Cambridge IGCSE Mathematics - International 0607 — 2010 Oct/Nov Paper 1 · Variant 1

This document consists of 10 printed pages and 2 blank pages. IB10 11_0607_01/2RP © UCLES 2010 [Turn over *5564235406* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/01 Paper 1 (Core) October/November 2010 45 minutes Candidates answer on the Question Paper Additional Materials: Geometrical Instruments 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. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40. www.XtremePapers.com

2 © UCLES 2010 0607/01/O/N/10 Formula List Area, A, of triangle, base b, height h. A = 1 2 bh Area, A, of circle, radius r. A = πr2 Circumference, C, of circle, radius r. C = 2πr Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of prism, cross-sectional area A, length l. V =Al Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3

3 © UCLES 2010 0607/01/O/N/10 [Turn over For Examiner's Use Answer all the questions. 1 (a) Find the lowest common multiple of 6 and 9. Answer(a) [1] (b) Work out 52 – 23. Answer(b) [2] 2 (a) Samir and Josef divide $250 in the ratio 2 : 3. Calculate how much money each receives. Answer(a) Samir $ Josef $ [2] (b) A recipe for 3 people needs 600 g of pasta. Work out how much pasta is needed for 8 people. Answer(b) g [2]

4 © UCLES 2010 0607/01/O/N/10 For Examiner's Use 3 P(2, 3) and Q(4, 7) are two points. (a) Find the gradient of the line joining P and Q. Answer(a) [2] (b) Find the co-ordinates of the midpoint of the line joining P and Q. Answer(b) ( , ) [1] 4 60° NOT TO SCALE O A circle, centre O, has an area of 600 cm2. Find the area of the shaded sector. Answer cm2 [2]

5 © UCLES 2010 0607/01/O/N/10 [Turn over For Examiner's Use 5 The heights of a number of students were measured. The results are shown in the cumulative frequency diagram. 120 110 100 90 80 70 60 50 40 30 20 10 0 155 150 160 165 170 175 180 185 190 Height (cm) Cumulative frequency (a) How many students were measured? Answer(a) [1] (b) Find the interquartile range. Answer(b) cm [2]

6 © UCLES 2010 0607/01/O/N/10 For Examiner's Use 6 Diagram 1 Diagram 2 Diagram 3 Diagram 4 (a) Draw Diagram 4 in this sequence. [1] (b) (i) Write down, as a sequence, the number of dots in each diagram. Answer(b)(i) , , , [1] (ii) Write down the nth term of this sequence. Answer(b)(ii) [1] 7 Solve the simultaneous equations 2x = y + 8 and 3x + 2y = 5 . Answer x = y = [4]

7 © UCLES 2010 0607/01/O/N/10 [Turn over For Examiner's Use 8 (a) B D A 70° E C x° NOT TO SCALE In the diagram DE is parallel to BC. AD = DE and angle ABC = 70°. Find the value of x. Answer(a) x = [2] (b) y° 20° z° O Q P NOT TO SCALE The diagram shows a circle, centre O, with a tangent drawn at P. Angle OQP = 20°. Find the values of y and z. Answer(b) y = [1] z = [1]

8 © UCLES 2010 0607/01/O/N/10 For Examiner's Use 9 (a) Expand the brackets and simplify. 3(x – y) – 2(x – 5y) Answer(a) [2] (b) Factorise completely. 3x2 + 9xy2 Answer(b) [2] (c) Write as a single fraction. 2 3 5 x x − Answer(c) [2]

9 © UCLES 2010 0607/01/O/N/10 [Turn over For Examiner's Use 10 5 m 5 m 4 m NOT TO SCALE A cuboid has a square base of side 5 m and a height of 4 m. (a) Calculate the volume of the cuboid. Answer(a) m3 [1] (b) Calculate the total surface area of the cuboid. Answer(b) m2 [2]

10 © UCLES 2010 0607/01/O/N/10 For Examiner's Use 11 Student A B C D E F G H Test 1 25 20 40 25 50 20 30 40 Test 2 30 25 35 25 40 30 35 40 The table shows the marks scored by 8 students in two mathematics tests. The marks for students A to F are shown on the scatter diagram below. Test 2 Test 1 40 30 20 10 10 20 30 40 50 0 (a) On the diagram, plot the marks for students G and H. [1] (b) The mean for Test 1 is 31.25. Calculate the mean for Test 2. Answer(b) [2] (c) Plot the mean point on the scatter diagram. [1] (d) Draw the line of best fit on the scatter diagram. [1]

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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 0607/01/O/N/10 BLANK PAGE

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 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/01 Paper 1 (Core), maximum raw mark 40 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 0607 01 © UCLES 2010 1 (a) (b) 18 17 B1 B2 If B0 award M1 for 52 = 25 or 23 = 8 seen [3] 2 (a) Samir 100 Josef 150 B2 If B0 award M1 for 250 ÷ 5 seen or implied by 50 (b) 1600 B2 If B0 award M1 for 3 600 seen or implied by 200 [4] 3 (a) 2 4 3 7 − − M1 For using the gradient formula or sketch 2 4 oe A1 (b) (3, 5) B1 [3] 4 100 cm2 B2 If B0 award M1 for 60 ÷ 360 or 360 ÷ 60 seen, oe [2] 5 (a) (b) 120 10 B1 B2 If B0 award B1 for either 165 or 175 seen [3] 6 (a) (b) (c) Correct diagram 1, 4, 9, 16 n2 or n × n oe cao B1 B1ft B1 ft on their last number [3] 7 For rearranging equation(s) oe For coefficients of x and y equal if using elimination method or correct substitution x = 3, y = −2 www 4 M1 M1 A1A1 Independent [4] 8 (a) (b) 55° 140° 70° B2 B1 B1 If B0 award M1 for 180 – 70 seen or implied by 110° [4]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0607 01 © UCLES 2010 9 (a) (b) 3x – 3y – 2x + 10y x + 7y 3x(x + 3y2) B1 B1ft B2 For correctly multiplying out Dependent on 4 terms Award B1 for any other correct factorising (c) 15 3 10 x x − oe 15 7x M1 A1 [6] 10 (a) (b) 100 2 × 25 + 4 × 20 130 B1 M1 A1 [3] 11 (a) (b) Both points correctly plotted 32.5 P1 B2 Tolerance is 1mm for parts (a) (c) and (d) If B0 award M1 for 260 seen or implied. If working shown condone one error or omission. (c) Correct point P1ft or 8 ∑f seen (d) Correct ruled line passing through mean point L1ft For line though their mean point and intercepting vertical axis between 10 and 25 [5]