Cambridge IGCSE Mathematics (with coursework) 0581 — 2011 Oct/Nov Paper 1 · Variant 1

This document consists of 11 printed pages and 1 blank page. IB11 11_0581_11/FP © UCLES 2011 [Turn over *6795341079* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/11 Paper 1 (Core) October/November 2011 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 2011 0581/11/O/N/11 For Examiner's Use 1 A S The diagram shows the map of part of an orienteering course. Sanji runs from the start, S, to the point A. Write as a column vector. Answer           [1] 2 When Ali takes a penalty, the probability that he will score a goal is 5 4 . Ali takes 30 penalties. Find how many times he is expected to score a goal. Answer [2] 3 The ratio of Anne’s height : Ben’s height is 7 : 9. Anne’s height is 1.4 m. Find Ben’s height. Answer m [2]

3 © UCLES 2011 0581/11/O/N/11 [Turn over For Examiner's Use 4 The distance between the centres of two villages is 8 km. A map on which they are shown has a scale of 1 : 50 000. Calculate the distance between the centres of the two villages on the map. Give your answer in centimetres. Answer cm [2] 5 10 8 6 4 2 0 Black Silver Red Favourite colour Green Blue Frequency The bar chart shows the favourite colours of students in a class. (a) How many students are in the class? Answer(a) [1] (b) Write down the modal colour. Answer(b) [1]

4 © UCLES 2011 0581/11/O/N/11 For Examiner's Use 6 Use your calculator to find 1.5 3.1 5.75 45 + × . Answer [2] 7 (a) Calculate 60% of 200. Answer(a) [1] (b) Write 0.36 as a fraction. Give your answer in its lowest terms. Answer(b) [2] 8 A circle has a radius of 50 cm. (a) Calculate the area of the circle in cm2. Answer(a) cm2 [2] (b) Write your answer to part (a) in m2. Answer(b) m2 [1]

5 © UCLES 2011 0581/11/O/N/11 [Turn over For Examiner's Use 9 30 25 20 15 10 5 0 6 am 9 am Noon Time 3 pm 6 pm Temperature (°C) The graph shows the temperature in Paris from 6 am to 6 pm one day. (a) What was the temperature at 9 am? Answer(a) °C [1] (b) Between which two times was the temperature decreasing? Answer(b) and [1] (c) Work out the difference between the maximum and minimum temperatures shown. Answer(c) °C [1] 10 (a) Write down the mathematical name of a quadrilateral that has exactly two lines of symmetry. Answer(a) [1] (b) Write down the mathematical name of a triangle with exactly one line of symmetry. Answer(b) [1] (c) Write down the order of rotational symmetry of a regular pentagon. Answer(c) [1]

6 © UCLES 2011 0581/11/O/N/11 For Examiner's Use 11 Without using your calculator, work out       + 4 1 3 2 2 1 . Show all your working clearly and give your answer as a fraction. Answer [3] 12 y x 1 0 – 1 – 2 – 3 – 4 2 9 8 7 6 5 4 3 2 1 The diagram shows the graph of y = (x + 1)2 for −4 Y x Y 2. (a) On the same grid, draw the line y = 3. [1] (b) Use your graph to find the solutions of (x + 1)2 = 3. Give each solution correct to 1 decimal place. Answer(b) x = or x = [2]

7 © UCLES 2011 0581/11/O/N/11 [Turn over For Examiner's Use 13 NOT TO SCALE The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size. Calculate the size of one of these angles. Answer [3] 14 (a) Expand and simplify. 2(3x – 2) + 3(x – 2) Answer(a) [2] (b) Expand. x(2x2 – 3) Answer(b) [2]

8 © UCLES 2011 0581/11/O/N/11 For Examiner's Use 15 50 40 30 20 10 0 10 20 30 40 Mathematics test mark English test mark 50 60 70 80 The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English test by 15 students. (a) Describe the correlation. Answer(a) [1] (b) The mean for the Mathematics test is 47.3 . The mean for the English test is 30.3 . Plot the mean point (47.3, 30.3) on the scatter diagram above. [1] (c) (i) Draw the line of best fit on the diagram above. [1] (ii) One student missed the English test. She received 45 marks in the Mathematics test. Use your line to estimate the mark she might have gained in the English test. Answer(c)(ii) [1]

9 © UCLES 2011 0581/11/O/N/11 [Turn over For Examiner's Use 16 (a) A B C D E 110° NOT TO SCALE In the diagram, AB is parallel to DE. Angle ABC = 110°. Find angle BDE. Answer(a) Angle BDE = [2] (b) t ° y° z° 50° O B A T NOT TO SCALE TA is a tangent at A to the circle, centre O. Angle OAB = 50°. Find the value of (i) y, Answer(b)(i) y = [1] (ii) z, Answer(b)(ii) z = [1] (iii) t. Answer(b)(iii) t = [1]

10 © UCLES 2011 0581/11/O/N/11 For Examiner's Use 17 y° 8 m 3 m NOT TO SCALE The diagram shows a ladder, of length 8 m, leaning against a vertical wall. The bottom of the ladder stands on horizontal ground, 3 m from the wall. (a) Find the height of the top of the ladder above the ground. Answer(a) m [3] (b) Use trigonometry to calculate the value of y. Answer(b) y = [2]

11 © UCLES 2011 0581/11/O/N/11 For Examiner's Use 18 (a) Lucinda invests $500 at a rate of 5% per year simple interest. Calculate the interest Lucinda has after 3 years. Answer(a) $ [2] (b) Andy invests $500 at a rate of 5% per year compound interest. Calculate how much more interest Andy has than Lucinda after 3 years. Answer(b) $ [4]

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 2011 0581/11/O/N/11 BLANK PAGE

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 0581/11 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. • 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 11 © 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      − 4 3 1 2 24 or 24 out of 30 2 M1 for 5 4 × 30 3 1.8 2 M1 for 1.4 ÷ 7 or SC1 for answer 180 4 16 2 B1 for 1cm to 0.5km oe or 800 000 (cm) or figs 16 5 (a) 25 1 (b) Green cao 1 6 7.5(0) cao 2 M1 for 6.4 75 . 258 7 (a) 120 1 (b) 25 9 cao 2 B1 for100 36 or 50 18 8 (a) 7853 to 7855 or 7850 or 7860 www 2 M1 for π × 502 (b) 0.7853 to 0.7855 or 0.785 or 0.786 1ft Their (a) ÷ 10 000 evaluated 9 (a) 15 1 (b) 2 (pm), 6 (pm) 1 (c) 15 1 Allow −15 10 (a) Rectangle or rhombus 1 Either one or both given (b) Isosceles (triangle) 1 (c) 5 cao 1

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 11 © University of Cambridge International Examinations 2011 11 k k 24 11 final answer www Method 1 (Addition first) B1 12 8 +12 3 or 12 3 8 + oe M1 12 their 2 11 their 1 × × A1 Method 2 (Multiplication first) B1 6 2 + 8 1 or 3 1 + 8 1 oe M1 bd bc ad + for their d c b a + A1 If M0, SC1 if 12 11 is only followed by 24 11 or if zero, SC1 if work is entirely in decimals with answer of 3 458 .0 & to 45835 .0 12 (a) Correct ruled line 1 (b) −2.7, 0.7 1, 1ft B2ft their ruled line through (0, 3) for two intersections given to 1 decimal place or B1 for –2.70 to –2.75 and 0.70 to 0.75 or B1ft their ruled line through (0, 3) for two intersections not given to 1 decimal place 13 135 cao 3 M1 for 720 or (6 – 2) × 180 oe seen in working and M1 for equation 180 + 4x = their 720 or M1 for (360 − 180) ÷ 4 (= 45) oe seen in working and M1 dep for 180 − their 45 14 (a) 9x − 10 final answer 2 B1 for 6x − 4 or 3x − 6 or for answer of 9x + j, or kx − 10 (b) 2x3 – 3x final answer 2 B1 for answer in form 2x3 + m or n – 3x 15 (a) Negative 1 Ignore embellishments (b) Correct point 1 (c) (i) Accurate ruled line 1 (ii) English mark 1ft Follow through their (c)(i) 16 (a) 70 2 B1 for angle ABD = 70° stated or seen on the diagram (b) (i) (y =) 80 1 (ii) (z =) 40 1 (iii) (t =) 10 1ft Follow through 90 − their y or 50 − their z

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 11 © University of Cambridge International Examinations 2011 17 (a) 7.42 or 7.416... cao 3 M2 for ( ) 2 2 3 8 − or complete alternate method or M1 for x2 + 32 = 82 or better (b) 67.97 to 68(.0) cao 2 M1 for cos (y) = 8 3 oe 18 (a) 75 2 M1 for 100 3 5 500 × × oe or SC1 for answer of 575 (b) 3.81(25) 4 M2 for 500 × 1.05 × 1.05 × 1.05 or M1 for 500 × 1.05 × 1.05 A1 for 578.81(25) or 78.81(25) seen and A1ft for value of 500(1.05)3 – 500 – their (a)