Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 May/June Paper 1 · Variant 1

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 56. MATHEMATICS 0581/11 Paper 1 (Core) May/June 2014 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education This document consists of 12 printed pages. [Turn over IB14 06_0581_11/RP © UCLES 2014 *3049769181* PAPA CAMBRIDGE

2 0581/11/M/J/14 © UCLES 2014 1 Work out. 10 – 3 × 2 Answer … [1] __________________________________________________________________________________________ 2 Write down the prime numbers between 20 and 30. Answer … [1] __________________________________________________________________________________________ 3 NOT TO SCALE 163° 59° x° (a) Find the value of x. Answer(a) x = … [1] (b) One of the angles is 163°. What type of angle is this? Answer(b) … [1] __________________________________________________________________________________________ 4 A city has a population of fi ve hundred and six thousand. Write the size of the population (a) in fi gures, Answer(a) … [1] (b) in standard form. Answer(b) … [1] __________________________________________________________________________________________

3 0581/11/M/J/14 © UCLES 2014 [Turn over 5 p = 16.83 4.8 1.98276 # (a) In the spaces provided, write each number in this calculation correct to 1 signifi cant fi gure. Answer(a) … × … … [1] (b) Use your answer to part (a) to estimate the value of p. Answer(b) … [1] __________________________________________________________________________________________ 6 Solve the equation. 8 n 2 - = 11 Answer n = … [2] __________________________________________________________________________________________ 7 a = 3 - 4 e o b = 1 5 - e o Work out a – 2b. Answer f p [2] __________________________________________________________________________________________ 8 The width, w cm, of a carpet is 455 cm, correct to the nearest centimetre. Complete the statement about the value of w. Answer … Ğ w < … [2] __________________________________________________________________________________________

4 0581/11/M/J/14 © UCLES 2014 9 y = 2 x x 2 + 2 2 Find the value of y when x = 6. Give your answer as a mixed number in its simplest form. Answer y = … [2] __________________________________________________________________________________________ 10 Use your calculator to work out 4 3 + 2–1. Give your answer correct to 2 decimal places. Answer … [2] __________________________________________________________________________________________ 11 The diagram shows a cuboid. 8 cm 15 cm h NOT TO SCALE The volume of this cuboid is 720 cm3. The width is 8 cm and the length is 15 cm. Calculate h, the height of the cuboid. Answer h = … cm [2] __________________________________________________________________________________________

5 0581/11/M/J/14 © UCLES 2014 [Turn over 12 The scatter diagram shows the rainfall and the average temperature in a city for the month of June, over a period of 10 years. 30 25 20 15 10 5 0 5 10 15 Rainfall (cm) Temperature (°C) 20 25 30 (a) What type of correlation does this scatter diagram show? Answer(a) … [1] (b) Describe the relationship between the rainfall and the average temperature. Answer(b) … … [1] __________________________________________________________________________________________

6 0581/11/M/J/14 © UCLES 2014 13 The graph can be used to convert between miles and kilometres. 80 70 60 50 40 30 20 10 0 10 20 30 Miles Kilometres 40 50 A train travels 24 miles in 20 minutes. Find its average speed in kilometres per hour. Answer … km/h [2] __________________________________________________________________________________________

7 0581/11/M/J/14 © UCLES 2014 [Turn over 14 127° a° b° A D E B C NOT TO SCALE The diagram shows an isosceles triangle ABC. DCB is a straight line and is parallel to AE. Angle DCA = 127°. Find the value of (a) a, Answer(a) a = … [2] (b) b. Answer(b) b = … [1] __________________________________________________________________________________________ 15 Carlo changed 800 euros (€) into dollars for his holiday when the exchange rate was €1 = $1.50 . His holiday was then cancelled. He changed all his dollars back into euros and he received €750. Find the new exchange rate. Answer €1 = $ … [3] __________________________________________________________________________________________

8 0581/11/M/J/14 © UCLES 2014 16 (a) Simplify the expressions. (i) p 3 × p 7 Answer(a)(i) … [1] (ii) t 5 ÷ t 8 Answer(a)(ii) … [1] (b) (h3) k = h12 Find the value of k. Answer(b) k = … [1] __________________________________________________________________________________________ 17 O P R Q 17 cm 9 cm NOT TO SCALE The diagram shows a circle, centre O. P, Q and R are points on the circumference. PQ = 17 cm and QR = 9 cm. (a) Explain why angle PQR is 90°. Answer(a) … … [1] (b) Calculate the length PR. Answer(b) PR = … cm [2] __________________________________________________________________________________________

9 0581/11/M/J/14 © UCLES 2014 [Turn over 18 In this question, do not use your calculator and show all the steps in your working. (a) Show that 3 5 1 – 2 8 5 = 40 23 . Answer(a) [2] (b) Work out 8 7 ÷ 40 23 . Give your answer as a mixed number in its simplest form. Answer(b) … [2] __________________________________________________________________________________________ 19 The table shows the average monthly temperature (°C) for Fairbanks, Alaska. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temperature (°C) –23.4 –19.8 –11.7 –0.8 9.2 15.4 16.9 13.8 7.5 –5.8 –21.4 –21.8 (a) Find (i) the difference between the highest and the lowest temperatures, Answer(a)(i) … °C [1] (ii) the median. Answer(a)(ii) … °C [2] (b) A month is chosen at random from the table. Find the probability that its average temperature is below zero. Answer(b) … [1] __________________________________________________________________________________________

10 0581/11/M/J/14 © UCLES 2014 20 A bus company in Dubai has the following operating times. Day Starting time Finishing time Saturday 06 00 24 00 Sunday 06 00 24 00 Monday 06 00 24 00 Tuesday 06 00 24 00 Wednesday 06 00 24 00 Thursday 06 00 24 00 Friday 13 00 24 00 (a) Calculate the total number of hours that the bus company operates in one week. Answer(a) … h [3] (b) Write the starting time on Friday in the 12-hour clock. Answer(b) … [1] __________________________________________________________________________________________

11 0581/11/M/J/14 © UCLES 2014 [Turn over 21 The diagram shows a circle inside a square. The circumference of the circle touches all four sides of the square. (a) Calculate the area of the circle when the side of the square is 15 cm. Answer(a) … cm2 [2] (b) Draw all the lines of symmetry on the diagram. [2] __________________________________________________________________________________________ Question 22 is printed on the next page.

12 0581/11/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. 22 B C A 27 m 34 m North NOT TO SCALE In the diagram, B is 27 metres due east of A. C is 34 metres from A and due south of B. (a) Using trigonometry, calculate angle ACB. Answer(a) Angle ACB = … [2] (b) Find the bearing of C from A. Answer(b) … [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0581 MATHEMATICS 0581/11 Paper 1 (Core), maximum raw mark 56 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 11 © 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. Part Answers Mark Part Marks 1 4 1 2 23 29 1 3 (a) 138 1 (b) Obtuse 1 4 (a) 506 000 1 (b) 5.06 × 105 1FT Follow through their part (a) 5 (a) 20 2 5× 1 (b) 0.5 or 2 1 cao 1 6 30 2 M1 for n – 8 = 22 or 15 2 = n 7           −13 6 2 B1 for each component or for      − 10 2 or       −10 2 seen 8 454.5 455.5 1, 1 SC1 for both correct but reversed 9 18 1 18 2 M1 for 2 36 36 2 + or better 10 1.37 2 B1 for 0.866… or 2 3 or 0.5 or 2 1 or B1 for 1.366… as final answer 11 6 2 M1 for 720 = 8 × 15 × h or better

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 11 © Cambridge International Examinations 2014 12 (a) Negative 1 (b) More rain [suggests] lower temperature oe 1 13 114 to 117 2 B1 for 38 to 39 seen or 72 [mph] 14 (a) 74 2 M1 Angle B = 180 – 127 (b) 53 1FT 127 – their part (a) 15 1.6[0] 3 M1 for 800 × 1.5 and M1 for their 1200 ÷ 750 16 (a) (i) p10 1 (ii) t−3 or 3 1 t 1 (b) 4 1 17 (a) Angle [in a] semi-circle 1 (b) 19.2 or 19.23 to 19.24 2 M1 for 172 + 92 18 (a) 5 16 and 8 21 oe 40 8 and 40 25 oe M1 40 105 40 128 − oe 40 25 40 8 40 40 − + oe M1 or 40 21 5 40 16 8 their their × − × oe with numerators evaluated (b) 23 40 8 7 × oe M1 23 12 1 cao A1 19 (a) (i) 40.3 1 (ii) −3.3 2 M1 for attempt at ordering seen (b) 12 7 oe isw 1

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 11 © Cambridge International Examinations 2014 20 (a) 119 3 M2 for 18 × 6 + 11 oe or B1 for 18 or 11 or 108 (b) [0]1 [00] pm cao 1 21 (a) 177 or 176.7 to 176.74 2 M1 for π × 7.52 (b) 4 correct lines of symmetry drawn 2 B1 for 2 correct and no extra lines 22 (a) 52.6 2 M1 for sin [ ] = 34 27 (b) 127 or 127.4[…] 2FT 180 – their part (a) B1 for [BAC =] 90 − their part (a)