Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 Oct/Nov Paper 3 · Variant 3

This document consists of 16 printed pages. IB10 11_0581_33/FP © UCLES 2010 [Turn over *1239600127* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/33 Paper 3 (Core) October/November 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/O/N/10 For Examiner's Use 1 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 Number of children 4 5 6 Frequency The number of children in each of 40 families was recorded. The bar chart shows the results. (a) Complete the frequency table. Number of children 0 1 2 3 4 5 6 Frequency 4 6 [3] (b) Find (i) the mode, Answer(b)(i) [1] (ii) the median, Answer(b)(ii) [2]

3 © UCLES 2010 0581/33/O/N/10 [Turn over For Examiner's Use (iii) the mean. Answer(b)(iii) [3] (c) A pie chart showing the information has been started. (i) Calculate the angles of the sectors for 3 and 4 children. Answer(c)(i) , [3] (ii) Complete the pie chart accurately. 2 children 1 child 0 children 6 children 5 children [1]

4 © UCLES 2010 0581/33/O/N/10 For Examiner's Use 2 Eduardo lives in Argentina and travels to Uruguay for a holiday. (a) His flight from Buenos Aires to Montevideo takes 55 minutes. The plane departs at 17 35. (i) Write down the arrival time. Answer(a)(i) [1] (ii) The distance between Buenos Aires and Montevideo is 230 km. Calculate the average speed of the plane. Answer(a)(ii) km/h [3] (b) At the airport, Eduardo changed some Argentine pesos (ARS). He received 9121 Uruguay pesos (UYU). (i) The exchange rate was ARS 1 = UYU 6.515. Calculate how many Argentine pesos Eduardo changed. Answer(b)(i) ARS [2] (ii) Eduardo spent 1890 Uruguay pesos on meals. Calculate this as a percentage of the UYU 9121. Answer(b)(ii) % [1] (iii) At the end of his holiday, Eduardo has UYU 610 remaining. He changes this into Argentine pesos when the exchange rate is UYU 1 = ARS 0.149. Calculate how much Eduardo receives in Argentine pesos. Give your answer to the nearest whole number. Answer(b)(iii) ARS [2]

5 © UCLES 2010 0581/33/O/N/10 [Turn over For Examiner's Use 3 G H F I y x 12 11 10 9 8 7 6 5 4 3 2 1 –1 –2 –3 0 –1 1 2 3 4 5 6 7 8 9 10 –2 –3 –4 –5 (a) Describe fully the single transformation that maps (i) flag F onto flag G, Answer(a)(i) [2] (ii) flag F onto flag H, Answer(a)(ii) [2] (iii) flag F onto flag I. Answer(a)(iii) [3] (b) On the grid, draw (i) the reflection of flag F in the y-axis, [2] (ii) the enlargement of flag F, centre (0, 0) and scale factor 4. [2]

6 © UCLES 2010 0581/33/O/N/10 For Examiner's Use 4 North 200 m 75 m NOT TO SCALE B North North C A Dariella walks 200 m from A to B. She then turns through 90° and walks 75 m from B to C. (a) Calculate (i) the distance AC, Answer(a)(i) m [2] (ii) angle CAB. Answer(a)(ii) Angle CAB = [2] (b) The bearing of B from A is 065°. Find the bearing of (i) C from A, Answer(b)(i) [1] (ii) A from C, Answer(b)(ii) [1] (iii) C from B. Answer(b)(iii) [2]

7 © UCLES 2010 0581/33/O/N/10 [Turn over For Examiner's Use 5 C D A B The diagram shows a quadrilateral ABCD. (a) Using a straight edge and compasses only, construct (i) the perpendicular bisector of AB, [2] (ii) the bisector of angle ADC. [2] (b) Draw accurately the locus of points, inside the quadrilateral, that are 2 cm from BC. [2] (c) Shade the region, inside the quadrilateral, which is nearer to B than to A and nearer to DC than to DA and more than 2 cm from BC. [1]

8 © UCLES 2010 0581/33/O/N/10 For Examiner's Use 6 6 cm 12 cm 20 cm 8 cm D A B C NOT TO SCALE The diagram shows a prism of length 20 cm. The cross-section of the prism is a trapezium, ABCD, with AB parallel to DC. AB = 12 cm, DC = 8 cm and the perpendicular distance between AB and DC is 6 cm. (a) Calculate (i) the area of the trapezium ABCD, Answer(a)(i) cm2 [2] (ii) the volume of the prism. Answer(a)(ii) cm3 [1]

9 © UCLES 2010 0581/33/O/N/10 [Turn over For Examiner's Use (b) The prism is solid and made of brass. (i) One cubic centimetre of brass has a mass of 8.5 grams. Calculate the mass of the prism. Give your answer in kilograms. Answer(b)(i) kg [2] (ii) Brass costs $2.26 for one kilogram. How much will the brass cost to make this prism? Give your answer correct to 2 decimal places. Answer(b)(ii) $ [2]

10 © UCLES 2010 0581/33/O/N/10 For Examiner's Use 7 Alex has d dollars to spend. He buys a book which costs $9 less than 2 times d. (a) Write down an algebraic expression, in terms of d, for the cost of the book. Answer(a) $ [2] (b) The actual cost of the book is $7.80. Find the value of d. Answer(b) d = [2] (c) How much does Alex have left after buying the book? Answer(c) $ [1]

11 © UCLES 2010 0581/33/O/N/10 [Turn over For Examiner's Use 8 The area, A, of a sector of a circle of radius r is given by the formula below. A = 5 π 2 r (a) Calculate the area when the radius is 7.5 cm. Answer(a) cm2 [2] (b) Make r the subject of the formula. Answer(b) r = [3] (c) Calculate r when A = 4.8 cm2. Answer(c) r = cm [2]

12 © UCLES 2010 0581/33/O/N/10 For Examiner's Use 9 (a) (i) Complete the table for y = 12 – x2. x 0 1 2 3 4 y 12 11 – 4 [2] (ii) On the grid, draw the graph of y = 12 – x2 for 0 Y x Y 4. y x 12 11 10 9 8 7 6 5 4 3 2 1 0 –1 –2 –3 –4 1 2 3 4 5 6 7 8 [3] (iii) Use your graph to solve the equation 12 – x2 = 0. Answer (a)(iii) x = [1]

13 © UCLES 2010 0581/33/O/N/10 [Turn over For Examiner's Use (b) (i) Complete the table for y = 12 , x x ≠ 0 . x 1 2 3 4 5 6 7 8 y 12 6 4 2.4 1.7 [3] (ii) On the grid opposite, draw the graph of y = 12 x for 1 Y x Y 8. [3] (c) Write down the co-ordinates of the points of intersection of the two graphs. Answer(c) ( , ) , ( , ) [2]

14 © UCLES 2010 0581/33/O/N/10 For Examiner's Use 10 F E A B D C G H NOT TO SCALE ABCDEFGH is a regular octagon. (a) Show that angle BCD = 135°. Answer (a) [2] (b) Find (i) angle DEB, Answer(b)(i) Angle DEB = [1] (ii) angle FEB. Answer(b)(ii) Angle FEB = [1]

15 © UCLES 2010 0581/33/O/N/10 [Turn over For Examiner's Use (c) F E A B D Q R P S C G H NOT TO SCALE The sides of the octagon are extended to form the square PQRS. The length of each side of the octagon is 12 cm and the length of BP is 8.485 cm. Calculate the area of (i) triangle BPC, Answer(c)(i) cm2 [2] (ii) the octagon ABCDEFGH. Answer(c)(ii) cm2 [3] Question 11 is printed on the next page.

16 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/O/N/10 For Examiner's Use 11 (a) (i) 0, 1, 1, 2, 3, 5, 8, …. This sequence has the rule: After the first two terms, any term is the sum of the two previous terms. The first two terms are 0 and 1, the 3rd term is 0 + 1 = 1, the 4th term is 1 + 1 = 2, the 5th term is 1 + 2 = 3 and so on. Show that the 8th term is 13. Answer(a)(i) [1] (ii) Each of the following sequences have the same rule as part (a)(i). For each sequence write down the missing terms. 2, 5, 7, , [1] 4, 3, 7, , [1] 5, 2, , [1] 0, , 3, [1] 1, , , 9, [1] , , 5, 7 [1] (b) For the following sequences find the next term and the n th term. (i) 1, 3, 5, 7, 9, n th term = [3] (ii) 1, 4, 9, 16, 25, n th term = [2] (iii) 1, 1 2 , 3 1 , 4 1 , 5 1 , n th term = [2]

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 0581/33 Paper 3 (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 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 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) 10, 9, 5, 5, 1 (b) (i) 2 (ii) 2.5 3 1 2 B2 for 4 correct, B1 for 3 correct M1 for evidence of finding mid-value of 20 pieces of data (iii) 2.6 3 M1 for evidence of ∑fx then M1dep for ÷ 40 (c) (i) 81 or 45 45 or 81 (ii) Correct angles of 81° and 45° 2ft 1ft 1ft ft their 9 or their 5 M1 for their 9 or their 5 ÷ 40 × 360 Correct or ft 126 – their first angle ft only if add up to 126 2 (a) (i) 18 30 oe (ii) 251 (250.9…) (b) (i) 1400 (ii) 20.7(2…) (iii) 91 1 3 2 1 2 M1 for distance ÷ time (any units) and M1 for 55 ÷ 60 oe M1 for 9121 ÷ 6.515 B1 for 90.89 or 90.9 or 90.8 or 610 × 0.149 or B1 (indep) for correct rounding to integer if from a decimal 3 (a) (i) Translation      − 3 5 1, 1 (ii) Reflection in line y = 4 (iii) Rotation, (2, 2.5), 180° or half- turn (b) (i) Correct reflection in y-axis (ii) Correct enlargement, (0, 0), factor 4 1, 1 1, 1, 1 2 2 Line can be labelled on diagram Centre could be labelled on diagram SC1 for reflection in x-axis SC1 for any enlargement centre (0, 0) or factor 4

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 33 © UCLES 2010 4 (a) (i) 214 (213.6…) (ii) 20.6 or (20.55 – 20.56) (b) (i) (0)44 ((0)44.4…) (ii) 224 (224.4…) (iii) 335 2 2 1ft 1ft 2 M1 for 752 + 2002 M1 for tan = 75/200 or sin = 75/their (i) or cos = 200/their (i) B1 65 – their (a)(ii) if < 65 180 + their (b)(i) B1 for 65 below B or 25 above B, may be on diagram 5 (a) (i) Accurate perpendicular bisector of AB with arcs (ii) Accurate bisector of angle ADC (b) Ruled line 2 cm from and parallel to BC (c) Correct region shaded cao 2 2 2 1 SC1 if accurate without arcs or accurate bisector of wrong side with arcs SC1 if accurate without arcs or accurate bisector of wrong angle with arcs SC1 if not ruled Dependent on at least SC1 in (a)(i), (a)(ii) and (b) 6 (a) (i) 60 (ii) 1200 (b) (i) 10.2 (ii) 23.05 2 1ft 2ft 2ft M1 for full method for area with correct values ft their (i) × 20 SC1 for figs 102 or M1 for (a)(ii) × 8.5 ÷ 1000 ft their (a)(ii) × 8.5 ÷ 1000 and SC in same way ft their (b)(i) × 2.26 M1 for 23.052 or 23.1 or (b)(i) × 2.26 or B1ind for correctly rounding to 2 dp an answer with more than 2 dp 7 (a) 2d – 9 (b) 8.4(0) (c) 0.6(0) 2 2 1ft SC1 for 9 – 2d M1 for their (a) = 7.8(0) ft their (b) – 7.80, only if positive 8 (a) 35.3 art 2 M1 for substituting r = 7.5 in formula (b) π A 5 3 M1 for correctly multiplying by 5 M1 for correctly dividing by π M1 for correctly taking a square root (c) 2.76 art cao 2 M1 for substituting 4.8 in their (b) or if working backwards from original formula, substituting and reaching r2 = 5 × 4.8 ÷ π

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 33 © UCLES 2010 9 (a) (i) 8, 3 (ii) 5 points correctly plotted Smooth curve through their 5 points (iii) 3.4 Y x Y 3.6 (b) (i) 3, 2, 1.5 (ii) 8 points correctly plotted Smooth branch of rectangular hyperbola through 12 points (c) (1 < x Y 1.2, 10.6 Y y < 11) (2.6 Y x < 3, 4.2 Y y Y 4.5) 1, 1 2ft 1 1ft 1, 1, 1 2ft 1 1ft 1ft P1 for 4 correct points ft ft their intersection with x-axis B1 each P1 for 6 or 7 points ft to same accuracy intersections of their two graphs 10 (a) 360 ÷ 8 (= 45) Then 180 – their 45 (= 135) (b) (i) 45 (ii) 90 (c) (i) 35.99 to 36.(0) (ii) 695 to 696.4 1 1dep 1 1 2 3ft Alt method 180 × (8 – 2) Then their 1080 ÷ 8 (= 135) M1 for 0.5 × 8.485 × 8.485 M1 for (12 + 8.485 + 8.485)2 M1ind for correct collection of area with or without values indicated 11 (a) (i) 5 + 8 (= 13) (ii) 12, 19 10, 17 7, 9 3, 6 4, 5 3, 2 (b) (i) 11 2n – 1 (ii) 36 n2 1 1 1 1 1 1 1 1 2 1, 1 B1 for 2n ± k or jn – 1 (j ≠ 0) (iii) 6 1 n 1 1, 1