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Monday 16 June 2014 – Morning - MEI

Monday 16 june 2014 MorningA2 GCE MATHEMATICS (MEI)4753/01 Methods for Advanced Mathematics (C3)QUESTION PAPER*1243053592*INSTRUCTIONS TO CANDIDATEST hese instructions are the same on the Printed Answer Book and the Question Paper. The Question Paper will be found inside the Printed Answer Book. Write your name, centre number and candidate number in the spaces provided on the Printed Answer Book. Please write clearly and in capital letters. Write your answer to each question in the space provided in the Printed Answer Book. Additional paper may be used if necessary but you must clearly show your candidate number, centre number and question number(s). Use black ink. HB pencil may be used for graphs and diagrams only. Read each question carefully. Make sure you know what you have to do before starting your answer.

4753 Mark Scheme June 2014 1 1. Annotations and abbreviations Annotation in scoris Meaning Blank Page – this annotation must be used on all blank pages within an answer booklet (structured or

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Transcription of Monday 16 June 2014 – Morning - MEI

1 Monday 16 june 2014 MorningA2 GCE MATHEMATICS (MEI)4753/01 Methods for Advanced Mathematics (C3)QUESTION PAPER*1243053592*INSTRUCTIONS TO CANDIDATEST hese instructions are the same on the Printed Answer Book and the Question Paper. The Question Paper will be found inside the Printed Answer Book. Write your name, centre number and candidate number in the spaces provided on the Printed Answer Book. Please write clearly and in capital letters. Write your answer to each question in the space provided in the Printed Answer Book. Additional paper may be used if necessary but you must clearly show your candidate number, centre number and question number(s). Use black ink. HB pencil may be used for graphs and diagrams only. Read each question carefully. Make sure you know what you have to do before starting your answer.

2 Answer all the questions. Do not write in the bar codes. You are permitted to use a scientific or graphical calculator in this paper. Final answers should be given to a degree of accuracy appropriate to the FOR CANDIDATESThis information is the same on the Printed Answer Book and the Question Paper. The number of marks is given in brackets [ ] at the end of each question or part question on the Question Paper. You are advised that an answer may receive no marks unless you show sufficient detail of the working to indicate that a correct method is being used. The total number of marks for this paper is 72. The Printed Answer Book consists of 16 pages . The Question Paper consists of 4 pages . Any blank pages are TO EXAMS OFFICER / INVIGILATOR Do not send this Question Paper for marking; it should be retained in the centre or recycled.

3 Please contact OCR Copyright should you wish to re-use this is an exempt CharityTurn over OCR 2014 [M/102/2652]DC (LK/SW) 75645/5 Candidates answer on the Printed Answer supplied materials: Printed Answer Book 4753/01 MEI Examination Formulae and Tables (MF2)Other materials required: Scientific or graphical calculatorDuration: 1 hour 30 minutes24753/01 Jun14 OCR 2014 Section A (36 marks)1 Evaluate ()sindx x13061-ry, giving your answer in exact form. [3]2 Find the exact gradient of the curve lncosyx12=-^h at the point with x-coordinate 61r. [5]3 Solve the equation x x324-=. [4]4 Fig. 4 shows the curve ()fyx=, where (),fcosxabxx02 GGr=+, and a and b are positive constants. The curve has stationary points at (0, 3) and (,) 4 (i) Find a and b. [2] (ii) Find ()fx1-, and state its domain and range.

4 [5]5 A spherical balloon of radius r cm has volume cmV3, where Vr343r=. The balloon is inflated at a constant rate of cms1031-. Find the rate of increase of r when r8=. [5]6 The value V of a car t years after it is new is modelled by the equation eVAkt=-, where A and k are positive constants which depend on the make and model of the car. (i) Brian buys a new sports car. Its value is modelled by the equation Calculate how much value, to the nearest 100, this car has lost after 1 year. [2] (ii) At the same time as Brian buys his car, Kate buys a new hatchback for 15 000. Her car loses 2000 of its value in the first year. Show that, for Kate s car, k = correct to 3 significant figures. [3] (iii) Find how long it is before Brian s and Kate s cars have the same value. [3]7 Either prove or disprove each of the following statements.

5 (i) If m and n are consecutive odd numbers, then at least one of m and n is a prime number. [2] (ii) If m and n are consecutive even numbers, then mn is divisible by 8. [2]34753/01 Jun14 Turn over OCR 2014 Section B (36 marks)8 Fig. 8 shows the curve ()fyx=, where ()fxxx22=+.xyOFig. 8 (i) Show algebraically that ()fx is an odd function. Interpret this result geometrically. [3] (ii) Show that ())(fxx22232=+l. Hence find the exact gradient of the curve at the origin. [5] (iii) Find the exact area of the region bounded by the curve, the x-axis and the line x1=. [4] (iv) (A) Show that if yxx22=+, then yx12122=+. [2] (B) Differentiate yx12122=+ implicitly to show that ddxyxy233=. Explain why this expression cannot be used to find the gradient of the curve at the origin. [4][Question 9 is printed overleaf.]

6 ]44753/01 Jun14 OCR 2014 Copyright InformationOCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website ( ) after the live examination OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.

7 OCR 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 Fig. 9 shows the curve eyxx2=- together with the straight line ymx=, where m is a constant, with m0111. The curve and the line meet at O and P. The dashed line is the tangent at = mxPOy=xe 2xFig. 9 (i) Show that the x-coordinate of P is lnm21-. [3] (ii) Find, in terms of m, the gradient of the tangent to the curve at P. [4] You are given that OP and this tangent are equally inclined to the x-axis. (iii) Show that me2=-, and find the exact coordinates of P. [4] (iv) Find the exact area of the shaded region between the line OP and the curve. [7]end oF QueSTion pAperMonday 16 june 2014 MorningA2 GCE MATHEMATICS (MEI)4753/01 Methods for Advanced Mathematics (C3)PRINTED ANSWER BOOKINSTRUCTIONS TO CANDIDATEST hese instructions are the same on the Printed Answer Book and the Question Paper.

8 The Question Paper will be found inside the Printed Answer Book. Write your name, centre number and candidate number in the spaces provided on the Printed Answer Book. Please write clearly and in capital letters. Write your answer to each question in the space provided in the Printed Answer Book. Additional paper may be used if necessary but you must clearly show your candidate number, centre number and question number(s). Use black ink. HB pencil may be used for graphs and diagrams only. Read each question carefully. Make sure you know what you have to do before starting your answer. Answer all the questions. Do not write in the bar codes. You are permitted to use a scientific or graphical calculator in this paper. Final answers should be given to a degree of accuracy appropriate to the FOR CANDIDATESThis information is the same on the Printed Answer Book and the Question Paper.

9 The number of marks is given in brackets [ ] at the end of each question or part question on the Question Paper. You are advised that an answer may receive no marks unless you show sufficient detail of the working to indicate that a correct method is being used. The total number of marks for this paper is 72 The Printed Answer Book consists of 16 pages . The Question Paper consists of 4 pages . Any blank pages are indicated.*475301*OCR is an exempt CharityTurn over OCR 2014 [M/102/2652]DC (LK) 75646/5 Candidates answer on this Printed Answer supplied materials: Question Paper 4753/01 (inserted) MEI Examination Formulae and Tables (MF2)Other materials required: Scientific or graphical calculator*1243393355*Duration: 1 hour 30 minutes2 OCR 2014 Section A (36 marks)13 Turn over OCR 20142 4 OCR 201435 Turn over OCR 20144 (i)4 (ii)6 OCR 201457 Turn over OCR 20146 (i)6 (ii)8 OCR 20146 (iii)9 Turn over OCR 20147 (i)7 (ii)10 OCR 2014 Section B (36 marks)8 (i)11 Turn over OCR 20148 (ii)12 OCR 20148 (iii)13 Turn over OCR 20148 (iv) (A) 8 (iv) (B) 14 OCR 20149 (i)9 (ii)(answer space continued on next page)15 Turn over OCR 20149 (ii) (continued)9 (iii)16 OCR 2014 OCR 2014 Contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.

10 OCR 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 (iv) Oxford Cambridge and RSA Examinations GCE Mathematics (MEI) Unit 4753: Methods for Advanced Mathematics Advanced GCE Mark Scheme for june 20144753 Mark Scheme june 2014 1 1. Annotations and abbreviations Annotation in scoris Meaning Blank Page this annotation must be used on all blank pages within an answer booklet (structured or unstructured) and on each page of an additional object where there is no candidate response. and BOD Benefit of doubt FT Follow through ISW Ignore subsequent working M0, M1 Method mark awarded 0, 1 A0, A1 Accuracy mark awarded 0, 1 B0, B1 Independent mark awarded 0, 1 SC Special case ^ Omission sign MR Misread Highlighting Other abbreviations in mark scheme Meaning E1 Mark for explaining U1 Mark for correct units G1 Mark for a correct feature on a graph M1 dep* Method mark dependent on a previous mark, indicated by * cao Correct answer only oe Or equivalent rot Rounded or truncated soi Seen or implied www Without wrong working 4753 Mark Scheme june 2014 2 2.


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