Thursday 14 June 2012 Morning
|
|
- Clifton Stokes
- 5 years ago
- Views:
Transcription
1 Thursday 14 June 01 Morning A GCE MATHEMATICS (MEI) 4757 Further Applications of Advanced Mathematics (FP3) QUESTION PAPER * * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book 4757 MEI Examination Formulae and Tables (MF) Other materials required: Scientific or graphical calculator Duration: 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and the Question Paper. The Question Paper will be found in the centre of 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 any three 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 context. INFORMATION FOR CANDIDATES This 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 7. The Printed Answer Book consists of 0 pages. The Question Paper consists of 8 pages. Any blank pages are indicated. INSTRUCTION TO EXAMS OFFICER / INVIGILATOR Do not send this Question Paper for marking; it should be retained in the centre or recycled. Please contact OCR Copyright should you wish to re-use this document. OCR 01 [K/10/665] DC (NF) 47955/4 OCR is an exempt Charity Turn over
2 Option 1: Vectors 1 A mine contains several underground tunnels beneath a hillside. The hillside is a plane, all the tunnels are straight and the width of the tunnels may be neglected. A coordinate system is chosen with the z-axis pointing vertically upwards and the units are metres. Three points on the hillside have coordinates A(15, 60, 0), B( 75, 100, 40) and C(18, 138, 35.6). (i) Find the vector product AB AC and hence show that the equation of the hillside is x y + 5z = 650. [5] The tunnel T A begins at A and goes in the direction of the vector 15i + 14j k; the tunnel T C begins at C and goes in the direction of the vector 8i + 7j k. Both these tunnels extend a long way into the ground. (ii) Find the least possible length of a tunnel which connects B to a point in T A. [6] (iii) Find the least possible length of a tunnel which connects a point in T A to a point in T C. [6] (iv) A tunnel starts at B, passes through the point (18, 138, p) vertically below C, and intersects T A at the point Q. Find the value of p and the coordinates of Q. [7] Option : Multi-variable calculus You are given that g(x, y, z) = x + y z + xz + yz + 4z 3. (i) Find g x, g g and y z. The surface S has equation g(x, y, z) = 0, and P(, 1, 1) is a point on S. (ii) Find an equation for the normal line to the surface S at the point P. (iii) A point Q lies on this normal line and is close to P. At Q, g(x, y, z) = h, where h is small. Find the constant c such that PQ c h. [5] (iv) Show that there is no point on S at which the normal line is parallel to the z-axis. [5] (v) Given that x + y + z = k is a tangent plane to the surface S, find the two possible values of k. [8] OCR Jun1
3 3 Option 3: Differential geometry 3 A curve has parametric equations x = a(1 cos 3 θ), y = a sin 3 θ, for 0 where a is a positive constant. θ π 3, The arc length from the origin to a general point on the curve is denoted by s, and ψ is the acute angle defined by tan ψ = dy dx. (i) Express s and ψ in terms of θ, and hence show that the intrinsic equation of the curve is s = 3 a sin ψ. [9] (ii) For the point on the curve given by θ = π, find the radius of curvature and the coordinates of the centre 6 of curvature. [9] (iii) Find the area of the curved surface generated when the curve is rotated through π radians about the y-axis. [6] OCR Jun1 Turn over
4 4 Option 4: Groups 4 (i) Show that the set P = {1, 5, 7, 11}, under the binary operation of multiplication modulo 1, is a group. You may assume associativity. A group Q has identity element e. The result of applying the binary operation of Q to elements x and y is written xy, and the inverse of x is written x 1. (ii) Verify that the inverse of xy is y 1 x 1. [] Three elements a, b and c of Q all have order, and ab = c. (iii) By considering the inverse of c, or otherwise, show that ba = c. [] (iv) Show that bc = a and ac = b. Find cb and ca. (v) Complete the composition table for R = {e, a, b, c}. Hence show that R is a subgroup of Q and that R is isomorphic to P. The group T of symmetries of a square contains four reflections A, B, C, D, the identity transformation E and three rotations F, G, H. The binary operation is composition of transformations. The composition table for T is given below. A B C D E F G H A E G H F A D B C B G E F H B C A D C F H E G C A D B D H F G E D B C A E A B C D E F G H F C D B A F G H E G B A D C G H E F H D C A B H E F G (vi) Find the order of each element of T. (vii) List all the proper subgroups of T. [5] OCR Jun1
5 5 Option 5: Markov chains This question requires the use of a calculator with the ability to handle matrices. 5 In this question, give probabilities correct to 4 decimal places. A random walk is modelled as a Markov chain with five states A, B, C, D, E representing the possible positions, from left to right, of an object. At each step the object moves as follows. If the object is at A, it moves one place to the right (to B). If the object is at E, it moves one place to the left (to D). Otherwise, the probability that the object moves one place to the left is 0.4, and the probability that it moves one place to the right is 0.6. Steps occur at intervals of one minute, and the time taken to move may be neglected. The object starts at A, so after the first step (one minute later) the object is at B. (i) Which of the five states are reflecting barriers? [1] (ii) Write down the transition matrix P. [] (iii) State the possible positions of the object after 10 steps, and give the probabilities that the object is in each of these positions. (iv) Find the probability that after 15 steps the object is in the same position as it was after 13 steps. (v) Find the number of steps after which the probability that the object is at D exceeds 0.69 for the first time. (vi) Find the limits of P n and P n +1 as the positive integer n tends to infinity. (vii) For the interval of 100 minutes between the 00th step and the 300th step, find the expected length of time for which the object is at each of the five positions. (viii) At a certain instant, the object arrives at D. Find the expected number of successive occasions that the object moves to E (and then back to D). Hence find the expected time after this instant when the object first moves to C. OCR Jun1
6 14 4 (iv) 4 (v) R e a b c e a b c OCR 01
7 4757 Mark Scheme June 01 1 (i) Evaluation of vector product [ 73 ] A Give for one component correct x y5z (15) ( 60) 5(0) For x y5z d Equation of ABC is x y5z 650 E1 Evidence of substitution required [5] 1 (ii) Appropriate vector product AB d A A Give if one error AB d A for any non-zero multiple correctly obtained d A AB d A Distance is d A Distance is 180 m [6] OR Obtaining a value of Distance is (10) ( 13) ( 4) Distance is 180 m 5
8 4757 Mark Scheme June 01 1 (iii) Vector product of direction vectors d [ 7 ] 7 1 A Give if one error Appropriate scalar product ˆ AC. d Fully correct method for finding 1 3 distance Distance is 14.8 m [6] 1 (iv) p 40 Must use different parameters Both equations correct 5, 5 Obtaining value of or ( p 40) Or other method for finding p p 6 Q is (15 375, , 0 50) Q is (390, 90, 30) [7] (i) g x z x g 4y z y g z x y 4 z 6
9 4757 Mark Scheme June 01 (ii) g g g At P,,, 4 x y z 1 Normal line is r (iii) If Q is (, 1, 1 ) g g g h g x y z x y z ( )( ) ( )( ) ( 4)( ) [ 1 ] (iv) FT PQ ( ) ( ) ( ) For direction of normal line 6 FT Allow c A0 for c 1 1 [5] g g Require 0 x y x z, y 1 z 1 FT Requires some substitution in RHS or h on LHS z z z z z 4z3 0 Obtaining equation in one variable 5z 8z6 0 Discriminant is Hence there are no such points E1 Correctly shown [5] Or 5x 8x60 or 10y 8y3 0 or 14 0 Dependent on quadratic with negative discriminant Condone omission of r = Allow for x etc g ( ) z 7
10 4757 Mark Scheme June 01 (v) g g g Require ( ) Allow if 1 x y z x z 4yz zxy 4 FT x y, y z (4z 4) (z) z... 4z3 0 Obtaining equation in one variable 5z 8z3 0 Or 5x 8x0 or 5y 4y 0 Or 4 0 Points (0, 0, 1) and ( 1.6, 0.8, 0.6) Obtaining at least one point k 001 or k Obtaining a value of k k 1, 1.8 [8] 3 (i) dx dy 3acos sin, 3asin cos d d dx dy (3a sin cos ) (cos sin ) d d (3asin cos ) Implies previous if values of x, y, z not seen s 3asin cosd FT requires workable integral form 3 asin ( c) s 0when0 c 0 Or dy 3asin cos tan dx 3a cos sin tan Hence and s 3 asin E1 Correctly shown [9]... used Required for final E1 0 8
11 4757 Mark Scheme June 01 3 (ii) ds 3asin cos d OR 1 3 When,, 3a 6 6 Radius of curvature is a Condone use of even if 6 not established in (i) 9a 3 3a When, x, y Obtaining second derivatives 3 3a 15a x, y 8 8 May be implied by later work 3 ( x y ) xy xy 3 81a 7a a 15a 3 3a 3 3a Applying formula for or Radius of curvature is a 1 sin Obtaining gradient or normal vector Normal vector is n ˆ cos 3 Correct normal vector a c a Must use unit normal here a a Centre of curvature is a 1, 4 4 [9] Not necessarily unit vector 9
12 4757 Mark Scheme June 01 3 (iii) Surface area is xds 3 3 a(1 cos )(3asincos )d FT Correct limits required a (sincos sincos )d a sin cos a 80 [6] Integrating For 1sin and 1cos (i) P Table shows closure Identity is 1 All elements are self-inverse Condone no mention of inverse of 1 4 (ii) 1 1 ( xy)( y x ) 1 1 Or ( y x )( xy) x( yy ) x xex xx e E1 So y x is the inverse of xy [] 4 (iii) a a, b b, c c, c ( ab) b a For any one of these Hence c ba E1 [] At least one trigonometric term Or equivalent 10
13 4757 Mark Scheme June 01 4 (iv) bc b( ba) 1 Or ba c a b c Any correct first step bc ea a E1 ac a( ab) eb b E1 cb a, ca b 4 (v) R e a b c e e a b c a a e c b b b c e a c c b a e R is closed Hence R is a subgroup E1 No need to mention identity or inverses Same pattern as P; hence R and P are isomorphic E1 Dependent on (only) 4 (vi) Eleme A B C D E F G H nt B3 Give for 3 correct; B for 6 correct Order (vii) Ignore { E } and T in the marking { E, A}, { E, B}, { E, C}, { E, D}, { E, G } B Give for 3 correct { E, F, G, H } { E, A, B, G } { E, C, D, G } [5] Deduct 1 mark (from this B) for each subgroup of order given in excess of five Deduct 1 mark (from this ) for each subgroup of order 3 or more given in excess of three 11
14 4757 Mark Scheme June 01 5 Pre-multiplication by transition matrix Allow tolerance of in probabilities throughout this question (i) A and E are reflecting barriers [1] 5 (ii) P B Give for three columns correct [] 5 (iii) For P or P 10 P Using first or second column of P or P Possible positions are A, C, E P( A) , P( C) , P( E) (iv) , P P Using first or second column of P or P, and diagonal elements from P Probability is Allow for ( ) 1
15 4757 Mark Scheme June 01 5 (v) Considering powers of P P...., P Appropriate element exceeding After 17 steps 5 (vi) n Limit of P is Give for any non-zero element B correct to 3 dp n1 Limit of P is Give for any non-zero element n n1 B SC If P and P interchanged, correct to 3 dp award (vii) Expected time at A is Condone for A: 6. B: 15.4 C: 3.1 D: 34.6 E: 0.8 (min) A Give for one correct 5 (viii) 1 Expected number is For Expected time is 11.5 For minutes 13
16 4757 Mark Scheme June 01 5 Post-multiplication by transition matrix Allow tolerance of in probabilities throughout this question (i) A and E are reflecting barriers [1] 5 (ii) P B Give for three rows correct [] 5 (iii) P For P or 9 P Possible positions are A, C, E P( A) , P( C) , P( E) Using first or second row of P or 9 P 14
17 4757 Mark Scheme June 01 5 (iv) P Using first or second row of P or..... P, and diagonal elements from P P Allow for ( ) Probability is (v) P....., P..... Considering powers of P Appropriate element exceeding After 17 steps 15
18 4757 Mark Scheme June 01 5 (vi) n Limit of P is Give for any non-zero element B correct to 3 dp Limit of P n1 is Give for any non-zero element n n1 B SC If P and P interchanged, correct to 3 dp award (vii) Expected time at A is Condone for A: 6. B: 15.4 C: 3.1 D: 34.6 E: 0.8 (min) A Give for one correct 5 (viii) 1 Expected number is For Expected time is 11.5 For minutes 16
MEI STRUCTURED MATHEMATICS 4757
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 4757 Further Applications of Advanced Mathematics
More informationFurther Applications of Advanced Mathematics (FP3) THURSDAY 14 JUNE 2007
ADVANCED GCE UNIT 4757/01 MATHEMATICS (MEI) Further Applications of Advanced Mathematics (FP3) THURSDAY 14 JUNE 2007 Afternoon Time: 1 hour 30 minutes Additional materials: Answer booklet (8 pages) Graph
More informationMATHEMATICS (MEI) FRIDAY 6 JUNE 2008 ADVANCED GCE 4757/01. Further Applications of Advanced Mathematics (FP3) Afternoon Time: 1 hour 30 minutes
ADVANCED GCE 757/01 MATHEMATICS (MEI) Further Applications of Advanced Mathematics (FP) FRIDAY JUNE 008 Additional materials (enclosed): None Additional materials (required): Answer Booklet (8 pages) Graph
More information* * MATHEMATICS (MEI) 4757 Further Applications of Advanced Mathematics (FP3) ADVANCED GCE. Wednesday 9 June 2010 Afternoon PMT
ADVANCED GCE MATHEMATICS (MEI) 4757 Further Applications of Advanced Mathematics (FP3) Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet MEI Examination Formulae and
More informationWednesday 3 June 2015 Morning
Oxford Cambridge and RSA Wednesday 3 June 015 Morning AS GCE MATHEMATICS (MEI) 475/01 Concepts for Advanced Mathematics (C) QUESTION PAPER * 3 6 7 4 8 0 7 8 7 * Candidates answer on the Printed Answer
More informationWednesday 7 June 2017 Morning
Oxford Cambridge and RSA Wednesday 7 June 017 Morning AS GCE MATHEMATICS (MEI) 475/01 Concepts for Advanced Mathematics (C) QUESTION PAPER *6863001043* Candidates answer on the Printed Answer Book. OCR
More informationWednesday 18 June 2014 Afternoon
Wednesday 8 June 04 Afternoon A GCE MATHEMATICS (MEI) 4754/0A Applications of Advanced Mathematics (C4) Paper A QUESTION PAPER * 4 3 4 5 9 5 9 * Candidates answer on the Printed Answer Book. OCR supplied
More informationMATHEMATICS 4722 Core Mathematics 2
ADVANCED SUBSIDIARY GCE MATHEMATICS 4722 Core Mathematics 2 QUESTION PAPER Candidates answer on the Printed Answer Book OCR Supplied Materials: Printed Answer Book 4722 List of Formulae (MF1) Other Materials
More informationThursday 12 June 2014 Afternoon
Thursday June 4 Afternoon AS GCE MATHEMATICS (MEI) 476/ Mechanics QUESTION PAPER * 3 3 4 7 4 7 9 8 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book 476/ MEI Examination
More informationConcepts for Advanced Mathematics (C2) THURSDAY 15 MAY 2008
ADVANCED SUBSIDIARY GCE 47/0 MATHEMATICS (MEI) Concepts for Advanced Mathematics (C) THURSDAY MAY 008 Additional materials: Answer Booklet (8 pages) Insert for Question 3 MEI Examination Formulae and Tables
More informationMATHEMATICS 4723 Core Mathematics 3
ADVANCED GCE MATHEMATICS 4723 Core Mathematics 3 QUESTION PAPER Candidates answer on the printed answer book. OCR supplied materials: Printed answer book 4723 List of Formulae (MF1) Other materials required:
More informationWednesday 25 May 2016 Morning
Oxford Cambridge and RSA Wednesday 5 May 016 Morning A GCE MATHEMATICS (MEI) 476/01 Mechanics QUESTION PAPER * 6 6 9 6 6 0 4 1 9 * Candidates answer on the Printed Answer Book. OCR supplied materials:
More informationWednesday 30 May 2012 Afternoon
Wednesday 30 May 2012 Afternoon FSMQ ADVANCED LEVEL 6993 Additional Mathematics QUESTION PAPER *6916300612* Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book 6993
More informationThursday 12 June 2014 Afternoon
Thursday 12 June 2014 Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER * 3 1 3 4 0 1 4 0 0 1 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book 4728/01
More informationTuesday 10 June 2014 Morning
Tuesday 0 June 20 Morning AS GCE MATHEMATICS 736/0 Decision Mathematics PRINTED ANSWER BOOK *33365809* Candidates answer on this Printed Answer Book. OCR supplied materials: Question Paper 736/0 (inserted)
More informationMonday 6 June 2016 Afternoon
Oxford Cambridge and RSA Monday 6 June 2016 Afternoon FSMQ ADVANCED LEVEL 6993/01 Additional Mathematics QUESTION PAPER * 6 3 6 1 2 5 5 7 4 1 * Candidates answer on the Printed Answer Book. OCR supplied
More informationMonday 14 January 2013 Morning
Monday 14 January 2013 Morning A2 GCE MATHEMATICS 4729/01 Mechanics 2 QUESTION PAPER * 4 7 3 3 8 1 0 1 1 3 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book 4729/01
More informationConcepts for Advanced Mathematics (C2) WEDNESDAY 9 JANUARY 2008
ADVANCED SUBSIDIARY GCE 4752/01 MATHEMATICS (MEI) Concepts for Advanced Mathematics (C2) WEDNESDAY 9 JANUARY 2008 Additional materials: Answer Booklet (8 pages) MEI Examination Formulae and Tables (MF2)
More information* * MATHEMATICS (MEI) 4757 Further Applications of Advanced Mathematics (FP3) ADVANCED GCE. Wednesday 9 June 2010 Afternoon
ADVANCED GCE MATHEMATICS (MEI) 757 Further Applications of Advanced Mathematics (FP) Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet MEI Examination Formulae and Tables
More information4754A A A * * MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper A ADVANCED GCE. Tuesday 13 January 2009 Morning
ADVANCED GCE MATHEMATICS (MEI) Applications of Advanced Mathematics (C) Paper A 75A Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae
More informationTwo boats, the Rosemary and the Sage, are having a race between two points A and B. t, where 0 t (i) Find the distance AB.
5 8 In this question, positions are given relative to a fixed origin, O. The x-direction is east and the y-direction north; distances are measured in kilometres. Two boats, the Rosemary and the Sage, are
More informationWednesday 18 May 2016 Morning
Oxford Cambridge and RSA Wednesday 18 May 2016 Morning A2 GCE MATHEMATICS 4729/01 Mechanics 2 QUESTION PAPER * 6 3 9 5 6 4 5 6 6 1 * Candidates answer on the Printed Answer Book. OCR supplied materials:
More information4754A * * A A. MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper A ADVANCED GCE. Friday 14 January 2011 Afternoon
ADVANCED GCE MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper A 4754A Candidates answer on the answer booklet. OCR supplied materials: 8 page answer booklet (sent with general stationery)
More informationFriday 21 June 2013 Morning
Friday 21 June 2013 Morning A2 GCE MATHEMATICS 4729/01 Mechanics 2 QUESTION PAPER * 4 7 3 3 4 0 0 6 1 3 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book 4729/01
More informationThe 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 72.
ADVANCED SUBSIDIARY GCE UNIT 4752/0 MATHEMATICS (MEI) Concepts for Advanced Mathematics (C2) THURSDAY 7 JUNE 2007 Morning Time: hour 0 minutes Additional materials: Answer booklet (8 pages) Graph paper
More informationTuesday 18 June 2013 Morning
Tuesda 8 June 0 Morning A GCE MATHEMATICS (MEI) 475/0 Methods for Advanced Mathematics (C) QUESTION PAPER * 4 7 5 6 6 0 6 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed
More informationMonday 10 June 2013 Morning
Monday 10 June 2013 Morning A2 GCE MATHEMATICS (MEI) 4762/01 Mechanics 2 QUESTION PAPER * 4 7 1 5 7 9 0 6 1 3 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book
More information* * MATHEMATICS 4721 Core Mathematics 1 ADVANCED SUBSIDIARY GCE. Monday 11 January 2010 Morning QUESTION PAPER. Duration: 1 hour 30 minutes.
ADVANCED SUBSIDIARY GCE MATHEMATICS 4721 Core Mathematics 1 QUESTION PAPER Candidates answer on the Printed Answer Book OCR Supplied Materials: Printed Answer Book 4721 List of Formulae (MF1) Other Materials
More informationMATHEMATICS 4728 Mechanics 1
ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 Mechanics 1 QUESTION PAPER Candidates answer on the printed answer book. OCR supplied materials: Printed answer book 4728 List of Formulae (MF1) Other materials
More informationFriday 17 June 2016 Afternoon
Oxford Cambridge and RSA Friday 17 June 016 Afternoon AS GCE MATHEMATICS (MEI) 4761/01 Mechanics 1 QUESTION PAPER * 6 3 7 0 1 8 0 6 1 * Candidates answer on the Printed Answer Book. OCR supplied materials:
More informationMATHEMATICS 4725 Further Pure Mathematics 1
ADVANCED SUBSIDIARY GCE MATHEMATICS 4725 Further Pure Mathematics 1 QUESTION PAPER Candidates answer on the printed answer book. OCR supplied materials: Printed answer book 4725 List of Formulae (MF1)
More information* * MATHEMATICS (MEI) 4753/01 Methods for Advanced Mathematics (C3) ADVANCED GCE. Thursday 15 January 2009 Morning. Duration: 1 hour 30 minutes
ADVANCED GCE MATHEMATICS (MEI) 475/0 Methods for Advanced Mathematics (C) Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Eamination Formulae and Tables
More information* * MATHEMATICS (MEI) 4751 Introduction to Advanced Mathematics (C1) ADVANCED SUBSIDIARY GCE. Monday 11 January 2010 Morning QUESTION PAPER
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 475 Introduction to Advanced Mathematics (C) QUESTION PAPER Candidates answer on the Printed Answer Book OCR Supplied Materials: Printed Answer Book 475 MEI Examination
More information* * MATHEMATICS (MEI) 4757 Further Applications of Advanced Mathematics (FP3) ADVANCED GCE. Monday 13 June 2011 Morning
ADVANCED GCE MATHEMATICS (MEI) 4757 Further Applications of Advanced Mathematics (FP) Candidates answer on the answer booklet. OCR supplied materials: 8 page answer booklet (sent with general stationery)
More information4754A A A * * MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper A ADVANCED GCE. Friday 15 January 2010 Afternoon PMT
ADVANCED GCE MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper A 4754A Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet MEI Examination Formulae and
More informationOXFORD CAMBRIDGE AND RSA EXAMINATIONS A2 GCE 4733/01. MATHEMATICS Probability & Statistics 2 QUESTION PAPER
OXFORD CAMBRIDGE AND RSA EXAMINATIONS A2 GCE 4733/01 MATHEMATICS Probability & Statistics 2 QUESTION PAPER TUESDAY 10 JUNE 2014: Morning DURATION: 1 hour 30 minutes plus your additional time allowance
More informationWednesday 8 June 2016 Morning
Oxford Cambridge and RSA Wednesday 8 June 2016 Morning AS GCE MATHEMATICS 4732/01 Probability & Statistics 1 QUESTION PAPER * 4 8 2 7 1 9 3 8 2 8 * Candidates answer on the Printed Answer Book. OCR supplied
More informationConcepts for Advanced Mathematics (C2) THURSDAY 15 MAY 2008
ADVANCED SUBSIDIARY GCE 4752/0 MATHEMATICS (MEI) Concepts for Advanced Mathematics (C2) THURSDAY 5 MAY 2008 Additional materials: Answer Booklet (8 pages) Insert for Question 3 MEI Examination Formulae
More informationMATHEMATICS 4729 Mechanics 2
ADVANCED GCE MATHEMATICS 4729 Mechanics 2 QUESTION PAPER Candidates answer on the printed answer book. OCR supplied materials: Printed answer book 4729 List of Formulae (MF1) Other materials required:
More informationFriday 23 June 2017 Morning
Oxford Cambridge and RSA Friday 23 June 2017 Morning A2 GCE MATHEMATICS (MEI) 4754/01B Applications of Advanced Mathematics (C4) Paper B: Comprehension QUESTION PAPER *7350982488* Candidates answer on
More informationOXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 4752 Concepts for Advanced Mathematics (C2)
More informationThe 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 72.
ADVANCED GCE UNIT MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper A THURSDAY 4 JUNE 7 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF)
More informationMATHEMATICS (MEI) MONDAY 2 JUNE 2008 ADVANCED GCE 4753/01. Methods for Advanced Mathematics (C3) Morning Time: 1 hour 30 minutes
ADVANCED GCE 475/0 MATHEMATICS (MEI) Methods for Advanced Mathematics (C) MONDAY JUNE 008 Additional materials (enclosed): None Additional materials (required): Answer Booklet (8 pages) Graph paper MEI
More information* * MATHEMATICS (MEI) 4764 Mechanics 4 ADVANCED GCE. Thursday 11 June 2009 Morning. Duration: 1 hour 30 minutes. Turn over
ADVANCED GCE MATHEMATICS (MEI) 4764 Mechanics 4 Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae and Tables (MF2) Other Materials
More informationMEI STRUCTURED MATHEMATICS 4756
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 4756 Further Methods for Advanced Mathematics
More informationMATHEMATICS (MEI) 4776/01 Numerical Methods
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4776/01 Numerical Methods * OCE / 1 332 6 * Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae
More informationThe 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 72.
ADVANCED GCE UNIT MATHEMATICS (MEI) Applications of Advanced Mathematics (C) Paper A TUESDAY 3 JANUARY 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables
More informationApplications of Advanced Mathematics (C4) Paper A WEDNESDAY 21 MAY 2008
ADVANCED GCE 4754/01A MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper A WEDNESDAY 1 MAY 008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Examination Formulae and Tables
More informationADVANCED SUBSIDIARY GCE MATHEMATICS (MEI)
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 475 Concepts for Advanced Mathematics (C) Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Insert for Questions 5 and (inserted)
More informationFriday 24 June 2016 Morning
Oxford Cambridge and RSA Friday June 6 Morning A GCE MATHEMATICS (MEI) 75/A Applications of Advanced Mathematics (C) Paper A QUESTION PAPER *68656* Candidates answer on the Printed Answer Book. OCR supplied
More informationMATHEMATICS (MEI) 4776/01 Numerical Methods
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4776/01 Numerical Methods *OCE/T61324* Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet MEI Examination Formulae and Tables
More information* * MATHEMATICS (MEI) 4755 Further Concepts for Advanced Mathematics (FP1) ADVANCED SUBSIDIARY GCE. Thursday 15 January 2009 Morning
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4755 Further Concepts for Advanced Mathematics (FP) Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination
More informationFriday 17 June 2016 Afternoon
Oxford Cambridge and RSA Friday 17 June 016 Afternoon AS GCE MATHEMATICS (MEI) 4761/01 Mechanics 1 QUESTION PAPER * 6 3 7 0 1 8 0 6 1 * Candidates answer on the Printed Answer Book. OCR supplied materials:
More informationNATIONAL QUALIFICATIONS
Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -
More informationThursday 22 May 2014 Morning
Thursday 22 May 2014 Morning AS GCE MEI STATISTICS G241/01 Statistics 1 (Z1) QUESTION PAPER * 1 3 0 5 7 1 6 6 1 6 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer
More informationMATHEMATICS (MEI) 4776 Numerical Methods
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4776 Numerical Methods * OCE / V 0 221 5 * Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae
More informationWednesday 3 June 2015 Morning
Oxford Cambridge and RS Wednesday 3 June 2015 Morning FSMQ DVNCED LEVEL 6993/01 dditional Mathematics QUESTION PPER * 4 3 9 6 2 8 1 0 5 5 * Candidates answer on the Printed nswer ook. OCR supplied materials:
More informationTime: 1 hour 30 minutes
Paper Reference (complete below) Centre No. Surname Initial(s) Candidate No. Signature Paper Reference(s) 6663 Edexcel GCE Pure Mathematics C Advanced Subsidiary Specimen Paper Time: hour 30 minutes Examiner
More informationA Level Further Mathematics B (MEI) Y435 Extra Pure Sample Question Paper SPECIMEN
A Level Further Mathematics B (MEI) Y435 Extra Pure Sample Question Paper Date Morning/Afternoon Time allowed: 1 hour 15 minutes OCR supplied materials: Printed Answer Booklet Formulae Further Mathematics
More information* * MATHEMATICS (MEI) 4761 Mechanics 1 ADVANCED SUBSIDIARY GCE. Wednesday 21 January 2009 Afternoon. Duration: 1 hour 30 minutes.
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4761 Mechanics 1 Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae and Tables (MF2) Other
More informationWednesday 24 May 2017 Morning Time allowed: 1 hour 30 minutes
Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature AS MATHEMATICS Unit Pure Core 2 Wednesday 24 May 2017 Morning Time allowed: 1 hour 30 minutes
More informationMATHEMATICS (MEI) 4761 Mechanics 1
ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4761 Mechanics 1 QUESTION PAPER Candidates answer on the printed answer book. OCR supplied materials: Printed answer book 4761 MEI Examination Formulae and Tables
More information* * MATHEMATICS (MEI) 4763 Mechanics 3 ADVANCED GCE. Wednesday 26 January 2011 Afternoon PMT
ADVANCED GCE MATHEMATICS (MEI) 4763 Mechanics 3 Candidates answer on the answer booklet. CR supplied materials: 8 page answer booklet (sent with general stationery) MEI Examination Formulae and Tables
More informationGENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) B294B
H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper 4 Section B (Higher Tier) B294B * OCE / 14195* Candidates answer on the Question Paper OCR Supplied Materials: None Other Materials
More informationThe 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 72.
ADVANCED GCE UNIT / MATHEMATICS (MEI Further Methods for Advanced Mathematics (FP THURSDAY JUNE Additional materials: Answer booklet (8 pages Graph paper MEI Eamination Formulae and Tables (MF Morning
More informationFurther Concepts for Advanced Mathematics (FP1) FRIDAY 11 JANUARY 2008
ADVANCED SUBSIDIARY GCE 4755/0 MATHEMATICS (MEI) Further Concepts for Advanced Mathematics (FP) FRIDAY JANUARY 008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Examination Formulae and
More informationWednesday 11 January 2012 Morning
THIS IS A LEGACY SPECIFICATION H Wednesday 11 January 2012 Morning GCSE MATHEMATICS B (MEI) B293B Paper 3 Section B (Higher Tier) *B216700112* Candidates answer on the Question Paper. OCR supplied materials:
More informationThursday 22 May 2014 Morning
Thursday May 014 Morning A GCE MATHEMATICS (MEI) 4763/01 Mechanics 3 QUESTION PAPER * 3 1 8 8 3 7 0 8 8 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book 4763/01
More informationB293A. MATHEMATICS B (MEI) Paper 3 Section A (Higher Tier) GENERAL CERTIFICATE OF SECONDARY EDUCATION. Friday 9 January 2009 Morning WARNING
H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper 3 Section A (Higher Tier) B293A *CUP/T61573* Candidates answer on the question paper OCR Supplied Materials: None Other Materials
More informationB278A MATHEMATICS C (GRADUATED ASSESSMENT) MODULE M8 SECTION A GENERAL CERTIFICATE OF SECONDARY EDUCATION. Monday 8 March 2010 Morning WARNING
M8 GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS C (GRADUATED ASSESSMENT) MODULE M8 SECTION A B278A * OCE / 1 9558* Candidates answer on the Question Paper OCR Supplied Materials: None Other Materials
More informationMonday 4 March 2013 Morning
H Monday 4 March 2013 Morning GCSE MATHEMATICS B J567/04 Paper 4 (Higher Tier) *J533620313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical instruments
More informationThe 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 72.
ADVANCED SUBSIDIARY GCE UNIT 761/01 MATHEMATICS (MEI) Mechanics 1 MONDAY 1 MAY 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF) Morning Time: 1 hour
More informationMATHEMATICS (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
More informationTHIS IS A LEGACY SPECIFICATION
THIS IS A LEGACY SPECIFICATION H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper 3 Section B (Higher Tier) B293B * OCE / 1 794 9 * Candidates answer on the question paper. OCR supplied
More informationMATHEMATICS Unit Pure Core 2
General Certificate of Education June 2008 Advanced Subsidiary Examination MATHEMATICS Unit Pure Core 2 MPC2 Thursday 15 May 2008 9.00 am to 10.30 am For this paper you must have: an 8-page answer book
More informationThursday 26 May 2016 Morning
Oxford Cambridge and RSA H Thursday 26 May 2016 Morning GCSE MATHEMATICS A A502/02 Unit B (Higher Tier) * 5 9 9 9 0 5 4 4 9 7 * Candidates answer on the Question Paper. OCR supplied materials: None Other
More informationCambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level *8790810596* ADDITIONAL MATHEMATICS 4037/13 Paper 1 October/November 2017 2 hours Candidates answer on the Question Paper. No Additional Materials
More informationIntroduction to Advanced Mathematics (C1) THURSDAY 15 MAY 2008
ADVANCED SUBSIDIARY GCE 471/01 MATHEMATICS (MEI) Introduction to Advanced Mathematics (C1) THURSDAY 1 MAY 008 Additional materials: Answer Booklet (8 pages) MEI Examination Formulae and Tables (MF) Morning
More informationWednesday 25 January 2012 Afternoon
Wednesday 25 January 2012 Afternoon A2 GCE MATHEMATICS 4737 Decision Mathematics 2 QUESTION PAPER *4733040112* Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer Book
More informationThe 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 72.
ADVANCED SUBSIDIARY GCE UNIT 4776/01 MATHEMATICS (MEI) Numerical Methods WEDNESDAY 20 JUNE 2007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF2) Afternoon
More informationMETHODS IN MATHEMATICS B392/02 Methods in Mathematics 2 (Higher Tier)
THIS IS A NEW SPECIFICATION H GENERAL CERTIFICATE OF SECONDARY EDUCATION METHODS IN MATHEMATICS B392/02 Methods in Mathematics 2 (Higher Tier) *B315650611* Candidates answer on the question paper. OCR
More informationCore Mathematics C34
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Tuesday 20 June 2017 Afternoon Time: 2 hours 30 minutes
More information* * MATHEMATICS (MEI) 4758/01 Differential Equations ADVANCED GCE. Wednesday 18 May 2011 Morning
ADVANCED GCE MATHEMATICS (MEI) 4758/0 Differential Equations Candidates answer on the answer booklet. OCR supplied materials: 8 page answer booklet (sent with general stationery) MEI Examination Formulae
More informationB294A. MATHEMATICS B (MEI) Paper 4 Section A (Higher Tier) GENERAL CERTIFICATE OF SECONDARY EDUCATION. Friday 11 June 2010 Morning WARNING
H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper 4 Section A (Higher Tier) B294A * OCE / 1 0368* Candidates answer on the Question Paper OCR Supplied Materials: None Other Materials
More informationWednesday 6 November 2013 Morning
H Wednesday 6 November 2013 Morning GCSE MATHEMATICS A A501/02 Unit A (Higher Tier) *A516800313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Scientific
More informationMEI STRUCTURED MATHEMATICS 4753/1
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiar General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 4753/ Methods for Advanced Mathematics (C3)
More informationAdvanced Subsidiary General Certificate of Education Advanced General Certificate of Education
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS Applications of Advanced Mathematics (C4)
More informationB293A. MATHEMATICS B (MEI) Paper 3 Section A (Higher Tier) GENERAL CERTIFICATE OF SECONDARY EDUCATION. Tuesday 12 January 2010 Morning WARNING
H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper 3 Section A (Higher Tier) B293A *OCE/14183* Candidates answer on the Question Paper OCR Supplied Materials: None Other Materials Required:
More informationMonday 9 June 2014 Morning
H Monday 9 June 2014 Morning GCSE APPLICATIONS OF MATHEMATICS A381/02 Applications of Mathematics 1 (Higher Tier) * 3 0 5 2 7 0 0 6 9 1 * Candidates answer on the Question Paper. OCR supplied materials:
More informationTime: 1 hour 30 minutes
*CUP/T38891* ADVANCED SUBSIDIARY GCE 4776/01 MATHEMATICS (MEI) Numerical Methods MONDAY 16 JUNE 2008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF2)
More informationThursday 11 June 2015 Afternoon
Oxford Cambridge and RSA H Thursday 11 June 2015 Afternoon GCSE METHODS IN MATHEMATICS B392/02 Methods in Mathematics 2 (Higher Tier) *4856252055* Candidates answer on the Question Paper. OCR supplied
More informationThe 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 72.
ADVANCED GCE UNIT 7/ MATHEMATICS (MEI Further Methods for Advanced Mathematics (FP THURSDAY 7 JUNE 7 Additional materials: Answer booklet (8 pages Graph paper MEI Examination Formulae and Tables (MF Morning
More informationThe 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 72.
ADVANCED SUBSIDIARY GCE UNIT 475/0 MATHEMATICS (MEI) Introduction to Advanced Mathematics (C) THURSDAY 7JUNE 007 Additional materials: Answer booklet (8 pages) MEI Examination Formulae and Tables (MF)
More informationThe 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 72.
ADVANCED GCE UNIT 4753/0 MATHEMATICS (MEI) Methods for Advanced Mathematics (C3) MONDAY JUNE 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF) Afternoon
More informationTHIS IS A LEGACY SPECIFICATION
THIS IS A LEGACY SPECIFICATION H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper 3 Section A (Higher Tier) B293A *OCE/26262* Candidates answer on the question paper. OCR supplied materials:
More informationTuesday 9 June 2015 Morning
Oxford Cambridge and RSA Tuesday 9 June 2015 Morning AS GCE MATHEMATICS (MEI) 4761/01 Mechanics 1 QUESTION PAPER * 3 2 6 8 2 8 9 3 4 4 * Candidates answer on the Printed Answer Book. OCR supplied materials:
More informationWARNING You are not allowed to use a calculator in Section A of this paper. This document consists of 15 printed pages and 1 blank page.
GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS C (GRADUATED ASSESSMENT) HIGHER TERMINAL PAPER SECTION A MONDAY 2 JUNE 2008 H B252A Afternoon Time: 1 hour *CUP/T52253* Candidates answer on the question
More informationMonday 10 November 2014 Morning
H Monday 0 November 04 Morning GCSE METHODS IN MATHEMATICS B9/0 Methods in Mathematics (Higher Tier) * 0 4 0 9 7 6 6 * Candidates answer on the Question Paper. OCR supplied materials: None Other materials
More information* * MATHEMATICS (MEI) 4767 Statistics 2 ADVANCED GCE. Monday 25 January 2010 Morning. Duration: 1 hour 30 minutes. Turn over
ADVANCED GCE MATHEMATICS (MEI) 4767 Statistics 2 Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae and Tables (MF2) Other Materials
More informationB294B. MATHEMATICS B (MEI) Paper 4 Section B (Higher Tier) GENERAL CERTIFICATE OF SECONDARY EDUCATION. Monday 1 June 2009 Morning.
H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper Section B (Higher Tier) B29B *OCE/T75117* Candidates answer on the question paper OCR Supplied Materials: None Other Materials Required:
More information