Friday 18 January 2013 Afternoon

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1 Frida 18 Januar 013 Afternoon A GCE MATHEMATICS (MEI) 75/01B Applications of Advanced Mathematics (C) Paper B: Comprehension QUESTION PAPER * * Candidates answer on the Question Paper. OCR supplied materials: Insert (inserted) MEI Eamination Formulae and Tables (MF) Other materials required: Scientific or graphical calculator Rough paper Duration: Up to 1 hour * B * INSTRUCTIONS TO CANDIDATES The insert will be found in the centre of this document. Write our name, centre number and candidate number in the boes above. Please write clearl and in capital letters. Use black ink. HB pencil ma be used for graphs and diagrams onl. Answer all the questions. Read each question carefull. Make sure ou know what ou have to do before starting our answer. Write our answer to each question in the space provided. Additional paper ma be used if necessar but ou must clearl show our candidate number, centre number and question number(s). Do not write in the bar codes. The insert contains the tet for use with the questions. You are permitted to use a scientific or graphical calculator in this paper. Final answers should be given to a degree of accurac appropriate to the contet. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. You ma find it helpful to make notes and do some calculations as ou read the passage. You are not required to hand in these notes with our question paper. You are advised that an answer ma receive no marks unless ou show sufficient detail of the working to indicate that a correct method is being used. The total number of marks for this paper is 18. This document consists of 8 pages. An blank pages are indicated. OCR 013 [T/10/653] DC (RW/SW) 6006/ OCR is an eempt Charit Turn over

2 BLANK PAGE PLEASE DO NOT WRITE ON THIS PAGE OCR 013

3 3 1 On the grid below mark all three possible positions of the point P with integer coordinates for which t_ P,X i = and t_ P,Y i = 3. [3] 1 Y 0 X 6 This question is concerned with generalised taicab geometr. On the grid below, show the locus of a point P where t_ P,Ai = t_ P,Bi. [3] B A 0 OCR 013 Turn over

4 3 (i) Describe the following locus of a point P, using the notation t_ P,A i and t_ P,Bi as appropriate. B (5, ) 0 A (1, 0) [1] (ii) Describe the following locus of a point P, using the notation t_ P,Ai as appropriate. 6 A [1] OCR 013

5 5 3 (i) 3 (ii) PLEASE DO NOT WRITE IN THIS SPACE OCR 013 Turn over

6 6 Referring to Fig. 5, or otherwise, find the value of n_, i. [] 5 In lines 5 and 55 it sas there are 35 minimum distance routes from A _ 0, 0i to B _, 3i. Determine how man of these routes pass through the point with coordinates _ 3, i, eplaining our reasoning. [] 5 OCR 013

7 6 Fig. 7 is reproduced below C (, 3) (i) Two points on this locus have -coordinate 0.7. Write down the coordinates of each of these points. [] (ii) In lines 77 to 78 it sas adding a second taicab circle with centre _, 0i and radius shows that in generalised taicab geometr two different circles can have an infinite number of points in common! On the cop of Fig. 7 given below, draw the taicab circle with centre _, 0i and radius. [1] 6 (i) 6 (ii) 8 6 C (, 3) OCR 013 Turn over

8 8 7 In lines 3 and it sas that if the Pthagorean distance between two points A and B is d_ A,Bi then the taicab distance satisfies the inequalities d_ A,Bi G t_ A,Bi G # d_ A,Bi. This question is about using this result in generalised taicab geometr. (i) Given that A is the point _ 0, 0i, describe all possible positions of B for which d_ A,Bi = t_ A,Bi. [1] (ii) Given that A is the point _ 0, 0i, describe all possible positions of B for which t_ A,Bi = # d_ A,Bi. [] 7 (i) 7 (ii) Copright Information OCR is committed to seeking permission to reproduce all third-part content that it uses in its assessment materials. OCR has attempted to identif and contact all copright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copright acknowledgements are reproduced in the OCR Copright Acknowledgements Booklet. This is produced for each series of eaminations and is freel available to download from our public website ( after the live eamination series. If OCR has unwittingl failed to correctl acknowledge or clear an third-part content in this assessment material, OCR will be happ to correct its mistake at the earliest possible opportunit. For queries or further information please contact the Copright Team, First Floor, 9 Hills Road, Cambridge CB 1GE. OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of Universit of Cambridge Local Eaminations Sndicate (UCLES), which is itself a department of the Universit of Cambridge. OCR 013

MATHEMATICS (MEI) 4752 Concepts for Advanced Mathematics (C2)

ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4752 Concepts for Advanced Mathematics (C2) QUESTION PAPER Candidates answer on the printed answer book. OCR supplied materials: Printed answer book 4752 MEI Examination