### Maths Topics

#### Exponentials and logarithms

### Print based materials

Print Materials to assist with any pre-requisite mathematics required in USQ courses. These materials are based on USQ's Tertiary Preparation Program. Mathematics modules are presented in increasing level of difficulty and complexity from Level A through to Level D.

**Generalising Numbers** (part of module)

- Gradients of line graphs (including finding the gradient of a given line, and drawing a line given the gradient)
- Linear equations (including special lines, and what if two lines cross)
- Introduction to curve
- Parabolic equations (including the axis of symmetry)
**Exponential equations (including a special number)**- When two graphs meet

**Exponential and logarithmic functions**

- Exponential functions (including the function and its graph, case studies, average rate of change and the inverse of the exponential function)
- Logarithmic functions (including the function and its graph, case studies, average rate of change and properties of logarithms)
- Putting it all together – solving equations and real world applications

**Relations and functions** (part of module)

- What are functions
- Function toolbox (including functional notation, zero conditions of a function, average rate of change of a function, continuity and the inverse of a function)
- Families of functions (including polynomial functions (which include the constant function, the linear function, the quadratic function, and other polynomial functions),
**exponential and logarithmic functions**, rational functions and functions over an integral domain (including arithmetic and geometric sequences)

**Algebra, functions and geometry**

- Inequalities and the real number line (including operations on inequalities, and linear inequalities of two variables)
- Quadratic Equations and Completing the Square
- Functions (including polynomials, rational functions, other important non-linear functions, solving simultaneous equations algebraically and graphically inverse Functions and continuity)

### Videos:

**Index Laws** (print handout)

This 17 minute video introduces:

- Power (or Index) laws
- Power (or index) rules
- Using power (or index rules to simplify expressions.

**An introduction to logarithms **(printable handout)

This 12 minute video shows an introduction to logarithms. It has examples of using different bases and applying the different logarithms laws.

**Solving equations using logarithms** (printable handout)

This 7 minute video works through some examples of using logarithms to solve equations.

You can also get help Mastering your calculator – free, easy to follow online booklets on a range of scientific calculators.