Wednesday, 12 April 2017

OXFORD MATHEMATICS TUTORING - UNDER DEVELOPMENT

THIS MATERIAL IS UNDER DEVELOPMENT, PL. IGNORE AT THIS STAGE AND POINT

OXFORD MATHEMATICS

MATHEMATICS I. Consultant, Dr. Yeap Ban Har; Authors: Teh Keng Seng  * Loh Cheng Yee

 

CONTENTS

1. Factors and Multiples 

    Factors and Multiples                                                                                                   Prime Numbers and Composite Numbers                                                              Index Notations Highest Common Factors (HCF)                                                    Least Common Multiple (LCM)                                                        Squares and Square Roots                                                                                                     Cubes and Cubes Roots                                                                        Mental Estimation                                                                                                   The Use of Calculators                                                                                        Summary                                                                                                             Review Examples 1                                                                                      Review Questions 1

Read: http://www.wikihow.com/Factor-a-Number

http://www.basic-mathematics.com/what-is-factoring.html https://www.reference.com/math/factoring-math-c304f5269f44762a https://www.mathsisfun.com/divisibility-rules.html http://www.answers.com/Q/What_are_the_divisibility_rules_for_1-13 https://brilliant.org/wiki/divisibility-rules/

2. Integers

   Negative Numbers                                                                               Integers                                                                                                           The Number Line                                                                                           Absolute Value of an Integers                                                                Addition of Integers                                                                                   Subtraction of Integers                                                                        Multiplication of Integers                                                                                          Division of Integers                                                                                       Rules for Operating on Integers                                                                       Summary                                                                                                         Review Examples 2                                                                            Review Questions 2

Read: https://www.google.com/search?rct=j&q=integers#dobs=integers https://en.wikipedia.org/wiki/Integer https://www.khanacademy.org/math/in-sixth-grade-math/integers-india https://www.khanacademy.org/math/in-sixth-grade-math/integers-india http://whatis.techtarget.com/definition/integer

 

3. Rational Numbers

    Rational Numbers                                                                                 Ordering of Rational Numbers                                                                         Addition and Subtraction of Rational Numbers                                                       Multiplication and Division of Rational Numbers                                          Arithmetical Operations on Rational Numbers                                               Problem Solving Involving Rational Numbers                                              Terminating and Recurring Decimals                                                                              Use of Calculators on Real Numbers                                                                Summary                                                                                                         Review Examples 3                                                                            Review Questions 3

Read: https://www.google.com/search?rct=j&q=rational%20numbers https://en.wikipedia.org/wiki/Rational_number https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers/alg-1-irrational-numbers/v/introduction-to-rational-and-irrational-numbers              http://www.mathwarehouse.com/arithmetic/numbers/rational-and-irrational-numbers-with-examples.php https://www.google.com/search?rct=j&q=rational%20numbers#q=is+0+a+rational+number&*   https://www.google.com/search?rct=j&q=rational%20numbers#q=irrational+number&*

4. Estimation and Approximation

    Estimation and Rounding                                                                             Approximation in Measurement and Accuracy                                                Rounding Off a number to a given Number of Decimal Places     Accuracy and Significant Figures                                                        Rounding a Number to Given Number of Significant Figures                           Rounding and Truncation Errors                                                                  Summary                                                                                                         Review Examples 4                                                                            Review Questions 4  

Read: https://www.google.com/search?rct=j&q=estimation%20and%20approximation https://www.skillsyouneed.com/num/estimation.html https://www.youtube.com/watch?v=woth8j3XbWw http://www.cimt.org.uk/projects/mepres/book9/bk9_14.pdf https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=difference+between+approximation+and+estimation&*

5. Fundamental Algebra

   Notation in Algebra                                                                         Evaluation of Algebraic Expressions                                                     Some Rules in Algebra                                                                             Use of Brackets in Simplification                                                        Addition and Subtraction of Algebraic Expressions                              Linear Algebraic Expressions with Fractional Coefficients               Factorization Fractions to Grouping                                                  Summary                                                                                                         Review Examples 5                                                                            Review Questions 5   

Read:   https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=Fundamental+Algebra+&*    https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebra+rules+to+remember&*     https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebra+rules+for+kids&*   https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebra+rules+of+operation&* 

 

Revision Exercise I

 

6. Number Sequence

Number Sequence                                                                             General Term in a Number Sequence                                                Problem Solving                                                                                               Summary                                                                                                         Review Examples 6                                                                           Review Questions 6   

Read:  https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=Number+Sequence&* https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=number+sequence+meanings&* https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=number+sequence+formula&* https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=number+patterns+in+mathematics&*

 

7. Algebraic Equations

   Open Sentences                                                                                           Simple  Equations                                                                                Solving Simple Equations                                                                Formulae                                                                                       Construction of Formulae                                                                      Writing Algebraic Expressions                                                              Problem Solving with Algebra                                                        Inequalities                                                                                        Properties of Inequalities                                                                  Equations and Inequalities                                                                 Summary                                                                                                         Review Examples 7                                                                           Review Questions 7

Read:   https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebra+equations&*   https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebraic+equation+definition&*   https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebraic+equations+examples+with+answers&*  https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=hard+algebra+questions&* 

 

 

8. Properties and Area of Simple Geometrical Figures

    Units of Area                                                                                               Area of Parallelogram                                                                                Area of Trapezium                                                                              Summary                                                                                                          Review Examples 8                                                                                                      Review Questions 8

Read:  https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=geometric+figures&*  https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebra+problems+with+answers&* 

 

9. Volume and Surface Area

    Concept of Volume                                                                              Volume of Fluids                                                                                     Right Prisms                                                                                        Surface of a Prism                                                                                 Cylinders                                                                                              Volume of Cylinder                                                                              Surface Area of a Cylinder                                                                Summary                                                                                                          Review Examples 9                                                                                                      Review Questions 9 

Read: https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=volume&*&dobs=volume  https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=algebra+practice+questions&*   https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=surface+area&*&dobs=surface%20area https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=surface+area+of+a+triangular+prism&*  https://www.google.com/search?rct=j&q=estimation%20and%20approximation#q=surface+area+cylinder&*      

 

Revision Exercise II

10. Ratio, Rate and Speed

    Ratio                                                                                            Equivalence Ratio                                                                              Increase and Decrease in Ratio                                                         Average Rate                                                                                        Time                                                                                                      Speed and Average Speed                                                                  Problems Involving Speed and Average Speed                                 Summary                                                                                                          Review Examples 10                                                                                                      Review Questions 10     

11. Percentages

    Percentages Fractions and Decimals                                              Expressing One Quantity as a Percentage of Another                   Comparing Two Quantities by Percentages                                     Percentage Greater that 100%                                                         Increasing and Decreasing a Quantity by a Given Percentage           Discount                                                                                        Commission                                                                                          Value Added Tax and GST                                                                 Summary                                                                                                          Review Examples 11                                                                                                      Review Questions 11

12. Functions and Graphs

    Rectangular Coordinates  in Two Dimensions                                           The Rectangular or Cartesian Plane                                              Coordinates of a Point                                                                               The Idea of Functions                                                                         Ordered Pairs Satisfying a Functions                                                   Gradient of a Straight Line                                                                Summary                                                                                                          Review Examples 12                                                                                                      Review Questions 12  

13.Statistics

   Introduction to Numerical Data Collection.                                                    Organization and Interpretation of Data                                                         Collection of Data Using a Questionnaire                                            Pictogram                                                                                                  Bar Graphs                                                                                       Collection of Data Through Observation                                                      Pie Chart                                                                                              Collection of Data through Interviews                                                       Line Graphs                                                                                      Frequency Tables and Histograms                                                   Collection of Data by Measuring                                                      Collection of Data by Using Electronic Means  and the Internet           Grouped Frequency Tables                                                              Summary                                                                                                          Review Examples 13                                                                                                      Review Questions 13

Revision Exercise III

14. Basic Geometrical Concepts and Properties

    Points                                                                                                        Lines, Rays, Line Segments                                                               Planes                                                                                              Intersecting Lines                                                                                 Angles                                                                                                       The Protractor and Angle Measure                                                     Different Kind of Angles                                                            Complementary Angles                                                                     Supplementary Angles                                                                        Adjacent Angles on a Line                                                                 Vertically opposite Angles                                                                    Parallel Lines, Alternate Angles, Corresponding Angles , Interior Angles                   Summary                                                                                                          Review Examples 14                                                                                                      Review Questions 14

15. Angle Properties of Polygons

    Polygons                                                                                             Triangles                                                                                                   Angle Properties of Triangles                                                              Exterior and Interior Opposite Angles                                           Quadrilaterals                                                                                               Convex Polygons                                                                                    Sum of the Interior Angles of a Convex Polygons                                      Sum of the Exterior Angles of a Convex Polygons                           Summary                                                                                                          Review Examples 15                                                                                                     Review Questions 15

16. Geometrical Constructions

    Geometrical Constructions                                                                    Use of Compasses                                                                              Bisecting an Angle                                                                                Bisecting a Line Segment                                                                   Summary                                                                                                          Review Examples 16                                                                                                     Review Questions 16

Revision Exercise IV

 

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 MATHEMATICS II. Consultant, Dr. Yeap Ban Har; Authors: Teh Keng Seng  * Loh Cheng Yee

 

CONTENTS

1. Congruence and Similarity

   Congruent Figures and Objects                                                             Similar Figures and Objects                                                                                      Similarity and Enlargement                                                                     Similarity and Scale Drawings                                                                                Summary                                                                                                          Review Examples 1                                                                                                     Review Questions 1

 

2. Direct and Inverse Proportions

    Direct Proportions                                                                                More on Direct Proportion                                                                                Graphical Representation  of Direct Proportion                                                      Other Forms of Direct Proportion                                                                    Inverse Proportion                                                                                                  More on Inverse                                                                                         Proportion Graphical                                                                                  Representation of Inverse Proportion                                                             Other Forms of Inverse Proportions                                                                Summary                                                                                                          Review Examples 2                                                                                                     Review Questions 2

3. Expansionism and Factorization of Algebraic Expression

    Expansion of Algebraic Expressions                                                                 Further Algebraic Expansions                                                                             Perfect Squares and Difference of Two Squares                                              Factorization of Algebraic Expressions                                                         Factorization Using Algebraic Identities                                                          Factorization of Quadratic Expression                                                                Problem Solving Involving                                                                           Quadratic Equations                                                                                    Summary                                                                                                          Review Examples 3                                                                                                     Review Questions 3

Revision Exercise I

 

 4. Algebraic Manipulation and Formulae

    Simple Algebraic Fraction                                                                               Multiplication and Division of Algebraic Fractions                                                               Further Examples on Simplification of Algebraic Fractions                                                             Addition and Subtraction of Algebraic Fractions                                                     Further Addition and Subtraction of Algebraic Fractions                                            Equations Involving Algebraic Fractions                                                          Problem Solving Involving Algebraic Fractions                                               Changing the  subject of a Formula                                                                Changing Further Examples on Changing the  subject of a Formula                                                Finding an Unknown in a Formula                                                                  Summary                                                                                                          Review Examples 4                                                                                                     Review Questions 4

5. Simultaneous Linear Equations

    Simultaneous Linear Equations                                                                Solving Simultaneous Linear Equations                                                         Using Elimination Method                                                                          More Examples on Elimination                                                                        Solving Simultaneous Linear Equations                                                             Using Substitution Method                                                                              Problem Solving Involving                                                        Simultaneous Equations                           s                                                    Summary                                                                                                          Review Examples 5                                                                                                    Review Questions 5

6. Pythagoras’ Theorem

    Pythagoras’ Theorem                                                                              Application of Pythagoras’ Theorem                                                                Summary                                                                                                          Review Examples 6                                                                                                    Review Questions 6

Revision Exercise II

7. Volume and Surface Area

   Pyramids                                                                                                          Volume of Pyramids                                                                                                 Total Surface Area of Pyramid and Cone                                                            Volume of Cones                                                                                                     Surface Area of Cone                                                                                              Volume of Sphere                                                                                                Surface of Cone                                                                                       Surface Area of Sphere                                                                                                   Summary                                                                                                          Review Examples 7                                                                                                    Review Questions 7

8. Graphs of Linear Equations in Two Unknowns

    Choice of Appropriate Scales for Graphs                                                               Graphs of Equations of the form y = c                                                                Graphs of Equations of the form x = a                                                                  Graphs of Equations of the form y                                                                                 Graphs of Equations of the form mx y = mx + c                                                                 Solving Simultaneous Linear Equations Using Graphical Method  Summary                                                                                                          Review Examples 8                                                                                                    Review Questions 8

                                                                  

9. Graphs of Quadratic Equations

    Quadratic Equation in Two  Variables of the Form y = ax2 (a <>  0) Graphs of General Quadratic Equations in Two Variables                           Problems  Involving Quadratic Graphs                                                            Summary                                                                                                          Review Examples 9                                                                                                    Review Questions 9 

Revision Exercise III

 

10. Set Languages and Notation

   Introduction to Sets                                                                                       Number of Elements to a Set                                                                                    Venn Diagram                                                                             Intersection to Sets                                                                                                 Union of Sets                                                                                                                Summary                                                                                                          Review Examples 10                                                                                                    Review Questions 10

11. Statistics

   Collection, Organisation and Interpretation of Data                                          Dot Diagram                                                                                                                   Grouped Data                                                                                                          Stem and Leaf Diagram                                                                                     Mode                                                                                                         The Mean,                                                                                                       Median                                                                                                  Comparison of the Mean, Median and Mode                                                                                Average for Grouped Data                                                                                          Using Calculator to find Mean                                                                  Summary                                                                                                          Review Examples 11                                                                                                    Review Questions 11

12. Probability

    Introduction                                                                                          Experimentation and Sample Space                                                                               Definition of Probability                                                                                 Summary                                                                                                          Review Examples 12                                                                                                    Review Questions 12

Revision Exercise IV

 

 

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MATHEMATICS III. Consultant, Dr. Yeap Ban Har; Authors: Teh Keng Seng  * Loh Cheng Yee

 

CONTENTS

1. Solution in Quadratic Equations

Solving Quadratic Equations by Factorization (Revision)                       Solution by Completing the Square                                                    General Solution to a Quadratic Equation                                          Equations Reducible to Quadratic Equations                                   Summary                                                                                                          Review Examples 1                                                                                                   Review Questions 1

2.  Indices and Standard Form

Multiplication Law of Indices                                                                  Division Law of Indices                                                                          Power Law of Indices                                                                           More Law of Indices                                                                                  Zero and Negative Indices                                                                Fractional Indices                                                                                    The Standard Form                                                                           Common Practices Used in Every Day                                                      Life Situations                                                                                           Use of Calculator                                                                               Summary                                                                                                          Review Examples 2                                                                                                   Review Questions 2

3. Linear Inequalities

Solving Inequalities                                                                             Difference  between < and s                                                                Problem Solving Involving Inequalities                                                     Linear Inequalities in One Variable                                                    Summary                                                                                                          Review Examples 3                                                                                                   Review Questions 3

Revision Exercise I

4. Coordinate Geometry.

Revision Length of Line Segment                                                               Gradient of a Straight Line                                                                  Equation of a Straight Line                                                               Summary                                                                                                          Review Examples 4                                                                                                   Review Questions 4

5. Matrices

Introduction                                                                                                 Some Special Matrices                                                                        Addition and Subtraction of Matrices                                                         Rules for Matrix Addition and Subtraction                                      Multiplication of a Matrix by a Real Number                                     Multiplication of Matrices                                                                          Use of Matrices in Solving  Everyday Life Problem                              Summary                                                                                                          Review Examples 5                                                                                                   Review Questions 5

6. Application of Mathematics in Practical Situations

Profit and Loss as Compound Interest                                                          Hire Purchase Money Exchange                                                         Taxation Personal and Household Finances                                 Interpretation and Use of Tables and Charts Strategies in Problem Solving Summary                                                                                                          Review Examples 6                                                                                                   Review Questions 6

7 Graphs and Their Applications

Application of Graphs in Practical Situations                                        Conversion Graphs                                                                                Travel Graphs                                                                                     Drawing of Graphs                                                                              Problem Solving Involving Linear Graphs                                              Summary                                                                                                          Review Examples 7                                                                                                   Review Questions 7

Revision Exercise II

 

8. Congruent and Similar Triangles

Congruent Triangles Congruent Tests Simple Application of Congruent Triangles Similar Triangles Test for Similarity between Two Triangles Summary                                                                                                          Review Examples 8                                                                                                   Review Questions 8

9. Area and Volume of Similar Figures and Solids

Area of Similar Figures                                                                            Volume of Similar Solids                                                                   Summary                                                                                                          Review Examples 9                                                                                                   Review Questions 9

10 Trigonometrical Ratios

Trigonometrical Ratios                                                                                Volume of Trigonometrical Ratios                                                             Use of Calculator                                                                                  Solving Right-Angled Triangles Using  Trigonometrical Ratios              Finding the Volume of an Angle with Trigonometrical Ratios Practical Applications of Trigonometry                                                             Summary                                                                                                          Review Examples 10                                                                                                   Review Questions 10

 

Revision Exercise III

 

11. Further Trigonometry

 Trigonometrical Ratios Area of a Triangle the Sign Rule                        Cosine Rule                                                                                    Bearings Three Dimensional Problems                                         Further Examples                                                                              Three Dimensional Problems                                                      Summary                                                                                                          Review Examples 11                                                                                                   Review Questions 11

12.  Mensuration – Arc Length, Sector Area, Radian Measure

Area and Circumference of a Circle (Revision)                                         Length of Arc and Area of Sector                                                        The Radian (rad)                                                                              Radian Arc Length and Area of Sector                                       Summary                                                                                                          Review Examples 12                                                                                                   Review Questions 12

 

13.  Geometrical Properties of Circles

Symmetrical Properties of Circles                                                             Angles in Opposite Segment of a Circle                                         Problems on Angle Properties of Circles                                      Tangents                                                                                       Tangents from an External Point                                                      Summary                                                                                                          Review Examples 13                                                                                                   Review Questions 13

 

Revision Exercise IV

 

MATHEMATICS IV. Consultant, Dr. Yeap Ban Har; Authors: Teh Keng Seng  * Loh Cheng Yee

 

CONTENTS

1. Graphical Solution of Equations

Graphs of Cubic Functions                                                                         Graph of Reciprocal Functions Graph of y = / (a/x2)                          Graph of the Exponential Functions                                                     Sketches of Some Important Graphs                                              Graph of the form y = (+-)(x – a) (x -b )                                        Graphical Solution of Quadratic Equations                                  Summary                                                                                                          Review Examples 1                                                                                                  Review Questions 1

2. Further Graphs and Graphs Applied to Kinematics

Linear Distance- Time Graphs                                                               Gradients of a Curve                                                                        Gradient of a Distance- Time Curve                                              Speed-Time Graphs                                                                       Graphs in Practical Solutions                                                      Summary                                                                                                          Review Examples 2                                                                                                  Review Questions 2

3. Vectors in Two Dimensions

Scalar and Vector Quantities                                                            Technologies and Notations of Vectors                                             Equal Vectors                                                                                 Vectors which are Opposite                                                          Column Vectors                                                                                  Zero Vectors                                                                                   Subtraction of Vectors                                                                       Scalar Multiple  of a Vector                                                                 Scalar Multiple of a Vector Expression of a Given                             Vector in Terms of Two Vectors                                                       Review                                                                                         Summary Examples 3                                                                                                  Review Questions 3

4. Standard Deviation and Mean

Mean (Revision)                                                                                    Standard Deviation                                                                           Summary                                                                                                          Review Examples 4                                                                                                  Review Questions 4

5. Cumulative Frequency Distribution

Cumulative Frequency Table                                                                Cumulative Frequency Curve                                                        Median, Quartiles and Percentiles                                            Interquartile Range                                                                                Box and Whisker Plots                                                                Summary                                                                                                          Review Examples 5                                                                                                  Review Questions 5

6. More on Probability

Revision                                                                                                 Possible Outcomes in a Sample Space                                         Simple Combined Events and Possibility Diagrams                            Simple Combined Events and Tree Diagram                                 Addition of Probability and Mutually Exclusive Events              Multiplication of Probabilities and Independent Events               Summary                                                                                                          Review Examples 6                                                                                                 Review  Questions 6

7. Revision  

Arithmetic 1: Numbers, Percentages, Time                                         Arithmetic 2: Rate, Ratio, Proportion. Speed and Map Problems          Arithmetic 3: Simple and Compound Interest. Money Exchange. Financial Transactions

Algebra 1:  Simplification, Substitution. Expansion and Factorization  Algebra 2: Algebraic Manipulation and Indices                                                           Algebra 3: Inequalities                                                                            Algebra 4: Quadratic Equations                                                      Measurement (2-Dimensional Problems)                                           Measurement (3-Dimensional Problems)                                            Coordinate Geometry                                                                            Geometry 1: Geometrical Properties of Angles and Angle Properties of Polygons                                                                                          Geometry 2: Congruence and Similarity                                              Geometry 3: Angle Properties of Circles                                                  Graphs and Graphical Solution                                                          Pythagoras Theorem and Trigonometry                                                  Bearing and Trigonometry                                                                      Number Sequence and Problem Solving                                                    Sets and Van Diagrams                                                                         Matrices Vectors                                                                                     Statistics 1: Data Handling and Averages                                                Statistics 2: Data Analysis                                                                    Probability

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CORE MATHS for Advanced Level L. BOSTOCK & S. CHANDLER

CONTENTS

 

Chapter-1       Algebra-1

Multiplying, adding and subtracting algebraic expressions. Expanding subtracting algebraic function. Algebraic division.

  

Chapter-2       Surds, indices and logarithms

Square, Cube and other roots. Rational and irrational numbers. Surds. Rxxxx a denominator. Law of Indices. Definition of algorithm including…..Law of algorithms.

 

 Chapter-3       Equations 1

Solving quadratic equations by factorization, by completing the square by the formula. Factor theorem. Solving cubic equations by using the factor theorem. Solution of simultaneous equations, three linear equations and one linear and one quadratic equation.

 

Chapter-4       Equations 2

The nature of roots of a quadratic equation. Solving equations containing x as a power. Solving equations containing logarithm.

Summary A

Examination Questions A

Chapter-5       Reasoning and Proof

The need for proof. Mathematical Reasoning and deduction.

Chapter-6      Coordinate Geometry I

Cartesian coordinate. The length, mid point and gradient of a line joining two points. Parallel and perpendicular lines.

Chapter-7      Triangles

Trigonometric of acute and obtuse angles. The Sine endpoint casein rule and its use including the ambiguous case. The Cosine rule of a triangle.

Chapter-8      Coordinate Geometry 2

The equation of a straight line in the form of y = mx + c and in the form of Ax + By + c = 0. Finding the equation of a straight line. The angle between a line and x-axis. Reduction of a relationship to a linear law.

Chapter-9      Circles

Parts of a circle. Relationship between angles in circles. Tangents to circles and their properties. 

 

Chapter-10      Circular measure

Radians. The length of an arc of a circle. The area of a sector of a circle.

 

Summary B

Examination Questions B

 

Chapter-11      Functions 1

Definition of a function. Domain and range. Quadratic, cubic and rational functions.

 

Chapter-12      Inequalities

Solving inequalities involving linear, quadratic and rational functions.

 

Chapter-13      Differentiations 1

The gradient of a curve. Differentiations from first principles. Differentiation of constant, of a multiple of x, of xn , and their sums and differences. Gradients pf tangents and normal.

 

Chapter-14      Tangents, normal and stationary values

Equations of tangents and normals. Stationary values. Turning points and their nature. Points of inflexion.

Chapter-15      Trigonometric functions

General definition of an angle. Trig ratio of 300, 450 and 600. The sine, cosine and tangent functions, their properties and relationships. One-way stretches of curves. The reciprocal trigonometric function. Graphical solution of trig. Equations.

Chapter-16      Trigonometry I

The identity cos2θ + sin2θ 1 and its equivalent. Solving trig equations. ± ≤ ± π θ

 

Summary C

Examination questions C

 

Chapter-17      Exponential and logarithmic functions

Exponential growth and decay. The exponential function. Changing the base of a logarithm. The logarithm function. The derivative of ex and log x.

Chapter-18      Function 2

Curve Sketching using transformation. Even, odd and periodic functions. The modulus function. Equation and inequalities.

Chapter-19      Sequences

Sequences. The behavior of a sequence. Recurrence relationship. Arithmetic progression. Geometric progression.

Chapter-20      Integration 1

Integration as the sequence of differentiation. Integration as a process of summation. Finding areas by integration. Definite integration. Integration of 1/x. The trapezium rule, the mid-ordinate and Simpson’s rule. 

Summary D

Examination questions D

Chapter-21      Differentiations 2

Differentiating a function of a function (the chain rule) a product of two functions and a quotient of two functions.

Chapter-22      Trigonometry 2

Compound angle identities. Double angle identities. General solution of trig equations.

Chapter-23      Trigonometry 3

Expressing a cos θ + b sin θ as r cos (θ + α) and equivalent forms. Inverse trigonometric functions.  

Chapter-24      Differentiations 3

Differentiating trigonometric functions. Extending the chain rule.

Chapter-25      Differentiations 4

Differentiating implicit functions. Using logarithm to simplify differentiation. 

Differentiating ax. Parametric equations. Finding the gradient of a curve given grammatically.

Chapter-26      Differentiations 5

Small increments. Small percentage increases. Comparative rate of change.

Summary E

Examination questions E

Chapter-27      Method of Proof

Proof by contradiction. Use of a counter example.

Chapter-28      Coordinate Geometry 3

Loci. The equation of a circle. Finding equations of tangents to circles. Parametric equations of a circle and of an ellipse.

Chapter-29      Integration 2

Standard integrals. Integration by recognition and change of variable. Integration by parts. Indefinite integrals.

Chapter-30      Algebra 2

Partial fractions. Dividing one polynomial by another. Using partial fractions to simplify differentiation. The remainder theorem. Intersection of curves and coincident points of intersection.

Chapter-31      Integration 3

Interpreting fractions by recognition and by using partial fractions. Integration. Integrating compound trigonometric fractions.

Chapter-32      Integration 4

Classifying an integral. Solving first order differentiation equations and separable variables.

Chapter-33      Integration 5

Rates of increase. Forming and solving naturally occurring differential equations. Finding areas and volumes revo theoelution.

Summary F

Examination questions F

Chapter-34      Series

The expansion (1 + x)n when n is a positive integer when n has any value(the binomial theorem). Using the binomial theorem to find approximation. Maclaurin’s theorem. 

Chapter-35      Equations 3

Methods for solving trigonometric equations. Polynomial equations with a repeated root. Equations involving square roots. Locating an interval in which the root of an equation lies. Iterative methods for finding an approximate solution. xn + 1 = g(xn). Newton Raphson.

 Chapter-36      Vectors

Differentiation of a vector. Multiplying a vector by a scalar. Adding vectors. Adding vectors. The angle between two vectors. The position vector of a mid point of a line. Cartesian coordinates in three dimensions. The Cartesian unit vectors I, J and K. Scalar product. The Cartesian and vector equations of a line. Intersecting parallel and skewed lines. The cartesian and vector equations of a line. The cartesian and vector equations of a plane.

Summary G

Examination questions G

Answers

A level- Advance Level Mathematics- PURE MATHEMATICS I

Hugh Neill and Douglas Quadling

CONTENTS

Introduction

1. Coordinates, points and lines

2. Surds and Indices

3. Functions and Graphs

4. Quadratics

5. Inequalities

Revision Exercises I

6. Differentiations

7. Applications of differentiations

8. Sequences

9. The binomial theorem

10. Trigonometry

11. Combining and inverting functions

12. Extending differentiation

Revision Exercises 2

 

13. Vectors

14. Geometric Sequence

15. Second derivative

16. Integration

17. Volume of revolution

18. Radians

Revision Exercises 3

Practice Examinations

Answers

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