Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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) May/June 2013 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certifi cate of Secondary Education This document consists of 11 printed pages and 1 blank page. [Turn over IB13 06_0581_12/FP © UCLES 2013 *9639292645* www.XtremePapers.com

2 0581/12/M/J/13 © UCLES 2013 For Examiner's Use 1 0 0.5 1.0 Write down the number the arrow points to on the scale. Answer … [1] _____________________________________________________________________________________ 2 100 164 200 343 999 Write down the cube number from this list. Answer … [1] _____________________________________________________________________________________ 3 Write down the next prime number after 23. Answer … [1] _____________________________________________________________________________________ 4 Calculate the number of seconds in 3 hours. Answer … s [1] _____________________________________________________________________________________

3 0581/12/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 5 The diagram shows the net of a solid. Write down the mathematical name of this solid. Answer … [1] _____________________________________________________________________________________ 6 Bryony asks her friends how many pets they have. She is going to use this table to record her results. Number of pets Frequency 0 – 1 1 – 2 2 – 3 3 or more Explain what is wrong with this frequency table. Answer … … [1] _____________________________________________________________________________________ 7 (a) Draw an acute angle. Label the acute angle with the letter a. [1] (b) Write down the mathematical name of angle b. b Answer(b) … [1] _____________________________________________________________________________________

4 0581/12/M/J/13 © UCLES 2013 For Examiner's Use 8 3 rows 2 rows 1 row Complete the table for 4 rows and 5 rows. Number of rows 1 2 3 4 5 Number of cans 1 3 6 [2] _____________________________________________________________________________________ 9 The probability that the school hockey team will win its next match is 0.45 . The probability that it will lose its next match is 0.3 . Work out the probability that the school hockey team will draw its next match. Answer … [2] _____________________________________________________________________________________ 10 a = 4 7 e o b = 5 - 2 e o Write each of the following as a single vector. (a) 6a Answer(a) e o [1] (b) a + b Answer(b) e o [1] _____________________________________________________________________________________

5 0581/12/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 11 A B C 8 cm NOT TO SCALE Triangle ABC has a height of 8 cm and an area of 42 cm². Calculate the length of BC. Answer BC = … cm [2] _____________________________________________________________________________________ 12 (a) Use your calculator to work out 65 – 1.72 . Write down all the numbers displayed on your calculator. Answer(a) … [1] (b) Write your answer to part (a) correct to 2 signifi cant fi gures. Answer(b) … [1] _____________________________________________________________________________________

6 0581/12/M/J/13 © UCLES 2013 For Examiner's Use 13 The exterior angle of a regular pentagon is 72°. (a) Write down the interior angle of a regular pentagon. Answer(a) … [1] (b) The diagram shows three pentagons which fi t together. Uta thinks that three regular pentagons will fi t together in the same way. Explain how you know she is wrong. Answer(b) … … [1] _____________________________________________________________________________________ 14 B A 11 10 9 8 7 6 5 4 3 2 1 1 0 2 3 4 5 6 7 8 9 10 11 12 13 y x Describe fully the single transformation that maps shape A onto shape B. Answer … [3] _____________________________________________________________________________________

7 0581/12/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 15 (a) 128° x° NOT TO SCALE A straight line intersects two parallel lines as shown. Find the value of x. Answer(a) x = … [2] (b) 30° 128° y° NOT TO SCALE Calculate the value of y. Answer(b) y = … [1] _____________________________________________________________________________________ 16 (a) The average distance of the Moon from the Earth is 384 400 km. Write this distance in standard form. Answer(a) … km [1] (b) Calculate (4.3 × 108 ) + (2.5 × 107 ) . Give your answer in standard form. Answer(b) … [2] _____________________________________________________________________________________

8 0581/12/M/J/13 © UCLES 2013 For Examiner's Use 17 = < > Write one of the three symbols between each pair of numbers. Each symbol can be used more than once. (a) 30% … 3 1 [1] (b) –2 … –3 [1] (c) π … 10 [1] _____________________________________________________________________________________ 18 (a) –3 – 4 –7 2 5 Choose three different numbers from the list to complete this calculation. … + … + … = – 6 [1] (b) Find the value of 5x – 3y when x = –2 and y = 4. Answer(b) … [2] _____________________________________________________________________________________

9 0581/12/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 19 Without using a calculator, work out 7 6 ÷ 1 3 2 . Write down all the steps in your working. Answer … [3] _____________________________________________________________________________________ 20 A B C O NOT TO SCALE A, B and C are points on the circumference of a circle centre O. AC is a straight line. (a) Explain why angle ABC is 90°. Answer(a) … [1] (b) The diameter of the circle is 3 cm. Calculate the area of this circle. Answer(b) … cm2 [2] _____________________________________________________________________________________

10 0581/12/M/J/13 © UCLES 2013 For Examiner's Use 21 Carol invests $6250 at a rate of 2% per year compound interest. Calculate the total amount Carol has after 3 years. Answer $ … [3] _____________________________________________________________________________________ 22 Solve the equation. 5(2y – 17) = 60 Answer y = … [3] _____________________________________________________________________________________ 23 (a) Simplify y 0. Answer(a) … [1] (b) Make v the subject of E = 2 1 mv 2. Answer(b) v = … [3] _____________________________________________________________________________________

11 0581/12/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 24 8 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –8 –6 –7 –8 –9 –5 –4 –3 –2 –1 1 0 2 3 4 5 6 7 8 9 y x S (a) On the grid (i) plot the point (–5 , –2) and label it P, [1] (ii) draw the line y = 2x. [1] (b) (i) Write down the order of rotational symmetry of shape S. Answer(b)(i) … [1] (ii) Draw the image of shape S after a rotation through 90° clockwise about (0, 0). [2] _____________________________________________________________________________________

12 0581/12/M/J/13 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. University of 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 © UCLES 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 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 May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.XtremePapers.com

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 12 © Cambridge International Examinations 2013 Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Qu Answers Mark Part Marks 1 0.65 cao 1 2 343 1 3 29 1 4 10800 1 5 cuboid 1 Accept [rectangular] prism. 6 Overlapping class intervals oe 1 7 (a) (b) Any acute angle with angle indicated Obtuse 1 1 8 10, 15 1, 1 If 10 not correct allow SC1 for x, x + 5 9 0.25 oe 2 M1 for 1– (0.45 + 0.3) or better or SC1 for 0.52 as final answer 10 (a) (b)       42 24      − 9 1 1 1 11 10.5 www 2 M1 for 42 = 2 1 × BC × 8 or better 12 (a) (b) 5.17225... 5.2 1 1FT FT their (a) 13 (a) (b) 108° 3 × 108 ≠ 360 oe 1 1 14 Enlargement [Centre] (5,4) [Scale factor] 3 1 1 1

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 12 © Cambridge International Examinations 2013 Qu Answers Mark Part Marks 15 (a) (b) 52 22 2 1 M1 for 180 – 128 or 128 or 52 marked on diagram in a correct position. 16 (a) (b) 3.844 × 105 4.55 × 108 1 2 B1 for figs 455 seen 17 (a) (b) (c) < > < 1 1 1 18 (a) (b) –4, –7, [+]5 in any order –22 1 2 M1 for –10 and –12 seen SC1 for –10 +12 seen 19 with 2 correct steps seen k k 35 18 3 B1 for k k 3 5 and M1 for 5 3 7 6 their × 20 (a) (b) Angle or triangle [in a] semi-circle 7.068 to 7.07 1 2 M1 for π × 1.52 seen 21 6632.55 cao final answer 3 M2 for 3 100 2 1 6250      + × oe or M1 for 2 100 2 1 6250      + × oe SC2 for answer 382.55 final answer 22 14.5 oe 3 M2 for complete correct method or M1 for one correct step 23 (a) (b) 1 [v =] m E 2 or m E 5.0 or m E 2 1 1 3 M2 for v2 = m E 2 or M1 for mv2 = 2E or ½ v2 = m E

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 12 © Cambridge International Examinations 2013 Qu Answers Mark Part Marks 24 (a) (i) (ii) (b) (i) (ii) P in correct position at (– 5, – 2) y = 2x drawn 2 S rotated correctly 1 1 1 2 SC1 if rotated 90acw or 90cw about wrong centre.