Mathematics (JAN13MFP401) General Certificate of Education Advanced Level Examination January Unit Further Pure TOTAL

Size: px
Start display at page:

Download "Mathematics (JAN13MFP401) General Certificate of Education Advanced Level Examination January Unit Further Pure TOTAL"

Transcription

1 Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 4 Wednesday 30 January 2013 General Certificate of Education Advanced Level Examination January am to am For this paper you must have: * the blue AQA booklet of formulae and statistical tables. You may use a graphics calculator. Time allowed * 1 hour 30 minutes MFP4 Instructions * Use black ink or black ball-point pen. Pencil should only be used for drawing. * Fill in the es at the top of this page. * Answer all questions. * Write the question part reference (eg (a), (b)(i) etc) in the left-hand margin. * You must answer each question in the space provided for that question. If you require extra space, use an AQA supplementary answer book; do not use the space provided for a different question. * around each page. * Show all necessary working; otherwise marks for method may be lost. * Do all rough work in this book. Cross through any work that you do not want to be marked. Information * The marks for questions are shown in brackets. * The maximum mark for this paper is 75. Advice * Unless stated otherwise, you may quote formulae, without proof, from the booklet. * You do not necessarily need to use all the space provided. Question TOTAL Mark (JAN13MFP401) 6/6/6/ MFP4

2 2 Answer all questions. Answer each question in the space provided for that question. 1 Two planes have equations x þ 2y þ 2z ¼ 5 and px þ 3y ¼ 10 where p is a non-zero constant. Given that the acute angle, y, between the planes is such that cos y ¼ 2, find the 3 value of p. (5 marks) Answer space for question 1 (02)

3 3 Answer space for question 1 Turn over s (03)

4 4 2 It is given that A and B are 3 3 matrices such that detðabþ ¼24 and detða 1 Þ¼ 3 (a) State the value of det A. (1 mark) (b) A three-dimensional shape S, with volume 20 cm 3, is transformed using matrix B. Find the volume of the image of S. (3 marks) Answer space for question 2 (04)

5 5 Answer space for question 2 Turn over s (05)

6 6 3 (a) Expand and simplify, as far as possible, ða 4bÞða þ 3bÞ where a and b are vectors. (3 marks) (b) Given that a and b are perpendicular, deduce that jða 4bÞða þ 3bÞj ¼ ljajjbj where l is an integer. (2 marks) Answer space for question 3 (06)

7 7 Answer space for question 3 Turn over s (07)

8 8 4 The matrix A is given by (a) A ¼ p Given that A 2 6 ¼ , find the value of p and the value of q. (2 marks) 10 q 9 (b) Given that A 3 6A 2 þ 11A 6I ¼ 0, prove that A 1 ¼ 1 6 ða2 6A þ 11IÞ (2 marks) 2 3 r 2 2 (c) Given that A 1 ¼ , find the value of r and the value of s. 6 2 s 2 (2 marks) (d) Hence, or otherwise, find the solution of the system of equations x z ¼ k x þ 2y þ z ¼ 5 2x þ 2y þ 3z ¼ 7 giving your answers in terms of k. (3 marks) Answer space for question 4 (08)

9 9 Answer space for question 4 Turn over s (09)

10 10 Answer space for question 4 (10)

11 11 Answer space for question 4 Turn over s (11)

12 12 5 (a) By direct expansion, or otherwise, show that the value of is independent of k k 1 1 k þ 1 2 k 1 1 (4 marks) (b) State, with a reason, whether the vectors , and are linearly dependent or linearly independent. (2 marks) (c) (i) State, with a reason, whether the equations 2x þ y þ 6z ¼ 1 x þ y þ 4z ¼ 0 2x þ 2y þ z ¼ 1 are consistent or inconsistent. (2 marks) (ii) The three equations given in part (c)(i) are the Cartesian equations of three planes. State the geometrical configuration of these three planes. (1 mark) Answer space for question 5 (12)

13 13 Answer space for question 5 Turn over s (13)

14 14 Answer space for question 5 (14)

15 15 Answer space for question 5 Turn over s (15)

16 16 6 The linear transformations T 1 and T 2 are represented by the matrices 2 pffiffi M 1 ¼ and M 2 ¼ pffiffi respectively. (a) Give a full geometrical description of the transformations: (i) T 1 ; (ii) T 2. (2 marks) (3 marks) (b) Find the matrix which represents the transformation T 1 followed by T 2. (2 marks) (c) The linear transformation T 3 is represented by the matrix 2 k M 3 ¼ where k is a constant. For one particular value of k, T 3 has a line L of invariant points. (i) Find k. (ii) Find the Cartesian equations of L in the form x p ¼ y q ¼ z. (7 marks) r Answer space for question 6 (16)

17 17 Answer space for question 6 Turn over s (17)

18 18 Answer space for question 6 (18)

19 19 Answer space for question 6 Turn over s (19)

20 20 7 The matrix M is defined by 2 a 0 3 a 6 M ¼ a 0 2 (a) (b) where a is a real number. The distinct eigenvalues of M are l 1, l 2 and l 3 with corresponding eigenvectors v 1, v 2 and v Given that v 1 ¼ 4 1 5, find l 1. (2 marks) Given that v 2 ¼ 4 0 5, find the value of a. (3 marks) 2 (c) Given that l 3 ¼ 6, find a possible eigenvector v 3. (3 marks) (d) The matrix M can be expressed as UDU 1, where D is a diagonal matrix. Write down possible matrices D and U. (3 marks) Answer space for question 7 (20)

21 21 Answer space for question 7 Turn over s (21)

22 22 Answer space for question 7 (22)

23 23 Answer space for question 7 Turn over s (23)

24 24 8 The four vertices of a parallelogram ABCD have coordinates (a) (i) Að1, 0, 2Þ, Bð3, 1, 5Þ, Cð7, 2, 4Þ and Dð5, 3, 1Þ ƒ! ƒ! Find AB AD. (3 marks) p (ii) Show that the area of the parallelogram is p ffiffiffiffiffi 10, where p is an integer to be found. (2 marks) (b) The diagonals AC and BD of the parallelogram meet at the point M. The line L passes through M and is perpendicular to the plane ABCD. Find an equation for the line L, giving your answer in the form ðr uþv ¼ 0. (4 marks) (c) The plane P is parallel to the plane ABCD and passes through the point Qð6, 5, 17Þ. (i) Find the coordinates of the point of intersection of the line L with the plane P. (6 marks) (ii) One face of a parallelepiped is ABCD and the opposite face lies in the plane P. Find the volume of the parallelepiped. (3 marks) Answer space for question 8 (24)

25 25 Answer space for question 8 Turn over s (25)

26 26 Answer space for question 8 (26)

27 27 Answer space for question 8 END OF S (27)

28 28 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Copyright ª 2013 AQA and its licensors. All rights reserved. (28)

Mathematics (JUN13MFP401) General Certificate of Education Advanced Level Examination June Unit Further Pure TOTAL

Mathematics (JUN13MFP401) General Certificate of Education Advanced Level Examination June Unit Further Pure TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 4 Tuesday 18 June 2013 General Certificate of Education Advanced

More information

Wednesday 24 May 2017 Morning Time allowed: 1 hour 30 minutes

Wednesday 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 A-level MATHEMATICS Unit Further Pure 4 Wednesday 24 May 2017 Morning Time allowed: 1 hour

More information

Mathematics (JAN13MFP101) General Certificate of Education Advanced Subsidiary Examination January Unit Further Pure TOTAL

Mathematics (JAN13MFP101) General Certificate of Education Advanced Subsidiary Examination January Unit Further Pure TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 1 Friday 18 January 2013 General Certificate of Education Advanced

More information

Mathematics (JAN12MPC401) General Certificate of Education Advanced Level Examination January Unit Pure Core TOTAL

Mathematics (JAN12MPC401) General Certificate of Education Advanced Level Examination January Unit Pure Core TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 4 Monday 23 January 2012 General Certificate of Education Advanced

More information

Mathematics (JUN11MFP101) General Certificate of Education Advanced Subsidiary Examination June Unit Further Pure TOTAL

Mathematics (JUN11MFP101) General Certificate of Education Advanced Subsidiary Examination June Unit Further Pure TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 1 Friday 20 May 2011 General Certificate of Education Advanced

More information

Mathematics MFP1. General Certificate of Education Advanced Subsidiary Examination. Unit Further Pure 1

Mathematics MFP1. General Certificate of Education Advanced Subsidiary Examination. Unit Further Pure 1 Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 1 General Certificate of Education Advanced Subsidiary Examination

More information

Mathematics MPC1 (JUN15MPC101) General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core TOTAL

Mathematics MPC1 (JUN15MPC101) General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 1 Wednesday 13 May 2015 General Certificate of Education Advanced

More information

Mathematics (JUN13MM0401) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL.

Mathematics (JUN13MM0401) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL. Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 4 Friday 21 June 2013 General Certificate of Education Advanced

More information

Mathematics (JUN12MPC101) General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core TOTAL

Mathematics (JUN12MPC101) General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 1 Wednesday 16 May 2012 General Certificate of Education Advanced

More information

Answer all questions. Answer each question in the space provided for that question. x 3. find the values of the constants p, q and r

Answer all questions. Answer each question in the space provided for that question. x 3. find the values of the constants p, q and r Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 4 Thursday 14 June 2012 General Certificate of Education Advanced

More information

(ii) Given that gðxþ ¼ð4x 1Þðax 2 þ bx þ cþ, find the values of the integers a, b and c. (3 marks)

(ii) Given that gðxþ ¼ð4x 1Þðax 2 þ bx þ cþ, find the values of the integers a, b and c. (3 marks) Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 4 Tuesday 15 June 2010 General Certificate of Education Advanced

More information

Mathematics (JUN10MFP301) General Certificate of Education Advanced Level Examination June Unit Further Pure TOTAL

Mathematics (JUN10MFP301) General Certificate of Education Advanced Level Examination June Unit Further Pure TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 3 Friday 11 June 2010 General Certificate of Education Advanced

More information

Mathematics MM04 (JUN15MM0401) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL

Mathematics MM04 (JUN15MM0401) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 4 Wednesday 24 June 2015 General Certificate of Education Advanced

More information

Mathematics MFP2 (JUN15MFP201) General Certificate of Education Advanced Level Examination June Unit Further Pure TOTAL

Mathematics MFP2 (JUN15MFP201) General Certificate of Education Advanced Level Examination June Unit Further Pure TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 2 Tuesday 16 June 2015 General Certificate of Education Advanced

More information

Mathematics (JUN14MM0501) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL.

Mathematics (JUN14MM0501) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL. Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 5 Thursday 12 June 2014 General Certificate of Education Advanced

More information

Mathematics (JUN12MM2B01) General Certificate of Education Advanced Level Examination June Unit Mechanics 2B TOTAL

Mathematics (JUN12MM2B01) General Certificate of Education Advanced Level Examination June Unit Mechanics 2B TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 2B Thursday 21 June 2012 General Certificate of Education Advanced

More information

Mathematics (JAN12MPC201) General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core TOTAL

Mathematics (JAN12MPC201) General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 2 Friday 13 January 2012 General Certificate of Education Advanced

More information

Mathematics (JUN11MPC301) General Certificate of Education Advanced Level Examination June Unit Pure Core TOTAL

Mathematics (JUN11MPC301) General Certificate of Education Advanced Level Examination June Unit Pure Core TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 3 Monday 13 June 2011 General Certificate of Education Advanced

More information

Mathematics (JAN11MM1B01) General Certificate of Education Advanced Subsidiary Examination January Unit Mechanics 1B TOTAL

Mathematics (JAN11MM1B01) General Certificate of Education Advanced Subsidiary Examination January Unit Mechanics 1B TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 1B Wednesday 19 January 2011 General Certificate of Education Advanced

More information

AS MATHEMATICS. Paper 1 PRACTICE PAPER SET 1

AS MATHEMATICS. Paper 1 PRACTICE PAPER SET 1 PRACTICE PAPER SET 1 Please write clearly, in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature AS MATHEMATICS Paper 1 Practice paper set 1 Time allowed: 1 hour 30

More information

Mathematics MM1B (JUN15MM1B01) General Certificate of Education Advanced Subsidiary Examination June Unit Mechanics 1B TOTAL

Mathematics MM1B (JUN15MM1B01) General Certificate of Education Advanced Subsidiary Examination June Unit Mechanics 1B TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 1B Friday 12 June 2015 General Certificate of Education Advanced

More information

Wednesday 14 June 2017 Morning Time allowed: 1 hour 30 minutes

Wednesday 14 June 2017 Morning Time allowed: 1 hour 30 minutes Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature A-level MATHEMATICS Unit Pure Core 3 Wednesday 14 June 2017 Morning Time allowed: 1 hour 30

More information

Mathematics (JUN12MM0301) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL.

Mathematics (JUN12MM0301) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL. Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 3 Friday 22 June 2012 General Certificate of Education Advanced

More information

Mathematics (JAN12MD0201) General Certificate of Education Advanced Level Examination January Unit Decision TOTAL.

Mathematics (JAN12MD0201) General Certificate of Education Advanced Level Examination January Unit Decision TOTAL. Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Decision 2 Wednesday 25 January 2012 General Certificate of Education Advanced

More information

Wednesday 17 May 2017 Morning Time allowed: 1 hour 30 minutes

Wednesday 17 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 1 Wednesday 17 May 2017 Morning Time allowed: 1 hour 30 minutes

More information

Mathematics (JUN13MM2B01) General Certificate of Education Advanced Level Examination June Unit Mechanics 2B TOTAL

Mathematics (JUN13MM2B01) General Certificate of Education Advanced Level Examination June Unit Mechanics 2B TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 2B Thursday 13 June 2013 General Certificate of Education Advanced

More information

Mathematics (JAN12MS2B01) General Certificate of Education Advanced Level Examination January Unit Statistics 2B TOTAL

Mathematics (JAN12MS2B01) General Certificate of Education Advanced Level Examination January Unit Statistics 2B TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Statistics 2B Wednesday 25 January 2012 General Certificate of Education Advanced

More information

Mathematics MS2B (JUN15MS2B01) General Certificate of Education Advanced Level Examination June Unit Statistics 2B TOTAL

Mathematics MS2B (JUN15MS2B01) General Certificate of Education Advanced Level Examination June Unit Statistics 2B TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Statistics 2B Friday 12 June 2015 General Certificate of Education Advanced

More information

Mathematics (JUN13MD0201) General Certificate of Education Advanced Level Examination June Unit Decision TOTAL.

Mathematics (JUN13MD0201) General Certificate of Education Advanced Level Examination June Unit Decision TOTAL. Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Decision 2 Thursday 13 June 2013 General Certificate of Education Advanced

More information

Mathematics (JAN11MM2B01) General Certificate of Education Advanced Level Examination January Unit Mechanics 2B TOTAL

Mathematics (JAN11MM2B01) General Certificate of Education Advanced Level Examination January Unit Mechanics 2B TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 2B Wednesday 26 January 2011 General Certificate of Education Advanced

More information

MATHEMATICS Unit Pure Core 2

MATHEMATICS 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 information

A-level MATHEMATICS. Paper 2. Exam Date Morning Time allowed: 2 hours SPECIMEN MATERIAL

A-level MATHEMATICS. Paper 2. Exam Date Morning Time allowed: 2 hours SPECIMEN MATERIAL SPECIMEN MATERIAL Please write clearly, in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature A-level MATHEMATICS Paper 2 Exam Date Morning Time allowed: 2 hours Materials

More information

Mathematics (JUN10MM0401) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL.

Mathematics (JUN10MM0401) General Certificate of Education Advanced Level Examination June Unit Mechanics TOTAL. Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Mechanics 4 Thursday 24 June 2010 General Certificate of Education Advanced

More information

Wednesday 24 May 2017 Morning Time allowed: 1 hour 30 minutes

Wednesday 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 information

Statistics Unit Statistics 1B

Statistics Unit Statistics 1B Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Question Mark General Certificate of Education Advanced Subsidiary Examination June 2013 1

More information

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core 1. Time allowed * 1 hour 30 minutes

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core 1. Time allowed * 1 hour 30 minutes General Certificate of Education Advanced Subsidiary Examination June 01 Mathematics Unit Pure Core 1 Wednesday 16 May 01 9.00 am to 10.0 am For this paper you must have: the blue AQA booklet of formulae

More information

AS MATHEMATICS MM1B. Unit Mechanics 1B. Tuesday 20 June 2017 Afternoon Time allowed: 1 hour 30 minutes. *jun17mm1b01*

AS MATHEMATICS MM1B. Unit Mechanics 1B. Tuesday 20 June 2017 Afternoon Time allowed: 1 hour 30 minutes. *jun17mm1b01* Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature AS MATHEMATICS Unit Mechanics 1B Tuesday 20 June 2017 Afternoon Time allowed: 1 hour 30 minutes

More information

Morning Time allowed: 1 hour 30 minutes

Morning Time allowed: 1 hour 30 minutes SPECIMEN MATERIAL Please write clearly, in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature AS MATHEMATICS Paper 1 Exam Date Morning Time allowed: 1 hour 30 minutes

More information

MATHEMATICS Unit Mechanics 1B

MATHEMATICS Unit Mechanics 1B General Certificate of Education June 2008 Advanced Subsidiary Examination MATHEMATICS Unit Mechanics 1B MM1B Monday 2 June 2008 9.00 am to 10.30 am For this paper you must have: an 8-page answer book

More information

Further Mathematics 8360/1. Level 2 (JUN ) Level 2 Certificate in Further Mathematics June Time allowed * 1 hour 30 minutes

Further Mathematics 8360/1. Level 2 (JUN ) Level 2 Certificate in Further Mathematics June Time allowed * 1 hour 30 minutes Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Level 2 Certificate in Further Mathematics June 2014 Further Mathematics 8360/1 Level 2 Paper

More information

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January 2012

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January 2012 General Certificate of Education Advanced Subsidiary Examination January 01 Mathematics MPC1 Unit Pure Core 1 Friday 13 January 01 9.00 am to 10.30 am For this paper you must have: the blue AQA booklet

More information

Level 2 Certificate in Further Mathematics FURTHER MATHEMATICS

Level 2 Certificate in Further Mathematics FURTHER MATHEMATICS Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature Level 2 Certificate in Further Mathematics FURTHER MATHEMATICS Level 2 Paper 1 Non-Calculator

More information

MATHEMATICS Unit Mechanics 3

MATHEMATICS Unit Mechanics 3 General Certificate of Education June 2009 Advanced Level Examination MATHEMATICS Unit Mechanics 3 MM03 Wednesday 17 June 2009 9.00 am to 10.30 am For this paper you must have: a 12-page answer book the

More information

Use black ink or black ball-point pen. Pencil should only be used for drawing. *

Use black ink or black ball-point pen. Pencil should only be used for drawing. * General Certificate of Education June 2008 Advanced Subsidiary Examination MATHEMATICS Unit Statistics 1A MS/SS1A/W STATISTICS Unit Statistics 1A Wednesday 21 May 2008 1.30 pm to 2.45 pm For this paper

More information

Statistics Unit Statistics 1B

Statistics Unit Statistics 1B Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Statistics 1B Statistics Unit Statistics 1B General Certificate of Education

More information

Statistics Unit Statistics 1B

Statistics Unit Statistics 1B Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Statistics 1B Statistics Unit Statistics 1B Friday 14 January 2011 General

More information

Statistics Unit Statistics 1B

Statistics Unit Statistics 1B Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Statistics 1B Statistics Unit Statistics 1B Friday 18 January 2013 General

More information

Surname Other Names Centre Number Candidate Number Candidate Signature. a clean copy of the Data Sheet (enclosed)

Surname Other Names Centre Number Candidate Number Candidate Signature. a clean copy of the Data Sheet (enclosed) Surname Other Names Centre Number Candidate Number Candidate Signature Use of Mathematics (Pilot) Algebra USE1 Leave blank General Certificate of Education Advanced Subsidiary Examination June 2015 Monday

More information

Tuesday 21 June 2016 Morning Time allowed: 1 hour 30 minutes

Tuesday 21 June 2016 Morning Time allowed: 1 hour 30 minutes Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature A-level MATHEMATICS Unit Statistics 2B Tuesday 21 June 2016 Morning Time allowed: 1 hour 30

More information

Mathematics (Modular) 43055/2H (Specification B) Module 5

Mathematics (Modular) 43055/2H (Specification B) Module 5 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier June 0 Mathematics (Modular) 43055/H

More information

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination June Unit Further Pure 1.

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination June Unit Further Pure 1. General Certificate of Education Advanced Subsidiary Examination June 011 Mathematics MFP1 Unit Further Pure 1 Friday 0 May 011 1.0 pm to.00 pm For this paper you must have: the blue AQA booklet of formulae

More information

AS FURTHER MATHEMATICS Paper 2 Statistics

AS FURTHER MATHEMATICS Paper 2 Statistics SPECIMEN MATERIAL Please write clearly, in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature AS FURTHER MATHEMATICS Paper 2 Statistics Exam Date Morning Time allowed:

More information

43005/1H. General Certificate of Secondary Education November 2008

43005/1H. General Certificate of Secondary Education November 2008 Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education November 2008 MATHEMATICS (MODULAR) (SPECIFICATION B) 43005/1H Module

More information

General Certificate of Education Advanced Level Examination January 2010

General Certificate of Education Advanced Level Examination January 2010 General Certificate of Education Advanced Level Examination January 2010 Mathematics MM2B Unit Mechanics 2B Wednesday 20 January 2010 1.30 pm to 3.00 pm For this paper you must have: an 8-page answer book

More information

Candidate Number. General Certificate of Secondary Education Higher Tier June 2013

Candidate Number. General Certificate of Secondary Education Higher Tier June 2013 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier June 2013 Pages 2 3 4 5 Mark Mathematics

More information

Statistics Unit Statistics 1A

Statistics Unit Statistics 1A Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Statistics 1A Statistics Unit Statistics 1A Thursday 27 May 2010 General Certificate

More information

Physics Unit 3 Investigative and Practical Skills in AS Physics PHY3T/Q09/test

Physics Unit 3 Investigative and Practical Skills in AS Physics PHY3T/Q09/test Surname Other Names Leave blank Centre Number Candidate Number Candidate Signature General Certificate of Education June 2009 Advanced Subsidiary Examination Physics Unit 3 Investigative and Practical

More information

43603F. General Certificate of Secondary Education Foundation Tier June Unit 3. (JUN F01) WMP/Jun12/43603F F

43603F. General Certificate of Secondary Education Foundation Tier June Unit 3. (JUN F01) WMP/Jun12/43603F F Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Foundation Tier June 2012 Pages 3 4 5 Mark Mathematics

More information

MATHEMATICS Unit Mechanics 2B

MATHEMATICS Unit Mechanics 2B General Certificate of Education January 2007 Advanced Level Examination MATHEMATICS Unit Mechanics 2 MM2 Tuesday 16 January 2007 9.00 am to 10.30 am For this paper you must have: an 8-page answer book

More information

Use blue or black ink or ball-point pen. Pencil should only be used for drawing. *

Use blue or black ink or ball-point pen. Pencil should only be used for drawing. * General Certificate of Education January 2007 Advanced Subsidiary Examination MATHEMATICS Unit Statistics 1B MS/SS1B STATISTICS Unit Statistics 1B Tuesday 23 January 2007 1.30 pm to 3.00 pm For this paper

More information

43005/1H. General Certificate of Secondary Education June 2008

43005/1H. General Certificate of Secondary Education June 2008 Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education June 2008 MATHEMATICS (MODULAR) (SPECIFICATION B) 43005/1H Module 5

More information

43603H. (MAR H01) WMP/Mar13/43603H. General Certificate of Secondary Education Higher Tier March Unit H

43603H. (MAR H01) WMP/Mar13/43603H. General Certificate of Secondary Education Higher Tier March Unit H Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier March 2013 Pages 3 4 5 Mark Mathematics

More information

Monday 27 June 2016 Morning Time allowed: 1 hour 30 minutes

Monday 27 June 2016 Morning Time allowed: 1 hour 30 minutes Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature A-level STATISTICS Unit Statistics 6 Monday 27 June 2016 Morning Time allowed: 1 hour 30 minutes

More information

General Certificate of Secondary Education Foundation Tier

General Certificate of Secondary Education Foundation Tier Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature Pages Mark General Certificate of Secondary Education Foundation Tier 3 4-5 GCSE Mathematics

More information

A-level FURTHER MATHEMATICS Paper 3 - Mechanics

A-level FURTHER MATHEMATICS Paper 3 - Mechanics SPECIMEN MATERIAL Please write clearly, in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature A-level FURTHER MATHEMATICS Paper 3 - Mechanics Exam Date Morning Time

More information

PHYA5/2D. General Certificate of Education Advanced Level Examination June Unit 5D Turning Points in Physics Section B

PHYA5/2D. General Certificate of Education Advanced Level Examination June Unit 5D Turning Points in Physics Section B Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2010 Question 1 2 Mark Physics

More information

PHY6T/Q10/test. General Certificate of Education Advanced Level Examination June Investigative and Practical Skills in A2 Physics

PHY6T/Q10/test. General Certificate of Education Advanced Level Examination June Investigative and Practical Skills in A2 Physics Centre Number Surname Other Names Candidate Signature Candidate Number For Teacher s Use Mark Stage 1 Section A 1 General Certificate of Education Advanced Level Examination June 2010 Section B 2 3 4 Physics

More information

abc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES

abc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES abc General Certificate of Education Mathematics Further Pure SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER

More information

Methods in Mathematics (Linked Pair Pilot)

Methods in Mathematics (Linked Pair Pilot) Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier January 2013 Pages 3 4 5 Mark Methods

More information

General Certificate of Education Advanced Level Examination January 2010

General Certificate of Education Advanced Level Examination January 2010 General Certificate of Education Advanced Level Examination January 010 Mathematics MFP4 Unit Further Pure 4 Monday January 010 9.00 am to 10.0 am For this paper you must have: a 1-page answer book the

More information

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core 2.

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core 2. General Certificate of Education Advanced Subsidiary Examination January 0 Mathematics MPC Unit Pure Core Monday January 0 9.00 am to 0.0 am For this paper you must have: the blue AQA booklet of formulae

More information

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core 2.

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core 2. General Certificate of Education Advanced Subsidiary Eamination January 0 Mathematics MPC Unit Pure Core Monday 0 January 0 9.00 am to 0.0 am For this paper you must have: the blue AQA booklet of formulae

More information

PHY6T/P10/test. General Certificate of Education Advanced Level Examination June Investigative and Practical Skills in A2 Physics

PHY6T/P10/test. General Certificate of Education Advanced Level Examination June Investigative and Practical Skills in A2 Physics Centre Number Surname Other Names Candidate Signature Candidate Number For Teacher s Use Mark Stage 1 Section A 1 General Certificate of Education Advanced Level Examination June 2010 Section B 2 3 4 Physics

More information

PHYA4/2. (JUN14PHYA4201) WMP/Jun14/PHYA4/2/E4. General Certificate of Education Advanced Level Examination June 2014

PHYA4/2. (JUN14PHYA4201) WMP/Jun14/PHYA4/2/E4. General Certificate of Education Advanced Level Examination June 2014 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A General Certificate of Education Advanced Level Examination June 2014 PHYA4/2 Question

More information

Condensed. Mathematics. General Certificate of Education Advanced Level Examination June Unit Further Pure 2. Time allowed * 1 hour 30 minutes

Condensed. Mathematics. General Certificate of Education Advanced Level Examination June Unit Further Pure 2. Time allowed * 1 hour 30 minutes General Certificate of Education Advanced Level Examination June 011 Mathematics MFP Unit Further Pure Monday 13 June 011 9.00 am to 10.30 am For this paper you must have: the blue AQA booklet of formulae

More information

Mathematics (JAN13MPC301) General Certificate of Education Advanced Level Examination January Unit Pure Core TOTAL

Mathematics (JAN13MPC301) General Certificate of Education Advanced Level Examination January Unit Pure Core TOTAL Centre Number Candidate Number For Eaminer s Use Surname Other Names Candidate Signature Eaminer s Initials Mathematics Unit Pure Core Wednesday January General Certificate of Education Advanced Level

More information

General Certificate of Secondary Education Foundation Tier June Time allowed 1 hour 30 minutes

General Certificate of Secondary Education Foundation Tier June Time allowed 1 hour 30 minutes Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark Mathematics General Certificate of Secondary Education Foundation Tier June 2015

More information

4301/1F. General Certificate of Secondary Education June MATHEMATICS (SPECIFICATION A) 4301/1F Foundation Tier Paper 1 Non-calculator

4301/1F. General Certificate of Secondary Education June MATHEMATICS (SPECIFICATION A) 4301/1F Foundation Tier Paper 1 Non-calculator Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education June 2008 MATHEMATICS (SPECIFICATION A) 4301/1F Foundation Tier Paper

More information

General Certificate of Secondary Education Higher Tier June Time allowed 1 hour 30 minutes

General Certificate of Secondary Education Higher Tier June Time allowed 1 hour 30 minutes Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark Mathematics General Certificate of Secondary Education Higher Tier June 2015 43603H

More information

PHYA1. General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity

PHYA1. General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: a pencil and a ruler a calculator a Data and

More information

43603F. (NOV F01) WMP/Nov12/43603F. General Certificate of Secondary Education Foundation Tier November Unit F

43603F. (NOV F01) WMP/Nov12/43603F. General Certificate of Secondary Education Foundation Tier November Unit F Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Foundation Tier November 2012 Pages 3 4 5 Mark Mathematics

More information

43055/2H. General Certificate of Secondary Education June 2009

43055/2H. General Certificate of Secondary Education June 2009 Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education June 2009 MATHEMATICS (MODULAR) (SPECIFICATION B) 43055/2H Module 5

More information

43603F. (NOV F01) WMP/Nov13/43603F/E4. General Certificate of Secondary Education Foundation Tier November Unit 3

43603F. (NOV F01) WMP/Nov13/43603F/E4. General Certificate of Secondary Education Foundation Tier November Unit 3 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark General Certificate of Secondary Education Foundation Tier November 2013 3 4 5 Mathematics

More information

General Certificate of Secondary Education Higher Tier

General Certificate of Secondary Education Higher Tier Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature General Certificate of Secondary Education Higher Tier Pages 3 4-5 Mark GCSE Mathematics Unit

More information

PHYA5/2D. General Certificate of Education Advanced Level Examination June Unit 5D Turning Points in Physics Section B

PHYA5/2D. General Certificate of Education Advanced Level Examination June Unit 5D Turning Points in Physics Section B Centre Number Surname Candidate Number For Examinerʼs Use Other Names Candidate Signature Examinerʼs Initials General Certificate of Education Advanced Level Examination June 2012 Question 1 2 Mark Physics

More information

Mathematics Past Paper Type Questions by Topic 43602H. Histograms. In the style of General Certificate of Secondary Education Higher Tier TOTAL

Mathematics Past Paper Type Questions by Topic 43602H. Histograms. In the style of General Certificate of Secondary Education Higher Tier TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials In the style of General Certificate of Secondary Education Higher Tier Pages 2 3 4 5 Mark Mathematics

More information

PHYA5/1. General Certificate of Education Advanced Level Examination June 2010

PHYA5/1. General Certificate of Education Advanced Level Examination June 2010 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A General Certificate of Education Advanced Level Examination June 2010 Unit 5 Nuclear

More information

ERRATUM NOTICE ERRATUM NOTICE

ERRATUM NOTICE ERRATUM NOTICE ERRATUM NOTICE General Certificate of Education January 2011 PHYSICS A Unit 1 Particles, Quantum Phenomena and Electricity PHYA1 Wednesday 12 January 2011 9.00 am to 10.15 am Instructions to Invigilators

More information

PHYA4/2. (JUN15PHYA4201) WMP/Jun15/PHYA4/2/E3 PMT. General Certificate of Education Advanced Level Examination June 2015

PHYA4/2. (JUN15PHYA4201) WMP/Jun15/PHYA4/2/E3 PMT. General Certificate of Education Advanced Level Examination June 2015 Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2015 Question 1 2 Mark Physics

More information

General Certificate of Secondary Education November MATHEMATICS (MODULAR) (SPECIFICATION B) 43055/1H Module 5 Higher Tier Paper 1 Non-calculator

General Certificate of Secondary Education November MATHEMATICS (MODULAR) (SPECIFICATION B) 43055/1H Module 5 Higher Tier Paper 1 Non-calculator Surname Other Names For Examinerʼs Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education November 2009 MATHEMATICS (MODULAR) (SPECIFICATION B) 43055/1H Module

More information

Exam Date Morning Time allowed: 1 hour 30 minutes

Exam Date Morning Time allowed: 1 hour 30 minutes NEW PRACTICE PAPER SET 1 Published September 2015 Please write clearly, in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature GCSE MATHEMATICS H Higher Tier Paper 1

More information

Physics Unit 3 Investigative and Practical Skills in AS Physics PHY3T/P09/test

Physics Unit 3 Investigative and Practical Skills in AS Physics PHY3T/P09/test Surname Other Names Leave blank Centre Number Candidate Number Candidate Signature General Certificate of Education June 2009 Advanced Subsidiary Examination Physics Unit 3 Investigative and Practical

More information

PHYA5/2AR (JUN15PHYA52AR01) General Certificate of Education Advanced Level Examination June Section B PMT TOTAL.

PHYA5/2AR (JUN15PHYA52AR01) General Certificate of Education Advanced Level Examination June Section B PMT TOTAL. Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2015 Question 1 2 Mark Physics

More information

PHYA4/2. (JAN13PHYA4201) WMP/Jan13/PHYA4/2. General Certificate of Education Advanced Level Examination January 2013

PHYA4/2. (JAN13PHYA4201) WMP/Jan13/PHYA4/2. General Certificate of Education Advanced Level Examination January 2013 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 4 Fields and Further Mechanics Section B General Certificate of Education Advanced

More information

General Certificate of Secondary Education Higher Tier

General Certificate of Secondary Education Higher Tier Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Pages 3 Mark General Certificate of Secondary Education Higher Tier 4 5 6 7 Mathematics (Linear) B Paper 1 Non-calculator

More information

PHYA5/2C. General Certificate of Education Advanced Level Examination June Section B. Monday 27 June am to 10.45am (JUN11PHYA52C01) PMT

PHYA5/2C. General Certificate of Education Advanced Level Examination June Section B. Monday 27 June am to 10.45am (JUN11PHYA52C01) PMT Centre Number Surname Candidate Number For Examinerʼs Use Other Names Candidate Signature Examinerʼs Initials General Certificate of Education Advanced Level Examination June 2011 Question 1 2 Mark Physics

More information

Mathematics (Linear) 43651H. (NOV H01) WMP/Nov12/43651H. General Certificate of Secondary Education Higher Tier November 2012.

Mathematics (Linear) 43651H. (NOV H01) WMP/Nov12/43651H. General Certificate of Secondary Education Higher Tier November 2012. Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier November 202 Pages 3 4 5 Mark Mathematics

More information

PHYA1. (JUN13PHYA101) WMP/Jun13/PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2013

PHYA1. (JUN13PHYA101) WMP/Jun13/PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2013 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

More information

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Mechanics 1B.

Condensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Mechanics 1B. General Certificate of Education Advanced Subsidiary Examination January 2011 Mathematics MM1B Unit Mechanics 1B Wednesday 19 January 2011 1.30 pm to 3.00 pm For this paper you must have: the blue AQA

More information

PHYA4/2. General Certificate of Education Advanced Level Examination June Unit 4 Fields and Further Mechanics Section B

PHYA4/2. General Certificate of Education Advanced Level Examination June Unit 4 Fields and Further Mechanics Section B Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A General Certificate of Education Advanced Level Examination June 2012 PHYA4/2 Question

More information