The Exponential Function e^x and Natural Log Functions

1. The exponential function e^x
2. Sketching exponential graphs based on transformations
3. The natural logarithmic function, ln x
4. Exam Questions - Natural log functions

Working with Functions

1. f(x) notation
2. Domain and range
3. Exam Questions - Domain and range
4. Combination of functions
5. The inverse of a function
6. Graphical relationship between f(x) and its inverse
7. Exam Questions - Inverse functions

Even and Odd and Periodic Functions

1. Even and odd and periodic functions

Modulus Functions, Equations and Inequalities

1. The modulus function
2. Graphing y=|f(x)|
3. Graphing y=f(|x|)
4. Exam Questions - Modulus functions graphing
5. Modulus equations
6. Exam Questions - Modulus equations
7. Modulus inequalities
8. Exam Questions - Modulus inequalities

Graph Transformations and Asymptotes

Standard Differentials

1. Exponential function e^x
2. The natural log function, ln(x)
3. The trig functions sin(x), cos(x) and tan(x)

The Chain Rule

1. Chain rule: Polynomial to a rational power
2. Chain rule: Exponential types
3. Chain rule: Natural log types
4. Chain rule: Trigonometric types

The Product and Quotient Rules

1. The product rule
2. The quotient rule

More Standard Differentials

1. The trig functions, sec(x), cosec(x) and cot(x)

The Reciprocal Function of dy/dx

1. The reciprocal function of dy/dx

Implicit Functions

1. Implicit functions
2. Tangents and normals
3. Stationary points
4. Exam Questions - Implicit functions

Connected Rates of Change

1. Connected rates of change
2. Using three connected rates of change
3. Connected rates of change cone type problems
4. Exam Questions - Connected rates of change

Integration – Common Functions

1. Integration:(ax+b)ⁿ types
2. Exam Questions - Integration:(ax+b)ⁿ types
3. Integrating exponential functions e^x, e^ax and e^(ax+b)
4. Exam Questions - Integrating exponential functions e^x, e^ax and e^(ax+b)
5. Integrating reciprocal functions 1/x and 1/(ax+b)
6. Exam Questions - Integrating reciprocal functions 1/x and 1/(ax+b)
7. Integrals of the form : f '(x)/f(x)
8. Integrals of the form : f'(x)e^f(x)

Integrals of Trigonometric Functions

1. Integrals of sin x, cos x, sec² x
2. Integrals of the form sin(ax+b), cos(ax+b), sec² (ax+b) types
3. Exam Questions - Trigonometric types

Integration by Substitution

1. Integration by substitution
2. Square root types
3. Integration of trigonometric functions by substitution
4. Integration of exponential types by substitution
5. Integration by substitution using limits
6. Integration of trigonometric functions by substitution with limits
7. Exam Questions - Integration by substitution

Integration by Parts

1. Integration by parts
2. Integration by parts (ln types)
3. Integration by parts using limits
4. Proof of the formula - Integration by parts
5. Exam Questions - Integration by parts

Solution of Equations by Numerical methods

1. Graphical methods
2. Change of sign
3. Bisection method for locating a root in a given interval
4. Linear interpolation method for locating a root in a given interval
5. Iteration
6. Exam Questions - Iteration
7. Newton-Raphson method for locating a root in a given interval
8. Exam Questions - Newton-Raphson