Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 May/June Paper 3 · Variant 3

This document consists of 12 printed pages. IB10 06_0581_33/FP © UCLES 2010 [Turn over *5413394739* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/33 Paper 3 (Core) May/June 2010 2 hours 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 104. www.XtremePapers.com

2 © UCLES 2010 0581/33/M/J/10 For Examiner's Use 1 A bookshop sold a total of 2750 books in January. (a) The ratio hardback books sold : paperback books sold was 4 : 7. Calculate how many paperback books were sold. Answer(a) [2] (b) 24% of the 2750 books sold were non-fiction. Calculate how many non-fiction books were sold. Answer(b) [2] (c) 330 cookery books were sold. Write 330 as a fraction of 2750 in its lowest terms. Answer(c) [2] (d) In February, the bookshop sold 14% more than the 2750 books sold in January. Calculate the number of books sold in February. Answer(d) [3] (e) The total value of the books sold in January was $9480 correct to the nearest 10 dollars. Write down the lower bound for this amount. Answer(e) $ [1] (f) 35000 books were sold in a year. Write this number in standard form. Answer(f) [1]

3 © UCLES 2010 0581/33/M/J/10 [Turn over For Examiner's Use 2 (a) Write down (i) five numbers which are multiples of 7, Answer(a)(i) , , , , [2] (ii) two common multiples of 4 and 7. Answer(a)(ii) and [2] (b) 10 12 13 16 17 23 25 39 From the list above, write down (i) a square number that is also an odd number, Answer(b)(i) [1] (ii) a prime number that is one more than a square number. Answer(b)(ii) [1] (c) n is an integer and n3 is between 60 and 70. Find the value of n. Answer(c) n = [1] (d) k and m are prime numbers. k2 + m = 23 Find k and m. Answer(d) k = m = [2]

4 © UCLES 2010 0581/33/M/J/10 For Examiner's Use 3 (a) Complete the table of values for y = 5 + x – x2. x −3 −2 −1 0 1 2 3 y −7 −1 5 3 [3] (b) On the grid below draw the graph of y = 5 + x – x2 for –3 Y x Y 3. 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –8 0 1 –1 –2 –3 2 3 y x [4] (c) Use your graph to solve the equation 5 + x – x2 = 2. Answer(c) x = or x = [2]

5 © UCLES 2010 0581/33/M/J/10 [Turn over For Examiner's Use (d) (i) Complete the table of values for y = 2x – 1. x −3 0 3 y [2] (ii) On the grid, draw the straight line y = 2x – 1 for –3 Y x Y 3. [2] (iii) Write down the gradient of y = 2x – 1. Answer(d)(iii) [1] (e) Write down the co-ordinates of the points where the line y = 2x – 1 intersects the graph of y = 5 + x – x2. Answer(e) ( , ) and ( , ) [2] 4 (a) Solve the equation. 3(x + 1) + 5(x – 3) = 48 Answer(a) x = [3] (b) Make f the subject of the formula g = 7f − 5. Answer(b) f = [2] (c) Factorise completely 6xy − 10yz. Answer(c) [2]

6 © UCLES 2010 0581/33/M/J/10 For Examiner's Use 5 Triangles DAB and DCB form a kite ABCD. Angle DAB = angle DCB = 90°. AD = DC = x cm and AB = BC = (x + 3) cm. (a) Complete the following statement. Triangle ADB is to triangle CDB. [1] (b) When x = 8, calculate angle DBC. Answer(b) Angle DBC = [2] (c) When x = 5, calculate (i) the area of triangle BCD, Answer(c)(i) cm2 [2] (ii) the area of the kite ABCD. Answer(c)(ii) cm2 [1] (d) For a different value of x, the perimeter of the kite is 62 cm. Write down and solve an equation to find this value of x. Answer(d) x = [3] A C D B x cm x cm (x + 3) cm (x + 3) cm NOT TO SCALE

7 © UCLES 2010 0581/33/M/J/10 [Turn over For Examiner's Use 6 In triangle ABC, BC = 9 cm and AC = 11 cm. The side AB has been drawn for you. A B (a) Using ruler and compasses only, complete the triangle ABC. [2] (b) Measure and write down the size of angle CAB. Answer(b) Angle CAB = [1] (c) For the constructions below, use a straight edge and compasses only. Leave in all your construction arcs. (i) Construct the bisector of angle ABC. Label the point P where the bisector crosses AC. [2] (ii) Construct the locus of points which are equidistant from A and from C. Label the point Q where the locus crosses AC. [2] (d) (i) Write down the length of PQ in centimetres. Answer(d)(i) cm [1] (ii) Shade the region inside the triangle which is nearer to AB than to BC and nearer to C than to A. [1] (e) Triangle ABC is a scale drawing. The 9 cm line, BC, represents a wall 45 metres long. The scale of the drawing is 1 : n. Find the value of n. Answer(e) n = [2]

8 © UCLES 2010 0581/33/M/J/10 For Examiner's Use 7 (a) The first four terms of a sequence are given below. 5 9 13 17 Write down (i) the next term, Answer(a)(i) [1] (ii) the 8th term, Answer(a)(ii) [1] (iii) an expression, in terms of n, for the nth term of the sequence. Answer(a)(iii) [2] (b) The first four terms of a different sequence are given below. 4 10 18 28 (i) Find the next term. Answer(b)(i) [1] (ii) The nth term of this sequence is n(n + p) where p is an integer. Find the value of p. Answer(b)(ii) p = [2] (iii) Find the 100th term of this sequence. Answer(b)(iii) [1]

9 © UCLES 2010 0581/33/M/J/10 [Turn over For Examiner's Use 8 Tom has 50 model cars. He has 10 blue cars and 19 red cars. He has no yellow cars. (a) Tom chooses a car at random. Write down the probability that it is (i) red, Answer(a)(i) [1] (ii) red or blue, Answer(a)(ii) [1] (iii) not blue, Answer(a)(iii) [1] (iv) yellow. Answer(a)(iv) [1] (b) The probability that a car is damaged is 1. How many cars are damaged? Answer(b) [1]

10 © UCLES 2010 0581/33/M/J/10 For Examiner's Use 9 The table below shows the number of visitors to a museum each day during one week. Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Number of visitors 64 34 75 77 85 96 38 (a) Work out the mean number of visitors per day during this week. Answer(a) [2] (b) Find the range. Answer(b) [1] (c) On the grid below, draw a bar chart to show the information given in the table. Use a vertical scale of 1 cm to represent 10 visitors. [5]

11 © UCLES 2010 0581/33/M/J/10 [Turn over For Examiner's Use 10 In this question give all your answers correct to 2 decimal places. (a) A bank has an exchange rate of $1= € 0.6513. (i) Jonathan changes $500 into euros (€). Calculate the amount Jonathan receives. Answer(a)(i) € [2] (ii) Arika changes €300 into dollars. Calculate the amount Arika receives. Answer(a)(ii) $ [3] (b) Dania borrows $325 for 2 years at a rate of 3.8% per year simple interest. Calculate the total amount Dania owes after 2 years. Answer(b) $ [3] (c) Lee borrows $550 for 2 years at a rate of 6% per year compound interest. Calculate the total amount Lee owes after 2 years. Answer(c) $ [3] Question 11 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 2010 0581/33/M/J/10 For Examiner's Use 11 Shapes A, B and C are shown on the grid. (a) Describe fully the single transformation which maps (i) shape A onto shape B, Answer(a)(i) [2] (ii) shape A onto shape C. Answer(a)(ii) [3] (b) On the grid draw the image of shape A after (i) a translation by the vector 6 4    , [2] (ii) an enlargement, scale factor 2, centre the origin. [2] A B C 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 0 2 1 3 5 –2 –1 –3 –5 –4 –6 –7 –8 4 6 y x

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2010 question paper for the guidance of teachers 0581 MATHEMATICS 0581/33 Paper 33 (Core), maximum raw mark 104 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 May/June 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 – May/June 2010 0581 33 © 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 art anything rounding to soi seen or implied Qu. Answers Mark Part Marks 1 (a) 1750 2 M1 2750 7 4 7 × + oe (b) 660 2 M1 100 2750 24× (c) 25 3 2 W1 for equivalent fractions (d) 3135 cao 3 M2 2750 100 114 × oe If M0 then M1 for 2750 100 14 × or 385 seen (e) (f) 9475 3.5 × 104 1 1 cao cao 2 (a) (i) (ii) (b) (i) (ii) (c) (d) Any 5 multiples of 7 Two multiples of 28 25 17 4 (k =) 2, (m =) 19 2 2 1 1 1 2 –1 each error or omission W1, W1 cao cao cao W1, W1

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0581 33 © UCLES 2010 3 (a) (b) (c) 3, 5, −1 7 points plotted reasonable freehand curve −1.3, 2.3 strict ft their intercept with y = 2 3 P3ft C1 2ft 1 each P2 for 5 or 6 points, P1 for 3 or 4 points W1 for either (d) (i) −7, −1, 5 2 W1 for 2 correct (ii) Correct ruled line 2 SC1 for freehand line, or ruled short line crossing curve twice Or their 3 points plotted (iii) 2 1 cao (e) (−3, −7) and ( 2, 3) 2ft 1 for either 4 (a) (x =) 7.5 3 W1 for correct bracket expansions M1ft for collecting their terms correctly (b) (f = ) 7 5 + g 2 M1 for one correct step seen (c) ) 5 3 ( 2 z x y − 2 W1 for ) 5 3 ( 2 yz xy − or ) 10 6 ( z x y − or ) ( 2 bz ax y + where a and b are integers 5 (a) Congruent 1 cao (b) 36° or 36.0o art 2 M1 for tan angle = 11 8 (c) (i) 20 2 M1 for ) 3 5 ( 5 2 1 + × × oe (ii) 40 1ft ft is 2 × their (c)(i) (d) 14 3 W1 for 62 3 3 = + + + + + x x x x o.e. M1ft for correct first step but must be from a linear equation k b ax = +

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0581 33 © UCLES 2010 6 (a) (b) (c) (i) (ii) (d) (i) (ii) (e) Point C constructed with arcs, AC = 11 cm BC = 9 cm 46° Bisector of angle ABC with 4 correct arcs and reaches AC Perpendicular bisector of AC, with correct arcs 0.7 to 0.8 cm Region of triangle between their constructions 500 2 1ft 2ft 2ft 1ft 1 2 W1 if correct without arcs W1 if accurate without arcs or accurate with arcs and short W1 if accurate without arcs ft their PQ provided on their AC dep on W1 and W1 in (c)(i) and (c)(ii) W1 for figs 5 or 9 and 4500 oe seen 7 (a) (i) (ii) (iii) (b) (i) (ii) (iii) 21 33 4n + 1 oe 40 3 10300 1 1 2 1 2 1ft cao cao W1 for 4n + j or kn + 1, where k not equal to zero, seen cao W1 for embedded answer or M1 for 1(1 + p) = 4 oe ft is 100 × (100 + their p ) evaluated 8 (a) (i) 50 19 1 Accept 0.38 or 38% (ii) 50 29 1 Accept 0.58 or 58% (iii) 50 40 oe 1 Accept 0.8 or 80% (iv) 0 1 Accept 50 0 , 0%, nil or zero (b) 50 or all 1

Page 5 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0581 33 © UCLES 2010 9 (a) (b) (c) 67 62 Correct labelled vertical scale Bars equal width (with consistent/without gaps), or lines All 7 bars/lines correct height 2 1 1 1 3ft M1 their 469 ÷ 7 cao W2ft for 5 or 6 bars correct, W1ft for 3 or 4 10 (a) (i) (ii) 325.65 460.62 or 460.61 2 3 M1 for 500 × 0.6513 soi M1 for 300 ÷ 0.6513 A1 for 460.6 or 461 or 460.617…. W1 indep for their visible answer corrected to 2dp (b) 349.70 3 M1 for 100 8.3 2 325 × × or 24.7(0) M1dep for their interest added to 325 (c) 617.98 3 M2 for 550 × 1.062 or M1 for 550 × 1.06 oe and M1 dep for second year Penalise accuracy only once in the question 11 (a)(i) (ii) (b)(i) Reflection in the x-axis (or y = 0) Rotation, about origin, 90° (anti- clockwise) Correct translation 1, 1 1, 1, 1 2 Accept (0,0) or O Accept (+) 90, − 270, ¼ turn W1 for correct shape and orientation translated by     0 6 or     4 0 or     6 4 (ii) Correct enlargement 2 W1 for correct orientation and size but wrong position