Mathematics Skills

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

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Generalising numbers - Algebra (Level A)

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

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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

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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)

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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

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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)

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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)

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Videos:

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. 

solving_eqns_1-image  solving_eqns_2-image  solving_eqns_3-image

solving_eqns_4-image  solving_eqns_5-image  solving_eqns_6-image

Rearranging Formulas: 

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

rearrange1    

Completing the square:

This video goes through examples of how to complete the square.

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Simplifying Indices:

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

simplifying_indices

Algebraic fractions:

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

algebriac_fractions

Graphing a straight line

This video works through the key features and examples of graphing straight lines.

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