Mathematics Skills: Algebra, functions and graphing

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)