) [0]67 1 (ii) 135 2 B1 for 9 (cm) (iii) Correct diagram 2 B1 for correct bearing B1 for correct length

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6 (a) Solve these equations. (i) x + 7 = 15 x = ................................................. [1] (ii) 5(3x + 8) = 10 x = ................................................. [3] (b) A club is arranging transport for its members. Speedy Coaches charge $625 plus $15 per member. The total cost, in dollars, for x members is given by the expression 15x + 625. (i) Sporty Coaches charge $117 plus $19 per member. Write an expression for the total cost, in dollars, for x members. .................................................. [2] (ii) The total cost is the same for both Speedy Coaches and Sporty Coaches. Write down an equation and solve it to find x. x = ................................................. [3]

Mark scheme: 6 (a) (i) 8 1 (ii) –2 3 M1 for first step correctly completed M1FT for second step correctly completed (b) (i) 19x + 117 2 B1 for 19x + c or mx + 117 (ii) 15x + 625 = their (b)(i) 1 127 2 M1FT for the first correct step of their linear equation

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7 y 8 7 6 5 B A 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 C –4 –5 –6 –7 –8 -2 (a) On the grid, draw the image of shape A after a translation by the vector [2] e -6 o. (b) (i) On the grid, draw the image of shape A after an enlargement, scale factor 2, centre (4, 4). [2] (ii) Write down the scale factor of the enlargement that maps the image in part (b)(i) back onto shape A. .................................................. [1] (c) Describe fully the single transformation that maps shape A onto shape B. ............................................................................................................................................................. ............................................................................................................................................................. [2] (d) Describe fully the single transformation that maps shape A onto shape C. ............................................................................................................................................................. ............................................................................................................................................................. [3]

Mark scheme: 7 (a) Correct image, points at 2 B1 for one correct movement either horizontal (0,–3), (0,–1), (2,–3) and (4,–1) or vertical (b) (i) Correct image, points at 2 B1 for correct scale factor and orientation but (0, 6), (8, 6), (4, 2) and (0, 2) incorrect centre (ii) 1 1 2 (c) Reflection 1 [in mirror line] x = –1 oe 1 (d) Rotation 1 [centre] (0, 0) oe 1 [angle] 180° oe 1 SC1,1,1 for Enlargement , SF = −1, centre (0, 0)

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8 Jared is building a house. (a) 11.8 m NOT TO SCALE 7.5 m 2.8 m 3.2 m 3.2 m The diagram shows the plan of the floor of the house. (i) Find the area of the floor. ............................................. m2 [3] (ii) For every square metre of floor area, it costs $2175 to build the house. Calculate the cost of building the house. Give your answer correct to 3 significant figures. $ .................................................. [2] (b) NOT TO SCALE 1.8 m x° 1.75 m The diagram shows a section of the roof. Using trigonometry, calculate the value of x. x = ................................................. [2] (c) Jared invests $50 000 for three years at a rate of 2% per year compound interest. Calculate the total amount Jared receives at the end of the three years. $ .................................................. [3] (d) Jared also built an apartment for $180 000. He sells it for $198 000. Calculate the percentage profit that he makes. ...............................................% [3]

Mark scheme: 8 (a) (i) 73.38 3 B1 for 5.4 or 4.7 soi M1 for a completely correct method (ii) 160 000 2FT B1FT for their (a)(i) × 2175 or 159601.5[0] (b) 45.8 or 45.80 to 45.81 2 M1 for tan [ =] 1.8 ÷ 1.75 (c) 53 060.4[0] 3 M2 for 50 000 × 1.023 oe or M1 for two years compound interest eg 50 000 × 1.022 oe implied by 52 020

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9 (a) Complete the table of values for y = 8 + 7x − x2. x 0 1 2 3 4 5 6 7 8 y 8 18 18 8 [3] (b) On the grid, draw the graph of y = 8 + 7x − x2 for 0 G x G 8. y 22 20 18 16 14 12 10 8 6 4 2 x 0 1 2 3 4 5 6 7 8 [4] (c) Write down the co-ordinates of the highest point of the curve. (................ , ................) [1] (d) (i) On the grid, draw the line y = 16. [1] (ii) Use your line to solve the equation 8 + 7x − x2 = 16. x = ........................ or x = ........................ [2]

Mark scheme: 9 (a) … 14 … 20 20 … 14 … 0 3 B2 for 3 or 4 correct B1 for 2 correct (b) Completely 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 (c) (3.5, h) 1 20 < h ⩽ 20.4 (d) (i) Correct ruled line 1 (ii) 1.4 5.6 1, 1FT FT their graph and line

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