Chapter 1 Algebra I
1.1 Sets and numbers
1.1.1 Set theory
1.1.2 Rational and irrational numbers
1.1.3 Real numbers
1.2 Indices
1.2.1 Laws of indices
1.2.2 Properties of indices
1.2.3 Exponential equations
1.3 Polynomials
1.4 Factorization
1.5 Solving quadratic equations-
1.6 Simultaneous equations
1.6.1 Simultaneous linear equations
1.6.2 Simultaneous equations.linear and non-linear
1.7 Summary
1.8 Further problems
Chapter 2 Coordinate Geometry
2 1 Introduction
2.1.1 The distance between two points
2.1.2 The midpoint of a line segment
2.1.3 The slope of a line joining two points
2 2 Equations of a straight line
2 3 Inequalities
2.3.1 Symbols
2.3.2 Properties
2.3.3 Solving linear inequalities involving one variable
2.3.4 Solving linear inequalities involving two variables
2.4 The equation of a circle
2.4.1 Terminology
2.4.2 Cartesian coordinates
2.5 Summary
2.6 Further problems
Chapter 3 Functions
3.1 Mappings and functions
3.1.1 Relations and mappings
3.1.2 Functions
3.1.3 Four ways to represent a function
3.1.4 Injective,surjective and bijective functions
3.1.5 Piecewise-defined functions
3.2 Inverse functions
3.2.1 How to find the inverse of a function
3.2.2 How to graph the inverse of a function
3.3 Composite functions
3.3.1 Arithmetic combinations of functions
3.3.2 Composition of functions
3.4 Transformation of graphs and functions
3.5 Odd, even and periodic functions
3.6 Exponentials
3.6.1 Graphs of exponential functions
3.6.2 Transformations of graphs of exponential functions
3.6.3 The natural basee
3.6.4 Properties of exponential functions
3.7 Logarithms
3.7.1 Graphs of logarithmic functions
3.7.2 Natural logarithmic functions
3.7.3 Properties of logarithmic functions
3.8 Summary
3.9 Further problems
Chapter 4 Algebra
4.1 Polynomial division
4.1.1 The concept of long division
4.1.2 The synthetic division
4.1.3 The polynomial remainder theorem
4.1.4 The factor theorem
4.2 Algebraic fractions
4.3 Curve sketching
4.4 Summary
4.5 Further problems
Chapter 5 Trigonometry
5.1 Angles and angle measurement
5.2 Trigonometric functions
5.2.1 Right triangle definitions
5.2.2 Unit circle definitions
5.3 Equations and identities
5.3.1 Pythagorean trigonometric identities
5.3.2 Addition and subtraction formulae
5.3.3 Functions of the complementary angle
5.3.4 Functions of the supplementary angle
5.3.5 Double angle formulae
5.3.6 Half angle formulae
5.4 The cosine and sine laws
5.4.1 Law of cosines
5.4.2 Law of sines
5.5 The area of a triangle
5.6 The factor formulae
5.7 General solutions of trigonometric equations
5.8 Summary
5.9 Further problems
Chapter 6 Vectors
6.1 Vector geometry
6.2 Vector algebra
6.2.1 Vectors in three dimensions
6.2.2 Vectors in two dimensions
6.3 The scalar product
6.3.1 The algebraic expression
6.3.2 Properties of the dot product
6.3.3 Applications of the dot product
6.4 The vector product
6.4.1 The algebraic expression
6.4.2 Geometric applications
6.5 Equations of a straight line
6.5.1 The vector equation of a straight line
6.5.2 The standard Cartesian equation of a straight line
6.6 Equations of a plane
6.6.1 The vector equation of a plane
6.6.2 The standard Cartesian equation of a plane
6.6.3 The distance from the origin to a given plane
6.6.4 The distance from an arbitrary point to a given plane
6.7 Summary
6.8 Further problems
Chapter 7 Mathematical arguments and proofs
7.1 Mathematical logic
7.2 Proof by exhaustion
7.3 Proof by counterexample
7.4 Proof by contradiction
7.5 Proof by induction
7.5.1 Principle of Mathematical Induction(PMI)

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