Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 Oct/Nov 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 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 0581/12 Paper 1 (Core) October/November 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 10 printed pages and 2 blank pages. [Turn over IB14 11_0581_12/FP © UCLES 2014 *8226397023* PAPA CAMBRIDGE

2 0581/12/O/N/14 © UCLES 2014 1 Insert one pair of brackets only to make the following statement correct. 6 + 5 × 10 – 8 = 16 [1] __________________________________________________________________________________________ 2 Calculate 1.26 0.72 8.24 2.56 - + . Answer … [1] __________________________________________________________________________________________ 3 Write down the order of rotational symmetry of this shape. Answer … [1] __________________________________________________________________________________________ 4 (a) Write down two whole numbers that have a product of –15. Answer(a) … and … [1] (b) During one year, the temperature in Ulaanbaatar varied from –33 °C to 27 °C. Find the range of the temperatures during that year. Answer(b) … °C [1] __________________________________________________________________________________________

3 0581/12/O/N/14 © UCLES 2014 [Turn over 5 Work out the value of 34 ÷ 3–2. Give your answer as an ordinary number. Answer … [2] __________________________________________________________________________________________ 6 Indira measures the length, l centimetres, of her desk as 95.6 cm, correct to the nearest millimetre. Complete the statement about the value of l. Answer … Y l < … [2] __________________________________________________________________________________________ 7 (a) Complete the following list of factors of 30. 1, 2, … , 5, … , 10, … , 30 [1] (b) Write down the prime factors of 30. Answer(b) … [1] __________________________________________________________________________________________ 8 (a) Write 640 000 in standard form. Answer(a) … [1] (b) Write 7.82 × 10–4 as an ordinary number. Answer(b) … [1] __________________________________________________________________________________________

4 0581/12/O/N/14 © UCLES 2014 9 Make y the subject of the formula. 8 + 5y – 3x = 0 Answer y = … [2] __________________________________________________________________________________________ 10 y x 4 3 2 1 –1 –2 –3 –4 0 –1 1 2 3 4 –2 –3 –4 A B Points A and B are shown on the grid. (a) Write as a column vector. Answer(a) = f p [1] (b) Write 3 as a column vector. Answer(b) 3 = f p [1] __________________________________________________________________________________________

5 0581/12/O/N/14 © UCLES 2014 [Turn over 11 Write the following in order of size, starting with the smallest. 37 15 0.41 40.4% 42 17 Answer … < … < … < … [2] __________________________________________________________________________________________ 12 (a) Simplify 5k – 7k + 4k. Answer(a) … [1] (b) Find the value of 8x – 3y when x = –2 and y = –5. Answer(b) … [2] __________________________________________________________________________________________ 13 For her holiday, Alyssa changed 2800 Malaysian Ringgits (MYR) to US dollars ($) when the exchange rate was 1 MYR = $0.325 . At the end of her holiday she had $210 left. (a) How many dollars did she spend? Answer(a) $ … [2] (b) She changed the $210 for 750 MYR. What was the exchange rate in dollars for 1 MYR? Answer(b) 1 MYR = $ … [1] __________________________________________________________________________________________

6 0581/12/O/N/14 © UCLES 2014 14 Without using a calculator, work out 1 6 1 ÷ 8 7 . Show all your working and give your answer as a fraction in its lowest terms. Answer … [3] __________________________________________________________________________________________ 15 Solve the simultaneous equations. You must show all your working. 9x + 2y = 8 5x + 6y = –20 Answer x = … y = … [3] __________________________________________________________________________________________

7 0581/12/O/N/14 © UCLES 2014 [Turn over 16 A bag contains different coloured counters. Sasha takes a counter at random, records its colour, and replaces it. She does this 90 times and records her results in the pie chart below. 136° 148° Red Green Blue (a) Write down the relative frequency of Sasha choosing a red counter. Answer(a) … [1] (b) Work out the number of times a green counter is chosen. Answer(b) … [3] __________________________________________________________________________________________

8 0581/12/O/N/14 © UCLES 2014 17 The scatter diagram shows the results of height plotted against shoe size for 8 people. 200 192 184 176 168 160 152 144 136 128 120 28 26 30 32 34 Shoe size 36 38 40 42 44 Height (cm) (a) Four more results are recorded. Shoe size 28 31 38 43 Height (cm) 132 156 168 198 Plot these 4 results on the scatter diagram. [2] (b) Draw a line of best fi t on the scatter diagram. [1] (c) What type of correlation is shown by the scatter diagram? Answer(c) … [1] __________________________________________________________________________________________

9 0581/12/O/N/14 © UCLES 2014 [Turn over 18 Find (a) the cube root of 729, Answer(a) … [1] (b) the two square roots of 225, Answer(b) … and … [2] (c) a common multiple of 6 and 9, Answer(c) … [1] (d) (–4)2. Answer(d) … [1] __________________________________________________________________________________________ 19 z° x° y° 24° A B E C D NOT TO SCALE The points B, C, D and E lie on a circle. AB and AC are equal length tangents to the circle. BD is a diameter of the circle and BC is parallel to ED. Angle BDE = 24°. Calculate the value of (a) x, Answer(a) x = … [2] (b) y, Answer(b) y = … [1] (c) z. Answer(c) z = … [2] __________________________________________________________________________________________

10 0581/12/O/N/14 © UCLES 2014 20 The diagram shows the plan, ABCD, of a park. The scale is 1 centimetre represents 20 metres. D A C B Scale: 1 cm to 20 m (a) Find the actual distance BC. Answer(a) … m [2] (b) A fountain, F, is to be placed ● 160 m from C and ● equidistant from AB and AD. On the diagram, using a ruler and compasses only, construct and mark the position of F. Leave in all your construction lines. [5] __________________________________________________________________________________________

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12 0581/12/O/N/14 © UCLES 2014 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. 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 October/November 2014 series 0581 MATHEMATICS 0581/12 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 October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components. PAPA CAMBRIDGE

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 12 © 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. Answer Mark Part marks 1 6 + 5 × (10 – 8) = 16 1 One pair of brackets only 2 20 1 3 8 1 4 (a) 5 and −3 or −5 and 3 or 1 and −15 or −1 and 15 1 (b) 60 1 5 729 2 B1 for 81 or 9 1 seen in the working or 0.111… or B1 for 36 in the working or on the answer line. 6 95.55 95.65 1, 1 If zero, SC1 for both correct but reversed or 955.5 [mm] and 956.5 [mm] in correct place 7 (a) 3 6 15 1 (b) 2 3 5 cao 1 8 (a) 6.4 × 105 1 (b) [0].000782 1 9 5 8 3 − x oe 2 B1 for 5y = 3x – 8 or −5y = 8 – 3x If B0 SC1 for 5 8 3 + x or 5 8 3 − −x 10 (a)      − 4 5 1 (b)      − 12 15 1FT FT for 3 × their (a) 11 40.4% 42 17 37 15 0.41 2 B1 for 3 in correct order or for 0.405… , 0.404 and 0.4047… or 0.4048

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 12 © Cambridge International Examinations 2014 12 (a) 2k 1 (b) −1 2 B1 for −16 or −15 or 15 seen in the working. 13 (a) 700 2 M1 for 2800 × 0.325 (b) 0.28 1 14 6 7 oe 7 8 6 7 × their oe or 3 4 3 1 1 cao must see working B1 M1 A1 Or M1 for 48 42 48 56 ÷ or equivalent division with fractions with common denominators cancelled 15 [x =] 2 [y =] −5 3 M1 for correct method to eliminate one variable A1 for x A1 for y If zero scored SC1 for correct substitution and evaluation to find the other variable. 16 (a) 360 136 oe 1 (b) 19 cao 3 B1 for 76 M1 for 90 360 76 × their 17 (a) 4 points correctly plotted 2 B1 for 3 correct (b) Correct ruled line of best fit 1 (c) Positive 1 18 (a) 9 cao 1 (b) 15 and −15 1, 1 (c) Any multiple of 18 1 (d) 16 1 19 (a) (b) (c) [x =] 66 2 B1 for angle BED = 90° soi [y =] 24 1 [z =] 48 2FT M1FT for angle ABC = 90° − their y

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 12 © Cambridge International Examinations 2014 20 (a) 102 to 106 2 B1 for 5.1 to 5.3 seen (b) Correct position of F with correct arcs for angle bisector 5 B2 for Correct ruled angle bisector of A with correct arcs or B1 for correct bisector with no/wrong arcs and B2 for Arc centre C, radius 8 cm or B1 for arc centre C with incorrect radius or correct conversion to 8 cm and B1 for marking position of F on their bisector and 8 cm from C or their arc centre C