Topic 2: Functions and equations

Functions

1. f(x) notation

Completing the Square

1. Completing the square
2. Applications of completing the square

Quadratic Equations

1. Solve by factorising
2. Solve by completing the square
3. Solve by the quadratic formula
4. Exam Questions - Solved by the quadratic formula
5. Solving quadratic equations in some function of x

Quadratic Equations – Roots and Discriminant

1. Roots and discriminant of a quadratic equation
2. Exam Questions - Roots and discriminant

Quadratic Graphs

1. Sketching quadratic graphs

Polynomials

1. Polynomials

Working with Functions

1. f(x) notation
2. Domain and range
3. Exam Questions - Domain and range
4. Even & Odd Functions
5. Combination of functions
6. The inverse of a function
7. Self inverse functions
8. Graphical relationship between f(x) and its inverse
9. Exam Questions - Inverse functions
10. Exam Questions - Functions

Sketching Cubic and Reciprocal Curves

1. Sketching cubic curves
2. Sketching reciprocal curves of the form y = k/x
3. The graph of f=1/f(x) given the graph of y=f(x)

Graph Transformations and Asymptotes

1. Basic graphs used in transformations
2. Translations of graphs
3. Reflections of graphs
4. Stretches of graphs
5. Exam Questions - Graph transformations

Graphs of Rational Functions

Exponential Functions and Logarithms

1. Exponential functions: what they are and their graphs
2. What do we mean by a log?
3. Rules of logs
4. Logarithms - Change of Base
5. Simplifying and expanding
6. Converting between Logarithmic and Power (Exponential) equations
7. Modelling exponential growth and decay
8. Exponential and log equations
9. Simultaneous equations
10. Solving inequalities
11. Exam Questions - Logarithms

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