# Introduction to Advanced Mathematics (C1) WEDNESDAY 9 JANUARY 2008

Save this PDF as:
Size: px
Start display at page:

## Transcription

2 Section A (6 marks) Make v the subject of the formula E = mv. [] Factorise and hence simplify x 7x + 4 x. [] (i) Write down the value of ( 4 )0. [] (ii) Find the value of 6. [] 4 Find, algebraically, the coordinates of the point of intersection of the lines y = x 5and6x + y = 7. [4] 5 (i) Find the gradient of the line 4x + 5y = 4. [] (ii) A line parallel to 4x + 5y = 4 passes through the point (0, ). Find the coordinates of its point of intersection with the x-axis. [] 6 When x + kx + 7isdividedby(x ), the remainder is. Find the value of k. [] 7 (i) Find the value of 8 C. [] (ii) Find the coefficient of x in the binomial expansion of ( x)8. [] 8 (i) Write 48 + intheforma b,wherea and b are integers and b is as small as possible. [] (ii) Simplify [] 9 (i) Prove that is a factor of n + 6n for all even positive integers n. [] (ii) Determine whether is a factor of n + 6n for all positive integers n. [] OCR /0 Jan08

3 Section B (6 marks) 0 (i) y O x Fig. 0 Fig. 0 shows a sketch of the graph of y = x. Sketch the graph of y =, showing clearly the coordinates of any points where it crosses the x axes. [] (ii) Find the value of x for which = 5. [] x (iii) Find the x-coordinates of the points of intersection of the graphs of y = x and y = x. Give your answers in the form a ± b. Show the position of these points on your graph in part (i). [6] (i) Write x 5x + 8 in the form (x a) + b and hence show that x 5x + 8 > 0 for all values of x. [4] (ii) Sketch the graph of y = x 5x + 8, showing the coordinates of the turning point. [] (iii) Find the set of values of x for which x 5x + 8 > 4. [] (iv) If f(x)=x 5x + 8, does the graph of y = f(x) 0 cross the x-axis? Show how you decide. [] [Question is printed overleaf.] OCR /0 Jan08

4 4 A circle has equation x + y 8x 4y = 9. (i) Show that the centre of this circle is C (4, ) and find the radius of the circle. [] (ii) Show that the origin lies inside the circle. [] (iii) Show that AB is a diameter of the circle, where A has coordinates (, 7) and B has coordinates (6, ). [4] (iv) Find the equation of the tangent to the circle at A. Give your answer in the form y = mx + c. [4] 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 (OCR) 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. 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 Cambridge. OCR /0 Jan08

5 475 Mark Scheme January (C) Introduction to Advanced Mathematics Section A E [ v = ][ ± ] www m x 4 x + or 7 x + www as final answer M for = or for [ v ][ ] E v m E = ± or m for a correct constructive first step and for v= [ ± ] k ft their v = k; if M0 then SC for E/ ½ m or E/m etc for (x 4)(x ) and for (x + )(x ) (i) (ii) /64 www for dealing correctly with each of reciprocal, square root and cubing (allow only for /64) eg M for 64 or 64 or / 4096 or ¼ or for /6 / or 4 or 4 or 4 - etc 4 4 6x + (x 5) = 7 0x = 7 x =.7 o.e. isw y =.6 o.e.isw 5 (i) 4/5 or 0.8 o.e. (ii) (5, 0) or 5 found www for subst or multn of eqns so one pair of coeffts equal (condone one error) simplification (condone one error) or appropriate addn/subtn to eliminate variable allow as separate or coordinates as requested graphical soln: M0 4 for 4/5 or 4/ 5 or 0.8 or 4.8/6 or correct method using two points on the line (at least one correct) (may be graphical) or for 0.8x o.e. for y = their (i) x + o.e. or 4x + 5y = k and (0, ) subst and for using y = 0 eg = 0.8x or ft their eqn or for given line goes through (0, 4.8) and (6, 0) and for 6 /4.8 graphical soln: allow for correct required line drawn and for answer within mm of (5, 0) 5 9

6 475 Mark Scheme January f() used + k + 7 = k = 6 or division by x as far as x + x obtained correctly or remainder = (4 + k) + 7 o.e. nd dep on first 7 (i) 56 for or more simplified (ii) 7 or ft from their (i)/8 for 7 or ft their (i)/8 or for 56 ( /) o.e. or ft; condone x in answer or in expression; 0 in qn for just Pascal s triangle seen 4 8 (i) 5 for 48 = 4 (ii) common denominator = (5 )(5 + ) = numerator = 0 9 (i) n = m n + 6n = m + m or = m(m + ) (ii) showing false when n is odd e.g. n + 6n = odd + even = odd B M B allow for allow only for 0/ 5 or any attempt at generalising; M0 for just trying numbers or for n + 6n = n (n + ) = even even and for explaining that 4 is a factor of even even or for is a factor of 6n when n is even and for 4 is a factor of n so is a factor of n or n (n + ) = odd odd = odd or counterexample showing not always true; for false with partial explanation or incorrect calculation 5 7

7 475 Mark Scheme January 008 Section B 0 i correct graph with clear asymptote x = (though need not be marked) G G for one branch correct; condone (0, ½ ) not shown SC for both sections of graph shifted two to left G allow seen calculated (0, ½ ) shown ii /5 or. o.e. isw for correct first step iii x = x x(x ) = o.e. x x [= 0]; ft their equiv eqn attempt at quadratic formula ± cao position of points shown B or equivs with ys or (x ) = o.e. or (x ) = ± (condone one error) on their curve with y = x (line drawn or y = x indicated by both coords); condone intent of diagonal line with gradient approx through origin as y = x if unlabelled 6 i (x.5) o.e (x.5) + 7/4 o.e. for clear attempt at.5 allow MA0 for (x.5) + 7/4 o.e. with no (x.5) seen min y = 7/4 o.e. [so above x axis] or commenting (x.5) 0 B ft, dep on (x a) + b with b positive; condone starting again, showing b 4ac < 0 or using calculus 4 ii correct symmetrical quadratic shape 8 marked as intercept on y axis tp (5/, 7/4) o.e. or ft from (i) G G G or (0, 8) seen in table iii x 5x 6 seen or used and 6 obtained x < and x > 6 isw or ft their solns or (x.5) [> or =].5 or ft 4 b also implies first if M0, allow B for one of x < and x > 6 iv min = (.5, 8.5) or ft from (i) so yes, crosses or for other clear comment re translated 0 down and for referring to min in (i) or graph in (ii); or for correct method for solving x 5x = 0 or using b 4ac with this and for showing real solns eg b 4ac = ; allow A0 for valid comment but error in 8.5 ft; allow for showing y can be neg eg (0, ) found and for correct conclusion

8 475 Mark Scheme January 008 i (x 4) 6 + (y ) 4 = 9 o.e. rad = 9 M B for one completing square or for (x 4) or (y ) expanded correctly or starting with (x 4) + (y ) = r : for correct expn of at least one bracket and for = r o.e. or using x gx + y fy+ c = 0 for using centre is (g, f) [must be quoted] and for r = g + f c ii 4 + o.e = 0 which is less than 9 allow for showing circle crosses x axis at and 9 or equiv for y (or showing one positive; one negative); 0 for graphical solutions (often using A and B from (iii) to draw circle) iii showing midpt of AB = (4, ) and showing AB = 9 or showing AC or BC = 9 or that A or B lie on circle iv or showing both A and B lie on circle (or AC = BC = 9), and showing AB = 9 or that C is midpt of AB or that C is on AB or that gradients of AB and AC are the same or equiv. or showing C is on AB and showing both A and B are on circle or AC = BC = 9 grad AC or AB or BC = 5/ o.e. grad tgt = /their grad AC tgt is y 7 = their m (x ) o.e. y = /5 x + /5 o.e. in each method, two things need to be established. Allow for the concept of what should be shown and for correct completion with method shown allow A0 for AB just shown as 6 not 9 allow A0 for stating mid point of AB = (4,) without working/method shown NB showing AB = 9 and C lies on AB is not sufficient earns marks only if M0, allow SC for accurate graph of circle drawn with compasses and AB joined with ruled line through C. may be seen in (iii) but only allow this if they go on to use in this part allow for m m = used eg y = their mx + c then (, 7) subst; M0 if grad AC used condone y = /5x + c and c = /5 o.e

### Introduction 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

### 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 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)

### MEI STRUCTURED MATHEMATICS 4751

OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 75 Introduction to Advanced Mathematics (C)

### MEI STRUCTURED MATHEMATICS 4751

OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 475 Introduction to Advanced Mathematics

### 4751 Mark Scheme June Mark Scheme 4751 June 2005

475 Mark Scheme June 2005 Mark Scheme 475 June 2005 475 Mark Scheme June 2005 Section A 40 2 M subst of for x or attempt at long divn with x x 2 seen in working; 0 for attempt at factors by inspection

### Concepts 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

### * * 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

### ADVANCED 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)

### Concepts 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

### * * 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

### Further 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

### 4751 Mark Scheme June Mark Scheme 4751 June 2005

475 Mark Scheme June 005 Mark Scheme 475 June 005 475 Mark Scheme June 005 Section A 40 subst of for x or attempt at long divn with x x seen in working; 0 for attempt at factors by inspection 6y [ x =

### 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 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

### 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 72.

ADVANCED SUBSIDIARY GCE UNIT 4755/01 MATHEMATICS (MEI) Further Concepts for Advanced Mathematics (FP1) MONDAY 11 JUNE 2007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae

### Examiner's Report Q1.

Examiner's Report Q1. For students who were comfortable with the pair of inequality signs, part (a) proved to be straightforward. Most solved the inequalities by operating simultaneously on both sets and

### * * 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

### Concepts 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)

### MATHEMATICS (MEI) 4751 Introduction to Advanced Mathematics (C1)

ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4751 Introduction to Advanced Mathematics (C1) QUESTION PAPER Candidates answer on the Printed Answer Book OCR Supplied Materials: Printed Answer Book 4751 MEI

### 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 72.

ADVANCED SUBSIDIARY GCE UNIT 755/0 MATHEMATICS (MEI) Further Concepts for Advanced Mathematics (FP) THURSDAY 8 JANUARY 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae

### Methods for Advanced Mathematics (C3) FRIDAY 11 JANUARY 2008

ADVANCED GCE 4753/0 MATHEMATICS (MEI) Methods for Advanced Mathematics (C3) FRIDAY JANUARY 008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Eamination Formulae and Tables (MF) Morning

### * * MATHEMATICS (MEI) 4755 Further Concepts for Advanced Mathematics (FP1) ADVANCED SUBSIDIARY GCE. Friday 22 May 2009 Morning

ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 755 Further Concepts for Advanced Mathematics (FP) Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination

### Time: 1 hour 30 minutes

Paper Reference(s) 666/0 Edexcel GCE Core Mathematics C Gold Level G Time: hour 0 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil Candidates

### 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 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

### A booklet Mathematical Formulae and Statistical Tables might be needed for some questions.

Paper Reference(s) 6663/01 Edexcel GCE Core Mathematics C1 Advanced Subsidiary Quadratics Calculators may NOT be used for these questions. Information for Candidates A booklet Mathematical Formulae and

### Time: 1 hour 30 minutes

Paper Reference(s) 666/0 Edexcel GCE Core Mathematics C Gold Level G Time: hour 0 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil Candidates

### 4751 Mark Scheme June fraction line; accept to power ½ with denominator appropriate brackets answer M1 for a triple decker fraction or for

1 Question Answer Marks Guidance A A 2 square root symbol must extend below condone missing end bracket in [ r ] or [ r ] as final fraction line; accept to power ½ with denominator x y x y appropriate

### Monday 19 May 2014 Morning

Monday 19 May 014 Morning AS GCE MATHEMATICS (MEI) 4751/01 Introduction to Advanced Mathematics (C1) QUESTION PAPER * 3 1 8 7 0 4 0 5 4 * Candidates answer on the Printed Answer Book. OCR supplied materials:

### Time: 1 hour 30 minutes

Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Silver Level S4 Time: 1 hour 0 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil

### 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 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

### Time: 1 hour 30 minutes

Paper Reference(s) 666/01 Edexcel GCE Core Mathematics C1 Silver Level S4 Time: 1 hour 0 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil

### Time: 1 hour 30 minutes

Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Silver Level S3 Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil

### 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 72.

ADVANCED SUBSIDIARY GCE UNIT 4761/01 MATHEMATICS (MEI) Mechanics 1 WEDNESDAY 10 JANUARY 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF) Afternoon

### * * 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

### Time: 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)

### Time: 1 hour 30 minutes

Paper Reference(s) 6663/0 Edexcel GCE Core Mathematics C Gold Level G5 Time: hour 30 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil Candidates

### Wednesday 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

### MATHEMATICS (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

### A booklet Mathematical Formulae and Statistical Tables might be needed for some questions.

Paper Reference(s) 6663/0 Edexcel GCE Core Mathematics C Advanced Subsidiary Inequalities Calculators may NOT be used for these questions. Information for Candidates A booklet Mathematical Formulae and

### MATHEMATICS (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

### Statistics 3 WEDNESDAY 21 MAY 2008

ADVANCED GCE 4768/01 MATHEMATICS (MEI) Statistics 3 WEDNESDAY 1 MAY 008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF) Afternoon Time: 1 hour 30 minutes

### * * MATHEMATICS (MEI) 4761 Mechanics 1 ADVANCED SUBSIDIARY GCE. Wednesday 27 January 2010 Afternoon. Duration: 1 hour 30 minutes.

ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 476 Mechanics Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae and Tables (MF) Other

### * * 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

### Mechanics 2 THURSDAY 17 JANUARY 2008

ADVANCED GCE 4762/01 MATHEMATICS (MEI) Mechanics 2 THURSDAY 17 JANUARY 2008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF2) Afternoon Time: 1 hour 0

### 6664/01 Edexcel GCE Core Mathematics C2 Bronze Level B2

Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Bronze Level B Time: 1 hour 30 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil

### 4754A 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

### Quadratic Equations. All types, factorising, equation, completing the square. 165 minutes. 151 marks. Page 1 of 53

Quadratic Equations All types, factorising, equation, completing the square 165 minutes 151 marks Page 1 of 53 Q1. (a) Factorise x 2 + 5x 24 Answer... (2) (b) Solve x 2 + 5x 24 = 0 Answer... (1) (Total

### 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 72.

ADVANCED GCE UNIT 758/0 MATHEMATICS (MEI) Differential Equations THURSDAY 5 JANUARY 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF) Morning Time:

### Morning Time: 1 hour 30 minutes Additional materials (enclosed):

ADVANCED SUBSIDIARY GCE 761/01 MATHEMATICS (MEI) Mechanics 1 FRIDAY 3 MAY 008 Morning Time: 1 hour 30 minutes Additional materials (enclosed): None Additional materials (required): Answer Booklet (8 pages)

### Time: 1 hour 30 minutes

Paper Reference(s) 666/0 Edecel GCE Core Mathematics C Bronze Level B4 Time: hour 0 minutes Materials required for eamination papers Mathematical Formulae (Green) Items included with question Nil Candidates

### Friday 13 January 2012 Morning

Friday 13 January 2012 Morning AS GCE MATHEMATICS (MEI) 4751 Introduction to Advanced Mathematics (C1) QUESTION PAPER *4733060112* Candidates answer on the Printed Answer Book. OCR supplied materials:

### Time: 1 hour 30 minutes

Paper Reference(s) 6663/0 Edecel GCE Core Mathematics C Silver Level S Time: hour 30 minutes Materials required for eamination Mathematical Formulae (Green) Items included with question papers Nil Candidates

### A 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

### Mechanics 1 THURSDAY 17 JANUARY 2008

ADVANCED SUBSIDIARY GCE 761/01 MATHEMATICS (MEI) Mechanics 1 THURSDAY 17 JANUARY 008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF) Afternoon Time:

### Time: 1 hour 30 minutes

Paper Reference(s) 6665/01 Edecel GCE Core Mathematics C Silver Level S Time: 1 hour 0 minutes Materials required for eamination papers Mathematical Formulae (Green) Items included with question Nil Candidates

### Monday 14 January 2013 Morning

Monday 14 January 013 Morning AS GCE MATHEMATICS (MEI) 4751/01 Introduction to Advanced Mathematics (C1) QUESTION PAPER * 4 7 3 3 9 5 0 1 1 3 * Candidates answer on the Printed Answer Book. OCR supplied

### Core Mathematics C1 Advanced Subsidiary

Paper Reference(s) 666/0 Edexcel GCE Core Mathematics C Advanced Subsidiary Monday 0 January 0 Morning Time: hour 0 minutes Materials required for examination Mathematical Formulae (Pink) Items included

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *0835058084* ADDITIONAL MATHEMATICS 0606/11 Paper 1 October/November 2012 2 hours Candidates

### 6664/01 Edexcel GCE Core Mathematics C2 Bronze Level B3

Paper Reference(s) 666/01 Edecel GCE Core Mathematics C Bronze Level B Time: 1 hour 0 minutes Materials required for eamination papers Mathematical Formulae (Green) Items included with question Nil Candidates

### Time: 1 hour 30 minutes

Paper Reference(s) 666/0 Edexcel GCE Core Mathematics C Bronze Level B4 Time: hour 0 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil Candidates

### Wednesday 16 May 2012 Morning

Wednesday 16 May 2012 Morning AS GCE MATHEMATICS (MEI) 4751 Introduction to Advanced Mathematics (C1) QUESTION PAPER *4715620612* Candidates answer on the Printed Answer Book. OCR supplied materials: Printed

### Examiners Report/ Principal Examiner Feedback. June GCE Core Mathematics C2 (6664) Paper 1

Examiners Report/ Principal Examiner Feedback June 011 GCE Core Mathematics C (6664) Paper 1 Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a

### 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

### Applications of Advanced Mathematics (C4) Paper B: Comprehension TUESDAY 22 JANUARY 2008 Time:Upto1hour

ADVANCED GCE 4754/01B MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper B: Comprehension TUESDAY JANUARY 008 Afternoon Time:Upto1hour Additional materials: Rough paper MEI Examination Formulae

### 6664/01 Edexcel GCE Core Mathematics C2 Bronze Level B4

Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Bronze Level B4 Time: 1 hour 30 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil

### GCE. Mathematics (MEI) Mark Scheme for June Advanced Subsidiary GCE Unit 4751: Introduction to Advanced Mathematics

GCE Mathematics (MEI) Advanced Subsidiary GCE Unit 4751: Introduction to Advanced Mathematics Mark Scheme for June 013 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading

### Specimen. Date Morning/Afternoon Time allowed: 1 hour 30 minutes

AS Level Mathematics B (MEI) H630/01 Pure Mathematics and Mechanics Sample Question Paper Date Morning/Afternoon Time allowed: 1 hour 30 minutes You must have: Printed Answer Booklet You may use: a scientific

### 6664/01 Edexcel GCE Core Mathematics C2 Gold Level G2

Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Gold Level G Time: 1 hour 30 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil Candidates

### Applications 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

### GCE. Mathematics (MEI) Mark Scheme for January Advanced Subsidiary GCE Unit 4751: Introduction to Advanced Mathematics

GCE Mathematics (MEI) Advanced Subsidiary GCE Unit 4751: Introduction to Advanced Mathematics Mark Scheme for January 2012 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading

### 4754A * * 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)

### GCE Mathematics. Mark Scheme for June Unit 4721: Core Mathematics 1. Advanced Subsidiary GCE. Oxford Cambridge and RSA Examinations

GCE Mathematics Unit 47: Core Mathematics Advanced Subsidiary GCE Mark Scheme for June 04 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a

### Equations (Linear, Quadratic, Simultaneous & Basic Algebra)

Equations (Linear, Quadratic, Simultaneous & Basic Algebra) Mark Scheme Level Subject Exam Board Maths Module Core 1 Topic Sub Topic A Level OCR - MEI Algebra Booklet Mark Scheme Equations (Linear, Quadratic,

### 6664/01 Edexcel GCE Core Mathematics C2 Silver Level S1

Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Silver Level S1 Time: 1 hour 0 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil

### 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 72.

ADVANCED GCE UNIT 476/01 MATHEMATICS (MEI) Mechanics WEDNESDAY 10 JANUARY 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF) Afternoon Time: 1 hour

### PhysicsAndMathsTutor.com

Question Answer Marks Guidance Question 1 (i) [radius =] 15 isw or 5 5 B1 [C =] (10, ) B1 condone x = 10, y = 1 (ii) verifying / deriving that (1, 0) is one of the intersections with the axes [] B1 using

### 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 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

### 2 grad AB = 8/4 or 2 or y = 2x 10 grad BC = 1/ 2 or ½ or y = ½ x product of grads = 1 [so perp] (allow seen or used) ii midpt E of AC = (6, 4.

x 2 + 9x 2 = 25 0x 2 = 25 x= ±( 0)/2 or.± (5/2) or ±5/ 0 oe y = [±] (5/2) o.e. eg y = [±] 22.5 A2 B for subst for x or y attempted or x 2 = 2.5 o.e.; condone one error from start [allow 0x 2 25 = 0 + correct

### MEI STRUCTURED MATHEMATICS 4753/1

OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 4753/1 Methods for Advanced Mathematics (C3)

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 2 4 2 8 1 9 0 7 2 * ADDITIONAL MATHEMATICS 0606/12 Paper 1 February/March 2016 2 hours Candidates

### MEI STRUCTURED MATHEMATICS 4752

OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 4752 Concepts for Advanced Mathematics (C2)

### * * 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

### Time: 1 hour 30 minutes

Paper Reference(s) 6666/0 Edexcel GCE Core Mathematics C4 Silver Level S Time: hour 0 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil Candidates

### Higher Unit 9 topic test

Name: Higher Unit 9 topic test Date: Time: 45 minutes Total marks available: 41 Total marks achieved: Questions Q1. (a) (i) Factorise x 2 12x + 27... (ii) Solve the equation x 2 12x + 27 = 0 (b) Factorise

### Wednesday 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

### physicsandmathstutor.com

ADVANCED SUBSIDIARY GCE UNIT 4732/01 MATHEMATICS Probability & Statistics 1 FRIDAY 12 JANUARY 2007 Morning Additional Materials: Answer Booklet (8 pages) List of Formulae (MF1) Time: 1 hour 30 minutes

### Specimen. Date Morning/Afternoon Time allowed: 1 hour 15 minutes. AS Level Further Mathematics A Y531 Pure Core Sample Question Paper INSTRUCTIONS

AS Level Further Mathematics A Y531 Pure Core Sample Question Paper Date Morning/Afternoon Time allowed: 1 hour 15 minutes OCR supplied materials: Printed Answer Booklet Formulae AS Level Further Mathematics

### Assessment Report. Level 2, Mathematics

Assessment Report Level 2, 2006 Mathematics Manipulate algebraic expressions and solve equations (90284) Draw straightforward non-linear graphs (90285) Find and use straightforward derivatives and integrals

### MATHEMATICS 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

### Linear Equations. 196 minutes. 191 marks. Page 1 of 50

Linear Equations 196 minutes 191 marks Page 1 of 50 Q1. The perimeter of this L-shape is 56 cm. Not drawn accurately Set up and solve an equation to work out the value of x. x =... (Total 4 marks) Page

### Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level * 2 2 1 1 9 6 0 6 4 7 * ADDITIONAL MATHEMATICS 4037/22 Paper 2 May/June 2016 2 hours Candidates answer on the Question Paper. No Additional

### GCE Mathematics (MEI) Mark Scheme for June Unit 4751: Introduction to Advanced Mathematics (C1) Advanced Subsidiary GCE

GCE Mathematics (MEI) Unit 4751: Introduction to Advanced Mathematics (C1) Advanced Subsidiary GCE Mark Scheme for June 2014 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading

### Specimen. Date Morning/Afternoon Time allowed: 1 hour 30 minutes. A Level Further Mathematics A Y541 Pure Core 2 Sample Question Paper INSTRUCTIONS

A Level Further Mathematics A Y541 Pure Core Sample Question Paper Date Morning/Afternoon Time allowed: 1 hour 30 minutes OCR supplied materials: Printed Answer Booklet Formulae A Level Further Mathematics

### 2009 Assessment Report. Mathematics Level 2

National Certificate of Educational Achievement 2009 Assessment Report Mathematics Level 2 90284 Manipulate algebraic expressions and solve equations 90285 Draw straightforward non linear graphs 90286

### Time: 1 hour 30 minutes

Paper Reference(s) 6684/01 Edexcel GCE Statistics S2 Gold Level G3 Time: 1 hour 30 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil Candidates

### Wednesday 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

### Report on the Examination

Version 1.0 General Certificate of Education (A-level) January 01 Mathematics MPC4 (Specification 660) Pure Core 4 Report on the Examination Further copies of this Report on the Examination are available