### Maths Topics

#### Algebra, functions and graphing

**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.

**Representing relationships** (Level A)

- Writing relationships in words
- Writing relationships as formulas
- Representing relationships as graphs
- Describing relationships

**Generalising numbers - Algebra** (Level A)

- Simplifying expressions
- Rearranging equations
- Solving equations Equations involving powers and roots including Pythagoras' Theorem
- Simultaneous equations

**Generalising numbers - Graphs **(Level A)

- 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

**Algebra: Tools for change **(Level B)

- Describing relationships
- Manipulating relationships (including grouping like terms, factors and factorization, algebraic fractions and working with powers)
- Special relationships (including equations, solving equations, rearranging formulas, inequations, absolute value, quadratic equations, factorisation of quadratic equations, the quadratic formula, quadratic equations in the real world, solving simultaneous equations using substitution and elimination)

**Relations and functions** (Level B)

- What are relations and functions (including domain and range of relations and functions and function notation)
- The linear function (including rate of change of a linear function, the inverse – undoing a function and when two linear functions meet)
- The quadratic function (including sketching parabolas and rate of change of a quadratic function)
- Other functions

**Relations and functions** (Level C)

- 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** (Level D)

- 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 for Algebra**

You can also watch some video snippets for some of algebra concepts.

**Introduction to Algebra: relationships as words **(print handout)

This 12 minute video covers

- translating from words to symbols (relationships)
- variables and expressions
- collecting like terms.

**Substituting and rearranging equations** (print handout)

This 12 minute video covers

- substituting values into equations
- rearranging equations.

**Expanding Brackets** (print handout)

This 19 minute video covers

- the distributive law
- expanding brackets (single, double and triple)
- common expressions to get to know.

**Algebra: factorising quadratic expressions** (print handout)

This 13 minute video covers

- simple factorisations (adding one set of brackets)
- factorings quadratic expressions (two brackets).

**Solving quadratic equations using factorisation** (print handout)

This 7 minute video covers

- quadratic equations
- solving quadratic equations using factorisation.

**Solving quadratic equations using the quadratic formula** (print handout)

This12 minute video covers

- quadratic equations
- the quadratic equation
- using the quadratic equation
- finding the number of solutions a quadratic equation will have.

**Solving simultaneous equations (using the substitution method)** (print handout)

This 15 minute video covers the use of substitution method to solve simultaneous equations (two unknown variables and two equations).

**Solving simultaneous equations (using the elimination method)** (print handout)

This 16 minute video covers the use of the elimination method to solve simultaneous equations (two unknown variables and two equations).

**Inequalities** (print handout)

This 12 minute video covers graphing inequalities and rearranging inequalities.

**Cancelling with algebraic fractions** (print handout)

This 5 minute video steps though cancelling when there is algebraic terms in both the numerator and the denominator.

**Videos for Graphing**

**Geometry** (print handout)

This 7 minute video covers common shapes and their characteristics.

**Pythagoras' Theorem** (print handout)

This 4 minute video covers using Pythagoras' Theorem.

**Relationships as graphs** (print handout)

This 8 minute video covers the Cartesian co-ordinate system and drawing graphs.

**Gradient** (print handout)

This 7 minute video covers how to

- find the gradient (or slope) of a straight (linear) line
- drawing a line using a point and the gradient.

**The linear equation** (print handout)

This 7 minute video covers

- the linear equation
- finding the gradient and \(y\)-intercept
- the slope-point equation
- equations to special lines (e.g. horizontal and vertical lines).

**Exponential graphs** (print handout)

This 3 minute video introduces the exponential equation for growth and decay along with with the corresponding graphs.

**Other videos which might be useful**

**Solving Equations: **

The purpose of these videos is to use flow-charts and a process called back tracking to solve equations. These videos build on each other.

**Rearranging Formulas:**

These presentations demonstrate how rearranging algebraic formula can be achieved using a flow-chart approach.

**Simplifying Indices**:

This video shows has worked examples of how to use the index laws to simply expressions.

**Algebraic fractions:**

This video steps though cancelling when there is algebraic terms in both the numerator and the denominator.

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