Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 May/June Paper 1 · 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 56. MATHEMATICS 0581/13 Paper 1 (Core) May/June 2014 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) This document consists of 11 printed pages and 1 blank page. [Turn over IB14 06_0581_13/RP © UCLES 2014 *1659043106* Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education PAPA CAMBRIDGE

2 0581/13/M/J/14 © UCLES 2014 1 –3°C 8°C –19°C 42°C –7°C Write down the lowest temperature from this list. Answer … °C [1] __________________________________________________________________________________________ 2 Change 6450 cm into metres. Answer … m [1] __________________________________________________________________________________________ 3 52° x° NOT TO SCALE In the diagram, a straight line intersects two parallel lines. Find the value of x. Answer x = … [1] __________________________________________________________________________________________ 4 Calculate. 0.2 56.2 34.8 - - Answer … [1] __________________________________________________________________________________________ 5 Write down the value of 70. Answer … [1] __________________________________________________________________________________________

3 0581/13/M/J/14 © UCLES 2014 [Turn over 6 Write 45 000 in standard form. Answer … [1] __________________________________________________________________________________________ 7 Four faces of a cube are drawn on the grid. Complete the net of this cube. [1] __________________________________________________________________________________________ 8 Write down all the prime numbers that are greater than 30 and less than 40. Answer … [1] __________________________________________________________________________________________ 9 a = 4 3 - e o b = 2 6 e o Write each of the following as a single vector. (a) 2a Answer(a) f p [1] (b) a – b Answer(b) f p [1] __________________________________________________________________________________________

4 0581/13/M/J/14 © UCLES 2014 10 (a) 1 4 8 12 27 40 Write down the number from this list which is both a cube number and has a factor of 4. Answer(a) … [1] (b) 1258 is a multiple of 34. Write down a different multiple of 34 between 1200 and 1300. Answer(b) … [1] __________________________________________________________________________________________ 11 –3 –5 1 0 3 Three different numbers from the list are added together to give the smallest possible total. Complete the sum below. … + … + … = … [2] __________________________________________________________________________________________ 12 The area of a square is 36 cm2. Calculate the perimeter of this square. Answer … cm [2] __________________________________________________________________________________________ 13 The mean of fi ve numbers is 6. Four of the numbers are 3, 4, 5, and 10. Work out the number that is missing from the list. Answer … [2] __________________________________________________________________________________________

5 0581/13/M/J/14 © UCLES 2014 [Turn over 14 Find the value of 3a – 5b when a = –4 and b = 2 . Answer … [2] __________________________________________________________________________________________ 15 Celine buys a bag of 24 tulip bulbs. There are 8 red bulbs and 5 white bulbs. All of the other bulbs are yellow. Celine chooses a bulb at random from the bag. (a) Write down the probability that the bulb is red or white. Answer(a) … [1] (b) Write down the probability that the bulb is yellow. Answer(b) … [1] __________________________________________________________________________________________ 16 Find the fraction that is half-way between 2 1 and 3 2 . Answer … [2] __________________________________________________________________________________________

6 0581/13/M/J/14 © UCLES 2014 17 Using a straight edge and compasses only, construct the perpendicular bisector of AB. All construction arcs must be clearly shown. A B [2] __________________________________________________________________________________________ 18 Michelle sells ice cream. The table shows how many of the different fl avours she sells in one hour. Flavour Vanilla Strawberry Chocolate Mango Number sold 6 8 9 7 Michelle wants to show this information in a pie chart. Calculate the sector angle for mango. Answer … [2] __________________________________________________________________________________________

7 0581/13/M/J/14 © UCLES 2014 [Turn over 19 Chris changes $1350 into euros (€) when €1 = $1.313 . Calculate how much he receives. Answer € … [2] __________________________________________________________________________________________ 20 A y x 7 6 5 4 3 2 1 –1 –2 –3 0 –1 1 2 3 4 5 –2 –3 –4 –5 –6 –7 Draw the image of triangle A after a translation by the vector 4 3 - e o. [2] __________________________________________________________________________________________

8 0581/13/M/J/14 © UCLES 2014 21 Each exterior angle of a regular polygon is 30°. Work out the number of sides the polygon has. Answer … [2] __________________________________________________________________________________________ 22 46° 74° 60° 46° x° 9.65 cm 9.65 cm 8.69 cm 7.22 cm y cm NOT TO SCALE These two triangles are congruent. Write down the value of (a) x, Answer(a) x = … [1] (b) y. Answer(b) y = … [1] __________________________________________________________________________________________

9 0581/13/M/J/14 © UCLES 2014 [Turn over 23 Without using a calculator, work out 1 4 1 – 9 7 . Write down all the steps in your working. Answer … [3] __________________________________________________________________________________________ 24 Solve the simultaneous equations. 2x + 3y = 29 5x + y = 27 Answer x = … y = … [3] __________________________________________________________________________________________

10 0581/13/M/J/14 © UCLES 2014 25 10 00 10 04 10 08 10 12 10 16 Time Distance (km) 10 20 10 24 10 28 10 32 4 3 2 1 0 Town Home William Toby Toby and William cycled into town. Their journeys are shown on the travel graph. (a) For how many minutes did Toby stop on his journey into town? Answer(a) … min [1] (b) Explain what happened at 10 20. Answer(b) … [1] (c) Work out how long William took to cycle into town. Answer(c) … min [1] (d) Calculate William’s speed in km/h. Answer(d) … km/h [2] __________________________________________________________________________________________

11 0581/13/M/J/14 © UCLES 2014 [Turn over 26 (a) Factorise completely. 15a3 – 5ab Answer(a) … [2] (b) Simplify. 3x2y3 × x4y Answer(b) … [2] (c) Multiply out the brackets and simplify. 3(x – 2) – 4(2x – 3) Answer(c) … [2] (d) Solve the equation. 8x + 9 = 3(x + 8) Answer(d) x = … [3] __________________________________________________________________________________________

12 0581/13/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. BLANK PAGE

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0581 MATHEMATICS 0581/13 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 13 © 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 Question Answers Mark Part Marks 1 –19 1 2 64.5[0] 1 3 128 1 4 −107 1 5 1 1 6 4.5 × 104 1 7 Cube net drawn correctly 1 8 31, 37 1 9 (a) (b)      − 8 6       − − 2 5 1 1 10 (a) (b) 8 1224 or 1292 1 1 11 –3, –5, 0 [=] –8 2 B1 for –3, –5 and 0 in any order seen on left hand side. or B1 for –8 seen on answer line in correct position 12 24 2 M1 for √36 × 4 oe or B1 for 6 seen 13 8 2 B1 for 6 × 5 or better 14 –22 2 M1 for 3×(–4) –5×2 or B1 for −12 or −10 seen in the working.

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 13 © Cambridge International Examinations 2014 15 (a) (b) 24 13 oe 24 11 oe 1 1 16 12 7 oe 2 B1 for 6 7 or ( 6 3 and 6 4 ) or 12 6 and12 8 etc., or 6 5.3 17 Perpendicular bisector with 2 pairs of correct arcs. 2 B1 for correct line or B1 for 2 pairs of correct arcs 18 84 2 M1 for 7 9 8 6 7 + + + or 7 9 8 6 360 + + + 19 1030 2 M1 for 1350 ÷ 1.313 20 Triangle at ( 2, −1) ( 2, 1) ( 1, −2) 2 B1 for translation by       −4 k or       k 3 21 12 2 M1 for 360 ÷ 30 22 (a) (b) 74 8.69 1 1

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 13 © Cambridge International Examinations 2014 23 4 5 oe 9 4 9 5 × × and 4 9 4 7 × × oe or better 36 17 oe working must be shown B1 M1 A1 Do not allow decimals for the B1, M1 or A1 e.g. 36 45 and 36 28 Follow through their 4 5 for the M1 mark. Alt method 1: B1 for 9 2 4 1 + M1 for 9 4 4 2 and 9 4 9 1 × × × × oe e.g. 36 8 and 36 9 Alt method 2: B1 for 1 9 7 4 1 + − M1 for oe e.g. 36 8 and 36 9 ISW converting fraction answer to decimal. 24 x = 4 y = 7 3 M1 for correct method to eliminate one variable or (substitution) correct rearrangement of one equation seen substituted into the second equation. A1 for one correct answer. If M0 SC1 for both answers satisfying one of the original equations 25 (a) (b) (c) (d) 6 They are at the same place at the same time 16 15 cao 1 1 1 2 M1 FT for 60 ) ( 4 × c their oe

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 13 © Cambridge International Examinations 2014 26 (a) 5a(3a2−b) 2 B1 for a(15a2 − 5b) or 5(3a3− ab) (b) 3x6 y4 2 B1 for x6 or y4 in a product on answer line (c) 6 – 5x as final answer nfww 2 B1 for 3x – 6 or – 8x + 12 seen or SC1 for 6 or – 5x seen in final answer nfww (d) 3 nfww 3 M2 for 5x = 15 or B1 for 3x +24 seen or M1 for 8x – 3x = 3 × 8 − 9 or better. If zero, SC1 for answer [x =] 5 1 −