Cambridge IGCSE Mathematics 0580 — 2014 May/June Paper 3 · Variant 3

3 The Wong family spend the day at the zoo. (a) The Wong family has 2 adults and 3 children aged 2, 5 and 11 years old. Admission Adults $8.50 Children 11-16 years $6.00 Children 3-10 years $4.50 Children under 3 years FREE Mr Wong pays for his family to go into the zoo using a $50 note. Work out the change he receives. Answer(a) $ ................................................ [3] (b) The dolphin show fi nishes at 11 05. It lasts for 1 hour and 20 minutes. Write down the time the dolphin show starts. Answer(b) ................................................ [1] (c) Torty the tortoise was born on 27 December 1898. Work out how many years old she was on 3 January 2003. Answer(c) ....................................... years [1] (d) Last year, the ratio snakes : lizards = 3 : 5 . There were 45 lizards. (i) Work out how many snakes there were last year. Answer(d)(i) ................................................ [2] (ii) This year, there are 3 more snakes and the same number of lizards. Write down the new ratio snakes : lizards. Give your answer in its simplest form. Answer(d)(ii) ....................... : ....................... [2] (e) Mr Wong hires a vehicle to drive around the zoo. The cost is $25 for the fi rst hour and $7.50 for every extra half hour. He pays $85 altogether. For how long does he hire the vehicle? Answer(e) ...................................... hours [3] (f) Mrs Wong wants to buy some food for the giraffes. Small Bag Medium Bag Large Bag 225g 250g 325g 60 cents 70 cents 90 cents Work out which bag is the best value for money. Show how you decide. Answer(f) ................................................ [3] (g) The diagram shows a map of the zoo. The scale is 1 centimetre represents 50 metres. North Entrance Scale: 1 cm to 50 m Flamingos North Exit (i) Measure the bearing of the fl amingos from the entrance. Answer(g)(i) ................................................ [1] (ii) Xanthe looks after all the animals within 200 m of the exit. Draw accurately the locus of points inside the zoo which are 200 m from the exit. [2] (iii) A shop, S, is on a bearing of 212° from the entrance and a bearing of 293° from the exit. Mark the point S on the map. [3] __________________________________________________________________________________________

Mark scheme: 3 (a) 22.5[0] 3 M1 for (2 × 8.5 + 6 + 4.50) M1 for 50 – their total (b) [0]9 45 1 (c) 104 1 45 (d) (i) 27 2 M1 for × 3 5 (ii) 2 : 3 cao 2 M1 for (their 27 + 3) : 45 or better If zero SC1 for 3 : 2 85− 25 (e) 5 3 M1 for soi by 8 7.50 their 8 M1 for + 1 2 (f) 3.75, 3.57... 3.61... [g / c] 3 M1 for 1 correct division, not evaluated small [bag] M1 for 2 further consistent correct divisions, not evaluated (g) (i) 105 1 (ii) correct locus drawn 2 M1 for any arc centre exit (iii) S marked correctly 3 B1 for indication of bearing of 212° B1 for indication of bearing of 293°

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4 The ages of 15 children who go to a swimming club are shown below. 10 11 10 12 12 13 11 12 12 12 12 10 11 11 11 (a) Complete the frequency table. You may use the tally column to help you. Age Tally Frequency 10 11 12 13 [2] (b) For the ages of the 15 children, fi nd (i) the range, Answer(b)(i) ................................................ [1] (ii) the mode, Answer(b)(ii) ................................................ [1] (iii) the median, Answer(b)(iii) ................................................ [1] (iv) the mean. Answer(b)(iv) ................................................ [2] (c) One child is chosen at random from the group. Write down the probability that the child’s age is (i) 10, Answer(c)(i) ................................................ [1] (ii) more than 13. Answer(c)(ii) ................................................ [1] __________________________________________________________________________________________

Mark scheme: 4 (a) Frequencies 3, 5, 6, 1 2 B1 for 4 frequencies adding to 15 and at least two correct values or B1 for three correct values SC1 for fully correct tallies and nothing in frequency column. (b) (i) 3 1 (ii) 12 1 (iii) 11 1 (iv) 11.3 (…) 2 M1 for (10 × their 3 +11 × their 5 + 12 × their 6 +13 × their 1)÷15 3 1 (c) (i) or or 0.2 1FT isw 15 5 (ii) 0 1 IGCSE – May/June 2014 0580 33

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5 (a) (i) Write down the name of a solid which is not a prism. Answer(a)(i) ................................................ [1] (ii) A prism has a cross-sectional area, A, and height, h. Write down an expression, in terms of A and h, for the volume of the prism. Answer(a)(ii) ................................................ [1] (b) The volume, V, of a cylinder with radius r and height h is V = πr2h . (i) Calculate the volume of a cylinder with radius 3 cm and height 12 cm. Answer(b)(i) ......................................... cm3 [2] (ii) Ravi puts 150 identical marbles in the cylinder. He fi lls the cylinder to the top with 160 cm3 of water. Find the volume of one marble. Give your answer correct to 2 signifi cant fi gures. Answer(b)(ii) ......................................... cm3 [4] (iii) Make r the subject of the formula V = πr2h . Answer(b)(iii) r = ................................................ [2] __________________________________________________________________________________________

Mark scheme: 5 (a) (i) one of e.g. cone, sphere, pyramid 1 (ii) Ah 1 (b) (i) 339 2 M1 π × 32 × 12 their 339 - 160 (ii) 1.2 cao 4 M2 FT for soi 150 or M1 FT for their 339 – 160 soi A1 for 1.19... If A0 scored then B1 for correct rounding of their 3 sig fig or more answer. v v (iii) r = 2 M1 for r2 = πh πh

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6 y 6 5 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 (a) On the grid, draw the graphs of (i) y = 5, [1] (ii) x = –3. [1] (b) (i) Write down the co-ordinates of the point of intersection of y = 5 and x = –3. Answer(b)(i) (...................... , ......................) [1] (ii) Write down the equation of a line parallel to y = 5. Answer(b)(ii) ................................................ [1] (c) (i) Complete the table of values for the function y = x2 – 3x . x –2 –1 0 1 2 3 4 5 y 4 0 0 4 [2] (ii) On the grid, draw the graph of y = x2 – 3x for –2 Y x Y 5 . y 11 10 9 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 [4] (iii) Write down the co-ordinates of the lowest point of the graph. Answer(c)(iii) (...................... , ......................) [1] __________________________________________________________________________________________

Mark scheme: 6 (a) (i) y = 5 drawn 1 (ii) x = –3 drawn 1 (b) (i) (–3, 5) cao 1 (ii) y = k oe 1 k ≠ 5 (c) (i) 10, –2 –2, 10 2 B1 for 3 correct (ii) 8 correct points plotted 3FT B2 FT for 6 or 7 correctly plotted points or B1 FT for 4 or 5 correctly plotted points correct curve drawn 1 For smooth correct curve, going below y = –2 (iii) (1.5 cao, k ) 1 where –2.5 < k < –2 IGCSE – May/June 2014 0580 33

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7 Today it is Simon’s birthday. (a) Simon is x years old. Katy is twice as old as Simon. Bob is 8 years younger than Simon. (i) Write expressions, in terms of x, for the ages of Katy and Bob. Answer(a)(i) Katy ................................................ Bob ................................................ [2] (ii) The sum of their three ages is 40 years. Write an equation in terms of x. Answer(a)(ii) ................................................ [1] (iii) Solve your equation for x. Answer(a)(iii) x = ................................................ [2] (b) Simon’s birthday cake weighs 600 grams. 1 He eats of the cake. 8 Katy eats 25% of the cake. Bob eats 0.3 of the cake. Find the weight of the cake that is left. Answer(b) ............................................. g [4] (c) Aunty Millie gives Simon $150 for his birthday. He invests the money in a bank at a rate of 6% per year compound interest. Calculate the total amount Simon will have after 3 years. Answer(c) $ ................................................. [3] (d) One of Simon’s presents is a bag of sweets. He decides to eat the sweets in a sequence. On day 1 he eats 1 sweet, on day 2 he eats 5 sweets, on day 3 he eats 9 sweets and so on. (i) Describe in words the rule for continuing the sequence 1, 5, 9, 13, 17 ..... . Answer(d)(i) ................................................................................................................................ [1] (ii) Write down an expression for the number of sweets he eats on day n. Answer(d)(ii) ................................................ [2] __________________________________________________________________________________________

Mark scheme: 7 (a) (i) 2x 1, 1 x – 8 (ii) x + 2x + x – 8 = 40 or better 1FT FT if algebraic (iii) 12 cao 2 M1 FT for ax = b and a and b not zero (b) 195 cao 4 B1 for 75 B1 for 150 B1 for 180 (c) 178.65 3 M2 for 150 × 1.063 oe or 178.7 or or 179 M1 for 150 × 1.06 × 1.06 (d) (i) Add 4 oe 1 (ii) 4n – 3 oe, final answer 2 M1 for 4n + k (k not -3), qn–3 (q not 0 or 4) seen

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8 (a) NOT TO SCALE h 10 cm The triangle has an area of 30 cm2 and a base of 10 cm. Calculate the perpendicular height h of the triangle. Answer(a) h = ......................................... cm [2] (b) D 8 cm C NOT TO SCALE 7 cm A B 14 cm AB is parallel to CD. AB is 14 cm and CD is 8 cm. The perpendicular distance between AB and CD is 7 cm. (i) Write down the mathematical name for the quadrilateral ABCD. Answer(b)(i) ................................................ [1] (ii) Calculate the area of ABCD. Answer(b)(ii) ......................................... cm2 [2] (c) An isosceles triangle has an angle of 40°. Tikka draws the triangle with angles 40°, 70° and 70°. Kanwarpreet draws a different correct triangle. What angles did Kanwarpreet use? Answer(c) 40°, .............. , .............. [2] __________________________________________________________________________________________ Question 9 is printed on the next page.

Mark scheme: 8 30× 2 (a) 6 2 M1 for oe or better 10 (b) (i) Trapezium 1 (14 + 8) (ii) 77 2 M1 for × 7 oe 2 (c) [40], 40, 100 1, 1

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9 C NOT TO A SCALE O B The diagram shows a circle with diameter AB and centre O. C is a point on the circumference of the circle. (a) Explain how you know that angle ACB is 90° without having to measure it. Answer(a) ........................................................................................................................................... [1] (b) AB = 13 cm and AC = 5 cm. Calculate the length BC. Answer(b) BC = .......................................... cm [3] (c) Calculate angle ABC. Answer(c) Angle ABC = ................................................ [2]

Mark scheme: 9 (a) Angle [in the] semi-circle [equals 1 90U] (b) 12 3 M2 for [BC == √(13 2 – 5 2) or better or M1 for 5 2 + BC 2 = 13 2 or better –1 5 (c) 22.6 2 M1FT for tan their 12 or –1 5 M1 for sin 13 or –1 their 12 M1FT for cos 13

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