Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 Oct/Nov 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) 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_13/FP © UCLES 2014 *6234365219* PAPA CAMBRIDGE

2 0581/13/O/N/14 © UCLES 2014 1 Write 0.13 as a fraction. Answer … [1] __________________________________________________________________________________________ 2 (a) Write in fi gures the number three hundred and four thousand six hundred and twenty. Answer(a) … [1] (b) Write your answer to part (a) correct to 3 signifi cant fi gures. Answer(b) … [1] __________________________________________________________________________________________ 3 (a) Write down the order of rotational symmetry of the diagram. Answer(a) … [1] (b) Draw the lines of symmetry on the diagram. [1] __________________________________________________________________________________________ 4 Calculate 3.71 9.25 26.4 + . Give your answer correct to 2 decimal places. Answer … [2] __________________________________________________________________________________________

3 0581/13/O/N/14 © UCLES 2014 [Turn over 5 A bag contains 20 counters. One counter is taken from the bag at random. The arrow on the probability scale shows the probability that this counter is blue. 0 0.5 1 (a) Work out the number of blue counters in the bag. Answer(a) … [1] (b) Find the probability that the counter is not blue. Answer(b) … [1] __________________________________________________________________________________________ 6 The temperature in a freezer is –20.5 °C. (a) The temperature in a fridge is 2.8 °C. Find the difference between the temperature in the fridge and the temperature in the freezer. Answer(a) … °C [1] (b) The temperature in the freezer rises by 5 °C. Find the temperature in the freezer now. Answer(b) … °C [1] __________________________________________________________________________________________ 7 Find the value of (a) 2744 3 , Answer(a) … [1] (b) 64. Answer(b) … [1] __________________________________________________________________________________________

4 0581/13/O/N/14 © UCLES 2014 8 m = 5 2 - e o n = 3 6 - e o Work out (a) m + n, Answer(a) f p [1] (b) 3n. Answer(b) f p [1] __________________________________________________________________________________________ 9 Without using a calculator, work out 5 4 – 3 2 . Give your answer as a fraction and show each step of your working. Answer … [2] __________________________________________________________________________________________ 10 Make x the subject of the formula y = 6x – 1. Answer x = … [2] __________________________________________________________________________________________

5 0581/13/O/N/14 © UCLES 2014 [Turn over 11 Write the following in order of size, smallest fi rst. 0.34 0.6 0.62 0.73 Answer … < … < … < … [2] smallest __________________________________________________________________________________________ 12 Work out 4 × 10–5 × 6 × 1012. Give your answer in standard form. Answer … [2] __________________________________________________________________________________________ 13 The four sector angles in a pie chart are 2x°, 3x°, 4x° and 90°. Find the value of x. Answer x = … [2] __________________________________________________________________________________________ 14 A train takes 65 minutes to travel 52 km. Calculate the average speed of the train in kilometres per hour. Answer … km/h [2] __________________________________________________________________________________________

6 0581/13/O/N/14 © UCLES 2014 15 (a) A parcel is in the shape of a cuboid of length 18 cm, width 10 cm and height 8 cm. Calculate the volume of the parcel. Answer(a) … cm3 [2] (b) The mass of the parcel is 1.7 kilograms. Change 1.7 kilograms to grams. Answer(b) … g [1] __________________________________________________________________________________________ 16 (a) Simplify. 5j + 2k + j – 3k Answer(a) … [2] (b) Factorise. 5p + 10 Answer(b) … [1] __________________________________________________________________________________________ 17 (a) Paolo thinks of a number. It has two digits. It is a common factor of 36 and 48. Write down Paolo’s number. Answer(a) … [1] (b) Maria thinks of a number. It has two digits. It is a common multiple of 15 and 20. Write down Maria’s number. Answer(b) … [1] (c) Kemar thinks of a number. It is between 1 and 2. It is an irrational number. Write down a number he could be thinking of. Answer(c) … [1] __________________________________________________________________________________________

7 0581/13/O/N/14 © UCLES 2014 [Turn over 18 Solve the equation. 3 2 5 x + = 8 Answer x = … [3] __________________________________________________________________________________________ 19 The scatter diagram shows the heights and masses of some fi ve-year-old boys. 30 25 20 15 10 90 95 100 105 110 115 Height (cm) Mass (kg) 120 125 130 135 (a) The height of one of the boys is likely to have been recorded incorrectly. Write down the mass of this boy. Answer(a) … kg [1] (b) What type of correlation does the scatter diagram show? Answer(b) … [1] (c) (i) Draw a line of best fi t on the scatter diagram. [1] (ii) Another boy had a height of 108 cm. His mass was not recorded. Use your line of best fi t to estimate the boy’s mass. Answer(c)(ii) … kg [1] __________________________________________________________________________________________

8 0581/13/O/N/14 © UCLES 2014 20 D A C B E (a) Draw the locus of the points which are 3 cm from E. [1] (b) Using a straight edge and compasses only, construct the bisector of angle DCB. [2] (c) Shade the region which is ● less than 3 cm from E and ● nearer to CB than to CD. [1] __________________________________________________________________________________________

9 0581/13/O/N/14 © UCLES 2014 [Turn over 21 C B A 8 cm 5 cm 32° NOT TO SCALE A, B and C lie on a circle with diameter AB. Angle CAB = 32°, AC = 8 cm and BC = 5 cm. (a) Work out the size of angle CBA. Answer(a) Angle CBA = … [2] (b) Work out the length of AB. Answer(b) AB = … cm [2] __________________________________________________________________________________________

10 0581/13/O/N/14 © UCLES 2014 22 This is an accurate drawing of quadrilateral ABCD. D C A B (a) Write down the mathematical name for quadrilateral ABCD. Answer(a) … [1] (b) Measure the size of the acute angle. Answer(b) … [1] (c) By taking suitable measurements from the diagram, work out the area of ABCD. Answer(c) … cm2 [3] __________________________________________________________________________________________

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12 0581/13/O/N/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

® 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 0581/13 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 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 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 Qu. Answers Mark Part Marks 1 100 13 oe 1 2 (a) (b) 304 620 305 000 1 1FT 3 (a) 2 1 (b) 1 4 9.61 2 B1 for 9.609[1…] or for their answer seen rounded to 2 d.p. 5 (a) (b) 5 0.75 oe 1 1 6 (a) (b) 23.3 –15.5 1 1 7 (a) (b) 14 1296 1 1 8 (a) (b)       4 2      − 18 9 1 1 9 15 10 12 − or 15 10 15 12 − oe 15 2 oe M1 A1 Answer must be a fraction

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 13 © Cambridge International Examinations 2014 10 6 1 + y oe 2 B1 for x y 6 1= + or 6 1 6 − = x y If B0 SC1 for 6 1 − y or 1 6 + y 11 6.0 6.0 7.0 34 .0 2 3 2 M1 for decimal conversion: 0.7[7…] or 0.8 for 6.0 and 0.36 for 0.62 and 0.343 for 0.73 or B1 for three in the correct order 12 8 10 4.2 × 2 B1 for 240 000 000 oe or B1 for 8 10 × k or k 10 4.2 × 13 30 2 M1 for 360 90 4 3 2 = + + + x x x oe 14 48 2 M1 for 52 ÷ 65 [× 60] oe implied by 0.8 15 (a) (b) 1440 1700 2 1 M1 for 18 × 10 × 8 16 (a) (b) k j − 6 ( ) 2 5 + p 2 1 B1 for ak j ± 6 or k bj − (a and b ≠ 0) 17 (a) (b) (c) 12 60 Irrational number between 1 and 2 1 1 1 18 9.5 or 2 19 3 M2 for ( ) 5 3 8 2 − × = x or better oe or M1 for 3 8 5 2 × = + x or better 19 (a) (b) (c) (i) (ii) 16 [kg] Positive Ruled line of best fit Correct reading from ruled line 1 1 1 1FT

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 13 © Cambridge International Examinations 2014 20 (a) (b) (c) Complete circle centre E radius 3 cm Correct ruled bisector with two pairs of correct arcs 1 2 1 B1 for correct bisector with no/wrong arcs dep on attempt at bisector of C and enclosed region 21 (a) (b) 58 9.43 to 9.44 2 2 B1 for ACB = 90o soi as angle at C or M1 for 5 8 tan M1 for [ ] 2 2 2 5 8 + = AB or AB 5 32 sin = or AB 8 32 cos = oe 22 (a) (b) (c) Trapezium 55o 21.4 or 19.55 to 23.37 nfww 1 1 3 B1 for [AB =] 7.2, [DC =] 4.7, and [height =] 3.6 seen and M1 for ( ) 2.7 7.4 6.3 5.0 + × × their their