#### New Additional Mathematics

New Additional Mathematics is written for students preparing for the GCE ‘O’ Level Additional Mathematics examination paper.

This book closely follows the revised syllabus and includes five new chapters on Sets, Matrices, Permutations and Combinations, Kinematics and Relative Velocity. Some Challenging questions (indicated by *) and Critical Thinking Problems (indicated by *) are placed at appropriate places for more able students. Suggestions on the use of IT and open tools to promote dynamic learning have been added where relevant (indicated by a laptop). These open tools include spreadsheets and graph plotters.

All basic concepts are explained and developed clearly through comprehensive illustrations and worked examples. Important concepts applied for problem solving in some examples are highlighted by short notes. Simple questions for direct application of basic concepts and formulae are given at the beginning of each graded exercise —students are encouraged to attempt these.

The main text contains clear presentation of basic concepts with simple illustrations, the derivation and application of useful formulae, important facts and the process of problem solving through examples.At the end of each chapter, all basic concepts, formulae and problem-solving methods are summarised in the Important Notes. This is followed by harder examples and more questions in the Miscellaneous Exercise.

To assist students in their revision and examination preparation, five sets of graded revision exercises are placed at various appropriate stages of learning, in addition to two assessment papers at the end of the book.

##### SPECIAL FEATURES

- Clear and concise explanation of concepts
- Relevant examples
- IT-based activities for exploration and extension
- Great variety of questions
- Questions that develop higher-order thinking skills
- Overview of each chapter
- Revision exercises and assessment papers
- Answers and index for easy reference

#### CONTENTS

- 1 SETS
- 1.1 Introduction to Sets
- 1.2 Intersection and Union of Sets
- 1.3 Applications
- Important Notes
- Miscellaneous Exercise 1
- 2 SIMULTANEOUS EQUATIONS
- 2.1 Simultaneous Linear Equations in Two Unknowns
- 2.2 Simultaneous Linear and Non-Linear Equations in Two Unknowns
- Important Notes
- Miscellaneous Exercise 2
- 3 INDICES , SURDS, and LOGARITHMS
- 3.1 Indices (Exponents) and Surds
- 3.2 Exponential Equations
- 3.3 Logarithms
- 3.4 Common and Natural Logarithms
- 3.5 Laws of Logarithms
- 3.6 Logarithmic Equations
- Important Notes
- Miscellaneous Exercise 3
- 4 QUADRATIC EXPRESSIONS and EQUATIONS
- 4.1 Maximum/Minimum Values of a Quadratic Expression
- 4.2 Roots of a Quadratic Equation
- 4.3 Solving Quadratic Inequalities
- Important Notes
- Miscellaneous Exercise 4
- 5. REMAINDER AND FACTOR THEOREMS
- 5.1 Polynomial Identities
- 5.2 Remainder Theorem
- 5.3 Factor Theorem
- 5.4 Solving Cubic Equations
- Important Notes
- Miscellaneous Exercise 5
- Revision Exercise 1
- Revision Exercise 2
- Revision Exercise 3
- Revision Exercise 4
- 6. MATRICES
- 6.1 Represent Information as a Matrix
- 6.2 Addition, Subtraction and Scalar Multiplication of Matrices
- 6.3 Multiplication of Matrices
- 6.4 Determinant and Inverse of a 2 x 2 Matrix
- 6.5 Solving Simultaneous Equations by a Matrix Method
- Important Notes
- Miscellaneous Exercise 6
- 7. COORDINATE GEOMETRY
- 7.1 Distance between Two Points
- 7.2 Midpoint of the Line Joining Two Points
- 7.3 Gradient of a Line Passing through Two Points
- 7.4 Equations of Straight Lines
- 7.5 Equations of Parallel and Non-Parallel Lines
- 7.6 Equations of Perpendicular Lines
- 7.7 Perpendiculat Bisector
- 7.8 Intersection of a Straight Line and a Curve
- Important Notes
- Miscellaneous Exercise 7
- 8. LINEAR LAW
- 8.1 Linear Law
- Important Notes
- Miscellaneous Exercise 8
- 9. FUNCTIONS
- 9.1 Introduction to Functions
- 9.2 Composite Functions
- 9.3 Inverse Functions
- 9.4 Absolute Valued Functions
- Important Notes
- Miscellaneous Exercise 9
- Revision Exercise 5
- Revision Exercise 6
- Revision Exercise 7
- Revision Exercise 8
- 10. TRIGONOMETRIC FUNCTIONS
- 10.1 Trigonometric Ratios and General Angles
- 10.2 Trigonometric Ratios of Any Angle
- 10.3 Graphs of the Sine, Cosine and Tangent Functions
- 10.4 Three More Trigonometric Functions
- Important Notes
- Miscellaneous Exercise
- 11. SIMPLE TRIGONOMETRIC IDENTITIES and EQUATIONS
- 11 .1 Simple Identities
- 11.2 Trigonometric Equations and More Graphs
- Important Notes
- Miscellaneous Exercise 11
- 12. CIRCULAR MEASURE
- 12.1 Radian Measure
- 12.2 Arc Length and Area of a Sector
- Important Notes
- Miscellaneous Exercise 12
- 13. PERMUTATIONS and COMBINATIONS
- 13.1 The Basic Counting Principle
- 13.2 Permutations
- 13.3 Combinations
- Important Notes
- Miscellaneous Exercise 13
- 14. BINOMIAL THEOREM
- 14.1 The Binomial Expansion of (1 + b)n
- 14.2 The Binomial Expansion of (a + b)n
- Important Notes
- Miscellaneous Exercise 1
- Revision Exercise 9
- Revision Exercise 10
- Revision Exercise 11
- Revision Exercise 12
- 15. DIFFERENTIATION and ITS TECHNIQUE
- 15.1 The Gradient Function
- 15.2 Function of a Function (Composite Function)
- 15.3 Product of Two Functions
- 15.4 Quotient of Two Functions
- 15.5 Equations of Tangent and Normal
- Important Notes
- Miscellaneous Exercise 15
- 16. RATES of CHANGE
- 16.1 Constant Rate and Variable Rate of Change
- 16.2 Related Rates of Change
- 16.3 Small Changes
- Important Notes
- Miscellaneous Exercise 16
- 17. HIGHER DERIVATIVES and APPLICATIONS
- 17.1 Determination of Maximum and Minimum Points
- 17.2 Maximum and Minimum Points
- 17.3 Maximum and Minimum Values
- Important Notes
- Miscellaneous Exercose 17
- 18. DERIVATIVES of TRIGONOMETRIC FUNCTIONS
- 18.1 Differentiatiion of Trigonometric Fuctions
- Important Notes
- Miscellaneous Exercise 18
- 19. EXPONENTIAL and LOGARITHMIC FUNCTIONS
- 19.1 Exponential Functions
- 19.2 Logarithmic Functions
- Important Notes
- Miscellaneous Exercise 19
- Revision Exercise 13
- Revision Exercise 14
- Revision Exercise 15
- Revision Exercise 16
- 20. INTEGRATION
- 20.1 Integration as the Reverse Process of Differention and Indefinite Integrals
- 20.2 Defnite Integrals
- 20.3 Integration of Trigonometric Functions
- 20.4 Integration of Exponential Functions
- Important Notes
- Miscellaneous Exercise 20
- 21. APPLICATIONS of INTEGRATION
- 21.1 Area between a Curve and an Axis
- 21.2 Area Bounded by Two Curves
- Important Notes
- Miscellaneous Exercise 21
- 22. KINEMATICS
- 22.1 Displacement, Velocity and Acceleration
- 22.2 Displacement-Time and Velocity-Time Graphs
- 22.3 Equations of Motion with Constant Acceleration (Optional)
- Important Notes
- Miscellaneous Exercise 22
- 23. VECTORS
- 23.1 Basic Concepts
- 23.2 Vectors Expressed in Terms of Two Non-Parallel Vectors
- 23.3 Position Vectors
- 23.4 Vectors in the Cartesian Plane
- Important Notes
- Miscellaneous Exercise 23
- 24. RELATIVE VELOCITY
- 24.1 Relative Motion in a Straight Line
- 24.2 Relative Motion in a Current
- 24.3 Relative Motion of Two Moving Objects
- Important Notes
- Miscellaneous Exercise 24
- Revision Exercise 17
- Revision Exercise 18
- Revision Exercise 19
- Revision Exercise 20
- Assessment Papers
- Answers
- Index