Cambridge International Examinations Cambridge International General Certificate of Secondary Education

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1 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/1 Paper (Extended) May/June hour 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 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. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level Certificate. This document consists of 1 printed pages. DC (AC/FD) 1016/ [Turn over

2 1 At noon the temperature was 4 C. At midnight the temperature was 5.5 C. Work out the difference in temperature between noon and midnight. Answer... C [1] Use your calculator to work out # ( ). Answer... [1] 3 Write in standard form. Answer... [1] 4 Expand and simplify. x (x + 3) + 5(x 7) Answer... [] 5 Paul and Sammy take part in a race. The probability that Paul wins the race is The probability that Sammy wins the race is 6%. Who is more likely to win the race? Give a reason for your answer. Answer... because... [] 0580/1/M/J/15

3 6 Rice is sold in 75 gram packs and 10 gram packs. The masses of both packs are given correct to the nearest gram. Calculate the lower bound for the difference in mass between the two packs. 3 Answer... g [] 7 Simplify. 6uw 3 4uw 6 Answer... [] 8 The point A has co-ordinates ( 4, 6) and the point B has co-ordinates (7, ). Calculate the length of the line AB. Answer AB =... units [3] 9 Without using a calculator, work out '. 7 Show all your working and give your answer as a fraction in its lowest terms. Answer... [3] 0580/1/M/J/15 [Turn over

4 4 10 Speed (metres per second) Time (minutes) A tram leaves a station and accelerates for minutes until it reaches a speed of 1 metres per second. It continues at this speed for 1 minute. It then decelerates for 3 minutes until it stops at the next station. The diagram shows the speed-time graph for this journey. Calculate the distance, in metres, between the two stations. Answer... m [3] 11 Find the nth term of each sequence. (a) 4, 8, 1, 16, 0,... Answer(a)... [1] (b) 11, 0, 35, 56, 83,... Answer(b)... [] 0580/1/M/J/15

5 1 p is inversely proportional to the square of (q + 4). p = when q =. Find the value of p when q =. 5 Answer p =... [3] 13 A car travels a distance of 180 metres at an average speed of 64 kilometres per hour. Calculate the time it takes for the car to travel this distance. Give your answer in seconds. Answer... s [3] 0580/1/M/J/15 [Turn over

6 6 14 Q b R NOT TO SCALE a P M S PQRS is a quadrilateral and M is the midpoint of PS. PQ = a, QR = b and SQ = a b. (a) Show that PS = b. Answer(a) [1] (b) Write down the mathematical name for the quadrilateral PQRM, giving reasons for your answer. Answer(b)... because [] 0580/1/M/J/15

7 7 15 y x Write down the 3 inequalities which define the unshaded region. Answer [4] 16 Georg invests $5000 for 14 years at a rate of % per year compound interest. Calculate the interest he receives. Give your answer correct to the nearest dollar. Answer $... [4] 0580/1/M/J/15 [Turn over

8 8 17 (a) Write 30 as a product of its prime factors. Answer(a)... [] (b) Find the lowest common multiple (LCM) of 30 and 45. Answer(b)... [] 18 Solve the simultaneous equations. You must show all your working. 5x + y = 3x 5y = 17.4 Answer x =... y =... [4] 0580/1/M/J/15

9 9 19 B 8 cm 10 cm 6 cm E x cm NOT TO SCALE A y cm C D 9 cm F Triangle ABC is similar to triangle DEF. Calculate the value of (a) x, Answer(a) x =... [] (b) y. Answer(b) y =... [] 0 Factorise completely. (a) yp + yt + xp + xt Answer(a)... [] (b) 7(h + k) 1(h + k) Answer(b)... [] 0580/1/M/J/15 [Turn over

10 cm NOT TO SCALE 4 cm The diagram shows a toy. The shape of the toy is a cone, with radius 4 cm and height 9 cm, on top of a hemisphere with radius 4 cm. Calculate the volume of the toy. Give your answer correct to the nearest cubic centimetre. [The volume, V, of a cone with radius r and height h is V = 3 1 πr h.] [The volume, V, of a sphere with radius r is V = 3 4 πr 3.] Answer... cm 3 [4] 0580/1/M/J/15

11 11 (a) Calculate 3 f pf p. 4 4 Answer(a) f p [] (b) Calculate the inverse of f p. Answer(b) f p [] Question 3 is printed on the next page. 0580/1/M/J/15 [Turn over

12 1 3 f(x) = 5 3x (a) Find f(6). Answer(a)... [1] (b) Find f(x + ). Answer(b)... [1] (c) Find ff(x), in its simplest form. Answer(c)... [] (d) Find f 1 (x), the inverse of f(x). Answer(d) f 1 (x) =... [] 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 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. 0580/1/M/J/15

13 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/3 Paper (Extended) May/June 015 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 1 hour 30 minutes 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. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level Certificate. This document consists of 1 printed pages. DC (CW/SW) / [Turn over

14 1 Ahmed and Babar share 40 g of sweets in the ratio 7 : 3. Calculate the amount Ahmed receives. Answer... g [] Factorise completely. 9x 6x Answer... [] 3 5 cm NOT TO SCALE cm x Calculate the value of x. Answer x =... [] 4 An equilateral triangle has sides of length 6. cm, correct to the nearest millimetre. Complete the statement about the perimeter, P cm, of the triangle. Answer... P... [] 0580/3/M/J/15

15 3 5 Factorise x 5x 3. Answer... [] 6 Find the matrix that represents a rotation through 90 clockwise about (0, 0). Answer f p [] 7 James buys a drink for euros ( ). Work out the cost of the drink in pounds ( ) when 1 = 1.5. Give your answer correct to decimal places. Answer... [3] 0580/3/M/J/15 [Turn over

16 4 8 Without using a calculator, work out Show all your working and give your answer as a fraction in its lowest terms. Answer... [3] 9 Solve the equation. 3(x + 4) = (4x 1) Answer x =... [3] 10 In a sale, the cost of a coat is reduced from $85 to $ Calculate the percentage reduction in the cost of the coat. Answer... % [3] 0580/3/M/J/15

17 11 5 C 100 NOT TO SCALE A 30 4 cm B Use the sine rule to calculate BC. Answer BC =... cm [3] 1 10 Speed (m/s) NOT TO SCALE 0 u 3u Time (seconds) A car starts from rest and accelerates for u seconds until it reaches a speed of 10 m/s. The car then travels at 10 m/s for u seconds. The diagram shows the speed-time graph for this journey. The distance travelled by the car in the first 3u seconds is 15 m. (a) Find the value of u. (b) Find the acceleration in the first u seconds. Answer(a) u =... [3] Answer(b)... m/s [1] 0580/3/M/J/15 [Turn over

18 6 13 Simplify. (a) 1x 1 3x 3 Answer(a)... [] (b) ( 56y 56 1 ) 8 Answer(b)... [] 14 Solve the equation. x + x = 0 Show your working and give your answers correct to decimal places. Answer x =... or x =... [4] 0580/3/M/J/15

19 7 15 The circumference of a circle is 30 cm. (a) Calculate the radius of the circle. Answer(a)... cm [] (b) The length of the arc of the semi-circle is 15 cm. Calculate the area of the semi-circle. Answer(b)... cm [] 0580/3/M/J/15 [Turn over

20 16 (a) In this part, you may use this Venn diagram to help you answer the questions. 8 F S In a class of 30 students, 5 study French (F), 18 study Spanish (S). One student does not study French or Spanish. (i) Find the number of students who study French and Spanish. Answer(a)(i)... [] (ii) One of the 30 students is chosen at random. Find the probability that this student studies French but not Spanish. Answer(a)(ii)... [1] (iii) A student who does not study Spanish is chosen at random. Find the probability that this student studies French. Answer(a)(iii)... [1] (b) P Q R On this Venn diagram, shade the region R (P Q ). [1] 0580/3/M/J/15

21 Cumulative frequency Time (seconds) students take a reaction time test. The cumulative frequency diagram shows the results. Find (a) the median, Answer(a)... s [1] (b) the inter-quartile range, Answer(b)... s [] (c) the number of students with a reaction time of more than 4 seconds. Answer(c)... [] 0580/3/M/J/15 [Turn over

22 10 18 P NOT TO SCALE 8 cm D C M 0 cm A 0 cm B The diagram shows a solid pyramid on a square horizontal base ABCD. The diagonals AC and BD intersect at M. P is vertically above M. AB = 0 cm and PM = 8 cm. Calculate the total surface area of the pyramid. Answer... cm [5] 0580/3/M/J/15

23 11 19 B M P b X NOT TO SCALE O a A OAPB is a parallelogram. O is the origin, OA = a and OB = b. M is the midpoint of BP. (a) Find, in terms of a and b, giving your answer in its simplest form, (i) BA, Answer(a)(i) BA =... [1] (ii) the position vector of M. Answer(a)(ii)... [1] (b) X is on BA so that BX : XA = 1 :. Show that X lies on OM. Answer(b) [4] Question 0 is printed on the next page. 0580/3/M/J/15 [Turn over

24 1 0 9 cm R NOT TO SCALE P 10 cm Q The area of triangle PQR is 38.5 cm. Calculate the length QR. Answer QR =... cm [6] 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 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. 0580/3/M/J/15

25 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 015 series 0580 MATHEMATICS 0580/1 Paper (Extended), maximum raw mark 70 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 015 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is the registered trademark of Cambridge International Examinations.

26 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/June Abbreviations 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 or x + 8x 35 final answer B1 for correct terms in final answer or M1 for x + 3x or 5x 35 5 Sammy and correct reason with 5.7% oe shown B1 for 5.7% or seen or conversion of 6% to fraction and common denominator 6 44 B1 for 75.5 or seen 7 3 4u w final answer B1 for correct elements in final answer or M for ( 4 7) + ( 6 ( ) ) oe or M1 for ( 4 7) oe or ( 6 ( ) ) oe B1 63 or 35 their or or 4 cao 5 5 M1 A or their or equivalent division with fractions with common denominators M for 1 (1 + 6) oe or M1 for 1 area correct If zero scored B1 for top speed = 70 m per min or total time = 360 sec Cambridge International Examinations 015

27 Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE May/June Question. Answer Mark Part Marks 11 (a) 4n oe final answer 1 (b) 3n + 8 oe final answer M1 for a quadratic expression as final answer or 3n + 8 oe in working M for ( + 4) = p( + 4) oe M1 for A1 for k = 7 k p = ( q + 4) M for M1 for working out distance speed 14 (a) a + b a or a ( a b) oe 1 e.g. figs or figs 180 their speed or for working out km/h to m/s conversion 1000 e.g. 64 oe or their oe (b) Parallelogram PM equal and parallel to QR or PM or PS parallel to QR and MR found = a so pairs of parallel sides 1 1 SC1 for answer trapezium with reason PM parallel to QR 15 y < 8 y [ 6 x oe and y [ x + oe 1 3 B for either y [ 6 x oe or y [ x + oe or SC for y = 6 x oe and y = x + oe or SC1 for y K 6 x or y = 6 x or y K x + or y = x + Cambridge International Examinations 015

28 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE May/June Question. Answer Mark Part Marks cao 4 B3 for or [9...] or or 6597 or B for [9...] or or B1 for If B1 scored or B0 scored and an attempt at compound interest is shown SC1 for their 6597[...] 5000 evaluated correctly provided answer positive and SC1 for their final answer rounded correctly to nearest $ from their more accurate answer 17 (a) 3 5 B1 for, 3, 5 as prime factors (b) 90 B1 for 90k or for listing multiples of each up to 90 or Correctly equating one set of coefficients Correct method to eliminate one variable x = 0.8 y = 3 M1 M1 A1 A1 Dependent on the coefficients being the same for one of the variables Correct consistent use of addition or subtraction using their equations If zero scored SC1 for values satisfying one of the original equations or if no working shown, but correct answers given 6 19 (a) 7.5 M1 for [ 10 ] oe 8 (b) 1 cao M1 for 8 9 oe or their (a) 0 (a) ( p + t)( y + x) final answer B1 for y ( p t) + x( p + t) p( y + x) + t( y + x) + or ( ) (b) 7( h + k)( h + k 3) final answer B1 for 7 ( h + k) 3( h + k) or ( h + k) ( 7( h + k) 1) Cambridge International Examinations 015

29 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE May/June Question. Answer Mark Part Marks 1 85 cao 4 1 M1 for π 4 9, 48π M1 for π 4, 18π 3 7π A1 for 84.8 to 84.9, 3 If A0 then B1 for their final answer rounded correctly to nearest whole number from their more accurate answer dependent on at least M1 (a) M1 for a matrix with correct elements (b) a b M1 for c d or 4 3 k soi 6 5 or det = soi 3 (a) 13 1 (b) 3x 1 or 5 3( + ) x 1 (c) 9x 10 cao M1 for 5 3( 5 3x) (d) 5 x 3 final answer oe M1 for correct first step e.g. y 5 y + 3 x = 5 or = x 3 3 better or or for interchanging x and y, e.g. not need to be the first step y 5 = 3x or x = 5 3y, this does Cambridge International Examinations 015

30 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 015 series 0580 MATHEMATICS 0580/ Paper (Extended), maximum raw mark 70 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 015 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is the registered trademark of Cambridge International Examinations.

31 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/June Abbreviations 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 [h] 30 [min] cao or (a) 7 1 (b) Any number except 3, 7 or oe M1 for 1 ( ) or 8000 nfww M1 for w = oe or 5w = oe 7 Parallel Same length n + 3 oe final answer M1 for a quadratic expression as final answer or n + 3 oe in working 9 3 M1 for 5. 5 & -. 5 & oe e.g..55 r 0.5 r oe, must be fraction 90 k or B1 for B1 for 10.5 or seen oe M1 for k soi 11 3 or 1 a 5 c b d or det = 5 soi Cambridge International Examinations 015

32 Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE May/June B or accept or their oe 5 8 M or their or equivalent division with fractions with common denominators 3 cao 10 A1 13 (a) 11 1 (b) 8 FT FT 30 their (a) or M1 for 4 7 = (x 1) + FG oe or 4(x 4) = (x 1) + FG oe or 7 + (x 4) = (x 1) + FG oe Allow x to be their (a) in each M for or M1 for [ 3] or or or (a) (i) x 3 final answer ( x + )(x 5) or 0.5 or or 3 B1 for a common denominator of (x + )(x 5) 1 B1 for 3(x 5) 4(x + ) or better x 7 or SC for final answer ( x + )(x 5) or SC1 for numerator of x 7 in final answer (a)(ii) 4 1 (b) 1.37 or 1.37[4 ] 1 17 (a) [y =] x + 3 cao 3 M for correct unsimplified equation or B1 for gradient = (11 3) (4 0) or better and B1 for c = 3 (b) 1 oe 1FT 1 their m Cambridge International Examinations 015

33 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE May/June (a) 78 3 M for (8 5) or 1 6 (5 + 8) oe (b) FT 15 their (a) or M1 for 5 1, 1 1 (8 5), 1 6 (5 + 8) or 1 8 ( ) 19 (a) 1 Correct circle, radius 4 cm centre C (b) B for correct bisector with pairs of correct arcs or B1 for correct bisector with no/wrong arcs C (c) 1 Correct complete boundary and correct shading. A B Dep on at least B1 in (b) 0 (a) (i) 4 1 (ii) {3, 9} 1 (iii) fewer than 6 numbers from {1, 3, 5, 7, 9, 11} or 1 (b) ξ 1 A B C 1 (a) m = n = 10 B1 for m = B1 for n = 10 If 0 scored SC1 for (x + ) in working or x + mx + m + n and equating coefficients m[x] = 4[x] or m + n = 6 (b) 1.16 or 1.16[ ] from completing square FT FT dep on negative n B1 for (x + their m) = their n or SC1 for correct answer from using formula or for both answers 1.16 and 5.16 whatever method used Cambridge International Examinations 015

34 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE May/June (a) 44 M1 for 48 soi (b) 4 M1 for 40 or 16 or both lines drawn from 15 and 45 across and down to the horizontal axis (c) 5 M1 for answer 55 or line or mark on graph indicating 55 3 (a) 0.4 or 5 1 (b) M for correct, complete, area statement 1 1 e.g oe or M1 for one area calculation 1 1 e.g or 0 8 or (c) 11.9 or to FT their (b) 10 4 (a) 9x 1 (b) x 5 M1 for correct first algebraic step e.g. 3 y 5 y 5 = 3x or = x + or better 3 3 or (c) 9x + 0 cao final answer M1 for 3(3x + 5) + 5 for interchanging x and y, e.g. x = 3y + 5, this does not need to be the first step Cambridge International Examinations 015

35 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 015 series 0580 MATHEMATICS 0580/3 Paper (Extended), maximum raw mark 70 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 015 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is the registered trademark of Cambridge International Examinations.

36 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/June Abbreviations 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 M1 for 40 (7 + 3) or better 3x (3x ) final answer B1 for 3(3x x) or x ( 9x 6) [ ] M1 for cos [ = ] 5 oe If 0 scored, SC1 for 6.15 and 6.5 seen or for correct answers reversed 5 ( x + 1)( x 3) B1 for ( x + a)( x + b), where ab = 3 or a + b = B1 for one correct column cao 3 B for or 1.6 or M1 for B1 135 or their oe 8 5 M or or equivalent division with 7 7 fractions with common denominators 7 8 or cao A1 9.8 oe 3 M for 1 + = 8x 3x or better or M1 for 3x + 1 or 8x or 0.58 to M for 100 or or M1 for or If zero scored SC1 for Cambridge International Examinations 015

37 Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE May/June Question Answer Mark Part Marks or 1.18 to sin 30 M for sin100 or M1 for correct implicit equation sin100 sin 30 e.g. = 4 BC 1 (a) 5 3 u 10 M for + u 10 = 15 oe or M1 for evidence that area represents distance e.g. u 10, 10 u or 3 u 10 (b) 1FT FT 10 their u correctly evaluated 13 (a) 4x 9 final answer B1 for answer kx 9 or 4x k (k 0 ) (b) y 3 final answer B1 for answer ky 3 or y k (k 0 ) ()( ) B1 If completing the square B1 for 1 x + oe 4 If in form p + r q or p r q B1 B1 for 1 x = p = 1, r = () or 4 or 1 x = B1 B1 If 0 scored for the last two B marks then SC1 for 1.3 and 0.8 or 1.81 to 1.80 and or to or 1.8 and 0.78 or 1.8 and 0.78 seen in the working 15 (a) 4.77 or to M1 for 30 []π (b) 35.7 or 35.8 or to 35.8 M1 for 0.5 π (their (a)) or 0.5 π (30 π) Cambridge International Examinations 015

38 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE May/June Question Answer Mark Part Marks 16 (a) (i) 14 M1 for any two of 1, 11, 14, 4 correctly placed on Venn diagram or for x + x + 18 x = 30 oe (ii) ( )( ) 11 5 their a i oe 1FT FT diagram or their from (iii) 11 their oe 1FT FT their diagram e.g their ( a)( i) or 1 (b) 1 17 (a) 6 1 (b) M1 for 7 identified as the UQ or 5 identified as the LQ or both lines drawn from the 150 and 50 across and down to the horizontal axis (c) 180 M1 for answer 0 or line or mark on graph indicating or M4 for or better or M3 for or better or M1 for and M1 for and M1 for Cambridge International Examinations 015

39 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE May/June Question Answer Mark Part Marks 19 (a) (i) b + a 1 (ii) b + 1 a 1 (b) [ OX = ] b ( b + a) oe M1 1 a + b oe 3 3 statements from: 1 OM = b + a oe or [ OX =] 1 ( b + a) oe 3 or OX = 3 OM oe A1 B B1 for any one of these statements or to M for sin[p] = or M1 for sin = 38.5 M3 for ( cos (their P)) or M for cos (their P) or M1 for a correct implicit expression e.g. cos(their P)= RQ 9 10 Note: 87.8, 87.81[ ] or 87.7[55 ] score 4 marks or M is foot of perpendicular from R to PQ M for perp.ht = or 7.7 or M1 for 1 10 [ ] = 38.5 M1 for PM = (9 7.7 )[ = or 4.66] M1 for QM = 10 their [ = 5.34 ] M1 for QR = ((their QM) ) Cambridge International Examinations 015