Cambridge IGCSE Mathematics (with coursework) 0581 — 2011 Oct/Nov Paper 1 · Variant 2

This document consists of 12 printed pages. IB11 11_0581_12/FP © UCLES 2011 [Turn over *5866757876* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/12 Paper 1 (Core) October/November 2011 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) 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 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. www.XtremePapers.com

2 © UCLES 2011 0581/12/O/N/11 For Examiner's Use 1 The temperature on Monday is 3 °C. On Tuesday it is 5 °C lower. Find the temperature on Tuesday. Answer °C [1] 2 Joseph changed 120 New Zealand dollars (NZ$) into Australian dollars (A$) when the exchange rate was NZ$1 = A$0.796 . Calculate the exact amount he received. Answer A$ [1] 3 A bus leaves a port every 15 minutes, starting at 09 00. The last bus leaves at 17 30. How many times does a bus leave the port during one day? Answer [2] 4 Write the following in order of size, starting with the smallest. 8 9 1.2 115% 1 6 1 Answer I I I [2]

3 © UCLES 2011 0581/12/O/N/11 [Turn over For Examiner's Use 5 Mortar is a mixture of cement, sand and lime in the ratio cement : sand : lime = 1 : 5 : 2. Calculate how much sand there is in a 12 kg bag of this mortar. Answer kg [2] 6 Find the cube root of 96. Give your answer correct to 2 decimal places. Answer [2] 7 Write these numbers in standard form. (a) 734 000 000 Answer(a) [1] (b) 0.000587 Answer(b) [1]

4 © UCLES 2011 0581/12/O/N/11 For Examiner's Use 8 The population, P, of Brunei in 2008 was 400 000 correct to the nearest 1000. Complete the statement about the value of P. Answer Y P I [2] 9 Use your calculator to find the value of (a) 30 × 2.52, Answer(a) [1] (b) 2.5 – 2. Answer(b) [1]

5 © UCLES 2011 0581/12/O/N/11 [Turn over For Examiner's Use 10 A C D B E 115° 20° y° x° NOT TO SCALE In the diagram, AB is parallel to CDE. Find the value of (a) x, Answer(a) x = [1] (b) y. Answer(b) y = [2] 11 75° x° 2x° 2x° NOT TO SCALE (a) For the diagram above, write down an equation in x. Answer(a) [1] (b) Solve your equation. Answer(b) x = [2]

6 © UCLES 2011 0581/12/O/N/11 For Examiner's Use 12 Jiwan incorrectly wrote 1 + 2 1 + 3 1 + 4 1 = 1 9 3 . Show the correct working and write down the answer as a mixed number. Answer [3] 13 Solve these simultaneous equations. 5x – 2y = 17 2x + y = 5 Answer x = y = [3]

7 © UCLES 2011 0581/12/O/N/11 [Turn over For Examiner's Use 14 A bag contains only red, yellow and blue counters. Bashira picks a counter at random from the bag, records its colour, and puts it back in the bag. She does this 60 times. (a) Complete the table for her results. Colour Frequency Relative frequency Red 19 Yellow Blue 28 [2] (b) Gita picks a counter at random from the same bag. Which colour counter is she most likely to pick? Answer(b) [1] 15 A cruise ship travels at 22 knots. [1 knot is 1.852 kilometres per hour.] Convert this speed into metres per second. Answer m/s [3]

8 © UCLES 2011 0581/12/O/N/11 For Examiner's Use 16 (a) Write down a common multiple of 8 and 14. Answer(a) [1] (b) (i) Complete the list of factors of 81. 1, , , , 81 [2] (ii) Write down the prime factor of 81. Answer(b)(ii) [1]

9 © UCLES 2011 0581/12/O/N/11 [Turn over For Examiner's Use 17 y x 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 0 –1 –2 –3 –4 –5 –6 5 6 4 3 2 1 B A The diagram shows two straight lines, A and B, drawn on a grid. (a) Write down the equation of line A. Answer(a) [1] (b) The equation of line B is y = 3x – 1 . (i) Draw a line parallel to line B that passes through the point (0, 2). [1] (ii) Write down the equation of your line in the form y = mx + c. Answer(b)(ii) y = [2]

10 © UCLES 2011 0581/12/O/N/11 For Examiner's Use 18 O A B 75° NOT TO SCALE (a) Triangle AOB is isosceles. OA = OB. Calculate angle AOB. Answer(a) Angle AOB = [1] (b) O A B NOT TO SCALE 75° AB is one side of a regular polygon with n sides. (i) Calculate n. Answer(b)(i) n = [2] (ii) Find the size of an interior angle of this polygon. Answer(b)(ii) [1]

11 © UCLES 2011 0581/12/O/N/11 [Turn over For Examiner's Use 19 (a) 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 0 A B C y x Three vertices of the quadrilateral ABCD are shown in the diagram. (i) Write down the co-ordinates of the point B. Answer(a)(i) ( , ) [1] (ii) On the grid, plot and label the point D so that quadrilateral ABCD has rotational symmetry of order 2. [1] (iii) Draw the quadrilateral ABCD. Draw in all the lines of symmetry on your quadrilateral. [1] (b) Write down the mathematical names of these quadrilaterals. P Q Answer(b) P Q [2] Question 20 is printed on the next page.

12 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. © UCLES 2011 0581/12/O/N/11 For Examiner's Use 20 In a survey of 60 cars, the type of fuel that they use is recorded in the table below. Each car only uses one type of fuel. Petrol Diesel Liquid Hydrogen Electricity 40 12 2 6 (a) Write down the mode. Answer(a) [1] (b) Olav drew a pie chart to illustrate these figures. Calculate the angle of the sector for Diesel. Answer(b) [2] (c) Calculate the probability that a car chosen at random uses Electricity. Write your answer as a fraction in its simplest form. Answer(c) [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2011 question paper for the guidance of teachers 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 must be read in conjunction with the question papers and the report on the examination. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the October/November 2011 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 12 © University of Cambridge International Examinations 2011 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 Qu. Answers Mark Part Marks 1 −2(°C) 1 2 95.52 1 3 35 2 M1 for 4 × 8 + 3 or 4 × 4 3 8 or 4 × 2 1 8 + 1 or 15 525 or 15 510 + 1 SC1 for answer 34 4 8 9 < 115% < 6 1 1 < 1.2 2 M1 for all decimals (or %), allow 1 error or B1 for 3 in correct order eg 115% < 8 9 < 6 1 1 < 1.2 SC1 for reverse order 5 7.5 2 M1 for 12 × 5 ÷ (1 + 5 + 2) oe 6 4.58 cao 2 B1 for 4.6(0) or 4.57 or 4.579 or 4.578 or 4.5789 or 4.5788… SC1 for 4.583 only 7 (a) 7.34 × 108 1 (b) 5.87 × 10–4 1 8 399 500 (≤ P <) 400 500 1, 1 SC1 for both correct reverse order 9 (a) 6.25 cao 1 (b) 0.16 cao 1 10 (a) (x =) 20 1 (b) (y =) 65 2 B1 for ABD = 65° or ADB = 95° 11 (a) x + 2x + 2x + 75 = 360 1 Allow 4x + x + 75 = 360 or 5x + 75 = 360 or 5x = 285 (b) (x =) 57 cao 2 M1 correct first step after 5x + 75 = 360 ie 5x = 360 − 75 or x + 15 = 72 If zero SC1 for correct solution to their linear equation seen in part (a) or in part (b) if (a) is blank

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 12 © University of Cambridge International Examinations 2011 12 212 1 cao with correct working 3 M1 (1+) 12 3 12 4 12 6 + + oe A1 (1)12 13 or 12 25 oe 13 (x =) 3 (y =) –1 www 3 M1 for consistent multiply and consistent add/ subtract as appropriate Allow computational but not method errors Likely 5x + 4x = 17 + 10 Other methods allowed A1 for correct x or y 14 (a) 13 1 (Red) 60 19 (Yellow) 60 13 their oe 1ft All needed for the mark isw cancelling or decimals after correct fractions seen (Blue) 60 28 oe (b) Blue 1ft Strict ft their highest frequency 15 11.3 3 M2 22 × 1.852 × 1000/3600 oe or M1 22 × figs 1852 or 22 × 1000/3600 16 (a) Any multiple of 56 1 (b) (i) 3, 9, 27 (in any order) 2 B1 for 2 correct (ii) 3 cao 1 17 (a) y = −2 or y + 2 = 0 1 (b) (i) Ruled line parallel to B through (0, 2) 1 Must at least go through (−1, –1) (ii) (y =) 3x + 2 cao final answer 2 B1 3x + j j ≠ –1 or 2 or kx + 2 k ≠ 3 SC1 for 3x + 2 then spoiled by the final answer 18 (a) 30 1 (b) (i) 12 2ft M1 for 360 ÷ their (a) (Any answer for (a) for method) Only ft for A1 if 360 ÷ their (a) is an integer Other methods allowed if complete (ii) 150 cao 1 19 (a) (i) (1, 5) 1 (ii) D at (5, 2) 1 (iii) Lines x = 3 and y = 3.5 only drawn 1 Dep on (a)(ii) Extra line(s) zero Lines should at least meet the sides (b) Kite Trapezium 1, 1 1 mark for each 20 (a) Petrol cao 1 (b) 72 2 M1 for 360 × 12 ÷ 60 (c) 10 1 2 B1 60 6 or 30 3 or 20 2 or 0.1 or 10%