Cambridge IGCSE Mathematics 0580 — 2016 Oct/Nov Paper 3 · Variant 1

1 (a) Juan and his family fly from London to Rio de Janeiro. (i) The plane departs at 10 20 and arrives in Rio de Janeiro 11 hours 40 minutes later. The local time in Rio de Janeiro is 5 hours behind the local time in London. Work out the time in Rio de Janeiro when the plane arrives. ................................................ [2] (ii) The total cost of the plane tickets is 3500 pounds (£). The exchange rate is £1 = 4.45 Brazilian Real. Calculate the cost of the tickets in Brazilian Real. ....................................... Real [1] (b) (i) Juan and his family go to a soccer match. He buys 2 adult tickets and 2 child tickets. The price of an adult ticket is 660 Brazilian Real. 2 The price of a child ticket is 3 of the price of an adult ticket. Calculate the total cost of the tickets. ....................................... Real [2] (ii) The length, x metres, of the soccer pitch is 105 m, correct to the nearest metre. Complete the statement about the value of x. .................................... G x 1 .................................... [2] (c) The table shows how Juan and his family spent their time in Rio de Janeiro. Sector angle in a Activity Percentage of time pie chart Watching soccer 10 36° Sleeping 108° Shopping Beach 25 90° Other 15 54° (i) Complete the table. [3] (ii) Complete the pie chart. Watching soccer Other Beach [1]

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 1700 or 5pm 2 B1 for 2200 or [0]5 20 or 10pm or 5:20am or 6h 40 (ii) 15 575 1 (b) (i) 2200 2 B1 for 440 10 or M1 for 660 × 2 + their 440 × 2 or × 660 3 or better (ii) 104.5 1 SC1 for both correct but reversed 105.5 1 (c) (i) 30 1 20 72 1 1 (ii) Correct pie chart 1 160 + 58 + 45 + 82 + 125 470

More questions on Ratio and proportion

2 Javier went to a carnival with his friends. (a) He played five games of darts. These are his scores. 160 58 45 82 125 (i) Work out his mean score. ................................................ [2] (ii) Find the range. ................................................ [1] (b) The 5000 tickets for the carnival are different colours. The table shows the number of tickets of each colour. Colour of ticket Red Green Blue Pink White Number of tickets 370 560 1800 1320 950 A ticket is picked at random. Find the probability that this ticket is Blue. ................................................ [1] (c) Five different types of food are sold at the carnival. Javier chooses one of these types of food. The table shows the probability that he chooses each type of food. Type of food Curry Fries Pasta Burger Salad Probability 0.15 0.23 0.4 0.07 Complete the table. [2] (d) Javier hires a four-seater bike. The hire cost is $8.50 for the first hour and then $7.75 for each extra hour. Calculate the cost of hiring the bike for 5 hours. $ ................................................ [2] (e) The table shows the number of drinks sold by one stall at the carnival. Drink Number sold Tea 70 Orange 60 Water 120 Coffee 180 Smoothie 40 Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency Tea Orange Water Coffee Smoothie [3]

Mark scheme: 160 + 58 + 45 + 82 + 125 470 2 (a) (i) 94 2 M1 for or 5 5 (ii) 115 1 1800 (b) oe isw 1 5000 (c) [0].15 oe 2 M1 for 1 – ( 0.15 + 0.23 + 0.4 + 0.07) or 1 – 0.85 (d) 39.5[0] 2 M1 for [8.50 +] (7.75 × 4) soi by 31 If zero scored, SC1 for 47.25 (e) Correct bar chart 3 B1 for any correct linear scale starting at zero soi B2 for all bars correct height and equal width, with equal gaps or no gaps or B1 for all bars correct height with unequal widths and/or gaps or at least three bars correct height with equal width, with equal gaps or no gaps

More questions on Averages and range

3 (a) 6 144 63 11 288 72 8 From the list, write down (i) the multiple of 7, ................................................ [1] (ii) the cube of 2, ................................................ [1] (iii) the prime number, ................................................ [1] (iv) the lowest common multiple (LCM) of 16 and 18. ................................................ [1] (b) Without using a calculator explain why the square of 4.86 must be between 16 and 25. ............................................................................................................................................................. [1] (c) Find the value of (i) 47, ................................................ [1] (ii) 120, ................................................ [1] (iii) 8.32 + 27. ................................................ [1] (d) Write 90 as the product of its prime factors. ................................................ [2]

Mark scheme: 3 (a) (i) 63 1 (ii) 8 1 (iii) 11 1 (iv) 144 1 (b) 42 [=] 16 52 [=] 25 1 (c) (i) 16384 1 (ii) 1 1 (iii) 74.1 or 74.08 to 74.09 1 (d) 2 × 32 × 5 or 2 × 3 × 3 × 5 2 B1 for prime factors 2 , 3 , 5 (and no others) identified or B1 for any correct product e.g. 9 × 10, 5 × 18, 6 × 3 × 5, 1 × 3 × 30

More questions on Types of number

4 y 6 5 A 4 3 2 1 x –6 –5 –4–4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 B –3 –4 –5 –6 The diagram shows two trapeziums, A and B, on a 1 cm2 grid. (a) Find the area of trapezium A. Give the units of your answer. ..................................... .............. [2] (b) (i) Describe fully the single transformation that maps trapezium A onto trapezium B. ..................................................................................................................................................... ..................................................................................................................................................... [3] 5 (ii) On the grid, translate trapezium A by the vector [2] 2 f- p. (iii) On the grid, enlarge trapezium A with centre (0, 0) and scale factor 0.5 . [2]

Mark scheme: 4 (a) 3 1 cm2 1 (b) (i) Rotation 1 90° [anticlockwise] oe 1 [Centre] (0,0) oe 1 5  k  (ii) Correct trapezium 2 B1 for translation of  or   k  −2  (iii) Correct trapezium 2 B1 for correct size and orientation but incorrect position

More questions on Transformations

5 (a) This graph shows Gianna’s journey to work. 20 Work 15 Distance from home 10 (km) 5 Home 0 07 00 07 30 08 00 08 30 09 00 Time (i) How far did Gianna travel to work? .......................................... km [1] (ii) Explain what happened at 07 10. ................................................ [1] (iii) Calculate the average speed for Gianna’s journey to work. ....................................... km/h [2] (b) Gianna earns $1320 each month. She divides her money in the ratio Bills : Leisure : Other = 12 : 5 : 7. Work out how much she spends on each. Bills = $ ................................................ Leisure = $ ................................................ Other = $ ................................................ [3] (c) Gianna invests $5000 for 3 years at a rate of 2.1% per year compound interest. Calculate the amount she will have at the end of the 3 years. Give your answer correct to 2 decimal places. $ ................................................ [4]

Mark scheme: 5 (a) (i) 17.5 1 (ii) She stopped oe 1 (iii) 8.75 2 M1FT for their (a)(i) ÷ 2 soi (b) 660 3 M2 for one correct value in correct place 275 1320 385 or × k where k is 5, 12 or 7 ( 5 + 12 + 7 ) or better in working 1320 or M1 for or better ( 5 + 12 + 7 ) If zero scored, SC1 for all correct answers in incorrect order (c) 5321.66 cao 4 M2 for 5000 × 1.0213 oe or M1 for 5000 × 1.021 × 1.021 oe A1 for 5321.661….. B1 indep for their answer corrected to 2 d.p. if their unrounded answer is shown to at least 3 d.p.

More questions on Interpreting statistical data

6 (a) Here are the first four terms of a sequence. 18 25 32 39 (i) Write down the next term. ................................................ [1] (ii) Explain how you worked out your answer. ..................................................................................................................................................... [1] (b) The nth term of another sequence is n2 + 3. Write down the first three terms of this sequence. ......................... , ......................... , ......................... [2] (c) Simplify. (i) 6a + 5h − 4a − 8h ................................................ [2] (ii) 5(x + 3) + 4(2x − 6) ................................................ [2] (d) Factorise. 6g + 15 ................................................ [1] (e) A rectangle has length (x + 6) cm and width 5 cm. The area of this rectangle is 85 cm2. Find the value of x. x = ............................................... [3]

Mark scheme: 6 (a) (i) 46 1 (ii) Add 7 oe 1 (b) 4, 7, 12 2 M1 for 2 correct or 3 , 4 , 7 (c) (i) 2a – 3h final answer 2 B1 for 2a or −3h (ii) 13x – 9 final answer 2 M1 for 5x + 15 or 8x – 24 or 13x or −9 (d) 3( 2g + 5) final answer 1 (e) 11 nfww 3 M2 for 5x = 55 or x + 6 = 17 or M1 for 5x + 30 [ = 85] or 5 (x + 6 ) [ = 85] or M1 for correct first step of incorrect linear equation if of the form ax + b = 85, a ≠ 1

More questions on Sequences

7 y 20 18 L 16 14 12 10 8 6 4 2 x –2 –1 0 1 2 3 –2 –4 –6 –8 (a) The line L is drawn on the grid. Find the equation of the line in the form y = mx + c. y = ............................................... [3] (b) (i) Complete the table of values for y = x2 + 2x + 4. x −2 −1 0 1 2 3 y 4 4 7 19 [2] (ii) On the grid above, draw the graph of y = x2 + 2x + 4 for –2 G x G 3 . [4] (c) For –2 G x G 3 , write down the x co-ordinate of the point of intersection of the curve y = x2 + 2x + 4 with the line L.

Mark scheme: 7 (a) −5x + 6 3 B2 for –5x (oe) + 6 or –5x + k or rise B1 for kx + 6 k ≠ 0 or [gradient = ] run k with correct values or [gradient =] ±5 k (b) (i) 3 12 1 , 1 (ii) Correct curve 4 B3FT for 5 or 6 correctly plotted points or B2FT for 3 or 4 correctly plotted points or B1FT for 1 or 2 correctly plotted points (c) 0.2 to 0.35 1 FT

More questions on Graphs of functions

8 (a) A cuboid measures 6 cm by 3 cm by 2 cm. (i) On this 1 cm2 grid, complete the net of the cuboid. [3] (ii) Calculate the volume of the cuboid. ........................................ cm3 [2] (b) Write down the mathematical name of this shape. ................................................ [1] (c) Mark an obtuse angle on this trapezium. [1] (d) A regular polygon has an exterior angle of 22.5°. Work out how many sides this polygon has. ................................................ [2] (e) NOT TO SCALE 20 cm 6 cm x cm The diagram shows a shape made from a semi-circle, radius 6 cm, and a right-angled triangle. (i) Show that x = 16. [2] (ii) Calculate the area of the shape. ........................................ cm2 [5]

Mark scheme: 8 (a) (i) Correct net 3 B2 for 3 or 4 correct faces in correct position or B1 for 1 or 2 correct faces in correct position (ii) 36 2 M1 for 6 × 3 × 2 oe (b) Hexagon 1 (c) Obtuse angle indicated 1 360 360 (d) 16 2 M1 for or = 22.5 22.5 n 180 ( n − 2 ) or = 157.5 oe n (e) (i) 20 2 − 12 2 M2 M1 for 202 = 122 + x2 or [x2 =] 202 – 122 π6 2 (ii) 153 or 152.5 to 152.6 5 M2 for soi by 56.5… . or 18 π 2 or M1 for π62 soi by 113 or 113.0…. or 113.1…. or 36 π M1 for 0.5 × 12 × 16 soi by 96 M1dep for their 56.5... + their 96 dep on at least M1 earned soi

More questions on Pythagoras’ theorem

9 (a) The area of Cuba, in square kilometres, is one hundred and five thousand eight hundred and six. Write this number in figures. ................................................ [1] (b) The population of an island is 103 000. Write this number in standard form. ................................................ [1] (c) The table shows some populations in 2014. Population Puerto Rico 3.68 × 106 St Maarten 4.61 × 104 Haiti 1.05 × 107 US Virgin Islands 1.07 × 105 (i) Write the population of St Maarten as an ordinary number. ................................................ [1] (ii) Complete the statement. The population of Haiti is approximately ...................... times the population of the US Virgin Islands. [1] (iii) Find the difference between the population of Haiti and the population of Puerto Rico. Give your answer in standard form. ................................................ [2] (d) In 2013 the population of a town was 30 405. In 2014 the population was 30 851. Calculate the percentage increase in the population. ............................................% [3]

Mark scheme: 9 (a) 105 806 1 (b) 1.03 × 105 1 (c) (i) 46 100 1 (ii) 100 1 (iii) 6.82 × 106 2 B1 for figs 682  30 851  (d) 1.47 or 1.466 to 1.467 3 M2 for  − 1  [×100] oe soi by 0.0146….  30 405  or 0.0147  30 851 or  × 100 [–100] oe soi by 101.46….  30 405  or 101.47  30 851  or M1 for   soi by 1.0146……. or 1.0147  30 405  Alternative method 30 851 − 30 405 M2 for [× 100 ] oe soi by 0.0146…. 30 405 or 0.0147 or B1 for 30 851 – 30 405 soi by 446

More questions on Standard form

10 The scale drawing shows the positions of two towns, X and Y. The scale is 1 centimetre represents 5 kilometres. North X North Y Scale: 1 cm to 5 km (a) Work out the actual distance from town X to town Y. .......................................... km [2] (b) Measure the bearing of town X from town Y. ................................................ [1] (c) An airport, A, is 22.5 km from town Y on a bearing of 050°. Mark and label the position of A on the scale drawing. [2]

Mark scheme: 10 (a) 35 2 B1 for 7 (b) 305 1 (c) Point marked in correct 2 B1 for point at 4.5 cm or 050 ° from Y position

More questions on Scale drawings