Cambridge IGCSE Mathematics - International 0607 — 2011 May/June Paper 1 · Variant 1

This document consists of 8 printed pages. IB11 06_0607_11/2RP © UCLES 2011 [Turn over *5403601149* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/11 Paper 1 (Core) May/June 2011 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 2011 0607/11/M/J/11 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 2011 0607/11/M/J/11 [Turn over For Examiner's Use Answer all the questions. 1 (a) Write 6.149 correct to 1 decimal place. Answer(a) [1] (b) Write 206 correct to 2 significant figures. Answer(b) [1] (c) Write 0.0023 in standard form. Answer(c) [1] 2 (a) List all four factors of 15. Answer(a) , , , [1] (b) Find the highest common factor of 15 and 21. Answer(b) [2] 3 (a) Write down the number of lines of symmetry of a regular pentagon. Answer(a) [1] (b) A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. Write down the mathematical name of this quadrilateral. Answer(b) [1]

4 © UCLES 2011 0607/11/M/J/11 For Examiner's Use 4 (a) Solve the equation 2(3x – 5) = x + 10 . Answer(a) x = [3] (b) −3 Y x I 4 Show this inequality on the number line below. –4 –5 –3 –2 –1 0 1 2 3 4 5 x [2] 5 The nth term of a sequence is 2n – 3. (a) Write down the first term and the second term of this sequence. Answer(a) , [2] (b) Write down the 100th term of this sequence. Answer(b) [1] (c) Paulo says that the number 44 is in the sequence. Is he correct? You must show your working. [2]

5 © UCLES 2011 0607/11/M/J/11 [Turn over For Examiner's Use 6 Shade the required regions in the Venn diagrams below. (a) P ∪ Q [1] (b) P′ ∩ Q [1] 7 The diagram shows two triangles. (a) Write down the value of x. Answer(a) x = [1] (b) Complete the following statement. The two triangles are [1] (c) Find the value of y. Answer(c) y = [2] 95° 30° 15 cm y cm 95° x° 30° 5 cm 2.5 cm NOT TO SCALE U P Q U P Q

6 © UCLES 2011 0607/11/M/J/11 For Examiner's Use 8 (a) Find the gradient of the line 2y = x + 3. Answer(a) [2] (b) Write down the gradient of a line parallel to the line 2y = x + 3. Answer(b) [1] 9 O x° NOT TO SCALE The area of the circle, centre O, is 100 cm2. The area of the shaded sector is 20 cm2. Find the value of x. Answer x = [2]

7 © UCLES 2011 0607/11/M/J/11 [Turn over For Examiner's Use 10 (a) Work out 3 27 . Answer(a) [1] (b) Factorise completely. 3y2 – 15y Answer(b) [2] 11 U T B 2 6 4 3 The Venn diagram shows the number of students who play tennis (T), basketball (B), both tennis and basketball or neither of these games. (a) How many students play basketball only? Answer(a) [1] (b) How many students do not play tennis? Answer(b) [1] (c) Find the probability that a student chosen at random plays tennis. Answer(c) [2]

8 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 0607/11/M/J/11 For Examiner's Use 12 (a) Graph B is a transformation of graph A. The equation of graph A is y = x3. Write down the equation of graph B. y x 0 A y x 0 3 B Answer(a) [2] (b) Graph D is a transformation of graph C. The equation of graph C is y = x2. Write down the equation of graph D. y x 0 C y x 0 3 D Answer(b) [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2011 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/11 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. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 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 – May/June 2011 0607 11 © University of Cambridge International Examinations 2011 1 (a) (b) (c) 6.1 210 2.3 × 10–3 B1 B1 B1 [3] 2 (a) (b) 1, 3, 5, 15 3 B1 B2 In any order If B0 then award B1 for factors of 21 seen [3] 3 (a) (b) 5 Parallelogram B1 B1 [2] 4 (a) (b) 6x – 10 = x + 10 5x = 20 x = 4 www3 x -5 -4 3 2 - - 1 0 1 2 3 4 5 - M1 M1 A1 B2 Independent B1 for line, B1 for both circles correct [5] 5 (a) (b) (c) –1, 1 197 2n – 3 = 44 or better Or using n = 23 and n = 24 n not an integer oe Or List of at least three terms (excluding –1 and 1) Stating ‘only odd numbers in sequence’ oe B1 B1 B1 M1 R1 Or M1 R1 E.g. n = 23.5 Allow ‘not in the sequence’ from correct values from n = 22, 23, 24 or n = 23, 24, 25 [5] 6 (a) P Q U B1 (b) P Q U B1 [2]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2011 0607 11 © University of Cambridge International Examinations 2011 7 (a) (b) 55° Similar or Enlargements of each other B1 B1 Ignore extra correct statements e.g. equal angles but not incorrect statements e.g. same (c) 7.5 B2 If B0 award B1 for y 5.2 15 5 = oe seen [4] 8 (a) 2 1 oe B2 If B0 award M1 for attempt to use y = mx + c or for 2 3 2 1 + = x y seen (b) 2 1 oe B1ft Strict follow through. Allow recovery only with new working. Single number only. [3] 9 72° B2 If B0 award M1 for 360 100 20 × soi [2] 10 (a) (b) 3 3y(y – 5) B1 B2 Allow 3y(1y – 5) and/or 3y(y – 5) If B0 award B1 for y(3y – 15) or 3(y2 – 5y) SC1 for 3y(y + 5) [3] 11 (a) (b) 4 7 B1 B1 (c) 15 8 oe isw B2 If B0 award B1 for 15 k or k 8 (k > 0) [4] 12 (a) (b) y = x3 + 3 y = (x – 3)2 B2 B2 If B0 award B1 for (y =) x3 ± constant (≠ 0) If B0 award B1 for (y =) (x ± constant)2 (≠ 0) [4]