Cambridge IGCSE Mathematics (with coursework) 0581 — 2011 Oct/Nov Paper 3 · Variant 3

This document consists of 16 printed pages. IB11 11_0581_33/FP © UCLES 2011 [Turn over *7377641899* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/33 Paper 3 (Core) October/November 2011 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 2011 0581/33/O/N/11 For Examiner's Use 1 Caroline goes to a shop. The shopping bill shows the items she buys. Item Cost ($) 1 packet of cereal 1.20 3 bottles of water at $0.45 each 1.35 2 cartons of milk at $0.82 each 4 kg of rice at $0.90 per kg 0.7 kg of apples at $2.40 per kg (a) Complete the shopping bill. [3] (b) (i) Calculate the total amount of money Caroline spends at the shop. Answer(b)(i) $ [1] (ii) Caroline pays with a $10 note. Calculate how much change she receives. Answer(b)(ii) $ [1]

3 © UCLES 2011 0581/33/O/N/11 [Turn over For Examiner's Use (c) Caroline arrived at the shop at 09 48. She was in the shop for 18 minutes. She then took 5 minutes to walk to a café. She was in the café for 20 minutes. (i) At what time did Caroline leave the café? Answer(c)(i) [2] (ii) Caroline then went to the library. She was in the library for 45 minutes. Work out the ratio time in the shop : time in the library. Give your answer in its simplest form. Answer(c)(ii) : [2] (d) When Caroline left home she had $36.50. She returned home with $12.74. Calculate $12.74 as a percentage of $36.50. Answer(d) % [1]

4 © UCLES 2011 0581/33/O/N/11 For Examiner's Use 2 James takes 12 science tests during one school term. These are his marks. 18 11 20 15 15 12 15 9 11 15 14 13 (a) Find (i) the range, Answer(a)(i) [1] (ii) the mode, Answer(a)(ii) [1] (iii) the median, Answer(a)(iii) [2] (iv) the mean. Answer(a)(iv) [2]

5 © UCLES 2011 0581/33/O/N/11 [Turn over For Examiner's Use (b) James sorts his marks into three levels. The levels are Satisfactory (less than 12), Good (12 to 16) and Excellent (more than 16). (i) Complete the frequency table to show this information. Level Satisfactory Good Excellent Frequency 7 [1] (ii) Complete the pie chart accurately and label each sector. Good [2] (c) What fraction of the marks were Satisfactory or Good? Give your answer in its lowest terms. Answer(c) [2]

6 © UCLES 2011 0581/33/O/N/11 For Examiner's Use 3 600 550 500 450 400 350 300 250 200 150 100 50 0 09 00 09 10 09 20 09 30 09 40 Time 09 50 10 00 10 10 Bruce’s home Park Jason’s home Distance from Bruce’s home (metres) One morning, Bruce walked from his home to Jason’s home and the two boys walked to the park. The distance-time graph shows Bruce’s journey. (a) How many minutes was Bruce at Jason’s home? Answer(a) min [1] (b) How far from the park were Bruce and Jason at 09 20? Answer(b) m [2] (c) Work out the speed at which Bruce and Jason walked to the park. Give your answer in km/h. Answer(c) km/h [3] (d) Bruce stayed at the park for 35 minutes. He then walked home at a speed of 60 metres per minute. Complete the graph to show Bruce’s time at the park and his journey home. [3]

7 © UCLES 2011 0581/33/O/N/11 [Turn over For Examiner's Use 4 (a) l W C On the grid, (i) draw the reflection of W in the line l, [2] (ii) rotate W anticlockwise through 90°, about the point C. [2] (b) y x 3 2 1 –1 –2 –3 –4 0 –1 1 2 3 4 5 6 7 –2 –3 –4 –5 P R Q (i) Describe fully the single transformation that maps P onto Q. Answer(b)(i) [2] (ii) Describe fully the single transformation that maps P onto R. Answer(b)(ii) [3]

8 © UCLES 2011 0581/33/O/N/11 For Examiner's Use 5 (a) A X B C D 140° 52° 92° NOT TO SCALE In the quadrilateral ABCD, angle BAD = 52°, angle ADC = 140° and angle DCB = 92°. AB is extended to X. (i) Calculate angle CBX. Answer(a)(i) Angle CBX = [2] (ii) The line BY bisects angle CBX. Complete the statement. The lines BY and AD are because [2] (b) 4x° x° O T U P NOT TO SCALE The diagram shows a circle, centre O. PT and PU are tangents to the circle at T and U. Angle TPU = x° and angle TOU = 4x°. Calculate the value of x. Answer(b) x = [3] (c) The exterior angle of a regular polygon is 20°. Calculate the number of sides of the polygon. Answer(c) [2]

9 © UCLES 2011 0581/33/O/N/11 [Turn over For Examiner's Use 6 (a) Complete the table for y = 4 + 2x O x2. x –2 –1 0 1 2 3 4 y 1 5 1 [2] (b) On the grid, draw the graph of y = 4 + 2x O x2 for –2 Y x Y 4 . y x 6 5 4 3 2 1 –1 –2 –3 –4 0 –1 –2 2 3 4 1 [4] (c) (i) Draw the line of symmetry of the graph. [1] (ii) Write down the equation of this line of symmetry. Answer(c)(ii) [1] (d) Use your graph to solve the equation 4 + 2x O x2 = 0. Answer(d) x = or x = [2]

10 © UCLES 2011 0581/33/O/N/11 For Examiner's Use 7 8 7 6 5 4 3 2 1 0 3 3 1 2 4 4 1 2 5 5 1 2 6 6 1 2 Shoe size Frequency The bar chart shows the frequencies of the shoe sizes for a group of students. (a) Use the information in the bar chart to complete the frequency table. Shoe size 3 3 2 1 4 4 2 1 5 5 2 1 6 6 2 1 Frequency 4 1 [2] (b) How many students are in the group? Answer(b) [1] (c) Calculate the mean shoe size. Answer(c) [3]

11 © UCLES 2011 0581/33/O/N/11 [Turn over For Examiner's Use 8 A B (a) Construct triangle ABC accurately, with AC = 10 cm and BC = 8 cm. The line AB has been drawn for you. [2] (b) (i) Using a straight edge and compasses only, construct the bisector of angle A. [2] (ii) The bisector of angle A meets BC at X. Measure the length of BX. Answer(b)(ii) BX = cm [1] (c) (i) Using a straight edge and compasses only, construct the perpendicular bisector of AB. [2] (ii) The perpendicular bisector of AB meets AC at Y and AX at Z. Measure angle CYZ. Answer(c)(ii) Angle CYZ = [1] (d) Shade the region inside triangle ABC which is • nearer to AB than to AC and • nearer to B than to A. [1]

12 © UCLES 2011 0581/33/O/N/11 For Examiner's Use 9 P Q R 12 cm 25 cm 5 cm NOT TO SCALE The diagram shows a solid triangular prism of length 25 cm. The cross-section of the prism is triangle PQR. PQ = 5 cm, QR = 12 cm and angle PQR = 90°. (a) (i) Calculate the volume of the prism. Answer(a)(i) cm3 [3] (ii) The prism is made from wood. The mass of 1 cm3 of the wood is 0.96 g. Calculate the mass of the prism. Give your answer in kilograms. Answer(a)(ii) kg [2]

13 © UCLES 2011 0581/33/O/N/11 [Turn over For Examiner's Use (b) (i) Show that PR = 13 cm. Answer(b)(i) [2] (ii) The prism is completely covered with plastic at a cost of $0.08 per square centimetre. By finding the total area of the two triangles and the three rectangles, calculate the total cost of the plastic used. Answer(b)(ii) $ [4]

14 © UCLES 2011 0581/33/O/N/11 For Examiner's Use 10 (a) Tatiana goes for a walk. (i) She walks for 15 minutes at a speed of 80 metres per minute. Calculate the distance she walks. Answer(a)(i) m [1] (ii) She then walks for a further p minutes at w metres per minute. Write down an expression, in terms of p and w, for the total distance Tatiana walks. Answer(a)(ii) m [1] (iii) Write down an expression, in terms of p and w, for Tatiana’s average speed, in metres per minute. Answer(a)(iii) m/min [2]

15 © UCLES 2011 0581/33/O/N/11 [Turn over For Examiner's Use (b) The volume, V, of a solid is given by the following formula. V = 3b(t + 2 1 m) (i) Find V when b = 4, t = 5 and m = 6 . Answer(b)(i) V = [2] (ii) Find b when t =3, m = 2 and V = 84. Answer(b)(ii) b = [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 2011 0581/33/O/N/11 For Examiner's Use 11 (a) Write down the next term in each of the following sequences. (i) 8, 15, 22, 29, [1] (ii) 3, 6, 12, 24, [1] (iii) 1, 4, 9, 16, [1] (iv) 0, 3, 8, 15, [1] (b) Write down an expression, in terms of n, for the nth term of (i) the sequence in part(a)(iii), Answer(b)(i) [1] (ii) the sequence in part(a)(iv). Answer(b)(ii) [1] (c) The nth term of a sequence is 7n –3 . (i) Write down the value of the 4th term. Answer(c)(i) [1] (ii) Which term has a value of 592? Answer(c)(ii) [2] (d) 1, 2, 2, 4, 8, 32, 256, …… Work out the next two terms of this sequence. Answer(d) , [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 0581/33 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. • 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 33 © 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 (a) 1.64 B1 3.6(0) B1 1.68 B1 (b) (i) 9.47 ft 1ft ft their table (ii) 0.53 ft 1ft ft their (i) (c) (i) 10 31 2 B1 for 43 seen (ii) 2 : 5 cao 2 B1 for 18 : 45 oe (d) 34.9 1 2 (a) (i) 11 1 (ii) 15 1 (iii) 14.5 2 M1 for ordering list or substantial part of list or 14 & 15 (iv) 14 2 M1 for (9 + 11 + 11 + 12 + 13 + 14 + 15 + 15 + 15 + 15 + 18 + 20) (b) (i) 3, …, 2 1 (ii) Angles of 90° and 60° 1ft ft only if total equals 12 Correct labels 1 (Dependent) (c) 6 5 cao 2 M1 for 12 10 or 12 their 7 3 their + from table 3 (a) 5 1 (b) 150 2 B1 for 450 seen or implied (c) 1.8 3 M2 for 25 .0 45 .0 oe (M1 for correct distance ÷ correct time) (d) Straight line (09 25, 600) to (10 00, 600) 1 Straight line (10 00, 600 to 10 10, 0) ft 2ft M1 for 600 ÷ 60 oe ft their graph 10 mins to time axis

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 33 © University of Cambridge International Examinations 2011 4 (a) (i) Correct reflection 2 B1 if reflected in other vertical line (ii) Correct rotation 2 B1 if rotated about C but clockwise through 90° or correct rotation about their reflected C (b) (i) Translation,       − − 1 9 2 B1 for translation B1 for column vector (ii) Enlargement , (centre) (0, 0), (sf) 2 1 3 B1 B1 B1 5 (a) (i) 104 2 M1 for 360 – (52 + 140 + 92) implied by 76 (ii) Parallel 1 Dependent on (i) correct Angle YBX = 52° oe 1 Dependent on word parallel already given (b) 36 3 M2 for 360 = 90 + 90 + x + 4x oe (B1 if angle T or U = 90° soi) (c) 18 2 M1 if angle sum = 360 soi or long method 6 (a) –4, …, 4, …, 4, …, –4 2 B1 for both –4s B1 for both 4s (b) 7 points plotted ft 3ft P2 for 5 or 6 points plotted ft P1 for 3 or 4 Reasonable curve through at least 6 points 1ft Only ft if shape parabola (c) (i) The line x = 1 drawn 1ft (ii) x = 1 1ft (d) –1.4 to –1.1, 3.1 to 3.4 2ft B1 B1ft if not in these ranges 7 (a) …, 5, 8, 7, 6, 4, 5, … 2 B1 for 4 or 5 correct (b) 40 1ft (c) 4.5375 or 4.537 or 4.538 or 4.54 www3 Allow 4.5 but only with working 3 M1 for 4 × 3 + 5 × 3.5 + 8 × 4 + 7 × 4.5 + 6 × 5 + 4 × 5.5 + 5 × 6 + 1 × 6.5 M1 dependent for dividing their 181.5 by their 40 (M1 + M1 implied by 175(.1625))

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 33 © University of Cambridge International Examinations 2011 8 (a) Correct construction with arcs 2 B1 for two correct lines without arcs or B1 for accurate arcs seen or B1 for 1 correct line with 2 arcs seen SC1 for AC = 8 and BC = 10 correct with arcs (b) (i) Correct construction with arcs 2ft ft their (a) B1ft for accurate line drawn without arcs or B1ft for accurate arcs seen or B1ft for accurate line with arcs bisecting another angle (ii) 4.2 to 4.5 1ft Strict ft their b(i) with intersection on opposite side of triangle (c) (i) Correct construction with arcs 2ft ft their (a) B1ft for accurate line drawn without arcs or B1ft for two pairs of accurate arcs seen or B1ft for accurate line with arcs, bisecting AB or AC (ii) 129° to 133° 1ft Strict ft from their C on triangle, their Y on one side of triangle and their Z on their intersection of b(i) and c(i) (d) Correct quadrilateral shaded 1 From their triangle 9 (a) (i) 750 3 M2 for 0.5 × 12 × 5 × 25 seen or implied (M1 for 0.5 × 12 × 5 or M1 for their area of cross-section × 25) (ii) 0.72 2ft ft their (i) × 0.00096 SC1 for 720 (or ft their (i) × 0.96) (b) (i) 52 + 122 M1 169 M1 (ii) 64.8(0) www4 4 M2 for 2 × 2 1 × 12 × 5 + 25 × 13 + 25 × 12 + 25 × 5 (M1 for any three correct) M1 for their area × 0.08 10 (a) (i) 1200 1 (ii) 1200 + pw 1ft ft their (i) + pw (iii) p pw + + 15 1200 2ft ft their (ii)/(15 + p) M1 for ÷ (15 + p) (b) (i) 96 2 M1 for 3 (4)(5 + 2 1 ×6) or better (ii) 7 3 M1 for 84 = 3b(3 + 2 1 ×2) or better A1 for equation 12b = 84 oe correct kb = l

Page 5 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 33 © University of Cambridge International Examinations 2011 11 (a) 36, 48, 25, 24 ft 4 B1 each ft their 25 – 1 (b) (i) n2 oe 1 (ii) n2 – 1 oe 1ft ft their (i) – 1, if expression in n (c) (i) 25 1 (ii) 85 2 M1 for 7n – 3 = 592 or better (d) 8192, 2 097 152 2 B1 each SC1ft 256 × their 8192