Cambridge IGCSE Mathematics 0580 — 2012 Oct/Nov Paper 1 · Variant 3

This document consists of 12 printed pages. IB12 11_0580_13/7RP © UCLES 2012 [Turn over *3457337604* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/13 Paper 1 (Core) October/November 2012 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.

2 © UCLES 2012 0580/13/O/N/12 For Examiner's Use 1 x° 196° NOT TO SCALE Find the value of x. Answer x = [1] 2 (a) Write down the order of rotational symmetry of this letter. H Answer(a) [1] (b) Draw the line of symmetry on this letter. A [1] 3 Work out. 43 O 49 Answer [2]

3 © UCLES 2012 0580/13/O/N/12 [Turn over For Examiner's Use 4 Simplify. (a) 5t O 2t + 4t Answer(a) [1] (b) r5 × r8 Answer(b) [1] 5 Samantha invests $600 at a rate of 2% per year simple interest. Calculate the interest Samantha earns in 8 years. Answer $ [2] 6 Show that 10 1 2 + 5 2 2 = 0.17. Write down all the steps in your working. Answer [2] 7 Pens cost p cents and rulers cost r cents. Write down an expression, in terms of p and r, for the cost of 5 pens and 11 rulers. Answer cents [2]

4 © UCLES 2012 0580/13/O/N/12 For Examiner's Use 8 Jamie needs 300 g of flour to make 20 cakes. How much flour does he need to make 12 cakes? Answer g [2] 9 Expand the brackets. y(3 O y3) Answer [2] 10 Maria pays $84 rent. The rent is increased by 5%. Calculate Maria’s new rent. Answer $ [2] 11 A carton contains 250 ml of juice, correct to the nearest millilitre. Complete the statement about the amount of juice, j ml, in the carton. Answer Y j I [2]

5 © UCLES 2012 0580/13/O/N/12 [Turn over For Examiner's Use 12 98 19.78 4.7 2 + (a) Rewrite this calculation with each number written correct to 1 significant figure. Answer(a) [1] (b) Work out the answer to your calculation in part (a). Do not use a calculator and show all your working. Answer(b) [1] 13 Factorise completely. 4xy + 12yz Answer [2] 14 Using a straight edge and compasses only, construct the locus of points which are equidistant from R and from T. [2] T R

6 © UCLES 2012 0580/13/O/N/12 For Examiner's Use 15 Find the value of 10.95 11.8 7.2 − . Give your answer correct to 4 significant figures. Answer [2] 16 Calculate the interior angle of a regular pentagon. You must show all your working. Answer [3] 17 Without using your calculator, work out 5 1 8 3 2 5 − . Give your answer as a fraction in its lowest terms. You must show all your working. Answer [3]

7 © UCLES 2012 0580/13/O/N/12 [Turn over For Examiner's Use 18 14 children played a game. The age of each child and the number of points they scored are plotted on the scatter diagram. 7 6 8 9 10 11 12 13 14 15 16 14 13 12 11 10 9 8 7 6 5 4 Points scored Age of child (a) Write down the number of points the child aged 11 scored. Answer(a) [1] (b) Draw a line of best fit on the scatter diagram. [1] (c) What type of correlation is shown? Answer(c) [1]

8 © UCLES 2012 0580/13/O/N/12 For Examiner's Use 19 y x 1 0 2 3 4 5 6 –6 –5 –4 –3 –2 –1 5 4 3 2 1 –1 –2 –3 –4 B L (a) On the grid mark the point (5, 1). Label it A. [1] (b) Write down the co-ordinates of the point B. Answer(b) ( , ) [1] (c) Find the gradient of the line L. Answer(c) [2]

9 © UCLES 2012 0580/13/O/N/12 [Turn over For Examiner's Use 20 (a) The probability that the school bus is late is 0.29 . Write down the probability that the school bus is not late. Answer(a) [1] (b) A fridge contains 12 beef pies, 3 vegetable pies and 5 chicken pies. One pie is taken at random from the fridge. Find the probability that it is (i) a vegetable pie, Answer(b)(i) [1] (ii) a beef pie or a vegetable pie, Answer(b)(ii) [1] (iii) a lamb pie. Answer(b)(iii) [1]

10 © UCLES 2012 0580/13/O/N/12 For Examiner's Use 21 C A B 8 cm 9 cm 12 cm NOT TO SCALE (a) (i) Construct an accurate drawing of triangle ABC. [2] (ii) On your drawing, mark accurately the midpoint of the side AB. Label it M. [1]

11 © UCLES 2012 0580/13/O/N/12 [Turn over For Examiner's Use (b) (i) Sketch the quadrilateral that has • opposite sides which are equal in length and parallel and • opposite angles which are equal and • diagonals which bisect each other at 90°. [1] (ii) Write down the mathematical name of this quadrilateral. Answer(b)(ii) [1] Question 22 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 2012 0580/13/O/N/12 For Examiner's Use 22 (a) In the diagram, the line AC touches the circle at B. A B C (i) Measure the length of the line AC. Answer(a)(i) AC = cm [1] (ii) Write down the mathematical name for the line AC. Answer(a)(ii) [1] (iii) Mark a point D on the circumference of the circle. [1] (b) The diameter of another circle is 3.6 cm. Calculate the circumference of this circle. Answer(b) cm [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2012 series 0580 MATHEMATICS 0580/13 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 should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2012 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2 Mark Scheme Syllabus Paper IGCSE – October/November 2012 0580 13 © Cambridge International Examinations 2012 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 74 1 2 (a) (b) 2 Correct line drawn 1 1 3 57 2 M1 64 or 7 4 (a) (b) 7t final answer r13 final answer 1 1 5 96 2 M1 for 600 × 2 × 8 oe 100 If zero SC1 696 6 100 1 + 25 4 or 0.12 + 0.42 oe 100 1 +100 16 = 0.17 or 0.01 + 0.16= 0.17 M1 M1 Independent 7 5p + 11r final answer 2 B1 5p or 11r seen 8 180 2 M1 for 20 12 300× oe 9 3y – y4 final answer 2 B1 for 3y or – y4 as part of two term expression 10 88.2(0) 2 M1 for 84 × 1.05 oe 11 249.5 [Y j <] 250.5 cao 2 B1 for either, or both correct but reversed 12 (a) (b) 100 20 52 + 4.5 cao 1 1

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2012 0580 13 © Cambridge International Examinations 2012 13 4y (x + 3z) final answer 2 B1 4(xy + 3yz ) or y (4x + 12z) or 2y (2x + 6z) 14 Accurate perpendicular bisector of RT with arcs. 2 B1 for 2 pairs of correct arcs B1 for correct line 15 8.471 cao 2 B1 for 8.47 or 8.4705 to 8.4706 or 17 144 or 17 8 8 16 108 3 M2 for 180 – (360 ÷ 5) or ( ) 5 2 5 180 − M1 for 360 ÷ 5 or 180 × 3 17 40 215 − 40 88 40 127 or 40 7 3 M2 A1       −40 8 40 15 3 OR M1 for 40 15 or 40 8 or 40 215 or 40 88 18 (a) (b) (c) 9 Ruled line of best fit drawn positive 1 1 1 19 (a) (b) (c) (5, 1) marked ( –1 , 0) 2 1 1 2 M1 correct rise over run 20 (a) (b) 0.71 oe (i) 20 3 oe or 0.15 or 15% (ii) 20 15 oe or 0.75 or 75% (iii) 0 1 1 1 1 21 (a) (b) (i) triangle with arcs (ii) Midpoint marked 5.8 – 6.2 cm (i) Correct sketch (ii) Rhombus or square cao 2 1ft 1 1 M1 1 side correct

Page 4 Mark Scheme Syllabus Paper IGCSE – October/November 2012 0580 13 © Cambridge International Examinations 2012 22 (a) (b) (i) 7.3 – 7.7 cm (ii) Tangent (iii) D marked on circumference 11.3 to 11.3112 1 1 1 2 M1 3.6 × π