Cambridge IGCSE Mathematics - International 0607 — 2014 May/June Paper 5 · Variant 2

This document consists of 7 printed pages and 1 blank page. IB14 06_0607_52/4RP © UCLES 2014 [Turn over *7695187803* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) May/June 2014 1 hour Candidates answer on the Question Paper. Additional Materials: Graphics Calculator 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, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. You must show all relevant working to gain full marks for correct methods, including sketches. In this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. At the end of the examination, fasten all your work securely together. The total number of marks for this paper is 24.

2 © UCLES 2014 0607/52/M/J/14 Answer all the questions. INVESTIGATION FRACTIONS WITHIN FRACTIONS This investigation looks at sequences of fractions. One way to form a sequence is by using fractions within fractions as shown below. 1 1 then 1 1 1 + 1 then 1 1 1 + 1 + 1 1 then and so on. 1 1 1 1 + 1 + 1 + 1 1 1 The first three terms of a sequence of fractions are 1, 2 1 , 3 2 . These terms are calculated in the following way. 1 1 1 + 1 + 1 1 2 1 + 1 3 2 1 1 = = = 2 3 1 1 1 + 1 1 + 1 1 = = 1 2 1 1 = 1 (a) (i) Fill in the box to complete the calculation of the 4th term. 3 2 1 5 3 1 1 1 1 1 + 1 + 1 + 1 1 1 2 3 5 1 + 1 + 1 1 + 1 1 = = = = =

3 © UCLES 2014 0607/52/M/J/14 [Turn over (ii) Show that the 5th term of this sequence of fractions is 8 5 . 1 1 = 1 1 1 + 1 + 1 + 1 + 1 1 (iii) Complete the table to show the first eight terms of this sequence of fractions. 1 1 2 1 3 2 5 3 8 5 21 13 (iv) Explain how you used a pattern to find the numerator and the denominator of the 8th term. Numerator Denominator

4 © UCLES 2014 0607/52/M/J/14 (b) The numbers 1, 1, 2, 3, 5, 8, 13, 21 are the first eight numbers in a sequence. (i) Work out the next five terms of this sequence. (ii) Write down the 12th term of the sequence of fractions in part (a). 2 Here is a different sequence of fractions. 2 1 + 2 1 + 1 + 2 2 1 + 2 1 + 2 1 + 2 2 2 , , , 1 2 , ... (a) Calculate the 2nd and 3rd terms in this sequence of fractions. Give your answers as single fractions. The 1st and 4th terms are given. 1 + 2 1 + 2 1 + 2 2 1 2 1 2 11 10 2 = = = = … … 2 1 + 2 1 + 1 + 2 2

5 © UCLES 2014 0607/52/M/J/14 [Turn over (b) Find the 5th term of this sequence. Give your answer as a single fraction. (c) Describe the connection between the numerator of a fraction and the denominator of the previous fraction in the sequence. (d) Describe the connection between the denominator of a fraction and the numerator and denominator of the previous fraction.

6 © UCLES 2014 0607/52/M/J/14 3 Here is a different sequence of fractions. The first three terms are 3, 4 3 , 7 12 . (a) Calculate the 4th and 5th terms. Give your answers as single fractions. 12 7 3 4 1 + 3 1 + 3 1 + 3 3 1 + 3 1 + 1 + 3 3 3 = = = = 12 7 3 1 1 + 3 1 + 3 = 3 4 3 1 3 1 = … 1 + 3 1 + 1 + 3 3 3 1 + 3 = … (b) Explain how you can use a pattern to find the numerator and the denominator of the 5th term of this sequence. Numerator Denominator

7 © UCLES 2014 0607/52/M/J/14 4 Here is a sequence in terms of n. n 1 + n 1 + 1 + n n 1 + n 1 + n 1 + n n n , , , 1 n , ... Calculate the first four terms in this sequence when n = 4. Give your answers as single fractions. … , … , … , …

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CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core), maximum raw mark 24 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 May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 52 © Cambridge International Examinations 2014 1 (a) (i) 3 2 1 1 + seen 1 (ii) 5 3 1 1 + seen 1 C opportunity (iii) 1 1 2 1 3 2 5 3 8 5 13 8 21 13 34 21 2 B1 each fraction (iv) [Numerator =] denominator of 7th or previous fraction or added the two previous numerators or denominator of (previous fraction + 1) oe [Denominator =] numerator + denominator of 7th or previous fraction or added the two previous denominators or numerator of (previous fraction + 1)oe 2 B1 each statement (b) (i) 34, 55, 89, 144, 233 2 B1 FT from incorrect 34 or M1 adding previous 2 terms 3 times C opportunity (ii) 233 144 1FT FT from their 144, 233 in (b)(i) 2 (a) 3 2 5 6 2 B1 B1FT their 3 2 C opportunity (b) 21 22 isw 2 B1 numerator B1 denominator If B0 scored, then M1 for a complete correct fraction shown (c) [Numerator =] 2 × previous denominator oe 1 (d) [Denominator =] numerator + denominator of previous fraction oe 1

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 52 © Cambridge International Examinations 2014 3 (a) 19 21 40 57 2 B1 each fraction FT their 19 21 C opportunity (b) [Numerator =] 3 × 19 = 57 or 3 × previous (4th term) denominator [Denominator =] 21 + 19 = 40 or previous (4th term) numerator + previous (4th term) denominator 2 B1 each statement 4 ]1[ 4 , 5 4 , 9 20 , 29 36 isw 3 B2 for two of 5 4 , 9 20 , 29 36 B1 for one of 5 4 , 9 20 , 29 36 C opportunity Communication seen in 3 or more of 1(a)(i), 1(b)(i), 2(a), 3(a), 4 2 C1 for 2