0.1  Rational Indices

0.2  Logarithms

0.3  Factorials

0.4  ∑ Notation
       A. Using ‘∑’Notation
       B. Properties of ‘∑’

1.1  Surds

1.2  Mathematical Induction
       A. Principle of Mathematical Induction
       B. Application to Proofs of Summation Formulae for Series
       C. Proofs of Divisibility

1.3  Binomial Theorem
       A. Pascal’s Triangle
       B. Binomial Theorem
       C. Proof of Binomial Theorem

2.1  Radian Measure
       A. Concept of Radian Measure
       B. Arc Length and Area of Sector

2.2  The Six Trigonometric Functions
       A. Reciprocals of the Basic Trigonometric Ratios
       B. Using a Calculator to Find the Values of the Six Trigonometric Ratios
       C. Graphs of the Six Trigonometric Functions

2.3  Trigonometric Identities

2.4  Trigonometric Formulae
       A. Compound Angle Formulae
       B. Double Angle Formulae
       C. Sum and Product Formulae

3.0  Review

3.1  Limit of a Sequence
       A. Basic Concept of the Limit of a Sequence
       B. The Limit of a Special Sequence: the Number e
       C. Natural Logarithm

3.2  Continuous and Discontinuous Functions
       A. Basic Concept
       B. Graphs of Continuous and Discontinuous Functions
       C. Some Special Continuous and Discontinuous Functions

3.3  Theorems on Limits
       A. Limit of a Function at a Certain Value
       B. More on Finding the Limits of Functions
       C. Two Important Limits

3.4  Limit of a Function at Infinity
       A. Basic Concept and Theorem
       B. Limits of Composite Functions

4.1  Derivative of a Function
       A. Slope of a Curve
       B. Concept of Derivatives
       C. Finding Derivatives from First Principles

4.2  Basic Rules of Differentiation
       A. Constant Rule
       B. Power Rule
       C. Constant Factor Rule
       D. Sum Rule and Difference Rule
       E. Product Rule
       F. Quotient Rule
       G. Chain Rule

4.3  More about Differentiation of Functions
       A. Trigonometric Functions
       B. Exponential Functions
       C. Logarithmic Functions

4.4  Implicit Differentiation
       A. Implicit Functions
       B. Logarithmic Differentiation

4.5  Second Derivatives

5.0  Review

5.1  Tangents and Normals
       A. Tangent at a Point
       B. Normal at a Point

5.2  Maxima and Minima
       A. The Concept of Maxima and Minima
       B. First Derivative Test
       C. Second Derivative Test

5.3  Graph Sketching of Rational Functions
       A. Symmetry in the Graphs of Even and Odd Functions
       B. Asymptotes
       C. Graph Sketching

5.4  Applications of Differentiation to Practical Problems
       A. Problems Related to Rates of Change
       B. Problems on Maximization and Minimization

6.1  Concept of Indefinite Integration

6.2  Basic Rules and Properties of Integration
       A. Power Rule
       B. Properties of Indefinite Integrals

6.3  More Integration Formulae
       A. Integration of
       B. Integration of Exponential Functions
       C. Integration of Trigonometric Functions

6.4  Applications of Indefinite Integration
       A. Geometrical Applications
       B. Physical Applications

6.5  Integration by Substitution

6.6  Integration Techniques Involving Trigonometric Functions
       A. Integration Involving Product of Sine and Cosine
       B. Integration Involving Powers of Trigonometric Functions
       C. Trigonometric Substitution

6.7  Integration by Parts

7.0  Review

7.1  The Concept of Definite Integration
       A. Definite Integral as the Limit of a Sum
       B. Properties of Definite Integrals

7.2  Fundamental Theorem of Calculus

7.3  Integration by Substitution

7.4  Integration by Parts

7.5  Other Properties of Definite Integrals
       A. Definite Integrals of Odd Functions and Even Functions
       B. Definite Integrals of Periodic Functions

8.0  Review

8.1  Areas of Plane Figures
       A. Area between a Curve and the x-axis
       B. Area between a Curve and the y-axis
       C. Area between Two Curves

8.2  Volumes of Solids of Revolution
       A. Solids of Revolution
       B. Disc Method
       C. Shell Method
       D. Revolution about Lines Parallel to a Coordinate Axis

9.1  Concept and Basic Operations of Matrices
       A. Concept of Matrices
       B. Basic Operations of Matrices

9.2  Multiplication of Matrices
       A. Concept of Matrix Multiplication
       B. Finding the Product of Matrices
       C. Properties of Matrix Multiplication

9.3  Determinants
       A. Concept of Determinants
       B. Expanding a Determinant
       C. Properties of Determinants

9.4  Inverse of a Matrix
       A. Concept of the Inverse of a Matrix
       B. The Adjoint Method to Find the Inverse of a Matrix
       C. Properties of Inverses of Matrices

10.0  Review

10.1  Solving Systems of Linear Equations
          A. Introduction
          B. System of Linear Equations of Order 2
          C. System of Linear Equations of Order 3
          D. Gaussian Elimination

10.2  General Solution of a System of Linear Equations
          A. Number of Solutions of a System of Linear Equations
          B. General Solution of a System of Linear Equations of  Order 2
          C. General Solution of a System of Linear Equations of  Order 3

10.3  System of Homogeneous Linear Equations

11.0  Review

11.1  Concept of Vectors
          A. Scalars and Vectors
          B. Geometrical Representation of Vectors
          C. Equality of Vectors
          D. Negative Vector
          E. Zero Vector

11.2  Basic Operations of Vectors
          A. Addition of Vectors
          B. Subtraction of Vectors
          C. Scalar Multiplication of Vectors

11.3  Position Vectors
          A. Concept of Position Vectors
          B. Section Formula for Vectors

11.4  Representation of Vectors in the Rectangular Coordinate System
          A. Representation of Vectors in a Plane
          B. Representation of Vectors in Space

11.5  Applications of Vectors
          A. Parallelism
          B. Division of a Line Segment

12.1  Scalar Products
          A. Definition of Scalar Product
          B. Scalar Products of Vectors in R3
          C. Properties of Scalar Products
          D. Applications of Scalar Products

12.2  Vector Products
          A. Definition of Vector Product
          B. Properties of Vector Products
          C. Vector Products of Vectors in R3
          D. Applications of Vector Products

12.3  Scalar Triple Products