PRE-LEAVING CERTIFICATE EXAMINATION, 2010
|
|
- Dina Burns
- 5 years ago
- Views:
Transcription
1 L.7 PRE-LEAVING CERTIFICATE EXAMINATION, 00 MATHEMATICS HIGHER LEVEL PAPER (300 marks) TIME : ½ HOURS Attempt SIX QUESTIONS (50 marks each). WARNING: Marks will be lost if all necessary work is not clearly shown. Answers should include the appropriate units of measurement, where relevant. 00 L.7 /8 Page of 5
2 . (a) Simplify fully (b) (i) Let g (x) = ax + bx + c, where a, b, c R. Given that k is a real number such that g (k) = 0, prove that x k is a factor of g (x). x t is a factor of x 3 + px + p. 3 t Show that p =. ( t + ) (c) Show that z 4z + 5 is a factor of z 3 + (i 4)z + (5 4i)z + 5i. Hence, find the three roots of z 3 + (i 4)z + (5 4i)z + 5i = 0.. (a) Solve the simultaneous equations x + y + z = 6 x y + 3z = 4 5x + y = 8. (b) (i) Let f (x) = 3tx 6x + (t ), where t R. Find the values of t for which f (x) = 0 has equal roots. Hence, for each value of t, find the roots of f (x) = 0. Find the range of values of x for which x 3 x + 4 >, where x R and x 4. (c) α and β are the roots of the equation x + 3ax + a = 0. (i) Find the value of α 3 + β 3. Find the quadratic equation whose roots are β α and α β. 00 L.7 /8 Page of 5
3 3. (a) i Let z =, where i =. i Express z in the form a + bi and plot it on an Argand diagram. k k simplifies to a constant. (b) (i) Show that ( k ) Let A = and B =. 9 Find the matrix C, such that CA = B. (c) (i) w is a complex number such that w w = + 4i where i =. Express w in the form p + qi, where p, q R. Use De Moivre s theorem to find the three roots of z 3 8 = 0. Give your answer in the form x + yi, with x and y fully evaluated. Hence, show that the sum of the three roots is zero. n n n + 4. (a) Show that + = for all natural numbers n (b) A sequence is defined by u n = (an + b)3 n, where a, b R. (i) Show that u n + 6u n + + 9u n = 0, for all n 0. Given that u 3 = 54 and u 4 = 405, find the value of a and the value b. (c) Let g(x) = + x + 5x +, where x <. 4x Show that g(x) =. ( x) 00 L.7 3/8 Page 3 of 5
4 5. (a) The sum to infinity of a geometric series is 0. The common ratio of the series is. Find the first term of the series. (b) (i) Solve log (3x + ) log (x ) =, x >, x R. In the expansion of (x + a) 8 35, the middle term is x 4. 8 Find the values of a, a R. (c) (i) Use induction to prove that n! < for all n 4, n N. n Hence, deduce that n = 4 n! < (a) Differentiate 4 3x with respect to x. (b) Let y = xe x. (i) dy d y Find and. Find the value of k R for which d y dy ky = 0. (c) Let f (x) = 5 3x x 3, x R. (i) Find the co-ordinates of the local maximum and local minimum points of the curve y = f (x). Show that the only real root of f (x) = 0 lies between and and hence draw a sketch of the curve y = f (x). (iii) Take x = as the first approximation of the real root of the equation f (x) = 0. Find, using the Newton-Raphson method, x, the second approximation. 00 L.7 4/8 Page 4 of 5
5 7. (a) Prove from first principles, the addition rule d du dv (u + v) = + where u = u(x) and v = v(x). (b) Given that y = ln x + for x >, x 4 dy find and express your answer in the form b a a x, where a, b N. (c) The parametric equations of a curve are x = cos t + t sin t y = sin t t cos t, where t 4 π. (i) dy Find in terms of t. Hence, show that x y = π is a tangent to the curve. 8. (a) Find (i) 3 x e3x. (b) Evaluate (i) 6 x x. 4x x. 4x + 0 (c) The diagram shows the curve y = x(x ) and the tangent to the curve at its local maximum point. (i) Find the area enclosed by the curve and the x-axis. Hence, find the area of the shaded region. 00 L.7 5/8 Page 5 of 5
6 Blank Page 00 L.7 6/8 Page 6 of 5
7 Blank Page 00 L.7 7/8 Page 7 of 5
8 Blank Page 00 L.7 8/8 Page 8 of 5
Mathematics (Project Maths Phase 2)
011. M9 S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 011 Sample Paper Mathematics (Project Maths Phase ) Paper 1 Higher Level Time: hours, 30 minutes 300
More information2013 Leaving Cert Higher Level Official Sample Paper 1
013 Leaving Cert Higher Level Official Sample Paper 1 Section A Concepts and Skills 150 marks Question 1 (5 marks) (a) w 1 + 3i is a complex number, where i 1. (i) Write w in polar form. We have w ( 1)
More informationH2 MATHS SET D PAPER 1
H Maths Set D Paper H MATHS Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e b The curve y ax c x 3 points, and, H Maths Set D Paper has a stationary point at x 3. It also
More informationSECTION A. f(x) = ln(x). Sketch the graph of y = f(x), indicating the coordinates of any points where the graph crosses the axes.
SECTION A 1. State the maximal domain and range of the function f(x) = ln(x). Sketch the graph of y = f(x), indicating the coordinates of any points where the graph crosses the axes. 2. By evaluating f(0),
More informationX100/701 MATHEMATICS ADVANCED HIGHER. Read carefully
X/7 N A T I O N A L Q U A L I F I C A T I O N S 9 T H U R S D A Y, M A Y. P M. P M MATHEMATICS ADVANCED HIGHER Read carefully. Calculators may be used in this paper.. Candidates should answer all questions.
More information9 11 Solve the initial-value problem Evaluate the integral. 1. y sin 3 x cos 2 x dx. calculation. 1 + i i23
Mock Exam 1 5 8 Solve the differential equation. 7. d dt te t s1 Mock Exam 9 11 Solve the initial-value problem. 9. x ln x, 1 3 6 Match the differential equation with its direction field (labeled I IV).
More informationMathematics 104 Fall Term 2006 Solutions to Final Exam. sin(ln t) dt = e x sin(x) dx.
Mathematics 14 Fall Term 26 Solutions to Final Exam 1. Evaluate sin(ln t) dt. Solution. We first make the substitution t = e x, for which dt = e x. This gives sin(ln t) dt = e x sin(x). To evaluate the
More informationDifferentiation Shortcuts
Differentiation Shortcuts Sections 10-5, 11-2, 11-3, and 11-4 Prof. Nathan Wodarz Math 109 - Fall 2008 Contents 1 Basic Properties 2 1.1 Notation............................... 2 1.2 Constant Functions.........................
More informationMath 142, Final Exam. 12/7/10.
Math 4, Final Exam. /7/0. No notes, calculator, or text. There are 00 points total. Partial credit may be given. Write your full name in the upper right corner of page. Number the pages in the upper right
More informationTHE NATIONAL UNIVERSITY OF IRELAND, CORK COLÁISTE NA hollscoile, CORCAIGH UNIVERSITY COLLEGE, CORK. Summer Examination 2009.
OLLSCOIL NA héireann, CORCAIGH THE NATIONAL UNIVERSITY OF IRELAND, CORK COLÁISTE NA hollscoile, CORCAIGH UNIVERSITY COLLEGE, CORK Summer Examination 2009 First Engineering MA008 Calculus and Linear Algebra
More informationP3.C8.COMPLEX NUMBERS
Recall: Within the real number system, we can solve equation of the form and b 2 4ac 0. ax 2 + bx + c =0, where a, b, c R What is R? They are real numbers on the number line e.g: 2, 4, π, 3.167, 2 3 Therefore,
More informationFall 2013 Hour Exam 2 11/08/13 Time Limit: 50 Minutes
Math 8 Fall Hour Exam /8/ Time Limit: 5 Minutes Name (Print): This exam contains 9 pages (including this cover page) and 7 problems. Check to see if any pages are missing. Enter all requested information
More informationG H. Extended Unit Tests A L L. Higher Still Advanced Higher Mathematics. (more demanding tests covering all levels) Contents. 3 Extended Unit Tests
M A T H E M A T I C S H I G H E R Higher Still Advanced Higher Mathematics S T I L L Extended Unit Tests A (more demanding tests covering all levels) Contents Extended Unit Tests Detailed marking schemes
More informationReview for the Final Exam
Math 171 Review for the Final Exam 1 Find the limits (4 points each) (a) lim 4x 2 3; x x (b) lim ( x 2 x x 1 )x ; (c) lim( 1 1 ); x 1 ln x x 1 sin (x 2) (d) lim x 2 x 2 4 Solutions (a) The limit lim 4x
More informationMth Review Problems for Test 2 Stewart 8e Chapter 3. For Test #2 study these problems, the examples in your notes, and the homework.
For Test # study these problems, the examples in your notes, and the homework. Derivative Rules D [u n ] = nu n 1 du D [ln u] = du u D [log b u] = du u ln b D [e u ] = e u du D [a u ] = a u ln a du D [sin
More informationCSSA Trial HSC Examination
CSSA Trial HSC Examination. (a) Mathematics Extension 2 2002 The diagram shows the graph of y = f(x) where f(x) = x2 x 2 +. (i) Find the equation of the asymptote L. (ii) On separate diagrams sketch the
More informationMathematics Extension 2
Mathematics Extension 03 HSC ASSESSMENT TASK 3 (TRIAL HSC) General Instructions Reading time 5 minutes Working time 3 hours Write on one side of the paper (with lines) in the booklet provided Write using
More informationMathematics (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 informationCore Mathematics C4 Advanced Level
Paper Reference(s) 6666/0 Edexcel GCE Core Mathematics C4 Advanced Level Thursday June 0 Afternoon Time: hour 0 minutes Materials required for examination Mathematical Formulae (Pink) Items included with
More informationIntegration - Past Edexcel Exam Questions
Integration - Past Edexcel Exam Questions 1. (a) Given that y = 5x 2 + 7x + 3, find i. - ii. - (b) ( 1 + 3 ) x 1 x dx. [4] 2. Question 2b - January 2005 2. The gradient of the curve C is given by The point
More informationSemester University of Sheffield. School of Mathematics and Statistics
University of Sheffield School of Mathematics and Statistics MAS140: Mathematics (Chemical) MAS15: Civil Engineering Mathematics MAS15: Essential Mathematical Skills & Techniques MAS156: Mathematics (Electrical
More informationEdexcel GCE Further Pure Mathematics (FP1) Required Knowledge Information Sheet. Daniel Hammocks
Edexcel GCE Further Pure Mathematics (FP1) Required Knowledge Information Sheet FP1 Formulae Given in Mathematical Formulae and Statistical Tables Booklet Summations o =1 2 = 1 + 12 + 1 6 o =1 3 = 1 64
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *122414780* FURTHER MATHEMATICS 9231/01 Paper 1 October/November 2007 Additional Materials: Answer Booklet/Paper
More informationFind the common ratio of the geometric sequence. (2) 1 + 2
. Given that z z 2 = 2 i, z, find z in the form a + ib. (Total 4 marks) 2. A geometric sequence u, u 2, u 3,... has u = 27 and a sum to infinity of 8. 2 Find the common ratio of the geometric sequence.
More informationReview For the Final: Problem 1 Find the general solutions of the following DEs. a) x 2 y xy y 2 = 0 solution: = 0 : homogeneous equation.
Review For the Final: Problem 1 Find the general solutions of the following DEs. a) x 2 y xy y 2 = 0 solution: y y x y2 = 0 : homogeneous equation. x2 v = y dy, y = vx, and x v + x dv dx = v + v2. dx =
More informationMathematics. Pre-Leaving Certificate Examination, Paper 1 Higher Level Time: 2 hours, 30 minutes. 300 marks L.17 NAME SCHOOL TEACHER
L.7 NAME SCHOOL TEACHER Pre-Leaving Certificate Examination, 205 Name/v Printed Checke To: Update Name/v Comple Paper Higher Level Time: 2 hours, 30 minutes 300 marks For examiner Question 2 School stamp
More informationUNIVERSITY OF SOUTHAMPTON
UNIVERSITY OF SOUTHAMPTON MATH03W SEMESTER EXAMINATION 0/ MATHEMATICS FOR ELECTRONIC & ELECTRICAL ENGINEERING Duration: 0 min This paper has two parts, part A and part B. Answer all questions from part
More informationTHE KING S SCHOOL. Mathematics Extension Higher School Certificate Trial Examination
THE KING S SCHOOL 2009 Higher School Certificate Trial Examination Mathematics Extension 1 General Instructions Reading time 5 minutes Working time 2 hours Write using black or blue pen Board-approved
More informationTopic 1 Part 3 [483 marks]
Topic Part 3 [483 marks] The complex numbers z = i and z = 3 i are represented by the points A and B respectively on an Argand diagram Given that O is the origin, a Find AB, giving your answer in the form
More informationMTH4101 CALCULUS II REVISION NOTES. 1. COMPLEX NUMBERS (Thomas Appendix 7 + lecture notes) ax 2 + bx + c = 0. x = b ± b 2 4ac 2a. i = 1.
MTH4101 CALCULUS II REVISION NOTES 1. COMPLEX NUMBERS (Thomas Appendix 7 + lecture notes) 1.1 Introduction Types of numbers (natural, integers, rationals, reals) The need to solve quadratic equations:
More informationSTEP Support Programme. Pure STEP 1 Questions
STEP Support Programme Pure STEP 1 Questions 2012 S1 Q4 1 Preparation Find the equation of the tangent to the curve y = x at the point where x = 4. Recall that x means the positive square root. Solve the
More information3 COMPLEX NUMBERS. 3.0 Introduction. Objectives
3 COMPLEX NUMBERS Objectives After studying this chapter you should understand how quadratic equations lead to complex numbers and how to plot complex numbers on an Argand diagram; be able to relate graphs
More informationAnnouncements. Topics: Homework:
Announcements Topics: - sections 7.5 (additional techniques of integration), 7.6 (applications of integration), * Read these sections and study solved examples in your textbook! Homework: - review lecture
More informationFurther Pure Mathematics F2
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Further Pure Mathematics F2 Advanced/Advanced Subsidiary Wednesday 7 June 2017 Morning Time: 1 hour 30
More informationPENRITH HIGH SCHOOL MATHEMATICS EXTENSION HSC Trial
PENRITH HIGH SCHOOL MATHEMATICS EXTENSION 013 Assessor: Mr Ferguson General Instructions: HSC Trial Total marks 100 Reading time 5 minutes Working time 3 hours Write using black or blue pen. Black pen
More informationMathematics Extension 2
00 HIGHER SCHOOL CERTIFICATE TRIAL EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Approved scientific calculators and templates
More informationLesson 3: Linear differential equations of the first order Solve each of the following differential equations by two methods.
Lesson 3: Linear differential equations of the first der Solve each of the following differential equations by two methods. Exercise 3.1. Solution. Method 1. It is clear that y + y = 3 e dx = e x is an
More information+ 2gx + 2fy + c = 0 if S
CIRCLE DEFINITIONS A circle is the locus of a point which moves in such a way that its distance from a fixed point, called the centre, is always a constant. The distance r from the centre is called the
More informationMATHEMATICAL METHODS
Victorian Certificate of Education 018 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER MATHEMATICAL METHODS Written examination 1 Friday 1 June 018 Reading time:.00 pm to.15 pm (15 minutes)
More informationMATHEMATICS - ORDINARY LEVEL
M7 AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 000 MATHEMATICS - ORDINARY LEVEL PAPER (300 marks) THURSDAY, 8 JUNE - MORNING, 930 to 00 Attempt SIX QUESTIONS (50 marks each) Marks
More informationPURE MATHEMATICS AM 27
AM Syllabus (014): Pure Mathematics AM SYLLABUS (014) PURE MATHEMATICS AM 7 SYLLABUS 1 AM Syllabus (014): Pure Mathematics Pure Mathematics AM 7 Syllabus (Available in September) Paper I(3hrs)+Paper II(3hrs)
More informationabc 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 informationMathematics (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 informationAdvanced Higher Grade
Prelim Eamination / 5 (Assessing Units & ) MATHEMATICS Advanced Higher Grade Time allowed - hours Read Carefully. Full credit will be given only where the solution contains appropriate woring.. Calculators
More informationPLC Papers Created For:
PLC Papers Created For: Quadratics intervention Deduce quadratic roots algebraically 1 Grade 6 Objective: Deduce roots algebraically. Question 1. Factorise and solve the equation x 2 8x + 15 = 0 Question
More informationSOLUTIONS FOR PRACTICE FINAL EXAM
SOLUTIONS FOR PRACTICE FINAL EXAM ANDREW J. BLUMBERG. Solutions () Short answer questions: (a) State the mean value theorem. Proof. The mean value theorem says that if f is continuous on (a, b) and differentiable
More informationt 2 + 2t dt = (t + 1) dt + 1 = arctan t x + 6 x(x 3)(x + 2) = A x +
MATH 06 0 Practice Exam #. (0 points) Evaluate the following integrals: (a) (0 points). t +t+7 This is an irreducible quadratic; its denominator can thus be rephrased via completion of the square as a
More informationTEST CODE: MMA (Objective type) 2015 SYLLABUS
TEST CODE: MMA (Objective type) 2015 SYLLABUS Analytical Reasoning Algebra Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinatorics: Permutations and combinations,
More informationCreated by T. Madas. Candidates may use any calculator allowed by the regulations of this examination.
IYGB GCE Mathematics MP Advanced Level Practice Paper M Difficulty Rating:.8750/1.176 Time: hours Candidates may use any calculator allowed by the regulations of this examination. Information for Candidates
More informationAPPENDIX : PARTIAL FRACTIONS
APPENDIX : PARTIAL FRACTIONS Appendix : Partial Fractions Given the expression x 2 and asked to find its integral, x + you can use work from Section. to give x 2 =ln( x 2) ln( x + )+c x + = ln k x 2 x+
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *5238158802* MATHEMATICS 9709/31 Paper 3 Pure Mathematics 3 (P3) October/November 2013 Additional Materials:
More informationFORM VI MATHEMATICS EXTENSION 2
CANDIDATE NUMBER SYDNEY GRAMMAR SCHOOL 207 Trial Examination FORM VI MATHEMATICS EXTENSION 2 Thursday 0th August 207 General Instructions Reading time 5minutes Writing time 3hours Write using black pen.
More informationMathematics Higher Level
L.7/0 Pre-Leaving Certificate Examination, 06 Mathematics Higher Level Marking Scheme Paper Pg. Paper Pg. 36 Page of 68 exams Pre-Leaving Certificate Examination, 06 Mathematics Higher Level Paper Marking
More informationUNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE General Certificate of Education Advanced Level FURTHER MATHEMATICS 9221/1 PAPER 1
,--, ~"\, \ "~. "',,~ \ ~ 1.f8P;)1!,'" ;i *.~ UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE General Certificate of Education Advanced Level FURTHER MATHEMATICS 9221/1 PAPER 1 MAY/JUNE SESSION 2001
More informationLimit. Chapter Introduction
Chapter 9 Limit Limit is the foundation of calculus that it is so useful to understand more complicating chapters of calculus. Besides, Mathematics has black hole scenarios (dividing by zero, going to
More informationAnswer all the questions
SECTION A ( 38 marks) Answer all the questions 1 The following information refer to the set A and set B. Set A = { -3, -2, 2, 3 } Set B = { 4, 9 } The relations between set A and set B is defined by the
More informationIntegration by Parts
Calculus 2 Lia Vas Integration by Parts Using integration by parts one transforms an integral of a product of two functions into a simpler integral. Divide the initial function into two parts called u
More information, B = (b) Use induction to prove that, for all positive integers n, f(n) is divisible by 4. (a) Use differentiation to find f (x).
Edexcel FP1 FP1 Practice Practice Papers A and B Papers A and B PRACTICE PAPER A 1. A = 2 1, B = 4 3 3 1, I = 4 2 1 0. 0 1 (a) Show that AB = ci, stating the value of the constant c. (b) Hence, or otherwise,
More informationECM Calculus and Geometry. Revision Notes
ECM1702 - Calculus and Geometry Revision Notes Joshua Byrne Autumn 2011 Contents 1 The Real Numbers 1 1.1 Notation.................................................. 1 1.2 Set Notation...............................................
More informationFurther Mathematics AS/F1/D17 AS PAPER 1
Surname Other Names Candidate Signature Centre Number Candidate Number Examiner Comments Total Marks Further Mathematics AS PAPER 1 CM December Mock Exam (AQA Version) Time allowed: 1 hour and 30 minutes
More informationCalifornia Subject Examinations for Teachers
California Subject Examinations for Teachers TEST GUIDE MATHEMATICS SUBTEST I Sample Questions and Responses and Scoring Information Copyright 204 Pearson Education, Inc. or its affiliate(s). All rights
More informationIYGB. Special Extension Paper A. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas
IYGB Special Extension Paper A Time: 3 hours 30 minutes Candidates may NOT use any calculator Information for Candidates This practice paper follows the Advanced Level Mathematics Core and the Advanced
More informationADDITIONAL MATHEMATICS 4037/01
Cambridge O Level *0123456789* ADDITIONAL MATHEMATICS 4037/01 Paper 1 For examination from 2020 SPECIMEN PAPER 2 hours You must answer on the question paper. No additional materials are needed. INSTRUCTIONS
More informationMathematics Extension 2
00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators may be used A table
More informationReview session Midterm 1
AS.110.109: Calculus II (Eng) Review session Midterm 1 Yi Wang, Johns Hopkins University Fall 2018 7.1: Integration by parts Basic integration method: u-sub, integration table Integration By Parts formula
More informationCoimisiún na Scrúduithe Stáit State Examinations Commission
M 9 Coimisiú a Scrúduithe Stáit State Examiatios Commissio LEAVING CERTIFICATE EXAMINATION, 006 MATHEMATICS HIGHER LEVEL PAPER 1 ( 00 marks ) THURSDAY, 8 JUNE MORNING, 9:0 to 1:00 Attempt SIX QUESTIONS
More informationAdvanced Mathematics Support Programme Edexcel Year 2 Core Pure Suggested Scheme of Work ( )
Edexcel Year 2 Core Pure Suggested Scheme of Work (2018-2019) This template shows how Integral Resources and AMSP FM videos can be used to support Further Mathematics students and teachers. This template
More informationUNIVERSITY 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
More informationThe marks achieved in this section account for 50% of your final exam result.
Section D The marks achieved in this section account for 50% of your final exam result. Full algebraic working must be clearly shown. Instructions: This section has two parts. Answer ALL questions in part
More informationSCORE. Exam 3. MA 114 Exam 3 Fall 2016
Exam 3 Name: Section and/or TA: Do not remove this answer page you will return the whole exam. You will be allowed two hours to complete this test. No books or notes may be used. You may use a graphing
More informationBook 4. June 2013 June 2014 June Name :
Book 4 June 2013 June 2014 June 2015 Name : June 2013 1. Given that 4 3 2 2 ax bx c 2 2 3x 2x 5x 4 dxe x 4 x 4, x 2 find the values of the constants a, b, c, d and e. 2. Given that f(x) = ln x, x > 0 sketch
More informationMath 113 Winter 2005 Key
Name Student Number Section Number Instructor Math Winter 005 Key Departmental Final Exam Instructions: The time limit is hours. Problem consists of short answer questions. Problems through are multiple
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 informationEdexcel Core Mathematics 4 Parametric equations.
Edexcel Core Mathematics 4 Parametric equations. Edited by: K V Kumaran kumarmaths.weebly.com 1 Co-ordinate Geometry A parametric equation of a curve is one which does not give the relationship between
More informationPURE MATHEMATICS AM 27
AM SYLLABUS (2020) PURE MATHEMATICS AM 27 SYLLABUS 1 Pure Mathematics AM 27 (Available in September ) Syllabus Paper I(3hrs)+Paper II(3hrs) 1. AIMS To prepare students for further studies in Mathematics
More informationg 0 (x) = u(x)v0 (x) v(x)u 0 (x) u (x) A g 0 ( 1) 1(3) (3) = = 5 4 : c) What can be said about the number and location of solutions to the equation f(
1A (10) 1. Suppose f(x) =x 3x. Use the definition of derivative to find f 0 (x). f 0 f(x + h) f(x) (x) h (x + h) 3(x + h) (x 3x) h x +4xh +h 3x 3h x +3x h 4xh +h 3h h 4x +h 3=4x 3 (9). Find an equation
More information2012 HSC Notes from the Marking Centre Mathematics Extension 2
Contents 01 HSC Notes from the Marking Centre Mathematics Extension Introduction...1 General comments...1 Question 11...1 Question 1... Question 13...3 Question 14...4 Question 15...5 Question 16...6 Introduction
More informationMATHEMATICAL METHODS (CAS) Written examination 1
Victorian Certificate of Education 2010 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words MATHEMATICAL METHODS (CAS) Written examination 1 Friday 5 November 2010 Reading time:
More informationPure Mathematics Paper II
MATHEMATICS TUTORIALS H AL TARXIEN A Level 3 hours Pure Mathematics Question Paper This paper consists of five pages and ten questions. Check to see if any pages are missing. Answer any SEVEN questions.
More informationLeamy Maths Community
Leaving Certificate Examination, 213 Sample paper prepared by Mathematics Project Maths - Phase 2 Paper 1 Higher Level Saturday 18 May Paper written by J.P.F. Charpin and S. King 3 marks http://www.leamymaths.com/
More informationDifferentiation Review, Part 1 (Part 2 follows; there are answers at the end of each part.)
Differentiation Review 1 Name Differentiation Review, Part 1 (Part 2 follows; there are answers at the end of each part.) Derivatives Review: Summary of Rules Each derivative rule is summarized for you
More information(b) g(x) = 4 + 6(x 3) (x 3) 2 (= x x 2 ) M1A1 Note: Accept any alternative form that is correct. Award M1A0 for a substitution of (x + 3).
Paper. Answers. (a) METHOD f (x) q x f () q 6 q 6 f() p + 8 9 5 p METHOD f(x) (x ) + 5 x + 6x q 6, p (b) g(x) + 6(x ) (x ) ( + x x ) Note: Accept any alternative form that is correct. Award A for a substitution
More informationMathematics 1052, Calculus II Exam 1, April 3rd, 2010
Mathematics 5, Calculus II Exam, April 3rd,. (8 points) If an unknown function y satisfies the equation y = x 3 x + 4 with the condition that y()=, then what is y? Solution: We must integrate y against
More informationNotes from the Marking Centre - Mathematics Extension 2
Notes from the Marking Centre - Mathematics Extension Question (a)(i) This question was attempted well, with most candidates able to calculate the modulus and argument of the complex number. neglecting
More informationx+1 e 2t dt. h(x) := Find the equation of the tangent line to y = h(x) at x = 0.
Math Sample final problems Here are some problems that appeared on past Math exams. Note that you will be given a table of Z-scores for the standard normal distribution on the test. Don t forget to have
More informationTEST CODE: MIII (Objective type) 2010 SYLLABUS
TEST CODE: MIII (Objective type) 200 SYLLABUS Algebra Permutations and combinations. Binomial theorem. Theory of equations. Inequalities. Complex numbers and De Moivre s theorem. Elementary set theory.
More informationObjective Mathematics
Multiple choice questions with ONE correct answer : ( Questions No. 1-5 ) 1. If the equation x n = (x + ) is having exactly three distinct real solutions, then exhaustive set of values of 'n' is given
More informationSolutionbank Edexcel AS and A Level Modular Mathematics
Page of Exercise A, Question The curve C, with equation y = x ln x, x > 0, has a stationary point P. Find, in terms of e, the coordinates of P. (7) y = x ln x, x > 0 Differentiate as a product: = x + x
More informationFinal Exam Study Guide
Final Exam Study Guide Final Exam Coverage: Sections 10.1-10.2, 10.4-10.5, 10.7, 11.2-11.4, 12.1-12.6, 13.1-13.2, 13.4-13.5, and 14.1 Sections/topics NOT on the exam: Sections 10.3 (Continuity, it definition
More informationNational Quali cations
National Quali cations AH08 X747/77/ Mathematics THURSDAY, MAY 9:00 AM :00 NOON Total marks 00 Attempt ALL questions. You may use a calculator. Full credit will be given only to solutions which contain
More informationEdexcel past paper questions. Core Mathematics 4. Parametric Equations
Edexcel past paper questions Core Mathematics 4 Parametric Equations Edited by: K V Kumaran Email: kvkumaran@gmail.com C4 Maths Parametric equations Page 1 Co-ordinate Geometry A parametric equation of
More informationFP1 practice papers A to G
FP1 practice papers A to G Paper Reference(s) 6667/01 Edexcel GCE Further Pure Mathematics FP1 Advanced Subsidiary Practice Paper A Time: 1 hour 30 minutes Materials required for examination Mathematical
More information3.4 Conic sections. Such type of curves are called conics, because they arise from different slices through a cone
3.4 Conic sections Next we consider the objects resulting from ax 2 + bxy + cy 2 + + ey + f = 0. Such type of curves are called conics, because they arise from different slices through a cone Circles belong
More informationCAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level FURTHER MATHEMATICS 9231/01 Paper 1 Additional materials: Answer Booklet/Paper Graph paper List of Formulae (MF10) May/June
More informationYou must have: Ruler graduated in centimetres and millimetres, pair of compasses, pen, HB pencil, eraser.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Thursday 12 January 2017 Morning Time: 2 hours Paper Reference AAL30/01
More informationNote: Final Exam is at 10:45 on Tuesday, 5/3/11 (This is the Final Exam time reserved for our labs). From Practice Test I
MA Practice Final Answers in Red 4/8/ and 4/9/ Name Note: Final Exam is at :45 on Tuesday, 5// (This is the Final Exam time reserved for our labs). From Practice Test I Consider the integral 5 x dx. Sketch
More informationSixth Term Examination Papers 9475 MATHEMATICS 3 THURSDAY 22 JUNE 2017
Sixth Term Examination Papers 9475 MATHEMATICS 3 THURSDAY 22 JUNE 207 INSTRUCTIONS TO CANDIDATES AND INFORMATION FOR CANDIDATES six six Calculators are not permitted. Please wait to be told you may begin
More informationphysicsandmathstutor.com Paper Reference Core Mathematics C4 Advanced Level Monday 23 January 2006 Afternoon Time: 1 hour 30 minutes
Centre No. Candidate No. Paper Reference(s) 6666/01 Edexcel GCE Core Mathematics C4 Advanced Level Monday 23 January 2006 Afternoon Time: 1 hour 30 minutes Materials required for examination Mathematical
More informationADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA
GRADE 1 EXAMINATION NOVEMBER 017 ADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA Time: hours 00 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists
More informationSixth Term Examination Papers 9470 MATHEMATICS 2 MONDAY 12 JUNE 2017
Sixth Term Examination Papers 9470 MATHEMATICS 2 MONDAY 12 JUNE 2017 INSTRUCTIONS TO CANDIDATES AND INFORMATION FOR CANDIDATES six six Calculators are not permitted. Please wait to be told you may begin
More information