Cambridge IGCSE Mathematics - International 0607 — 2017 May/June Paper 3 · Variant 2

This document consists of 16 printed pages. DC (LK/SW) 133449/5 © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 1 0 5 2 1 8 5 1 2 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2017 1 hour 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments 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. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For r, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, 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 96.

2 0607/32/M/J/17 © UCLES 2017 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = rr2 Circumference, C, of circle, radius r. C = 2rr Curved surface area, A, of cylinder of radius r, height h. A = 2rrh Curved surface area, A, of cone of radius r, sloping edge l. A = rrl Curved surface area, A, of sphere of radius r. A = 4rr2 Volume, V, of prism, cross-sectional area A, length l. V = Al Volume, V, of pyramid, base area A, height h. V = Ah 3 1 Volume, V, of cylinder of radius r, height h. V = rr2h Volume, V, of cone of radius r, height h. V = r h 3 1 2 r Volume, V, of sphere of radius r. V = r 3 4 3 r

3 0607/32/M/J/17 © UCLES 2017 [Turn over Answer all the questions. 1 (a) Write in words the number 70 302. … [1] (b) Work out . 13 683. Write down all the numbers on your calculator display. … [1] (c) Write 623.892 (i) correct to 2 decimal places, … [1] (ii) correct to 3 significant figures, … [1] (iii) correct to the nearest 100. … [1] (d) Find the value of x y 8 5 + when x 7 = and y 9 =- . … [2] (e) Solve. x 54 8 10 - = x = … [2]

4 0607/32/M/J/17 © UCLES 2017 2 Amir has 12 hens. (a) Each hen lays 5 eggs every week. (i) Work out the total number of eggs Amir collects each week. … [1] (ii) Amir sells the eggs at $2.10 for 10 eggs. He sells all the eggs. Work out how much money he receives. $ … [2] (iii) Cynthia buys 10 eggs and pays with a $5 note. Work out how much change she receives. $ … [1] (b) Food for the hens costs $20 for a 40 kg bag. Amir uses 8 kg of food each week. (i) Work out how much it costs him to feed the hens each week. $ … [2] (ii) Use your answer to part (a)(ii) to work out the profit that Amir makes each week. $ … [1]

5 0607/32/M/J/17 © UCLES 2017 [Turn over 3 U = {a, b, c, d, e, f, g, h} P = {a, c, e, f, g} Q = {b, d, f, g} (a) Write the elements of U in their correct position in the Venn diagram. P Q U [2] (b) Write down an element of P. … [1] (c) Write down the elements of a proper subset of Q. { … } [1] (d) Write down the elements of the complement of P. { … } [1] (e) Write down ( ) n P Q , l. … [1] (f) Using set notation, complete the statement. c … P [1] (g) On the diagram below, shade the region P Q + l . P Q U [1]

6 0607/32/M/J/17 © UCLES 2017 4 A M D B N C R P The diagram shows a rectangle ABCD. The points M, N, P and R are the midpoints of the sides. (a) On the diagram, label (i) an acute angle with the letter x , [1] (ii) a right angle with the letter y , [1] (iii) an obtuse angle with the letter z . [1] (b) Using the letters on the diagram, write down (i) two lines that are parallel, … and … [1] (ii) two lines that are perpendicular, … and … [1] (iii) two shapes that are congruent. … and … [1]

7 0607/32/M/J/17 © UCLES 2017 [Turn over 5 These are the first four terms of a sequence. 23 16 x 2 The difference between any two consecutive terms is the same. (a) Find the value of x. x = … [2] (b) Work out the 5th term of this sequence. … [1] (c) Find an expression for the nth term of this sequence. … [2] (d) Is 187 - a term in this sequence? Show how you decide. [3]

8 0607/32/M/J/17 © UCLES 2017 6 (a) Appointments with teachers are from 14 15 until 17 25. (i) Work out the total number of minutes between 14 15 and 17 25. … minutes [2] (ii) Each appointment is for 10 minutes. Find the maximum number of appointments that can be made for each teacher. … [1] (iii) A teacher has only 12 appointments. Work out the total number of minutes for his appointments as a percentage of the total possible number of minutes for appointments. … % [2] (b) The table shows the number of appointments for all the teachers. Teacher A B C D E F G H I J K L M Number of appointments 5 12 8 12 11 18 3 16 8 9 14 8 13 For these numbers of appointments, find (i) the range, … [1] (ii) the mode, … [1] (iii) the median. … [1]

9 0607/32/M/J/17 © UCLES 2017 [Turn over (c) One of the 13 teachers is chosen at random. Find the probability that this teacher has (i) exactly 12 appointments, … [1] (ii) more than 9 appointments. … [1] 7 . 3 1 0 55 2 2 7 1 r - - (a) From this list write down. (i) all the integers, … [2] (ii) an irrational number. … [1] (b) Use numbers from the list to complete the following statement. Q = { …} [2] (c) Write 0.55 as a fraction in its simplest form. … [2]

10 0607/32/M/J/17 © UCLES 2017 8 Ten students of different ages record the number of lengths of a pool they can swim. Age (years) 5 6 7 8 9 10 12 13 14 15 Number of lengths 1 3 4 10 9 7 14 15 18 20 (a) Complete the scatter diagram. The first six points have been plotted for you. 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1 2 3 4 5 6 7 8 Age (years) Number of lengths 9 10 11 12 13 14 15 16 [2] (b) What type of correlation is shown in the diagram? … [1]

11 0607/32/M/J/17 © UCLES 2017 [Turn over (c) Calculate (i) the mean of the ages, … years [1] (ii) the mean of the number of lengths. … [1] (d) On the scatter diagram, plot the mean point. [1] (e) On the scatter diagram, draw a line of best fit by eye. [2] (f) Use your line of best fit to estimate the number of complete lengths a student of age 11 years can swim. … [2]

12 0607/32/M/J/17 © UCLES 2017 9 Clarissa records the number of students absent from school each day. The results for one week are shown in the bar chart. 0 Monday Tuesday Wednesday Thursday Friday Number of absences 5 10 15 20 25 (a) Work out the total number of absences during the five days. … [1] (b) Write down which day had the most students absent. … [1]

13 0607/32/M/J/17 © UCLES 2017 [Turn over (c) Clarissa decides to draw a pie chart to show this information. (i) Show, using a calculation, that the sector angle for Monday is 88°. [1] (ii) Complete the pie chart. Label each sector clearly. Monday Friday 96° 88° [3]

14 0607/32/M/J/17 © UCLES 2017 10 80 m 100 m NOT TO SCALE C A B A track is in the shape of a right-angled triangle. m AB 100 = and m BC 80 = . (a) Find the length of AC. AC = … m [3] (b) Find the total length of the track. … m [1] (c) Use trigonometry to find the size of angle ABC. Angle ABC = … [2] (d) Margriet jogs around the track at an average speed of 9 km/h. (i) Change 9 km/h to metres/minute. … metres/minute [2] (ii) Calculate the number of minutes it takes her to jog around the track 5 times. … minutes [2]

15 0607/32/M/J/17 © UCLES 2017 [Turn over 11 NOT TO SCALE 2 cm 10 cm 20 cm 6 cm The diagram shows a wooden spinning top in the shape of a cone with a cylinder on top. The cone has radius 6 cm and height 20 cm. The cylinder has radius 2 cm and height 10 cm. (a) Find the total volume of the spinning top. … cm3 [3] (b) (i) Find the length of the slant height of the cone. … cm [2] (ii) The curved surface area of the cone is painted red. Find the area painted red. … cm2 [2] Question 12 is printed on the next page.

16 0607/32/M/J/17 © UCLES 2017 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. 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. 12 –1.5 2.5 x y –7 0 7 ( ) f x x x x 2 3 3 2 3 2 = - - + (a) On the diagram, sketch the graph of ( ) f y x = for . . x 1 5 2 5 G G - . [2] (b) Find the x co-ordinate of each point where the curve cuts the x-axis. x = … and x = … and x = … [3] (c) Find the y co-ordinate of the point where the curve cuts the y-axis. y = … [1] (d) Find the co-ordinates of the local maximum point. ( … , … ) [2]

® IGCSE is a registered trademark. This document consists of 6 printed pages. © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2017 MARK SCHEME Maximum Mark: 96 Published 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 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 2 of 6 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes. Types of mark M Method marks, awarded for a valid method applied to the problem. A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. B Mark for a correct result or statement independent of Method marks. When a part of a question has two or more ‘method’ steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation ‘dep’ is used to indicate that a particular M or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working nfww not from wrong working oe or equivalent rot rounded or truncated SC Special Case soi seen or implied

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 3 of 6 Question Answer Marks Part marks 1(a) Seventy thousand, three hundred [and] two 1 1(b) 2560.108032 or 2560.11 1 1(c)(i) 623.89 1 1(c)(ii) 624 1 1(c)(iii) 600 1 1(d) 11 2 M1 for 8 × 7 + 5 × –9 or 56 or – 45 seen 1(e) 5.5 or 11 2 2 M1 for correct first step e.g. 54 10 8 0 or 54 10 8 x x − − = = + 2(a)(i) 60 1 2(a)(ii) 12.6[0] 2 FT their (a)(i) M1 for ( )( ) a i 10 their 2(a)(iii) 2.9[0] 1 2(b)(i) 4 2 M1 for 40 8 soi or 20 40 soi 2(b)(ii) 8.6[0] 1 FT their (a)(ii) – their (b)(i) 3(a) 2 B1 for 2 or 3 correct regions 3(b) a or c or e or f or g 1 3(c) Any proper subset containing some (but not all) of b, d, f, g 1 3(d) {b, d, h } 1 FT from their Venn diagram 3(e) 1 1 FT from their Venn diagram 3(f) c ∈ P 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 4 of 6 Question Answer Marks Part marks 3(g) 1 4(a)(i) x in correct place 1 4(a)(ii) y in correct place 1 4(a)(iii) z in correct place 1 4(b)(i) Any pair of parallel lines 1 4(b)(ii) Any pair of perpendicular lines 1 4(b)(iii) Any 2 congruent shapes 1 Correct order of letters not required 5(a) 9 2 B1 for 7 or –7 seen 5(b) –5 1 5(c) 30 – 7n oe 2 B1 for k – 7n or 30 – kn, k ≠0 5(d) –187 = 30 – 7n (their c) –217 = –7n M1 n = 31 A1 Yes B1 1FT dependent on conclusion correct for their result. 6(a)(i) 190 2 B1 for 3 hours 10 minutes 6(a)(ii) 19 1 FT their (a)(i) 6(a)(iii) 63.2 or 63.15 to 63.16 2 M1 for ( )( ) 120 a i their or ( )( ) 12 a ii their 6(b)(i) 15 1 6(b)(ii) 8 1 6(b)(iii) 11 1 6(c)(i) 2 13 oe 1 6(c)(ii) 7 13 oe 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 5 of 6 Question Answer Marks Part marks 7(a)(i) 2, – 3 2 B1 for each If extras given, B1 for 1 correct and 1 incorrect or 2 correct and no more that 2 incorrect 7(a)(ii) 2 or π 1 7(b) 1 2, 3, 0.55, 17 − − 2 B1 for any 1 or more correct and no extras 7(c) 11 20 2 B1 for 55 100 8(a) All 4 points correctly plotted 2 B1 for 2 or 3 correctly plotted 8(b) Positive 1 8(c)(i) 9.9 1 8(c)(ii) 10.1 1 8(d) Mean point correctly plotted 1 FT their (c) 8(e) Appropriate line through mean point 2 M1 for ruled line within tolerance but not passing through their mean point or ruled line with positive gradient passing through their mean point 8(f) 12 2 B1FT from their decimal value or rounded up value from ruled line on graph 9(a) 90 1 9(b) Friday 1 9(c)(i) [ ] 22 360 88 90 × = oe 1 9(c)(ii) Correct pie chart 3 B2 for correct pie chart without labels or B1 for 1 correct angle 10(a) 60 3 M2 for 2 2 100 80 − or M1 for 1002 = 802 + AC2 or better 10(b) 240 1 FT 180 + their (a) 10(c) 36.9 or 36.86 to 36.87 2 M1 for cos[ ] = 80 100 oe 10(d)(i) 150 2 M1 for 9 × 1000 or 9 60 or 1000 60

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 6 of 6 Question Answer Marks Part marks 10(d)(ii) 8 2 M1 for 5 × their (b) oe or ( ) ( )( ) b d i their their 11(a) 880 or 879.6 to 879.8 3 M2 for 1 3 × π × 62 × 20 + π × 22 × 10 M1 for 1 3 × π × 62 × 20 or π × 22 × 10 11(b)(i) 20.9 or 20.88... 2 M1 for 202 + 62 11(b)(ii) 394 or 393.5 to 394.0 2 M1 for π × 6 × their(b) 12(a) Correct curve drawn 2 M1 for maximum and minimum in correct quadrants or B1 for axes intercepts approximately correct or correct shape in wrong position 12(b) – 1 1 0.5 1 2 1 12(c) 2 1 12(d) (– 0.366, 2.6[0]) or (–0.366… , 2.598…) 2 B1 for x co-ordinate B1 for y co-ordinate If 0 scored SC1 for (– 0.37, 2.6[0])