Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 May/June Paper 3 · Variant 3

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fl uid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specifi ed in the question, and if the answer is not exact, give the answer to three signifi cant fi gures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 104. MATHEMATICS 0581/33 Paper 3 (Core) May/June 2014 2 hours Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) This document consists of 16 printed pages. [Turn over IB14 06_0581_33/FP © UCLES 2014 *8295047221* Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education PAPA CAMBRIDGE

2 0581/33/M/J/14 © UCLES 2014 1 (a) D A B C y x 7 6 5 4 3 2 1 –1 –2 –3 –4 0 –1 1 2 3 4 5 6 –2 –3 –4 Four shapes, A, B, C and D, are shown on the grid. Describe fully the single transformation that maps shape A onto (i) shape B, Answer(a)(i) … … [2] (ii) shape C, Answer(a)(ii) … … [3] (iii) shape D. Answer(a)(iii) … … [3]

3 0581/33/M/J/14 © UCLES 2014 [Turn over (b) (i) Shade in one more square so that this shape has rotational symmetry of order 2. [1] (ii) Refl ect this shape in the line of symmetry shown. [2] __________________________________________________________________________________________

4 0581/33/M/J/14 © UCLES 2014 2 A group of students take part in their school’s sports day. (a) (i) The length, l m, that Anna throws the javelin is 23.6 metres correct to the nearest 10 centimetres. Complete the statement about l. Answer(a)(i) … Y l < … [2] (ii) Billy throws the hammer a distance of 8 metres on his fi rst throw. His second throw is 15% further. Calculate the distance of his second throw. Answer(a)(ii) … m [2] (iii) Carl runs 100 metres at a speed of 8 m/s. Calculate the time it takes him to run 100 m. Answer(a)(iii) … s [1] (iv) Change Carl’s speed of 8 m/s into km/h. Answer(a)(iv) … km/h [2] (b) Ten students take part in both the long jump and 100 m hurdles competitions. The results are shown in the table below. Student A B C D E F G H I J Distance in long jump (metres) 3.25 3.60 3.75 3.90 4.10 4.20 4.30 4.40 4.65 4.70 Time for 100 m hurdles (seconds) 17.3 17.4 16.7 16.1 16.5 15.8 15.3 14.8 15.5 15.0

5 0581/33/M/J/14 © UCLES 2014 [Turn over (i) Complete the scatter diagram. The fi rst six points have been plotted for you. 18.0 17.0 16.0 15.0 14.0 3.5 4.0 4.5 5.0 5.5 3.0 Distance in long jump (metres) Time for 100 m hurdles (seconds) [2] (ii) What type of correlation does this scatter diagram show? Answer(b)(ii) … [1] (iii) Describe the relationship between the distance in the long jump and the time for the 100 m hurdles. Answer(b)(iii) … [1] (iv) On the grid, draw the line of best fi t. [1] (v) Another student jumps 3.50 m in the long jump. Use your line of best fi t to estimate the time for this student in the 100 m hurdles. Answer(b)(v) … s [1] (vi) A different student jumps 5.20 m in the long jump. Explain why you should not use your scatter diagram to estimate their time in the 100 m hurdles. Answer(b)(vi) … [1] __________________________________________________________________________________________

6 0581/33/M/J/14 © UCLES 2014 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]

7 0581/33/M/J/14 © UCLES 2014 [Turn over (f) Mrs Wong wants to buy some food for the giraffes. Small Bag 225g 60 cents Medium Bag 250g 70 cents Large Bag 325g 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 Flamingos North Exit Scale: 1 cm to 50 m (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] __________________________________________________________________________________________

8 0581/33/M/J/14 © UCLES 2014 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] __________________________________________________________________________________________

9 0581/33/M/J/14 © UCLES 2014 [Turn over 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] __________________________________________________________________________________________

10 0581/33/M/J/14 © UCLES 2014 6 y x 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 0 –1 1 2 3 4 5 6 –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]

11 0581/33/M/J/14 © UCLES 2014 [Turn over (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 x 11 10 9 8 7 6 5 4 3 2 1 –1 –2 –3 –4 0 –1 1 2 3 4 5 6 –2 –3 [4] (iii) Write down the co-ordinates of the lowest point of the graph. Answer(c)(iii) (… , …) [1] __________________________________________________________________________________________

12 0581/33/M/J/14 © UCLES 2014 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. He eats 8 1 of the cake. 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]

13 0581/33/M/J/14 © UCLES 2014 [Turn over (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] __________________________________________________________________________________________

14 0581/33/M/J/14 © UCLES 2014 8 (a) h 10 cm NOT TO SCALE 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) NOT TO SCALE D C A B 8 cm 14 cm 7 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]

15 0581/33/M/J/14 © UCLES 2014 [Turn over (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.

16 0581/33/M/J/14 © UCLES 2014 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 9 A C B O NOT TO SCALE 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]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0581 MATHEMATICS 0581/33 Paper 3 (Paper 3), maximum raw mark 104 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. PAPA CAMBRIDGE

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 33 © Cambridge International Examinations 2014 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Qu. Answers Mark Part Marks 1 (a) (i) reflection y = –x oe 1 1 (ii) rotation [centre] (3, 2) 90° anticlockwise oe 1 1 1 (iii) Enlargement [Scale factor] 2 [Centre] (3,–3) 1 1 1 (b) (i) shaded square correct 1 (ii) Correct reflection 2 B1 for 7 or 8 corners correctly marked 2 (a) (i) 23.55, 23.65 2 B1 for 1 correct or both in reverse order (ii) 9.2[0] 2 M1 for 8 × 1.15 oe (iii) 12.5 1 (iv) 28.8 2 M1 for 1000 60 60 8 × × or better (b) (i) 4 points correct 2 B1 for 3 correct (ii) Negative 1 (iii) the longer the distance, the quicker the time oe 1 Or the shorter the distance the longer the time oe (iv) continuous ruled line of best fit 1 Dependent on at least 9 points on graph (v) 17.0 to 17.5 1FT FT dependent on negative line (vi) Outside the range [of the data] oe 1

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 33 © Cambridge International Examinations 2014 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 (d) (i) 27 2 M1 for 3 5 45 × (ii) 2 : 3 cao 2 M1 for (their 27 + 3) : 45 or better If zero SC1 for 3 : 2 (e) 5 3 M1 for 7.50 25 85− soi by 8 M1 for 1 2 8 + their (f) 3.75, 3.57... 3.61... [g / c] small [bag] 3 M1 for 1 correct division, not evaluated 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° 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 (c) (i) 15 3 or 5 1 or 0.2 1FT isw (ii) 0 1

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 33 © Cambridge International Examinations 2014 5 (a) (i) one of e.g. cone, sphere, pyramid 1 (ii) Ah 1 (b) (i) 339 2 M1 π × 32 × 12 (ii) 1.2 cao 4 M2 FT for 150 160 - 339 their soi 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. (iii) r = h v π 2 M1 for r2 = h v π 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 correct curve drawn 3FT 1 B2 FT for 6 or 7 correctly plotted points or B1 FT for 4 or 5 correctly plotted points For smooth correct curve, going below y = –2 (iii) (1.5 cao, k ) 1 where –2.5 < k < –2

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 33 © Cambridge International Examinations 2014 7 (a) (i) 2x x – 8 1, 1 (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 or 178.7 or 179 3 M2 for 150 × 1.063 oe or 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 8 (a) 6 2 M1 for 10 2 30× oe or better (b) (i) Trapezium 1 (ii) 77 2 M1 for 2 ) 8 14 ( + × 7 oe (c) [40], 40, 100 1, 1 9 (a) Angle [in the] semi-circle [equals 90U] 1 (b) 12 3 M2 for [BC == √(13 2 – 5 2) or better or M1 for 5 2 + BC 2 = 13 2 or better (c) 22.6 2 M1FT for tan –1 12 5 their or M1 for sin –1 13 5 or M1FT for cos –1 13 12 their