Cambridge IGCSE Mathematics - International 0607 — 2018 Oct/Nov Paper 4 · Variant 3

* 3 8 3 7 7 6 3 9 0 1 * This document consists of 16 printed pages. DC (SC/CGW) 156335/2 © UCLES 2018 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/43 Paper 4 (Extended) October/November 2018 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 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 120. Cambridge International Examinations Cambridge International General Certificate of Secondary Education

2 0607/43/O/N/18 © UCLES 2018 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/O/N/18 © UCLES 2018 [Turn over Answer all the questions. 1 (a) In a school there are 225 girls and 190 boys. (i) Work out the number of boys as a fraction of the total number of students. Give your answer in its lowest terms. … [2] (ii) Write the ratio number of girls : number of boys in its simplest form. … [2] (b) In a mathematics class there are 15 boys. The ratio number of girls : number of boys = 6 : 5. Find the number of girls in this class. … [2] (c) In a science class of 33 students there are 15 boys. (i) Find the number of boys as a percentage of the number of students in the class. … % [1] (ii) 20% of these boys did not complete an experiment. Work out the number of boys who did not complete the experiment. … [2] (d) This year the number of students studying mathematics is 390. This is an increase of 4% on the number of students who studied mathematics last year. Work out the number of students who studied mathematics last year. … [3]

4 0607/43/O/N/18 © UCLES 2018 2 –2 –3 –4 –5 –1 1 10 2 3 4 5 0 6 7 8 9 1 2 3 4 5 7 6 8 10 9 T P y x (a) Describe fully the single transformation that maps triangle T onto triangle P. … … [3] (b) Reflect triangle T in the y-axis. [1] (c) Translate triangle T by the vector 5 6 e o. [2] (d) Stretch triangle T, stretch factor 3 and x-axis invariant. [2]

5 0607/43/O/N/18 © UCLES 2018 [Turn over 3 (a) p 2 1 = - e o 3 2 q = e o Find (i) q p - , f p [1] (ii) 2p, f p [1] (iii) 2p . … [2] (b) A is the point (0, 2) and B is the point (2, 7). (i) Write AB as a column vector. f p [2] (ii) 2 BC AB = Find the co-ordinates of C. ( … , … ) [2]

6 0607/43/O/N/18 © UCLES 2018 4 (a) 4 –4 0 –3 3 x y ( )x x x 2 1 f = + , x 0 =Y (i) On the diagram, sketch the graph of ( ) y x f = for values of x between -3 and 3. [3] (ii) Find the co-ordinates of the local minimum point. ( … , … ) [2] (iii) Find the range of f( )x for x 0 2 . … [1] (iv) Write down the equations of the two asymptotes to the graph of ( ) y x f = . … … [2]

7 0607/43/O/N/18 © UCLES 2018 [Turn over (b) 5 –3 0 –2 3 x y (i) On the diagram, sketch the graph of (a) y 2 3 x = - for x 2 3 G G - , [2] (b) log y x 6 = for x 0 2 . [2] (ii) Solve the inequality logx 6 2 3 x 2 - . … [2]

8 0607/43/O/N/18 © UCLES 2018 5 The table shows the scores of 10 students in a mathematics test and in a physics test. Student A B C D E F G H I J Mathematics (x) 4 6 6 8 9 9 9 10 10 10 Physics (y) 5 5 6 9 9 8 7 9 10 7 (a) Find the median and the upper quartile of the physics scores. median = … upper quartile = … [2] (b) Write down the type of correlation between the mathematics scores and the physics scores. … [1] (c) Find the equation of the line of regression in the form y mx c = + . y = … [2] 6 23 cm 11 cm 50° x cm NOT TO SCALE Calculate (a) the area of the triangle, … cm2 [2] (b) the value of x. x = … [3]

9 0607/43/O/N/18 © UCLES 2018 [Turn over 7 (a) The population of a small town is decreasing at a rate of 5% every 10 years. The population is now 26 010. Calculate the population in 20 years time. Give your answer correct to the nearest 100. … [3] (b) The population was previously increasing at a rate of 2% each year. The population is now 26 010. (i) Calculate the population 2 years ago. … [2] (ii) Find the number of complete years since the population was last less than 20 000. … [4]

10 0607/43/O/N/18 © UCLES 2018 8 6 –5 0 –1 5 x y ( )x x x 1 4 f 2 = + - (a) On the diagram, sketch the graph of ( ) y x f = for x 1 5 G G - . [2] (b) Write down the equation of the line of symmetry of the graph of ( ) y x f = . … [1] (c) (i) Find the zeros of ( )x f . … [2] (ii) Solve the inequality ( )x 0 f 2 . … [1] (d) Solve the equation ( )x 1 0 f + = . x = … or x = … [2] (e) ( )x x 5 g = - On the diagram, sketch the graph of ( ) y x g = for x 1 5 G G - . [2] (f) On the diagram, shade the region where ( ) y x f G and ( ) y x g G . [1]

11 0607/43/O/N/18 © UCLES 2018 [Turn over 9 When Helena goes for a walk, she walks d kilometres. The probability that d 0 2 1 G is 5 1 and the probability that d 2 4 1 G is 4 1 . (a) Find the probability that d 4 2 . … [2] (b) If it rains, Helena never goes for a walk. If it does not rain, Helena always goes for a walk. On any day, the probability that it rains is 3 1 . (i) Complete the tree diagram showing the probabilities of the two events. Rain Distance (d km) Rain 0 < d G 2 2 < d G 4 d > 4 Not rain … … 1 3 1 5 1 4 [1] (ii) Find the probability that, on any day, Helena walks more than 2 km. … [3] (iii) Find the expected number of days that Helena walks more than 2 km, during a period of 90 days. … [1]

12 0607/43/O/N/18 © UCLES 2018 10 P C D A B 8 cm 6 cm NOT TO SCALE 7 cm The diagram shows a pyramid of height 7 cm on a rectangular base 8 cm by 6 cm. The point P is directly above the centre of the base. (a) Calculate the angle between the triangle PBC and the base ABCD. … [2] (b) Calculate the angle between PB and the base ABCD. … [3] (c) Calculate PC. PC = … cm [2]

13 0607/43/O/N/18 © UCLES 2018 [Turn over (d) Calculate angle PCB. Angle PCB = … [2] (e) X is a point on the line PC so that angle BXC = 60°. Calculate BX. BX = … cm [3] 11 The mass, m grams, of each of 200 potatoes is measured. The histogram shows the results. 2 1.5 1 Frequency density 0.5 0 0 50 100 150 Mass (grams) m 200 250 300 (a) Complete the frequency table. Mass (m grams) m 0 100 1 G m 100 150 1 G m 150 200 1 G m 200 300 1 G Frequency 20 [2] (b) Calculate an estimate of the mean. … g [2]

14 0607/43/O/N/18 © UCLES 2018 12 (a) (x + 1) cm (3x + 2) cm NOT TO SCALE The perimeter of the rectangle is 44 cm. Find the value of x. x = … [3] (b) y cm ( y −1) cm NOT TO SCALE The area of the rectangle is 272 cm2. Find the value of y. y = … [3]

15 0607/43/O/N/18 © UCLES 2018 [Turn over (c) w cm Area = 7 cm2 Area = 5 cm2 w cm v cm ( v + 1) cm NOT TO SCALE The two rectangles have the same length, w cm. Find the value of v. v = … [3] (d) 2p cm 3p cm Area = 9 cm2 Area = 10 cm2 NOT TO SCALE The perimeter of the larger rectangle is 2 cm more than the perimeter of the smaller rectangle. Find the value of p. p = … [4] Question 13 is printed on the next page.

16 0607/43/O/N/18 © UCLES 2018 13 ( )x x 1 f = - ( )x x 3 2 g = - ( )x x 4 h 2 = - ( )x x 3 2 k 2 = + (a) Find ( ) 0 h . … [1] (b) Find, giving your answer in its simplest form. (i) ( ( )) x g f … [2] (ii) ( ) ( ) ( ) x x x g f k # + … [3] (c) Find ( )x f 1 - . ( )x f 1 - = … [1] (d) Find x when (i) ( )x 2 g = , x = … [2] (ii) ( )x 3 h = . x = … [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.

This document consists of 8 printed pages. © UCLES 2018 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/43 Paper 4 (Extended) October/November 2018 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/43 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 2 of 8 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • the specific content of the mark scheme or the generic level descriptors for the question • the specific skills defined in the mark scheme or in the generic level descriptors for the question • the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate • marks are awarded when candidates clearly demonstrate what they know and can do • marks are not deducted for errors • marks are not deducted for omissions • answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

0607/43 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 3 of 8 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

0607/43 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 4 of 8 Question Answer Marks Partial Marks 1(a)(i) 38 83 cao 2 M1 for 190 225 190 + implied by correct unsimplified fraction 1(a)(ii) 45 : 38 final answer 2 M1 for 225 : 190 oe If 0 scored SC1 for 38 : 45 final answer 1(b) 18 2 M1 for 15 ÷ 5 soi by [1 part =] 3 1(c)(i) 45.5 or 45.45… 1 1(c)(ii) 3 2 M1 for 20 100 × 15 oe 1(d) 375 nfww 3 M2 for 390 ÷ 4 1 100   +     oe or M1 for recognising 390 as 104% 2(a) Rotation 90˚ clockwise oe (5, 1) 3 B1for each 2(b) Correct reflection (– 1, 1), (– 4, 1), (– 4, 3) 1 2(c) Correct translation (6, 7), (9, 7), (9, 9) 2 B1 for translation 5    k or 6    k 2(d) Correct stretch (1, 3), (4, 3), (4, 9) 2 B1 for stretch factor 3 displaced vertically or stretch with x-axis invariant but other factor. 3(a)(i) 1 3    1 3(a)(ii) 4 2     −   1 3(a)(iii) 4.47 or 4.472… 2 FT their (ii) M1 for ( ) 2 2 4 ( 2) + − their their 3(b)(i) 2 5    2 B1 for 2    k or 5    k If 0 scored, SC1 for 2 5       3(b)(ii) ( ) 6, 17 2 B1 for (6, k) or (k, 17)

0607/43 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 5 of 8 Question Answer Marks Partial Marks 4(a)(i) Correct sketch 3 B2 for correct shaped branches but branches joined or B1 for one branch correct shape (even if branches connected) 4(a)(ii) (0.707 or 0.7071… , 1.41 or 1.414…) 2 B1 for (0.707 or 0.7071… , k) or for(k , 1.41 or 1.414…) 4(a)(iii) f(x) ⩾ 1.41 or 1.414…. 1 FT their (ii) 4(a)(iv) x = 0 y = x oe 2 B1 for each 4(b)(i)(a) Correct sketches 2 B1 for increasing exponential graph with negative y-intercept. 4(b)(i)(b) 2 B1 for correct shape all to right of y-axis and x-intercept not too far from 1. 4(b)(ii) 0.556 or 0.5559… < x < 2.4[0] or 2.401… 2 B1 for both correct values seen 5(a) 7.5 9 2 B1 for each 5(b) Positive 1 5(c) [y = ]0.681 (or 0.6812…)x + 1.98 (or 1.982…) 2 B1 for 0.681 (or 0.6812…)x + k or for kx + 1.98 (or 1.982…) or for 0.68x + 2[.0] 6(a) 96.9 or 96.90… 2 M1 for 0.5 × 11 × 23 × sin50 oe 6(b) 18[.0] or 18.02… 3 B2 for 325 or 324.7… or M1 for 2 2 11 23 2 11 23 cos50 + −× × × oe 3 2 1 0 -1 -2 3 4 2 0 -2 -4 3 2 1 0 -1 -2 3 4 2 0 -2 -4 3 2 1 0 -1 -2 3 4 2 0 -2 -4 3 2 1 0 -1 -2 3 4 2 0 -2 -4 3 2 1 0 -1 2 4 2 0 -2 3 2 1 0 -1 2 4 2 0 -2 3 2 1 0 -1 2 4 2 0 -2 3 2 1 0 -1 2 4 2 0 -2

0607/43 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 6 of 8 Question Answer Marks Partial Marks 7(a) 23 500 3 B2 for 23 470 or 23 474. … or M1 for 26 010 × 2 5 1 100   −     oe If 0 scored, SC1 for 9300 or 9320 or 9324 or for their seen answer rounded to the nearest 100 7(b)(i) 25 000 cao nfww 2 M1 for 26 010 ÷ 2 2 1 100   +     7(b)(ii) 14 nfww 4 M3 for 26010 log(1.02) log 20000   =     n soi by 13 or 13.3 or 13.26 to 13.27 or for trial and improvement reaching n = 13 and 14 or M2for ( ) 26010 1.02 20000 = n oe or for trial and improvement at least 3 times or M1 for 26010 = 20000(1.02)n oe 8(a) Correct sketch 2 B1 for parabola vertex upwards but incorrect intersections with axes 8(b) x = 2 oe 1 8(c)(i) – 0.236 or – 0.2361 to – 0.2360 4.24 or 4.236… 2 B1 for each 8(c)(ii) – 0.236 or – 0.2361 to – 0.2360 < x < 4.24 or 4.236… 1 FT their (b)(i) 8(d) – 0.449 or – 0.4495 to – 0.4494 4.45 or 4.449… 2 B1 for each If 0 scored, B1 for y = –1 sketched 8(e) Correct line sketched, passing through (5, 0) 2 B1 for line with negative gradient or with y-intercept reasonably close to 5 but not through (0, 6) 8(f) Region below curve and below line shaded, continuing below x-axis 1 5 4 3 2 1 0 1 6 4 2 0 -2 -4 5 4 3 2 1 0 1 6 4 2 0 -2 -4 5 4 3 2 1 0 1 6 4 2 0 -2 -4 5 4 3 2 1 0 1 6 4 2 0 -2 -4

0607/43 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 7 of 8 Question Answer Marks Partial Marks 9(a) 11 20 oe 2 M1 for 1 1 1 5 4 − − 9(b)(i) 2 3 and 11 20 correctly placed 1 FT their (a) 9(b)(ii) 8 15 oe 3 M2 for 2 1 11 3 4 20   × +     their or 2 1 1 3 5   × −     oe or 1 2 1 1 3 3 5   − − ×     or M1 for 2 1 3 4   ×    or 2 11 3 20   ×    their or 1 2 1 3 3 5   + ×     or 1 11 4 20 + 9(b)(iii) 48 final answer 1 FT their (b)(ii) 10(a) 60.3 or 60.25 to 60.26 2 M1 for tan = 7 4 oe 10(b) 54.5 or 54.46… 3 M2 for tan = 2 2 7 1 6 8 2 + oe or M1 for 2 2 6 8 + or 32 + 42 oe 10(c) 8.6[0] or 8.602… 2 M1 for ( ) 2 2 7 5 + their oe 10(d) 69.6 or 69.58 to 69.59 2 M1 for cos = 3 their PC oe 10(e) 6.49 or 6.493… 3 M2 for 6sin( ) sin60 their(d) oe or M1 for sin 60 sin( ) 6 = their BX (d) 11(a) 70, 80, 30 2 B1 for 2 11(b) 156.25 2 M1 for mid-values soi

0607/43 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 8 of 8 Question Answer Marks Partial Marks 12(a) 4.75 3 B2 for 8x = 38 oe or M1 for 2{(3x + 2) + (x + 1)} = 44 or (3x + 2) + (x + 1) = 22 12(b) 17 cao 3 B2 for 16 and 17 seen or sketch showing 17 or ( 16)( 17) + − y y seen or 2 ( 1) ( 1) 4(1)( 272) 2(1) −− ± − − − oe or B1 for 17 seen or M1 for y(y – 1 ) = 272 or better or appropriate sketch but not indicating 17 12(c) 2.5 oe 3 M2 for vw = 5 and (v + 1)w = 7 oe or M1 for one of these equations oe 12(d) 1.69 or 1.690… only cao 4 M3 for 2 6 6 7[ 0] − − = p p oe or M2 for 9 10 2 2 2 2 3 2 3     + + = +         p p p p oe or M1 for 9 2p or 10 3p soi 13(a) 4 1 13(b)(i) 1 – 3x oe 2 M1 for 3(1 – x) – 2 13(b)(ii) 5x 3 B2 for 2 3 3 2 2 − + + − x x x or M1 for 2 (3 2)(1 ) 3 2 − − + + x x x 13(c) 1 – x oe 1 13(d)(i) 4 3 oe 2 M1 for 3x – 2 = 2 13(d)(ii) 1 ± , 7 ± nfww 3 M1 for 2 4 − x = 3 ± oe (implied by 1 and 7 ) A1 dep on M1 for two correct answers If 0 scored, SC1 for 7 ± or for 1 ±