Cambridge IGCSE Mathematics 0580 — 2015 May/June Paper 1 · Variant 2

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 fluid. 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 specified in the question, and if the answer is not exact, give the answer to three significant figures. 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 0580/12 Paper 1 (Core) May/June 2015 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) Cambridge International Examinations Cambridge International General Certificate of Secondary Education This document consists of 11 printed pages and 1 blank page. The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate. [Turn over DC (LK/SG) 103619/1 © UCLES 2015 CANDIDATE NAME CENTRE NUMBER CANDIDATE NUMBER * 9 3 8 0 7 5 3 2 6 8 *

2 0580/12/M/J/15 © UCLES 2015 1 A doctor starts work at 20 40 and finishes work at 06 10 the next day. How long is the doctor at work? Give your answer in hours and minutes. Answer … h … min [1] __________________________________________________________________________________________ 2 Write 53 400 000 in standard form. Answer … [1] __________________________________________________________________________________________ 3 Write down the gradient of the line y = –3x + 4. Answer … [1] __________________________________________________________________________________________ 4 Simplify 5x0. Answer … [1] __________________________________________________________________________________________ 5 y 0 x What type of correlation is shown on the scatter diagram? Answer … [1] __________________________________________________________________________________________

3 0580/12/M/J/15 © UCLES 2015 [Turn over 6 Write 64% as (a) a decimal, Answer(a) … [1] (b) a fraction in its simplest form. Answer(b) … [1] __________________________________________________________________________________________ 7 Expand the brackets and simplify. 5(x – 3) – 3(x – 5) Answer … [2] __________________________________________________________________________________________ 8 Write the following in order of size, starting with the smallest. 3–2 0.11 17 2 0.011 Answer … < … < … < … [2] smallest __________________________________________________________________________________________ 9 A biased 4-sided dice is rolled. The possible scores are 1, 2, 3 or 4. The probability of rolling a 1, 3 or 4 is shown in the table. Score 1 2 3 4 Probability 0.15 0.3 0.35 Complete the table. [2] __________________________________________________________________________________________

4 0580/12/M/J/15 © UCLES 2015 10 Factorise completely. 3x2y – 5xyz Answer … [2] __________________________________________________________________________________________ 11 A D E B C NOT TO SCALE The diagram shows two straight lines, AE and BD, intersecting at C. Angle ABC = angle EDC. Triangles ABC and EDC are congruent. Write down two properties of line segments AB and DE. Answer AB and DE are … and … [2] __________________________________________________________________________________________ 12 Without using a calculator, work out 5 4 ÷ 2 3 2 . Write down all the steps of your working and give your answer as a fraction in its simplest form. Answer … [3] __________________________________________________________________________________________

5 0580/12/M/J/15 © UCLES 2015 [Turn over 13 A B E D C F G (x – 4) cm (x – 1) cm 7 cm NOT TO SCALE (a) ABCD is a square. Find the value of x. Answer(a) x = … [1] (b) Square ABCD and isosceles triangle EFG have the same perimeter. Work out the length of FG. Answer(b) FG = … cm [2] __________________________________________________________________________________________

6 0580/12/M/J/15 © UCLES 2015 14 Bernard invests $480 at a rate of 4.5% per year compound interest. Calculate the amount he receives at the end of 3 years. Answer $ … [3] __________________________________________________________________________________________ 15 A random sample of 200 families was taken from the families in a city. The number of children in each family was recorded. The results are shown in the table below. Number of children in a family 0 1 2 3 4 5 or more Number of families 25 41 73 42 13 6 (a) Find the relative frequency of families with 2 children. Answer(a) … [1] (b) There are 5400 families in the city. Find an estimate of the number of families with 2 children. Answer(b) … [2] __________________________________________________________________________________________

7 0580/12/M/J/15 © UCLES 2015 [Turn over 16 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 B The diagram shows two points, A and B. (a) Write down the column vector . Answer(a) = f p [1] (b) = 2 5 - e o (i) On the grid, mark the point C. [1] (ii) Write down the co-ordinates of C. Answer(b)(ii) (… , …) [1] __________________________________________________________________________________________

8 0580/12/M/J/15 © UCLES 2015 17 D E A B F C 37° x° y° z° NOT TO SCALE In the diagram, ABF is parallel to EDC. Angle EDA = 37°, angle ADB is a right angle and BC = BD. Find the value of (a) x, Answer(a) x = … [1] (b) y, Answer(b) y = … [1] (c) z. Answer(c) z = … [2] __________________________________________________________________________________________ 18 (a) Write down the next two terms in the following sequence. 73, 66, 59, 52, … , … [2] (b) Write down an expression for the nth term of the sequence in part (a). Answer(b) … [2] __________________________________________________________________________________________

9 0580/12/M/J/15 © UCLES 2015 [Turn over 19 5 m 5 m 8 m 12 m NOT TO SCALE The diagram shows the front face of a barn. The width of the barn is 12 m. The height of the barn is 8 m. The sides of the barn are both of height 5 m. (a) Work out the area of the front face of the barn. Answer(a) … m2 [3] (b) The length of the barn is 15 m. Work out the volume of the barn. Answer(b) … m3 [1] __________________________________________________________________________________________ 15 m NOT TO SCALE

10 0580/12/M/J/15 © UCLES 2015 20 (a) A B C D E ABCDE is a pentagon. Explain why the diagram shows that the sum of the interior angles of a pentagon is 540°. Do not measure any angles. Answer(a)  [1] (b) Two interior angles of a pentagon are 79° and 53°. The other three angles are in the ratio 1 : 3 : 4. Calculate the size of each of these three angles. Answer(b) … , … , … [4] __________________________________________________________________________________________

11 0580/12/M/J/15 © UCLES 2015 21 The average monthly temperatures (°C) in Silvas, Turkey, are shown in the table below. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temperature (°C) – 4 –3 2 8 13 17 19 20 16 11 8 –1 (a) Which month is the coldest? Answer(a) … [1] (b) Work out the difference between the temperature in November and the temperature in December. Answer(b) … °C [1] (c) Find the median temperature. Answer(c) … °C [2] (d) Calculate the mean temperature. Give your answer correct to 2 significant figures. Answer(d) … °C [3] __________________________________________________________________________________________

12 0580/12/M/J/15 © UCLES 2015 BLANK PAGE 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. 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.

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 2015 series 0580 MATHEMATICS 0580/12 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 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0580 12 © Cambridge International Examinations 2015 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 Answer Mark Part marks 1* 9 [h] 30 [min] cao 1 2* 5.34 × 107 1 3 −3 1 4 5 1 5 Negative 1 6 (a) [0].64 1 (b) 25 16 cao 1 7 2x Final answer 2 B1 for 2x + j or kx [+0] as final answer or either 5x − 15 or −3x +15 in working 8 011 .0 0.11 3−2 17 2 2 M1 for correct change to decimals (or %) or B1 for 3 in correct order. 9* 0.2 oe 2 M1 for 1 – (0.15 + 0.3 + 0.35) 10 xy(3x – 5z) final answer 2 B1 for x(3xy – 5yz) or y(3x2 – 5xz) 11* Parallel Same length 1 1 12* 3 8 5 4 × their 8 3 oe 10 3 cao B1 M1 A1 or 15 40 accept 8 3 or 40 15 or 15 40 15 12 their ÷ or equivalent division with fractions with common denominators

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0580 12 © Cambridge International Examinations 2015 Qu Answer Mark Part marks 13* (a) 11 1 (b) 8 2FT FT 30 – 2 × their (a) or M1 for 4 × 7 = 2(x – 1) + FG oe or 4(x – 4) = 2(x – 1) + FG oe or 2 × 7 + 2(x – 4) = 2(x – 1) + FG oe Allow x to be their (a) in each case 14 548 or 547.8 or 547.75 to 547.76 3 M2 for 480 3 100 5.4 1      + oe or M1 for correct method for amount for 2 years. SC2 for [interest = $]68 or 67.8 or 67.75 to 67.76 15 (a) 200 73 oe 1 (b) 1971 2FT M1 for their (a) × 5400 (0 < their (a) <1) or 5400 ÷ 200 × 73 16 (a)       7 3 1 (b) (i) C marked at (−4, 0) 1 (ii) (−4, 0) 1FT Co-ordinates of their point C 17 (a) [x =] 37 1 (b) [y =] 53 1FT Follow through 90 – their (a) (c) [z =] 74 2FT M1 for eg 180 – 2× their angle BDC or 180 – 2× their (b) or 2 × their (a) 18 (a) 45, 38 1, 1FT Follow through their 45 – 7 (b) 80 – 7n oe 2 B1 for – 7n 19* (a) 78 3 M2 for 5 × 12 + 2 1 × 12 × (8 – 5) or 2 1 × 6 × (5 + 8) × 2 oe or M1 for 5 × 12 , 2 1 × 12 × (8 – 5) , 2 1 × 6 × (5 + 8) or 12 × 8 – (…) (b) 1170 1FT 15 × their (a)

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0580 12 © Cambridge International Examinations 2015 Qu Answer Mark Part marks 20 (a) 3 × 180 1 (b) 51, 153 204 4 M1 for 540 – (79 + 53) [= 408] M1 dependent for their 408 ÷ (1 + 3 + 4) A1 for 1 correct angle If zero, SC2 for 67.5, 202.5 and 270 or SC1 for 67.5 21 (a) Jan 1 (b) 9 1 (c) 9.5 2 M1 for correctly ordering at least 7 months from one end or identifying the middle two, 8 and 11 (d) 8.8 3 M1 for attempt to add the temperatures ÷ 12 A1 for 8.83[3…] After M1 A0, award SC1 for their mean correct to 2 sf