Cambridge IGCSE Mathematics (with coursework) 0581 — 2009 Oct/Nov Paper 1 · Variant 2

This document consists of 11 printed pages and 1 blank page. IB09 11_0581_12/RP © UCLES 2009 [Turn over *6066050202* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/12 Paper 1 (Core) October/November 2009 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic Calculator Mathematical tables (optional) Geometrical Instruments 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. 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 2009 0581/12/O/N/09 For Examiner's Use 1 Insert one pair of brackets to make the following equation correct. 2 × 8 − 5 − 4 = 15 [1] 2 Write the following numbers in order starting with the smallest. 2 7 0.283 28 % Answer < < [1] 3 Find the volume of a cube with sides of 3.8 cm. Answer cm3 [1] 4 North North 72° A B NOT TO SCALE The diagram shows the position of two airports, A and B. The bearing of B from A is 072°. Work out the bearing of A from B. Answer [2]

3 © UCLES 2009 0581/12/O/N/09 [Turn over For Examiner's Use 5 The number of spectators, N, at a football match is 16 000, correct to the nearest thousand. Complete the inequality for N in the answer space. Answer Y N < [2] 6 Work out the value of 2 2 1 3 11 ×1 . Show all your working and leave your answer as a fraction. Answer [2] 7 A B C Using a straight edge and compasses only, construct the locus of points which are equidistant from AB and from BC. Show clearly all your construction arcs. [2]

4 © UCLES 2009 0581/12/O/N/09 For Examiner's Use 8 4 8 25 5 2 0.3333 From the list above, write down (a) a prime number, Answer(a) [1] (b) an irrational number. Answer(b) [1] 9 A train sets off at 10 48 on a journey to Mumbai. The journey takes 4 hours 30 minutes. (a) Write down the time when the train arrives in Mumbai. Answer(a) [1] (b) The distance to Mumbai is 441 kilometres. Calculate the average speed of the train. Answer(b) km/h [2]

5 © UCLES 2009 0581/12/O/N/09 [Turn over For Examiner's Use 10 Solve the simultaneous equations 5x − 3y = 3, 6x − y = 14. Answer x = y = [3] 11 15 10 5 0 5 10 15 20 25 Kilometres Miles Distance can be measured in miles or kilometres. 24 kilometres is approximately equal to 15 miles. (a) Draw a straight line on the grid to show the conversion between kilometres and miles. [2] (b) Use your graph to estimate the number of kilometres equal to 7 miles. Answer (b) km [1]

6 © UCLES 2009 0581/12/O/N/09 For Examiner's Use 12 4 cm 7 cm NOT TO SCALE The diagram shows a triangular prism of length 7 cm. The cross-section is an equilateral triangle of side 4 cm. Complete an accurate net of the prism. One rectangular face has been drawn for you. [3]

7 © UCLES 2009 0581/12/O/N/09 [Turn over For Examiner's Use 13 –3 –2 –1 –1 –2 –3 –4 3 4 5 2 1 1 0 2 3 4 5 y x F G The points F and G are shown on the grid. (a) Write down the co-ordinates of the point F. Answer(a)( , ) [1] (b) Write as a column vector. Answer(b) = ( ) [1] (c) = _5 _3       . Mark and label the point H on the grid. [1]

8 © UCLES 2009 0581/12/O/N/09 For Examiner's Use 14 (a) Find the value of p when p3 = −27. Answer(a) p = [1] (b) Find the value of q when q −1 = 1 6 . Answer(b) q = [1] (c) Simplify 8s 2 ÷ 2s −1. Answer(c) [2] 15 J = 3 md (a) Find the value of d when J = 32 and m = 8. Answer(a) d = [2] (b) Make d the subject of the formula. Answer(b) d = [2]

9 © UCLES 2009 0581/12/O/N/09 [Turn over For Examiner's Use 16 As the earth rotates, a point on the equator moves round at a speed of 1669.8 kilometres/hour. (a) Write down this number in standard form, correct to 3 significant figures. Answer(a) [2] (b) Change 1669.8 kilometres/hour into metres/second. Answer(b) m/s [2] 17 (a) Factorise 3mp + 7p2. Answer (a) [1] (b) Simplify completely 8(3m + p) − 5(2m − 3p). Answer (b) [3]

10 © UCLES 2009 0581/12/O/N/09 For Examiner's Use 18 T P W Q R S 38° 105° NOT TO SCALE The lines PS and QT intersect at W. PQR is a straight line. Angle SPR = 38° and angle TQR = 105°. Write down the size of the following angles. In each case give a reason for your answer. (a) Angle PQW = because [2] (b) Angle PWQ = because [2] (c) Angle TWS = because [2]

11 © UCLES 2009 0581/12/O/N/09 For Examiner's Use 19 Silver Red Yellow Other The accurate pie chart shows information about the colours of 240 cars in a car park. (a) The sector angle for silver cars is 90°. Calculate the number of silver cars in the car park. Answer(a) [1] (b) There are 36 yellow cars in the car park. Showing all your working, calculate the sector angle for yellow cars. Answer(b) [2] (c) (i) Measure and write down the sector angle for red cars. Answer(c)(i) [1] (ii) Calculate the percentage of red cars in the car park. Answer(c)(ii) % [2]

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. 0581/12/O/N/09 BLANK PAGE

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2009 question paper for the guidance of teachers 0581 MATHEMATICS 0581/12 Paper 12 (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. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2009 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 2009 0581 12 © UCLES 2009 Qu. Answers Mark Part Marks 1 2 × 8 − (5 − 4) = 15 1 2 28% < 0.283 < 7 2 1 3 54.9 or 54.87 or 54.872 1 4 252 2 W1 for 108 or 72 correctly shown on the diagram at B. Or M1 for 180 + 72 or 360 − (180 − 72) soi 5 15500 Y N < 16500 1, 1 If zero, SC1 for correct but reversed 6 3 8 and 11 12 seen 33 96 oe fraction or 2 33 30 oe M1 A1 isw incorrect cancelling after 33 96 oe Final answer is a decimal, maximum M1. 7 Correct angle bisector (±2°) with two pairs of correct arcs. Line (±2 mm) from B. 2 W1 correct bisector without arcs or incorrect arcs or absent arcs. Line (±2 mm) from B. 8 (a) 25 or 5 (b) 8 isw 1 1 9 (a) 15 18 isw or 3.18 pm isw. (b) 98 1 2cao Not 03 18 or 3 18 alone. Not 15h(ours)18 M1 for 441 ÷ 4.5 (or 4h 30min or 270) Method mark is for formula with values. 10 (x =) 3 and (y =) 4 www 3 M1 for complete correct method for one value A1 for 1 correct answer. ww both correct W3 ww one correct W0 Reversed answer, look in working to be convinced of transcription error. 11 (a) Ruled line from (0, 0) to (24, 15) End point between (23.5, 15) and (24.5, 15). Start point within 1 mm of (0, 0) (b) 11 to 11.5 2 1ft W1 for correct freehand or short of (24, 15) but within allowed limits and to at least 7 miles. If zero SC1 Ruled line from (0, 0) to (23.5, 15) or to (24.5, 15) Answer in range. If 0 or W1 gained in part (a) follow through line with positive gradient only ± 1 mm

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2009 0581 12 © UCLES 2009 12 Correct net layout 2 accurate, 7 cm by 4 cm, rectangles on top and bottom. 2 accurate equilateral triangles at the sides (height 3.3 cm to 3.7 cm) 1 1 1 2 rectangles and 2 equilateral triangles (one on each side) in correct position to make a net. within 2 mm of central grid line 13 (a) (–2, 1) (b)       4 6 (c) H at (–1, 2) 1 1 1 All coordinates/components reversed. ie (a) (1, −2), (b)       6 4 , (c) (1, 0) mark 0, 0, SC1 14 (a) –3 final answer (b) 6 final answer (c) 4s3 or 3 4 − s final answer 1 1 2 W1 for 4sn (n ≠ 0) or ks3 (k ≠ 0) seen 15 (a) 12 (b) (d =) m J 3 2 2 M1 for 32 = 3 8d or better. M1 for 3J = md or m J = 3 d 16 (a) 1.67 × 103 (b) 464 or 463.8(3…..) 2 2 W1 for 1.67 × 10n (n ≠ 0) or 1.(…..) × 103 as answer If zero SC1 for figs 167 in answer. M1 for 1669.8 × 1000 ÷ 3600 17 (a) p(3m + 7p) final answer (b) 14m + 23p www 1 3 Ignore check by expansion. W1 for 24m + 8p and W1 for –10m + 15p If zero ww SC1 for 14m or (+)23p in answer 18 (a) 75 Angle(s) (on a straight) line (=) 180 (b) 67 Angle(s) (in a) triangle (sum to) 180 (c) 67 (vertically) opposite 1, 1 1ft,1 1ft,1 Or reference to straight line and 180 or exterior angle (of triangle is) sum of interior (opposite) angles

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2009 0581 12 © UCLES 2009 19 (a) 60 (b) 36 ÷ 240 × 360 oe 54 (c) (i) 116 to 118 (ii) 32.5 or their (c) (i) ÷ 3.6 1 M1 A1 1 2ft oe e.g. 36 × 90 ÷ 60 W2 54 with some relevant working shown M1 for their (c) (i) ÷ 360 × 100 Or for their (c) (i) × (60 ÷ 90) ÷ 240 × 100 Allow revised angle in range 116 – 118 seen with working