Cambridge IGCSE Mathematics - International 0607 — 2016 May/June Paper 4 · Variant 3

This document consists of 20 printed pages. DC (NF/SW) 115861/4 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 4 0 9 5 8 6 6 3 5 7 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/43 Paper 4 (Extended) May/June 2016 2 hours 15 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 p, 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 120.

2 0607/43/M/J/16 © UCLES 2016 Formula List For the equation ax bx c 0 2 + + = x a b b ac 2 4 2 ! = - - Curved surface area, A, of cylinder of radius r, height h. r A rh 2 = Curved surface area, A, of cone of radius r, sloping edge l. r A rl = Curved surface area, A, of sphere of radius r. r A r 4 2 = Volume, V, of pyramid, base area A, height h. V Ah 3 1 = Volume, V, of cylinder of radius r, height h. r V r h 2 = Volume, V, of cone of radius r, height h. r V r h 3 1 2 = Volume, V, of sphere of radius r. r V r 3 4 3 = sin sin sin A a B b C c = = cos a b c bc A 2 2 2 2 = + - sin bc A 2 1 Area = A C B c b a

3 0607/43/M/J/16 © UCLES 2016 [Turn over Answer all the questions. 1 (a) Write the number 13205.17268 (i) correct to 1 decimal place, … [1] (ii) correct to 3 significant figures, … [1] (iii) correct to the nearest 10, … [1] (iv) correct to the nearest 0.001. … [1] (b) Write the number 120 correct to the nearest 10. … [1] 2 (a) Factorise. x x 3 10 8 2 - - … [2] (b) Solve the inequality. x x 3 10 8 0 2 1 - - … [2] (c) Solve the equation. sin sin x x 3 10 8 0 2 - - = for x 0 360 ° ° 1 1 … [3]

4 0607/43/M/J/16 © UCLES 2016 3 y is directly proportional to x 1 3 + ^ h . y = 32 when x = 3. (a) Find the value of y when x = 4. y = … [3] (b) Find the value of x when . y 13 5 = . x = … [2] (c) Find x in terms of y. x = … [3]

5 0607/43/M/J/16 © UCLES 2016 [Turn over 4 A circle of radius r cm is inside a square, so that the circle touches the sides of the square. (a) (i) Find an expression for the area of the shaded region in terms of r and r. … [2] (ii) Calculate the area of the shaded region when r = 6. … cm2 [1] (b) Find an expression for the perimeter of the shaded region in terms of r and r. … [3]

6 0607/43/M/J/16 © UCLES 2016 5 A B NOT TO SCALE 12.4 cm 30° C The area of triangle ABC is 34.1 cm2. AB = 12.4 cm and angle ABC = 30°. (a) Show that BC = 11 cm. [1] (b) Find AC. AC = … cm [3]

7 0607/43/M/J/16 © UCLES 2016 [Turn over (c) Find angle CAB. Angle CAB = … [3] (d) Find the length of the perpendicular line from A to the line BC. … cm [2]

8 0607/43/M/J/16 © UCLES 2016 6 The heights of 400 students are given in the table. Height (h cm) Frequency h 145 155 1 G 26 h 155 160 1 G 66 h 160 165 1 G 82 h 165 170 1 G 118 h 170 175 1 G 82 h 175 190 1 G 26 (a) Calculate an estimate of the mean height of a student.  cm [2] (b) (i) Complete the frequency density column in this table. Height (h cm) Frequency Frequency density h 145 155 1 G 26 h 155 160 1 G 66 h 160 165 1 G 82 h 165 170 1 G 118 h 170 175 1 G 82 h 175 190 1 G 26 [2]

9 0607/43/M/J/16 © UCLES 2016 [Turn over (ii) On the grid below, draw an accurate histogram to show this information. Complete the scale on the frequency density axis. 0 140 150 160 170 Height (cm) h Frequency density 180 190 [4]

10 0607/43/M/J/16 © UCLES 2016 7 Sasha bought a house on 1st January 2013. By 1st January 2014 the value of the house had increased by 10%. By 1st January 2015 the value of the house had increased by a further 5% of its value on 1st January 2014. The value of the house on 1st January 2015 was $103 950. (a) Find how much Sasha paid for the house in 2013. $ … [4] (b) By 1st January each year, from 2015, the value of the house increases by 5% of its value on 1st January the previous year. The value of the house on 1st January 2015 was $103 950. Find the year in which the value of the house will first be greater than $200 000. … [3]

11 0607/43/M/J/16 © UCLES 2016 [Turn over 8 A B NOT TO SCALE C X D q 6p ABC is a triangle. AX AC 3 2 = and AD AB 2 1 =  AX p 6 = and DX q = . Find an expression, in terms of p and q, for (a) AD, … [2] (b) DC, … [2] (c) CB. … [3]

12 0607/43/M/J/16 © UCLES 2016 9 The transformation AB means transformation B followed by transformation A. (a) The transformation P is a rotation through 90° clockwise about the origin. The transformation Q is a rotation through 180° about the origin. The transformation R is a rotation through 270° clockwise about the origin. The transformation S is a reflection in the y-axis. The transformation T is a reflection in the x-axis. Write down the letter of the single transformation, P, Q, R, S or T, that is equivalent to each of the transformations QR, PQR, ST, SQ, PTP and TPP. QR = … PQR = … ST = … SQ = … PTP = … TPP = … [6]

13 0607/43/M/J/16 © UCLES 2016 [Turn over (b) –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 A –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 y x (i) Draw the image of triangle A after a reflection in the line y = x. Label this image B. [2] (ii) Draw the image of triangle B after a reflection in the x-axis. Label this image C. [1] (iii) Describe fully the single transformation that maps triangle C onto triangle A. … … [3]

14 0607/43/M/J/16 © UCLES 2016 10 A company is testing a new drug. Ten patients were examined and given a score before and after taking the drug. A decrease in score represents an improvement. The results are shown in the table. Patient A B C D E F G H I J Score before (x) 8 14 20 25 32 34 41 42 50 61 Score after ( y) 3 4 16 15 20 27 34 28 40 49 (a) (i) Complete the scatter diagram. The first four points have been plotted for you. 0 0 5 10 15 20 25 30 35 40 45 50 y x Score before Score after 10 20 30 40 50 60 70 [3] (ii) What type of correlation is shown by the scatter diagram? … [1]

15 0607/43/M/J/16 © UCLES 2016 [Turn over (b) Find (i) the mean score before taking the drug, … [1] (ii) the mean score after taking the drug. … [1] (c) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) Estimate the score after taking the drug when the score before taking the drug was 30. … [1] (iii) A patient has a score before taking the drug of 80. Explain why using the line of regression is unlikely to be reliable in predicting the score of the patient after taking the drug. … … [1]

16 0607/43/M/J/16 © UCLES 2016 11 8 –3 f (x) = 3 + 1 (x2 – 4x + 3) 0 –1 5 x y (a) On the diagram, sketch the graph of y = f(x) between x = −1 and x = 5. [4] (b) Write down the equations of the three asymptotes. … , … , … [3] (c) Write down the co-ordinates of the local maximum point. ( … , … ) [1] (d) The line y = x intersects the curve y x x 3 4 3 1 2 = + - + ^ h three times. Find the values of the x co-ordinates of these three points of intersection. x = … , x = … , x = … [3]

17 0607/43/M/J/16 © UCLES 2016 [Turn over 12 A D E NOT TO SCALE C B A, B, C and D lie on a circle. ADE and BCE are straight lines that intersect at E. BD = DE, angle BAD = 4x, angle BCD = 6x and angle BDC = 3x. Find (a) x, x = … [2] (b) angle CBD , Angle CBD = … [2] (c) angle CDE . Angle CDE = … [3]

18 0607/43/M/J/16 © UCLES 2016 13 60° Diagram 1 Diagram 2 Diagram 3 NOT TO SCALE 3 cm 60° 60° 3 cm 60° 3 cm 60° 60° Diagram 1 is a sector of a circle, radius 3 cm and sector angle 60°. Diagram 2 has a right-angled triangle, with an angle of 60°, drawn on a radius of this sector. Diagram 3 has a sector of a circle, with a sector angle 60°, drawn on the hypotenuse of the right-angled triangle. (a) Calculate the area of (i) Diagram 1, … cm2 [2] (ii) Diagram 2, … cm2 [3]

19 0607/43/M/J/16 © UCLES 2016 [Turn over (iii) Diagram 3. … cm2 [3] (b) Diagram 1, Diagram 2 and Diagram 3 are the first three diagrams in a pattern. There are 6 diagrams in the pattern. Diagram 4 has a right-angled triangle added to Diagram 3 in the same way as Diagram 2. Diagram 5 has a sector added to Diagram 4 in the same way as Diagram 3. Diagram 6 has a right-angled triangle added to Diagram 5 in the same way as Diagram 2. Find the area of Diagram 6. … cm2 [4] Question 14 is printed on the next page.

20 0607/43/M/J/16 © UCLES 2016 14 In this question, give all your answers as single fractions in terms of x and y. A bag contains x red balls and y blue balls. (a) Rosario chooses a ball at random from the bag, notes its colour and replaces it in the bag. He then chooses a ball from the bag a second time, notes its colour and replaces it in the bag. Find the probability, in terms of x and y, that the two balls chosen are (i) both red, … [2] (ii) one red and one blue. … [3] (b) Magda chooses a ball at random from the bag and does not replace it. She then chooses a ball from the bag a second time. Find the probability, in terms of x and y, that the two balls chosen are (i) both red, … [3] (ii) one red and one blue. … [3] 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.

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 6 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/43 Paper 4 (Extended) May/June 2016 MARK SCHEME Maximum Mark: 120 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 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 43 © Cambridge International Examinations 2016 Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question Answer Mark Part Marks 1 (a) (i) 13205.2 1 (ii) 13200 1 (iii) 13210 1 (iv) 13205.173 1 (b) 120 1 2 (a) (3 2)( 4) + − x x 2 SC1 for (3 )( ) + + x a x b where ab = –8 or a + 3b = –10 (b) 2 4 3 − < < x 2FT B1 for either correct (c) 221.8 or 221.8… 318.2 or 318.18 to 318.19 3 B2 for either correct or M1 for 2 2 sin where 1 1 3 3 x their their     = − −< − <         or M1 for sketch or M1 for 41.8 or –41.8 seen 3 (a) 62.5 3 B1 for 3 ( 1) = + y k x B1 for 0.5 = k OR M2 for 3 3 (4 1) 32 (3 1) + = + y (b) 2 2 B1FT for 3 1 27 + = x their (c) 3 2 1 = − x y oe final answer 3 M1 for division by their k M1 for cube root M1 for subtracting 1, must be final step

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 43 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 4 (a) (i) 2 2 4 π = − A r r oe final answer 2 M1 for 2 2 ar b r −π (ii) 30.9 or 30.88 to 30.90[…] 1 (b) 8 2 r r + π oe final answer 3 B1 for 8r oe B1 for 2 r π oe If B0 scored then M1 for 1 2 4 r r r + + × π oe 5 (a) 0.5 12.4 sin30 [ 34.1] x × × × = oe 1 (b) 6.21 or 6.205 to 6.206 3 B2 for 38.50 to 38.51 or M1 for 2 2 11 12.4 2 11 12.4 cos30 + −× × × (c) 62.3 or 62.4 or 62.33 to 62.41… 3 M2 for 11 sin30 sin 6.21 × = A their or 2 2 2 12.4 ( ( )) 11 cos 2 12.4 ( ) + − = × × their b A their b or M1 for 11 6.21 sin sin30 = their A oe (d) 6.2 2 M1 for 12.4 sin30 × oe 6 (a) 166 or 165.6 to 165.7 2 M1 for correct use of mid-pts at least 4 of (150, 157.5, 162.5, 167.5, 172.5,182.5) (b) (i) 2.6, 13.2, 16.4, 23.6, 16.4, 1.73 2 B1 for 4 or 5 correct (ii) Suitable vertical scale Correct column widths Correct heights 1 1 2FT dep B1 for 4 or 5 correct dep on at least B1 in (b)(i) 7 (a) 90 000 4 M3 for 1.05 1.1 103950 a × × = or better M2 for 103950 1.05 or 1.1 oe or M2 for 1.05 1.1 × M1 for 103 950 = 105% (b) 2028 3 M2 for 200000 1.05 103950 n = where n > 1 or M1 for 103950 1.05n × where n > 1 If 0 scored SC2 for 13.4 or 13.41… seen

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 43 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 8 (a) 6p – q 2 B1 for


 XD = –q or M1 for = +








 AD AX XD oe (b) 3p + q oe 2 M1 for


 AC = 9p or


 XC = 3p or correct route (c) 3p – 2q oe 3 M1 for


 BD = their (a) M1 for = +








 CB CD DB oe 9 (a) [QR =] P [PQR =] Q [ST =] Q [SQ =] T [PTP =] T [TPP =] S 6 B1 for each (b) (i) Points (2, 2) (2, 1) (5, 1) 2 B1 for (2, 1) or (5, 1) correct (ii) Points (2, –2) (2, –1) (5, –1) 1FT FT their B reflected in x-axis (iii) Rotation 90 [anticlockwise] oe [Centre] (0, 0) oe 1 1 1 10 (a) (i) Points correctly plotted 3 B2 for 4 or 5 correct points B1 for 2 or 3 correct points (ii) Positive 1 (b) (i) 32.7 1 (ii) 23.6 1 (c) (i) [ ] 5.57 0.892 = − + y x 2 B1 for –5.57 + kx, or B1 for a + 0.892x, If 0 scored SC1 for –5.6 + 0.89x (ii) 21.2 or 21.19… 1FT FT their (c)(i) using x = 30 (iii) Outside range oe 1

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 43 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 11 (a) Correct sketch 4 B1 Correct graph for 3 > x B1 Correct graph for 1 < x B1 Correct graph for 1 3 < < x B1 Approximately correct intercepts (b) x = 1 x = 3 y = 3 1 1 1 (c) (2, 2) 1 (d) 1.38, 2, 3.62 3 B1 for each 12 (a) 18 2 M1 for 4x + 6x = 180 (b) 18 2 M1 for 180 – 6x – 3x (c) 90 3 M2 for 180 – 3x – x – x or B1 for CED = x or DCE = 4x 13 (a) (i) 4.71 or 1.5π or 4.712 to 4.713 2 M1 for 2 60 π 3 360 × × (ii) 12.5 or 1.5 4.5 3 π + oe or 12.50 to 12.51 3 M2 for 3 0.5 3 sin60 (a) cos60 their × × × + oe or M1 for 3 cos60 (iii) 31.4 or 7.5 4.5 3 π + oe or 31.35 to 31.36 3 B1 for hyp = 6 M1 for 2 60 π ( 6) 360 × × their (b) 263 or 31.5 94.5 3 π + oe or 262.6 to 262.7 4 M3 for 1.5π 6π 24π + + + 4.5 3 18 3 72 3 × + × + × or M1 for 1.5π 6π 24π + + and M1 for 4.5 3 18 3 72 3 × + × + × or M1 for correct new triangle in diagram 4 or M1 for correct new sector in diagram 5 or M1 for correct new triangle in diagram 6

Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 43 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 14 (a) (i) 2 x x y     +   oe final answer 2 B1 for + x x y (ii) 2 2 ( ) × + xy x y oe final answer 3 M2 for ( ) ( ) × + + x y x y x y oe or B1 for + y x y seen (b) (i) ( 1) ( )( 1) − + + − x x x y x y oe final answer 3 B2 for 1 1 − + − x x y or B1 for 1 + − x y seen (ii) 2 ( )( 1) × + + − xy x y x y oe final answer 3 M2 for ( ) ( 1) × + + − x y x y x y oe or B1 for 1 + − y x y seen