Pre calculus
1. Functions
1.1 Definition of a function
1.2 Function notation and evaluating functions
1.3 Domain and range of functions
1.4 One to one and onto functions
1.5 Composition of functions
1.6 Inverse functions
1.7 Special functions (constant, polynomial, rational, absolute value)
1.8 The remainder theorem, factor theorem and the solution of cubic equations.
1.9 Applications of functions (depreciation, demand and supply curves, production levels)
1.10 Sketching graphs of function (constant, linear, quadratic, square root, absolute value)
1.11 Transforming graphs (horizontal and vertical shifts, reflection)
2. Solutions of inequalities
2.1 Systems of linear inequalities
2.2 Quadratic inequalities
2.3 Graphs of systems of inequalities
2.4 Applications of inequalities (profit, sales allocation, investment)
3. Complex Numbers
3.1 The definition of complex numbers
3.2 Addition, multiplication and division of complex numbers
4. Exponential and Logarithmic Functions
4.1 Graphs of exponential and logarithmic function
4.2 The natural exponential and natural logarithmic function
4.3 Basic properties of logarithmic
4.4 Solving exponential and logarithmic equations
4.5 Applications
5. Matrix Algebra
5.1 Matrix addition, multiplication and transposition
5.2 The determinant of a 3 x 3 matrix
5.3 The inverse of a 3 x 3 matrix
5.4 Matrix solution of 2 x 2 and 3 x 3 systems of linear equations
6. Sequences and Series
6.1 Definition of a sequence (general terms and recursive definition)
6.2 Types of sequences (constant, oscillating, arithmetic, geometric)
6.3 Sigma Notation
6.4 Arithmetic and Geometric Series
6.5 Sums of Arithmetic and Geometric Series including sums to infinity
Calculus
7. Limits
7.1 Concept of a Limit
7.2 Limits of Sequences
7.3 Limits of Polynomial and Rational Functions
7.4 One-Sided Limits
7.5 Limits to infinity
8. Continuity
8.1 Conditions for continuity at a point
8.2 Determination of continuity of polynomial and rational functions (at points and over intervals)
8.3 Finding points of discontinuity
9. Differentiation of Single Variable Functions
9.1 The concept of the derivative
9.2 Differentiation from first principles
9.3 Rules of differentiation (power, chain, product, quotient rules)
9.4 Differentiation of Exponential and Logarithmic Functions
10. Applications of Differentiation
10.1 Determination of gradients
10.2 Increasing and decreasing functions
10.3 Relative extrema (maxima/minima) using the first and second derivative tests
10.4 Concavity and Points of Inflection
10.5 Vertical and Horizontal Asymptotes
10.6 Sophisticated Graphing (polynomial, rational and other algebraic functions)
