Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 Oct/Nov Paper 1 · Variant 1

This document consists of 11 printed pages and 1 blank page. IB10 11_0581_11/FP © UCLES 2010 [Turn over *1925276261* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/11 Paper 1 (Core) October/November 2010 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 2010 0581/11/O/N/10 For Examiner's Use 1 On Monday the temperature was − 3°C. On Tuesday the temperature fell by 5°C. Write down the temperature on Tuesday. Answer °C [1] 2 Write 0.00387 in standard form. Answer [1] 3 The diagram is an accurate net for a solid shape. Write down the geometrical name for this solid shape. Answer [1] 4 On a map, a straight section of a canal is 3.5 cm long. The scale of the map is 1 cm to 5 km. Calculate the actual length of this straight section. Answer km [1]

3 © UCLES 2010 0581/11/O/N/10 [Turn over For Examiner's Use 5 Sophie invests $450 at a rate of 1.5% per year simple interest. Calculate the interest she earns after 8 years. Answer $ [2] 6 A B Using a straight edge and compasses only, construct the locus of points which are equidistant from point A and from point B. Show clearly all your construction arcs. [2]

4 © UCLES 2010 0581/11/O/N/10 For Examiner's Use 7 A box is 12 cm high, correct to the nearest centimetre. Complete the statement about the height, h cm, of the box. Answer Y=h I [2] 8 The metal used to make a coin is a mixture of steel and copper. The ratio mass of steel : mass of copper is 108 : 7. The coin has a total mass of 230 milligrams. Calculate the mass of copper in this coin. Answer milligrams [2] 9 F G H 6.3 m 53° NOT TO SCALE Calculate the length FG. Answer m [2]

5 © UCLES 2010 0581/11/O/N/10 [Turn over For Examiner's Use 10 Use your calculator to find the value of 25.63 . Write down your answer (a) as it appears on your calculator, Answer(a) [1] (b) correct to 4 significant figures. Answer(b) [1] 11 (a) The diagram shows a rhombus. Draw all the lines of symmetry. [2] (b) Shade two squares in the diagram above so that the figure has one line of symmetry and no rotational symmetry. [1] 12 Solve the simultaneous equations. 18 3 = + y x 34 2 4 = − y x Answer x = y = [3]

6 © UCLES 2010 0581/11/O/N/10 For Examiner's Use 13 y x 5 4 3 2 1 –1 –2 0 –1 –2 –3 –4 4 3 2 1 P Q The points P ( 3 , 1 ) and Q (−1 , −1) are marked on the grid. (a) Write down the vector . Answer(a) =         [1] (b) R and S are two more points. PR =      − 1 2 and PS = 3 PR . (i) Write down the vector PS . Answer(b)(i) PS =         [1] (ii) Mark the point S on the grid. [1]

7 © UCLES 2010 0581/11/O/N/10 [Turn over For Examiner's Use 14 Simplify the following. (a) 80 Answer(a) [1] (b) (x5)2 Answer(b) [1] (c) p–3 ÷ p4 Answer(c) [1] 15 A tourist changes $900 to euros (€) when the exchange rate is €1 = $1.356. Calculate the amount he receives. Give your answer correct to 2 decimal places. Answer € [3]

8 © UCLES 2010 0581/11/O/N/10 For Examiner's Use 16 (a) Write down all the common factors of 30 and 42. Answer(a) [2] (b) Write down the smallest number which is a multiple of both 12 and 18. Answer(b) [2] 17 Simon has ten cards, numbered 1 to 10. He chooses a card at random. Write down the probability that the number on the card is (a) 8, Answer(a) [1] (b) 12, Answer(b) [1] (c) an odd number, Answer(c) [1] (d) not a multiple of 3. Answer(d) [1]

9 © UCLES 2010 0581/11/O/N/10 [Turn over For Examiner's Use 18 35 cm 44 cm NOT TO SCALE A cylindrical tank, with radius 35 cm, is filled with water to a depth of 44 cm. (a) Calculate the area of the base of the tank. Answer(a) cm2 [2] (b) Calculate the volume of water in the tank. Answer(b) cm3 [1] (c) Change your answer to part (b) into litres. Answer(c) litres [1]

10 © UCLES 2010 0581/11/O/N/10 For Examiner's Use 19 In this question, you must show all the steps in your working. Without using a calculator, find the value of (a) 5 4 2 3 1 1 ÷ , Answer(a) [3] (b) 5 3 15 13 + . Give your answer as a mixed number. Answer(b) [3]

11 © UCLES 2010 0581/11/O/N/10 For Examiner's Use 20 w° p° t° A D C B M NOT TO SCALE 32° 67° The diagram shows a quadrilateral ABCD with DC parallel to AB. (a) Write down the geometrical name for a quadrilateral with only one pair of parallel sides. Answer(a) [1] (b) ABM is a straight line and DC = AC. Angle DCA = 32° and angle ACB = 67°. Find the values of p, t and w, giving a reason for each answer. Answer (b) p = because [2] t = because [2] w = because [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. © UCLES 2010 0581/11/O/N/10 BLANK PAGE

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2010 question paper for the guidance of teachers 0581 MATHEMATICS 0581/11 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. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2010 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 2010 0581 11 © UCLES 2010 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 −8 1 Accept negative or minus in place of ‘–’ 2 3.87 × 10-3 1 3 (Triangular) prism 1 4 17.5 1 5 54(.00) final answer 2 M1 for 100 5.1 8 450 × × oe or SC1 for 504(.00) 6 Perpendicular bisector of AB with 2 pairs of arcs 2 SC1 accurate, but without arcs 7 11.5, 12.5 1, 1 Independent SC1 if answers reversed 8 14 2 M1 for ( ) 7 7 108 230 × + or better or SC1 for 216 as answer (steel) 9 8.36(0) 2 M1 for 3.6 h = tan 53° or h 3.6 = tan 37° or better 10 (a) 5.062608(024) (b) 5.063 1 1ft ft (a) to 4sf only if their (a) is 5 digits or more 11 (a) 2 lines joining opposite vertices (b) Centre square and any other or 2 adjacent corner squares or 2 centre squares on adjacent edges 1, 1 1 Independent Accept reasonable freehand Any of these diagrams: May be rotated through 90, 180, 270 degrees

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 11 © UCLES 2010 12 (x = ) 7 (y =) −3 3 M1 for multiplying/dividing and adding/ subtracting or other complete correct method A1 for one correct variable 13 (a)       2 4 1 (b) (i)      − 3 6 1 (ii) S plotted at (−3 , 4 ) 1ft ft their PS 14 (a) 1 (b) x10 1 1 (c) 7 − p or 7 1 p 1 15 663.72 3 M2 for 663.716…. or M1 for 900 ÷ 1.356 and B1 for their longer wrong answer corrected to 2dp 16 (a) 1, 2, 3, 6 final answer cao (b) 36 only (as final answer) 2 2 B1 for only 3 factors as final answer or all 4 plus a wrong one as final answer B1 for any common multiple seen anywhere 17 (a) 10 1 1 (b) 0 1 Accept 10 0 but no other number than 10 (c) 10 5 oe 1 (d) 10 7 1 18 (a) 3846 to 3849 or 3850 (b) 169224 to 169356 or 169400 or 169000 (c) 169.2 to 169.4 or 169 2 1ft 1ft M1 for π × 352 or SC1 correct volume answer ft their (a) × 44 ft their (b) ÷ 1000

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 11 © UCLES 2010 19 (a) 14 5 3 4 × M2 M1 for 5 14 3 4 ÷ and M1 for ‘correct’ expression with their inverted 2nd fraction 21 10 A1 Allow 42 20 isw for attempt to cancel only (b) 15 13 + 15 3 3× or better or equivalent B2 If B0, then B1 for 15 13 + their 15 9 or equivalent pair of fractions 15 7 1 B1ft Independent ft their improper fraction given as a mixed number 20 (a) Trapezium (b) p = 32°, alternate t = 99°, exterior angle (of) triangle 1 1, 1 1ft, 1 Accept Z angles ft if t = p + 67 Accept angle of triangles and angles on straight line w = 74°, (base angle) isosceles triangle 1 , 1 Accept ) 32 180 ( 2 1 − with isosceles