Public Assessment of the HKDSE Mathematics Examination
|
|
- Catherine Thompson
- 5 years ago
- Views:
Transcription
1 Public Assessment of the HKDSE Mathematics Examination. Exam Format (a) The examination consists of one paper. (b) All questions are conventional questions. (c) The duration is hours and 30 minutes. Section Marks Number of Questions Other Details A 50 8 B Section A consists of short questions while Section B consists of long questions. Knowledge of the subject matter in the Compulsory Part together with the Foundation Part and the Non- Foundation Part of Secondary 3 Mathematics Curriculum is assumed.. Standards-referenced Reporting The HKDSE makes use of standards-referenced reporting, which means candidates levels of performance will be reported with reference to a set of standards as defined by cut scores on the variable or scale for a given subject. The following diagram represents the set of standards for a given subject: Cut scores U Variable/ scale Within the context of the HKDSE there will be five cut scores, which will be used to distinguish five levels of performance ( 5), with 5 being the highest. The Level 5 candidates with the best performance will have their results annotated with the symbols and the next top group with the symbol. A performance below the threshold cut score for Level will be labelled as Unclassified (U). II
2 Exam Strategies A. Time Allocation Section Suggested Time Allocation Approximate Time per Question A 80 minutes 6 0 minutes B 60 minutes 0 minutes In general, spend 7 minutes for every 5 marks. Allow 0 minutes for final checking. B. Answering Skills Skip the questions that you do not have confidence on. Go back to the skipped questions after you have finished the others. Show your formulas and steps rather than just writing down the answers. In case you do not get the correct answer, you can get marks for the correct methods used. Make sure your numerical answers are either exact or correct to 4 decimal places, unless otherwise specified. Give intermediate results correct to more significant figures or decimal places to avoid accumulated errors in the final answers. Make sure you give a unit, if any, to each answer. In answering questions involving curve sketching, Always use a pencil. Label significant items like graph titles and axis names. Show rough figures of the correct shapes and intercepts. In proving mathematical results, you should put down your workings in details. Pay attention to question wordings. Write down You can just write down the answer without showing your working steps. Hence You have to use the results obtained earlier to get the answer. III
3 Sample Paper Analysis The analysis is based on the Mathematics (Extended Part) Module sample paper issued by the Hong Kong Examination and Assessment Authority in 009. The paper consists of Section A (0 questions) and Section B (4 questions). Section A Section B. Binomial Theorem / /. Mathematical Induction 0(a) / 3. More about Trigonometric Functions 5, 0(b) / 4. Limits / 5. Differentiation / (a), (b), (c) 6. Applications of Differentiation, 6 / 7. Indefinite Integration 3, 4, 8(a) / 8. Definite Integration / 3 9. Applications of Definite Integration 8(b) (d) 0. Determinants / /. Matrices 0(a), 0(b). Systems of Linear Equations 7 / 3. Vectors / 4 4. Applications of Vectors 9 / IV
4 Useful Formulas. Binomial Theorem (a) Summation Notation n T ( i) T ( ) + T ( ) T ( n) i (b) Binomial Theorem (i) ( a + b) n n n n n n n 0 + C r a r b n n Cn b n C r a b r 0 C a + C a b + C a b +... n n - r r (ii) General term Cr a b, where n and r are integers.. More about Trigonometric Functions (a) (i) p rad. 80 (ii) Arc length rq, where q is measured in radians (iii) Area of a sector r θ rs, where s is the arc length. (b) Trigonometric Functions of General Angles Let P(x, y) be a point on the terminal side of an angle of rotation q. Then, sinθ y r cscθ r y cosθ x r secθ r x where r x + y tanθ y x cotθ x y, (c) Relationship between Trigonometric Functions (i) cscθ sinθ (iii) cotθ tanθ (ii) secθ cosθ sinθ (iv) tanθ cosθ cosθ (v) cotθ (vi) sin θ + cos θ sinθ (vii) + tan θ sec θ (viii) + cot θ csc θ (d) Compound Angle Formulas (i) sin(a + B) sin Acos B + cos Asin B (ii) sin(a - B) sin Acos B - cos Asin B (iii) cos(a + B) cos Acos B - sin Asin B (iv) cos(a - B) cos Acos B + sin Asin B tan A + tan B (v) tan( A + B) tan A tan B tan A tan B (vi) tan( A B) + tan A tan B (e) Double Angle Formulas (i) sin A sin Acos A (ii) cos A cos A sin A cos A sin A tan A (iii) tan A tan A (f) Product-to-sum Formulas: (i) sin A cos B [sin( A + B) + sin( A B)] (ii) cos Asin B [sin( A + B) sin( A B)] (iii) cos A cos B [cos( A + B) + cos( A B)] (iv) sin Asin B [cos( A + B) cos( A B)] (g) Sum-to-product Formulas: x + y x y (i) sin x + sin y sin cos x + y x y (ii) sin x sin y cos sin x + y x y (iii) cos x + cos y cos cos x + y x y (iv) cos x cos y sin sin 3. Limits (a) Limit of a Function Suppose lim f ( x ) and lim g ( x ) exist. x a x a (i) lim k k, k is a constant. x a (ii) lim kf ( x) k lim f ( x), k is a constant. x a x a (iii) lim[ f ( x) ± g( x)] lim f ( x) ± lim g( x) x a x a x a (iv) lim f ( x) g( x) lim f ( x) lim g( x) x a x a x a f (v) lim ( x ) lim f ( x) x a x a g( x) lim g( x) x a V
5 FORMULAS FOR REFERENCE A + B A B sin (A ± B) sin A cos B ± cos A sin B sin A + sin B sin cos cos (A ± B) cos A cos B ± A + B A B sin A sin B sin A sin B cos sin tan (A ± B) tan A ± tan B A + B A B cos A + cos B cos cos tan A tan B A + B A B sin A cos B sin (A + B) + sin (A - B) cos A cos B sin sin cos A cos B cos (A + B) + cos (A - B) sin A sin B cos (A - B) - cos (A + B) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Section A (50 marks) 3. Find d dx ( x + x) from first principles. (4 marks). Given that e x + ln y + 7xy, find dy dx when x 0 and y. (4 marks) 3. The slope at any point (x, y) of a curve is given by dy dx tangent to the curve, find the equation of the curve. 4 x ( x + ). If the straight line y 6 is a (4 marks) 4. If n is a positive integer and the coefficient of x in the expansion of ( x ) n + ( + x) n is 04, find the value(s) of n. (4 marks) M MOCK - 0 Hong Kong Educational Publishing Co.
6 Section B (50 marks). (a) Prove, by mathematical induction, that n(n + ) is divisible by 3 for all positive integers n. (3 marks) (b) Hence prove, by mathematical induction, that (n - n)(n - n + 4) is divisible by for all positive integers n >. (5 marks). Figure 3 In Figure 3, OPQ is an equilateral triangle with OP. M is the mid-point of PQ. A divides OP in the ratio : and B divides OQ in the ratio :. Let OP and OQ be p and q respectively. (a) Find p q. ( marks) (b) Hence find AB and express your answer in surd form if necessary. (3 marks) (c) By considering AB OM, find BCM and determine whether BCMQ is a cyclic quadrilateral. (3 marks) Go on to the next page M MOCK Hong Kong Educational Publishing Co.
7 Mathematics: Mock Exam Papers Extended Part Module Solution Guide (a) M M MM \ M 3M A M A (b) M ( M 3I) ( M 3I) M I (by (a)) M ( M 3I) ( M 3I) M I M ( M 3I) M M A (6) In (a), we have M 3-3M I. If we can rewrite it in the form MN I or NM I, then the matrix N should be the inverse of M. 9. Let (p, q) be the coordinates of A. The slope of the tangent to C dy : 3x + 4 dx dy 3p + 4 dx ( p, q) The equation of the tangent: y q ( 3p + 4)( x p) 3 y ( 3p + 4) x 3p 4 p + q...() Since the x-intercept of the tangent is, the tangent passes through (, 0). Substituting (, 0) into (), 0 3p + 4-3p 3-4p + q M i.e., q 3p 3-3p + 4p () Since A lies on C, q p 3 + 4p...(3) M () - (3): ( 3p 3p + 4 p 4) ( p + 4 p) 3 p 3p 4 0 ( p )( p + p + ) 0 M p or p + p + 0 (rejected) Substituting p into (3), q 3 + 4() 6 \ A (, 6 ) A (6) A M We can first show that p - is a factor of p 3-3p - 4 by using the factor theorem, then factorize p 3-3p - 4 by long division. 5 0 Hong Kong Educational Publishing Co.
8 Mock Exam 0 Alternative Solution Let the line x a cuts the x-axis at D. Area Area of sector OAB - Area of DOAD ( ) ( AOB) ( OA)( OD)sin AOB π ( ) 4 π ( ) sin 4 π 4 ( π ) 8 M M + A A (7) 0. (a) OM : MR : \ OM OR 3 + a b 3 a + b A 3 3 \ The candidate just gives a statement related to an undefined variable R, which is very confusing. Candidates should clearly define all variables when using mathematical expressions to formulate an statement. Let AM : MP : r and BM : MQ : s. Considering DOAP, ( )( OP) + ( r)( OA) OM + r b + ra + r Considering DOBQ, ( )( OQ) + ( s)( OB) OM + s a + sb + s A The candidate can use the correct method to find the ratio AM : MP with details and uses the section formula to find OM. Use the ratios AM : MP and BM : MQ to find OM. \ b + ra a + sb + r + s r s a + b a + b + r ( + r) ( + s) + s M 0 Hong Kong Educational Publishing Co.
ADDITIONAL MATHEMATICS
005-CE A MATH HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 005 ADDITIONAL MATHEMATICS :00 pm 5:0 pm (½ hours) This paper must be answered in English 1. Answer ALL questions in Section A and any FOUR
More informationMath Section 4.3 Unit Circle Trigonometry
Math 10 - Section 4. Unit Circle Trigonometry An angle is in standard position if its vertex is at the origin and its initial side is along the positive x axis. Positive angles are measured counterclockwise
More informationMATH 100 REVIEW PACKAGE
SCHOOL OF UNIVERSITY ARTS AND SCIENCES MATH 00 REVIEW PACKAGE Gearing up for calculus and preparing for the Assessment Test that everybody writes on at. You are strongly encouraged not to use a calculator
More informationThese items need to be included in the notebook. Follow the order listed.
* Use the provided sheets. * This notebook should be your best written work. Quality counts in this project. Proper notation and terminology is important. We will follow the order used in class. Anyone
More informationSection 6.2 Trigonometric Functions: Unit Circle Approach
Section. Trigonometric Functions: Unit Circle Approach The unit circle is a circle of radius centered at the origin. If we have an angle in standard position superimposed on the unit circle, the terminal
More information(c) cos Arctan ( 3) ( ) PRECALCULUS ADVANCED REVIEW FOR FINAL FIRST SEMESTER
PRECALCULUS ADVANCED REVIEW FOR FINAL FIRST SEMESTER Work the following on notebook paper ecept for the graphs. Do not use our calculator unless the problem tells ou to use it. Give three decimal places
More informationPublic Assessment of the HKDSE Mathematics Examination
Public Assessment of the HKDSE Mathematics Examination. Public Assessment The mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in the Compulsory Part is
More informationPublic Assessment of the HKDSE Mathematics Examination
Public Assessment of the HKDSE Mathematics Examination. Public Assessment The mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in the Compulsory Part is
More informationMA40S Pre-calculus UNIT C Trigonometric Identities CLASS NOTES Analyze Trigonometric Identities Graphically and Verify them Algebraically
1 MA40S Pre-calculus UNIT C Trigonometric Identities CLASS NOTES Analyze Trigonometric Identities Graphically and Verify them Algebraically Definition Trigonometric identity Investigate 1. Using the diagram
More information( ) ( ) ( ) ( ) MATHEMATICS Precalculus Martin Huard Fall 2007 Semester Review. 1. Simplify each expression. 4a b c. x y. 18x. x 2x.
MATHEMATICS 0-009-0 Precalculus Martin Huard Fall 007. Simplif each epression. a) 8 8 g) ( ) ( j) m) a b c a b 8 8 8 n f) t t ) h) + + + + k) + + + n) + + + + + ( ) i) + n 8 + 9 z + l) 8 o) ( + ) ( + )
More informationMATH 127 SAMPLE FINAL EXAM I II III TOTAL
MATH 17 SAMPLE FINAL EXAM Name: Section: Do not write on this page below this line Part I II III TOTAL Score Part I. Multiple choice answer exercises with exactly one correct answer. Each correct answer
More informationMATH 130 FINAL REVIEW
MATH 130 FINAL REVIEW Problems 1 5 refer to triangle ABC, with C=90º. Solve for the missing information. 1. A = 40, c = 36m. B = 53 30', b = 75mm 3. a = 91 ft, b = 85 ft 4. B = 1, c = 4. ft 5. A = 66 54',
More informationAP Calculus Summer Packet
AP Calculus Summer Packet Writing The Equation Of A Line Example: Find the equation of a line that passes through ( 1, 2) and (5, 7). ü Things to remember: Slope formula, point-slope form, slopeintercept
More informationChapter 5: Trigonometric Functions of Angles Homework Solutions
Chapter : Trigonometric Functions of Angles Homework Solutions Section.1 1. D = ( ( 1)) + ( ( )) = + 8 = 100 = 10. D + ( ( )) + ( ( )) = + = 1. (x + ) + (y ) =. (x ) + (y + 7) = r To find the radius, we
More informationCandidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.
Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;
More information( )( ) Algebra 136 Semester 2 Review. ( ) 6. g( h( x) ( ) Name. In 1-6, use the functions below to find the solutions.
Algebra 136 Semester Review In 1-6, use the functions below to find the solutions. Name f ( x) = 3x x + g( x) = x 3 h( x) = x + 3 1. ( f + h) ( x). ( h g) ( x) 3. h x g ( ) 4. ( gh) ( x). f g( x) ( ) 6.
More informationMath Worksheet 1 SHOW ALL OF YOUR WORK! f(x) = (x a) 2 + b. = x 2 + 6x + ( 6 2 )2 ( 6 2 )2 + 7 = (x 2 + 6x + 9) = (x + 3) 2 2
Names Date. Consider the function Math 0550 Worksheet SHOW ALL OF YOUR WORK! f() = + 6 + 7 (a) Complete the square and write the function in the form f() = ( a) + b. f() = + 6 + 7 = + 6 + ( 6 ) ( 6 ) +
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More informationChapter 3. Radian Measure and Circular Functions. Copyright 2005 Pearson Education, Inc.
Chapter 3 Radian Measure and Circular Functions Copyright 2005 Pearson Education, Inc. 3.1 Radian Measure Copyright 2005 Pearson Education, Inc. Measuring Angles Thus far we have measured angles in degrees
More informationMock Exam 3. 1 Hong Kong Educational Publishing Company. Section A. 1. Reference: HKDSE Math M Q1 (a) (1 + 2x) 2 (1 - x) n
Mock Eam Mock Eam Section A. Reference: HKDSE Math M 0 Q (a) ( + ) ( - ) n nn ( ) ( + + ) n + + Coefficient of - n - n -7 n (b) Coefficient of nn ( - ) - n + (- ) - () + (). Reference: HKDSE Math M PP
More informationDifferential Equaitons Equations
Welcome to Multivariable Calculus / Dierential Equaitons Equations The Attached Packet is or all students who are planning to take Multibariable Multivariable Calculus/ Dierential Equations in the all.
More informationName DIRECTIONS: PLEASE COMPLET E ON A SEPARATE SHEET OF PAPER. USE THE ANSWER KEY PROVIDED TO CORRECT YOUR WORK. THIS WILL BE COLLECTED!!!
FINAL EXAM REVIEW 0 PRECALCULUS Name DIRECTIONS: PLEASE COMPLET E ON A SEPARATE SHEET OF PAPER. USE THE ANSWER KEY PROVIDED TO CORRECT YOUR WORK. THIS WILL BE COLLECTED!!! State the domain of the rational
More informationLesson 33 - Trigonometric Identities. Pre-Calculus
Lesson 33 - Trigonometric Identities Pre-Calculus 1 (A) Review of Equations An equation is an algebraic statement that is true for only several values of the variable The linear equation 5 = 2x 3 is only
More informationCore Mathematics C1 (AS) Unit C1
Core Mathematics C1 (AS) Unit C1 Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation. Graphs of functions; sketching curves defined by simple equations.
More informationReview of Topics in Algebra and Pre-Calculus I. Introduction to Functions function Characteristics of a function from set A to set B
Review of Topics in Algebra and Pre-Calculus I. Introduction to Functions A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in set B.
More informationPROVINCIAL EXAMINATION MINISTRY OF EDUCATION, SKILLS AND TRAINING MATHEMATICS 12 GENERAL INSTRUCTIONS
INSERT STUDENT I.D. NUMBER (PEN) STICKER IN THIS SPACE JANUARY 1997 PROVINCIAL EXAMINATION MINISTRY OF EDUCATION, SKILLS AND TRAINING MATHEMATICS 12 GENERAL INSTRUCTIONS 1. Insert the stickers with your
More informationTrigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters
Trigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters α( alpha), β ( beta), θ ( theta) as well as upper case letters A,B,
More informationTHE COMPOUND ANGLE IDENTITIES
TRIGONOMETRY THE COMPOUND ANGLE IDENTITIES Question 1 Prove the validity of each of the following trigonometric identities. a) sin x + cos x 4 4 b) cos x + + 3 sin x + 2cos x 3 3 c) cos 2x + + cos 2x cos
More information2.Draw each angle in standard position. Name the quadrant in which the angle lies. 2. Which point(s) lies on the unit circle? Explain how you know.
Chapter Review Section.1 Extra Practice 1.Draw each angle in standard position. In what quadrant does each angle lie? a) 1 b) 70 c) 110 d) 00.Draw each angle in standard position. Name the quadrant in
More informationUsing the Definitions of the Trigonometric Functions
1.4 Using the Definitions of the Trigonometric Functions Reciprocal Identities Signs and Ranges of Function Values Pythagorean Identities Quotient Identities February 1, 2013 Mrs. Poland Objectives Objective
More informationReview for Cumulative Test 2
Review for Cumulative Test We will have our second course-wide cumulative test on Tuesday February 9 th or Wednesday February 10 th, covering from the beginning of the course up to section 4.3 in our textbook.
More informationD. 6. Correct to the nearest tenth, the perimeter of the shaded portion of the rectangle is:
Trigonometry PART 1 Machine Scored Answers are on the back page Full, worked out solutions can be found at MATH 0-1 PRACTICE EXAM 1. An angle in standard position θ has reference angle of 0 with sinθ
More information*n23494b0220* C3 past-paper questions on trigonometry. 1. (a) Given that sin 2 θ + cos 2 θ 1, show that 1 + tan 2 θ sec 2 θ. (2)
C3 past-paper questions on trigonometry physicsandmathstutor.com June 005 1. (a) Given that sin θ + cos θ 1, show that 1 + tan θ sec θ. (b) Solve, for 0 θ < 360, the equation tan θ + secθ = 1, giving your
More informationChapter 1. Functions 1.3. Trigonometric Functions
1.3 Trigonometric Functions 1 Chapter 1. Functions 1.3. Trigonometric Functions Definition. The number of radians in the central angle A CB within a circle of radius r is defined as the number of radius
More informationUnit 3 Trigonometry Note Package. Name:
MAT40S Unit 3 Trigonometry Mr. Morris Lesson Unit 3 Trigonometry Note Package Homework 1: Converting and Arc Extra Practice Sheet 1 Length 2: Unit Circle and Angles Extra Practice Sheet 2 3: Determining
More informationFind: sinθ. Name: Date:
Name: Date: 1. Find the exact value of the given trigonometric function of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: sinθ c a θ a a =
More informationPractice Problems for MTH 112 Exam 2 Prof. Townsend Fall 2013
Practice Problems for MTH 11 Exam Prof. Townsend Fall 013 The problem list is similar to problems found on the indicated pages. means I checked my work on my TI-Nspire software Pages 04-05 Combine the
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 informationFox Lane High School Department of Mathematics
Fo Lane High School Department of Mathematics June 08 Hello Future AP Calculus AB Student! This is the summer assignment for all students taking AP Calculus AB net school year. It contains a set of problems
More informationADDITIONAL MATHEMATICS
ADDITIONAL MATHEMATICS GCE NORMAL ACADEMIC LEVEL (016) (Syllabus 4044) CONTENTS Page INTRODUCTION AIMS ASSESSMENT OBJECTIVES SCHEME OF ASSESSMENT 3 USE OF CALCULATORS 3 SUBJECT CONTENT 4 MATHEMATICAL FORMULAE
More information1) SSS 2) SAS 3) ASA 4) AAS Never: SSA and AAA Triangles with no right angles.
NOTES 6 & 7: TRIGONOMETRIC FUNCTIONS OF ANGLES AND OF REAL NUMBERS Name: Date: Mrs. Nguyen s Initial: LESSON 6.4 THE LAW OF SINES Review: Shortcuts to prove triangles congruent Definition of Oblique Triangles
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *7292744436* ADDITIONAL MATHEMATICS 0606/23 Paper 2 May/June 2017 2 hours Candidates answer on the
More informationhttps://sites.google.com/site/dhseisen/
Name: Calculus AP - Summer Assignment 2017 All questions and concerns related to this assignment should be directed to Ms. Eisen on or before Wednesday, June 21, 2017. If any concerns should arise over
More informationLesson 22 - Trigonometric Identities
POP QUIZ Lesson - Trigonometric Identities IB Math HL () Solve 5 = x 3 () Solve 0 = x x 6 (3) Solve = /x (4) Solve 4 = x (5) Solve sin(θ) = (6) Solve x x x x (6) Solve x + = (x + ) (7) Solve 4(x ) = (x
More informationHonors Algebra 2 Chapter 14 Page 1
Section. (Introduction) Graphs of Trig Functions Objectives:. To graph basic trig functions using t-bar method. A. Sine and Cosecant. y = sinθ y y y y 0 --- --- 80 --- --- 30 0 0 300 5 35 5 35 60 50 0
More informationU6 A Level Maths PURE MOCK Tuesday 5 th February 2019 PM Time: 2 hours Total Marks: 100
Full name: Teacher name: U6 A Level Maths PURE MOCK Tuesday 5 th February 2019 PM Time: 2 hours Total Marks: 100 You must have: Mathematical Formulae and Statistical Tables, Calculator Instructions Use
More informationAlgebra 2 Honors Final Exam StudyGuide
Name: Algebra 2 Honors Final Exam StudyGuide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Simplify. 2. 3. 4. Asume that all absolute value symbols are
More informationMath Worksheet 1. f(x) = (x a) 2 + b. = x 2 6x = (x 2 6x + 9) = (x 3) 2 1
Names Date Math 00 Worksheet. Consider the function f(x) = x 6x + 8 (a) Complete the square and write the function in the form f(x) = (x a) + b. f(x) = x 6x + 8 ( ) ( ) 6 6 = x 6x + + 8 = (x 6x + 9) 9
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
PAPA CAMBRIDGE Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 1 0 4 5 3 8 9 2 1 * ADDITIONAL MATHEMATICS 0606/23 Paper 2 May/June 2014 2 hours
More informationA-Level Mathematics TRIGONOMETRY. G. David Boswell - R2S Explore 2019
A-Level Mathematics TRIGONOMETRY G. David Boswell - R2S Explore 2019 1. Graphs the functions sin kx, cos kx, tan kx, where k R; In these forms, the value of k determines the periodicity of the trig functions.
More informationPhysicsAndMathsTutor.com
PhysicsAndMathsTutor.com physicsandmathstutor.com June 2005 1. (a) Given that sin 2 θ + cos 2 θ 1, show that 1 + tan 2 θ sec 2 θ. (b) Solve, for 0 θ < 360, the equation 2 tan 2 θ + secθ = 1, giving your
More informationDRAFT. Appendix H. Grade 12 Prototype Examination. Pre-calculus 30. Course Code For more information, see the Table of Specifications.
Grade 1 Prototype Examination Pre-calculus 30 Course Code 846 Barcode Number DRAFT Appendix H For more information, see the Table of Specifications. Month Day Date of Birth November 013 AMPLE Pre-calculus
More informationCore Mathematics C34
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Monday 16 June 2014 Morning Time: 2 hours 30 minutes You
More informationSect 7.4 Trigonometric Functions of Any Angles
Sect 7.4 Trigonometric Functions of Any Angles Objective #: Extending the definition to find the trigonometric function of any angle. Before we can extend the definition our trigonometric functions, we
More informationCambridge 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
More informationFrom now on angles will be drawn with their vertex at the. The angle s initial ray will be along the positive. Think of the angle s
Fry Texas A&M University!! Math 150!! Chapter 8!! Fall 2014! 1 Chapter 8A Angles and Circles From now on angles will be drawn with their vertex at the The angle s initial ray will be along the positive.
More informationTrigonometry Final Exam Review
Name Period Trigonometry Final Exam Review 2014-2015 CHAPTER 2 RIGHT TRIANGLES 8 1. Given sin θ = and θ terminates in quadrant III, find the following: 17 a) cos θ b) tan θ c) sec θ d) csc θ 2. Use a calculator
More informationOutline schemes of work A-level Mathematics 6360
Outline schemes of work A-level Mathematics 6360 Version.0, Autumn 013 Introduction These outline schemes of work are intended to help teachers plan and implement the teaching of the AQA A-level Mathematics
More informationMonroe Township High School Mathematics Department
To: AP Calculus AB Re: Summer Project 017 Date: June 017 Monroe Township High School Mathematics Department To help begin your study of Calculus, you will be required to complete a review project this
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 informationC3 Exam Workshop 2. Workbook. 1. (a) Express 7 cos x 24 sin x in the form R cos (x + α) where R > 0 and 0 < α < 2
C3 Exam Workshop 2 Workbook 1. (a) Express 7 cos x 24 sin x in the form R cos (x + α) where R > 0 and 0 < α < 2 π. Give the value of α to 3 decimal places. (b) Hence write down the minimum value of 7 cos
More informationMath 132 Exam 3 Fall 2016
Math 3 Exam 3 Fall 06 multiple choice questions worth points each. hand graded questions worth and 3 points each. Exam covers sections.-.6: Sequences, Series, Integral, Comparison, Alternating, Absolute
More informationYou must have: Mathematical Formulae and Statistical Tables, calculator
Write your name here Surname Other names Pearson Edexcel Level 3 GCE Centre Number Mathematics Advanced Paper 2: Pure Mathematics 2 Candidate Number Specimen Paper Time: 2 hours You must have: Mathematical
More information2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2
29 April PreCalculus Final Review 1. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line: y = 3x + 13 2. Determine the domain of the function. Verify your result with
More informationMTH 122: Section 204. Plane Trigonometry. Test 1
MTH 122: Section 204. Plane Trigonometry. Test 1 Section A: No use of calculator is allowed. Show your work and clearly identify your answer. 1. a). Complete the following table. α 0 π/6 π/4 π/3 π/2 π
More informationLearning Objectives These show clearly the purpose and extent of coverage for each topic.
Preface This book is prepared for students embarking on the study of Additional Mathematics. Topical Approach Examinable topics for Upper Secondary Mathematics are discussed in detail so students can focus
More informationContact hour per week: 04 Contact hour per Semester: 64 ALGEBRA 1 DETERMINANTS 2 2 MATRICES 4 3 BINOMIAL THEOREM 3 4 LOGARITHMS 2 5 VECTOR ALGEBRA 6
BOARD OF TECHNICAL EXAMINATION KARNATAKA SUBJECT: APPLIED MATHEMATICS I For I- semester DIPLOMA COURSES OF ALL BRANCHES Contact hour per week: 04 Contact hour per Semester: 64 UNIT NO. CHAPTER TITLE CONTACT
More informationTrigonometric Ratios. θ + k 360
Trigonometric Ratios These notes are intended as a summary of section 6.1 (p. 466 474) in your workbook. You should also read the section for more complete explanations and additional examples. Coterminal
More informationCalculus First Semester Review Name: Section: Evaluate the function: (g o f )( 2) f (x + h) f (x) h. m(x + h) m(x)
Evaluate the function: c. (g o f )(x + 2) d. ( f ( f (x)) 1. f x = 4x! 2 a. f( 2) b. f(x 1) c. f (x + h) f (x) h 4. g x = 3x! + 1 Find g!! (x) 5. p x = 4x! + 2 Find p!! (x) 2. m x = 3x! + 2x 1 m(x + h)
More informationAlgebraic. techniques1
techniques Algebraic An electrician, a bank worker, a plumber and so on all have tools of their trade. Without these tools, and a good working knowledge of how to use them, it would be impossible for them
More informationCore Mathematics C12
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Tuesday 10 January 2017 Morning Time: 2 hours
More informationCore A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document
Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Background knowledge: (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers.
More informationNATIONAL QUALIFICATIONS
Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -
More informationCore Mathematics 2 Unit C2 AS
Core Mathematics 2 Unit C2 AS compulsory unit for GCE AS and GCE Mathematics, GCE AS and GCE Pure Mathematics C2.1 Unit description Algebra and functions; coordinate geometry in the (, y) plane; sequences
More informationChapter 5 Analytic Trigonometry
Chapter 5 Analytic Trigonometry Overview: 5.1 Using Fundamental Identities 5.2 Verifying Trigonometric Identities 5.3 Solving Trig Equations 5.4 Sum and Difference Formulas 5.5 Multiple-Angle and Product-to-sum
More informationSection 6.1 Angles and Radian Measure Review If you measured the distance around a circle in terms of its radius, what is the unit of measure?
Section 6.1 Angles and Radian Measure Review If you measured the distance around a circle in terms of its radius, what is the unit of measure? In relationship to a circle, if I go half way around the edge
More informationSec 4 Maths. SET A PAPER 2 Question
S4 Maths Set A Paper Question Sec 4 Maths Exam papers with worked solutions SET A PAPER Question Compiled by THE MATHS CAFE 1 P a g e Answer all the questions S4 Maths Set A Paper Question Write in dark
More informationAS and A-level Mathematics Teaching Guidance
ΑΒ AS and A-level Mathematics Teaching Guidance AS 7356 and A-level 7357 For teaching from September 017 For AS and A-level exams from June 018 Version 1.0, May 017 Our specification is published on our
More informationFundamental Trigonometric Identities
Fundamental Trigonometric Identities MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: recognize and write the fundamental trigonometric
More informationOdd Answers: Chapter Eight Contemporary Calculus 1 { ( 3+2 } = lim { 1. { 2. arctan(a) 2. arctan(3) } = 2( π 2 ) 2. arctan(3)
Odd Answers: Chapter Eight Contemporary Calculus PROBLEM ANSWERS Chapter Eight Section 8.. lim { A 0 } lim { ( A ) ( 00 ) } lim { 00 A } 00.. lim {. arctan() A } lim {. arctan(a). arctan() } ( π ). arctan()
More informationMath 1501 Calc I Summer 2015 QUP SOUP w/ GTcourses
Math 1501 Calc I Summer 2015 QUP SOUP w/ GTcourses Instructor: Sal Barone School of Mathematics Georgia Tech May 22, 2015 (updated May 22, 2015) Covered sections: 3.3 & 3.5 Exam 1 (Ch.1 - Ch.3) Thursday,
More informationAP CALCULUS AB SECTION I, Part A Time 55 Minutes Number of questions 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM
AP CALCULUS AB SECTION I, Part A Time 55 Minutes Number of questions 28 Time Began: Time Ended: A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM Directions: Solve each of the following problems, using
More informationName: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination 3 Secondary 4
Name: Inde Number: Class: CATHOLIC HIGH SCHOOL Preliminary Eamination 3 Secondary 4 ADDITIONAL MATHEMATICS 4047/1 READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work
More informationTrigonometric Identities Exam Questions
Trigonometric Identities Exam Questions Name: ANSWERS January 01 January 017 Multiple Choice 1. Simplify the following expression: cos x 1 cot x a. sin x b. cos x c. cot x d. sec x. Identify a non-permissible
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 information(c) log 1 4 (d) log 3 3. Use logarithm properties for expanding to rewrite the expression in
AP Calculus AB Summer Assignment for 2017-2018 School Year Mrs. Brennan In order to be prepared for next year and be ready to move on to new work, you must have skills required to do these problems with
More informationMath 370 Semester Review Name
Math 370 Semester Review Name These problems will give you an idea of what may be included on the final exam. Don't worry! The final exam will not be this long! 1) State the following theorems: (a) Remainder
More informationCore Mathematics C4. You must have: Mathematical Formulae and Statistical Tables (Pink)
Write your name here Surname Other names Pearson Edexcel GCE Centre Number Core Mathematics C4 Advanced Candidate Number Friday 24 June 2016 Morning Time: 1 hour 30 minutes Paper Reference 6666/01 You
More informationSec 4 Maths SET D PAPER 2
S4MA Set D Paper Sec 4 Maths Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e Answer all questions. Write your answers and working on the separate Answer Paper provided.
More informationCore Mathematics C4. You must have: Mathematical Formulae and Statistical Tables (Pink)
Write your name here Surname Other names Pearson Edexcel GCE Centre Number Core Mathematics C4 Advanced Candidate Number Friday 23 June 2017 Morning Time: 1 hour 30 minutes Paper Reference 6666/01 You
More information0 where A is the amount present initially. Estimate, to the nearest year, the
MATH 65 Common Final Exam Review SPRING 04. Cindy will require $9,000 in 4 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it
More informationPhysicsAndMathsTutor.com. Core Mathematics C4. You must have: Mathematical Formulae and Statistical Tables (Pink)
Write your name here Surname Other names Pearson Edexcel GCE Centre Number Core Mathematics C4 Advanced Candidate Number Friday 24 June 2016 Morning Time: 1 hour 30 minutes Paper Reference 6666/01 You
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 informationADDITIONAL MATHEMATICS
ADDITIONAL MATHEMATICS GCE Ordinary Level (Syllabus 4018) CONTENTS Page NOTES 1 GCE ORDINARY LEVEL ADDITIONAL MATHEMATICS 4018 2 MATHEMATICAL NOTATION 7 4018 ADDITIONAL MATHEMATICS O LEVEL (2009) NOTES
More informationName Date Period. Calculater Permitted MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PreAP Precalculus Spring Final Exam Review Name Date Period Calculater Permitted MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression.
More informationGeometry The Unit Circle
Geometry The Unit Circle Day Date Class Homework F 3/10 N: Area & Circumference M 3/13 Trig Test T 3/14 N: Sketching Angles (Degrees) WKS: Angles (Degrees) W 3/15 N: Arc Length & Converting Measures WKS:
More informationWORKBOOK. MATH 30. PRE-CALCULUS MATHEMATICS.
WORKBOOK. MATH 30. PRE-CALCULUS MATHEMATICS. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE Contributor: U.N.Iyer Department of Mathematics and Computer Science, CP 315, Bronx Community College, University
More informationMA 110 Algebra and Trigonometry for Calculus Spring 2017 Exam 3 Tuesday, 11 April Multiple Choice Answers EXAMPLE A B C D E.
MA 110 Algebra and Trigonometry for Calculus Spring 017 Exam 3 Tuesday, 11 April 017 Multiple Choice Answers EXAMPLE A B C D E Question Name: Section: Last digits of student ID #: This exam has twelve
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/02 Paper 2 Examination from 2013 SPECIMEN PAPER 2 hours Candidates
More informationMth 133 Trigonometry Review Problems for the Final Examination
Mth 1 Trigonometry Review Problems for the Final Examination Thomas W. Judson Stephen F. Austin State University Fall 017 Final Exam Details The final exam for MTH 1 will is comprehensive and will cover
More information