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Mathematics Skills

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Course: Study Support: Mathematics
Book: Mathematics Skills
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Date: Monday, 23 December 2024, 10:53 AM

Description

Mathematics Skills

Table of contents

Success in Maths at UniSQ

Many undergraduates courses at UniSQ have embedded within their structure mathematics at various levels.  The following programs will

  • assist you to identify your mathematical readiness
  • develop the necessary mathematical skills

Success in Maths for Aviation

To support you in your Aviation studies, UniSQ Support for Learning provides a range of activities to assist with mathematics skills.

Quick Videos and print resources to refresh your Maths skills

Arithmetic & Mental Maths

Order of operations (print handout)

This 6 minute video covers the importance of the order of operations with examples.

Image to click on to play the Order of Operations video.

There is also a QuickTip for Order of Operations with aviation examples.

Operations involving negative numbers (print handout)

This 10 minute video covers how to calculate with negative numbers.

Click on the image to play the video for Calculating with negative numbers.

Decimals (including percentages and rates) (print handout)

This 11 minute video covers

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages, including percentage increase and decrease
  • rates.

Click on the image to play the video for decimals (including percentages and rates).

There is also a QuickTip for percentages.

Other QuickTips and other print resources for Arithmetic and Mental Maths:

Graphs and graphing

Relationships as graphs (print handout)

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

Video to play the video for Relationships as 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.

Image to play the video: gradient

Algebra

Introduction to Algebra: relationships as words (print handout)

This12 minute video covers:

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

Click on the image to play the Introduction to algebra: relationships in words video.

Substituting and rearranging equations (print handout)

This 12 minute video covers

  • substituting values into equations
  • rearranging equations.

Click on the video to play the substituting and rearranging equations video.

There is also a QuickTip to help you rearrange equations.

Trigonometry

Pythagoras' Theorem (print handout)

This 4 minute video covers using Pythagoras' Theorem.

Image to play the video for Pythagoras' Theorem

Introduction to trigonometry (printable handout)

This 20 minute video introduces:

  • labeling triangles for trigonometry
  • Pythagoras' Theorem
  • trigonometric ratios
  • worked examples using trigonometric ratios

trig intro

Success in Maths for Economics

Economics requires a basic knowledge of arithmetic, algebra and graphing.

Current students can use our Readiness testing in mathematics (UConnect username and password required) to self assess your knowledge and skills and should take about half an hour to complete.

Current students can access the refreshment materials to review their basic maths skills with examples and activities. There are also four videos designed to assist you with the first four modules of this material.

Anyone can access the below videos to assist with preparation for Success in Maths for Economics.

Module 1: Arithmetic

This 17-minute video includes information on

  • useful keys on the calculator
  • order of calculation
  • percentage change
  • decimals, fractions, ratios
  • reading tables

SIME1

Module 2: Introductory graphing

This 8-minute video includes information on

  • types of graphs
  • setting up graphs, plotting points
  • graphing from a table of values, and areas of graphs

SIME2

Module 3: Algebra

This 15-minute video includes information on

  • what are variables
  • what are formulae
  • using substitutions and interpretation

SIME3

Module 4: Further Graphing

This 14-minute video includes information on

  • gradients
  • special lines
  • Production Productivity Frontier

SIME4

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

Net present Value QuickTip

Success in Maths for Finance

To support students enrolled in Finance studies, The Library provides a range of activities to assist you to develop your mathematics skills.

To assist you if you have had bad experiences at school, not enough exposure to mathematics or the exposure was a number of years ago we have developed a series of videos and quick tips.

These resources are based on the materials that is required for courses like FIN1103.

To view files, click on the topic you wish to refresh.  A copy of presentation is available for you to download (Print Handout).

Videos to watch

Have you got a maths bully in your brain? 

This 3-minute video shows how to overcome the maths bully you may have in your brain.

Link image for the Maths Bully video

Order of operations (print handout)

This 7 minute video covers the importance of the order of operations with examples.

image for the order of operations video

Fractions (print handout)

This 16-minute video covers:

  • Equivalent fractions
  • Mixed number and improper fractions
  • Addition, subtraction, multiplication and division of fractions

image for the the fractions video

Decimals (print handout)

This 11-minute video covers:

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages
  • rates

Image for the Decimals video

Index Laws (print handout)

This 12-minute video introduces:

  • Power (or index) notation
  • Power (or index) rules
  • Using power (or index) rules to simplify expressions.

image for the index laws video

Substituting and rearranging equations (print handout)

This 12-minute video covers:

  • substituting values into equations
  • rearranging equations
  • including a range of examples


Image for the substituting and rearranging equations video.

Quick Tips

You can also have a look at our general Mathematics QuickTips. Here a some of the most important quick tips for FIN1103:



Success in Maths for (Beginning) Engineering

Engineers require a sound knowledge of mathematics.

To assist you if you have had bad experiences at school, not enough exposure to mathematics or the exposure was a number of years ago we have developed a series of videos.

Please complete the online readiness test for ENM1500 to self assess if you need to work through the videos. These videos are based on the appendices in the ENM1500 materials.

If you are studying ENM1600, there is also a readiness test you can use to self assess your needs, including refreshment material.

To view files click on the topic you wish to refresh and choose the MP4 or iPad option. A copy of presentation is available for you to download (Print Handout).

Arithmetic

Calculating with negative numbers (print handout)

This 10 minute video covers how to calculate with negative numbers.

Calculating with negative numbers

Order of operations (print handout)

This 7 minute video covers the importance of the order of operations with examples.

SIMBE2

Fractions (print handout)

This 16 minute video covers:

  • Equivalent fractions
  • Mixed number and improper fractions
  • Addition, subtraction, multiplication and division of fractions.

fractions_image

Fractions in other forms - Decimals (print handout)

This 11 minute video covers:

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages
  • rates.

decimals-image

Algebra

Algebraic relationships (print handout)

This 9 minute video introduces:

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

relationships-image

Substituting and rearranging equations (print handout)

This 12 minute video covers:

  •  substituting values into equations
  • rearranging equations
  • including a range of examples.

Substituting and rearrange equations video

Inequalities (print Handout)

This 12 minute video covers graphing inequalities and rearranging inequalities.

Inequalities video

Index laws (print handout)

This 17 minute video introduces:

  • Power (or index) notation
  • Power (or index) rules
  • using power (or index) rules to simply expressions.

index laws image

Graphing and Geometry

Geometry (print handout)

This 8 minute video covers common shapes and their characteristics.

geometry-image

Pythagoras' Theorem (print handout)

This 4 minute video covers using Pythagoras’ Theorem.

pythagoras-image

Relationships as graphs (print handout)

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

relationships as graphs image

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.

gradient image

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).

linear-image

Exponential graphs (print handout)

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

exp-graph-image

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

Success in Maths for Nursing & Health

To support students enrolled in nursing studies, UniSQ provides a range of activities to assist with mathematics skills.

Current students can use our Readiness testing in mathematics (UConnect username and password required) to self assess your knowledge and skills and should take about half an hour to complete.

Current students can access the refreshment materials provide a review of basic maths skills with examples and activities.

Quick Videos to refresh your Maths skills

Arithmetic

Calculating with negative numbers (print handout)

This 10 minute video covers how to calculate with negative numbers.

Video link for Calculating with negative numbers.

Order of operations (print handout)

This 7 minute video covers the importance of the order of operations with examples.

Order of operations link to video

Fractions (print handout)

This 16 minute video covers:

  • Equivalent fractions
  • Mixed number and improper fractions
  • Addition, subtraction, multiplication and division of fractions.

Link to video about fractions

Fractions in other forms - Decimals (print handout)

This 11 minute video covers:

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages
  • rates.

Image to click on for a video about decimals (fractions in other forms)

Metric conversions for weight (print handout)

This 6 minute video covers how to use use metric conversions for weight, specifically for health students.

Video link for metric conversions for weight.

Single Digit Long Division (print handout)

This 4 minute video covers shows full working for doing long division by hand.

Long Division video

Algebra

Algebraic relationships (print handout)

This 9 minute video introduces:

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

image as a link to video to introduction to algebra: Relationships as words

Health QuickTips

You can also have a look at our general Mathematics QuickTips. There are also some Health specific QuickTips also:


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

Success in Maths for Paramedicine

To support students enrolled in paramedicine studies, The Library provides a range of activities to assist with mathematics skills.

Quick Videos to refresh your Maths skills

Arithmetic

Calculating with negative numbers (print handout)

This 10 minute video covers how to calculate with negative numbers.

link to video for calculating with negative numbers

Order of operations (print handout)

This 7 minute video covers the importance of the order of operations with examples.

Fractions (print handout)

This 16 minute video covers:

  • Equivalent fractions
  • Mixed numbers and improper fractions
  • Addition, subtraction, multiplication and division of fractions

Single Digit Long Division (print handout)

This 4 minute video shows full working for doing long division by hand.

Image to click on to run the video for the long division example.

Fraction in other forms (print handout)

This 11 minute video covers:

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages
  • rates.

Decimals: Fractions in other forms video link

Metric conversions for weight (print handout)

This 6 minute video covers how to use use metric conversions for weight, specifically for health students.

Metric conversions for weight

Algebra

Algebraic relationships (print handout)

This 9 minute video introduces:

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

Introduction to Algebra: relationships in words video

Health QuickTips

You can also have a look at our general Mathematics QuickTips. There are also some Health specific QuickTips also:

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

Success in Maths for Teaching

Educators require a basic knowledge of numbers, algebra, measurement, chance & data and space.

Current students can access the readiness test (UConnect username and password required) which is a self-test that will help you decide the level of support you may need in these areas. It should take about half an hour to complete.

Current students can also access refreshment materials which provide a review of basic mathematical skills with examples and activities.

There are also a number of videos designed to assist you with this refreshment material.


Calculating with negative numbers (printable handout)

This 10 minute video covers how to calculate with negative numbers.

Calculating with negative numbers title slide

Order of Operations (printable handout)

This 7 minute video covers the importance of the order of operations with examples.

Order of Operations video

Fractions (print handout)

This 16 minute video covers:

  • Equivalent fractions
  • Mixed numbers and improper fractions
  • Addition, subtraction, multiplication and division.

Fractions video

Fractions in other forms - Decimals (printable handout)

This 11 minute video covers:

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages
  • rates.

Decimals: Fractions in other forms video

Index Laws (printable handout)

This 12 minute video introduces:

  • Power (or index) notation
  • Power (or index) rules
  • using power (or index) rules to simply expressions.

Index Laws image

Introduction to algebra: Relationships as words (printable handout)

This 9 minute video introduces:

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

Introduction to Algebra: Relationships in words video

Relationships as graphs (printable handout)

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

link

Substituting and rearranging equations (printable handout)

This 12 minute video covers:

  •  substituting values into equations
  • rearranging equations
  • including a range of examples.

link

Using Pythagoras' Theorem (printable handout)

This 4 minute video covers using Pythagoras’ Theorem.

Pythagoras' Theorem video link

Simultaneous Equation: Substituting method (printable handout)

This 15 minute video will cover the use of the substitution method to solve a system of two equations with two unknown variables.

link

Gradients (printable 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.

link to play the video for finding the gradient (slope) of straight (linear) lines

The Linear Equation (printable 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).

image to play the video for The Linear Equation

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

Success in Maths for Science

Students studying science require a sound knowledge of mathematics.

To assist you if you have had bad experiences at school, not enough exposure to mathematics or the exposure was a number of years ago we have developed a series of videos.

These videos are based on the materials that is assumed in MAT1100.

To view files click on the topic you wish to refresh. A copy of presentation is available for you to download (Print Handout).

Arithmetic

Calculating with negative numbers (print handout)

This 10 minute video covers how to calculate with negative numbers.

SIMBE1

Order of operations (print handout)

This 6 minute video covers the importance of the order of operations with examples

SIMBE2

Fractions (print handout)

This 16 minute video covers:

  • Equivalent fractions
  • Mixed number and improper fractions
  • Addition, subtraction, multiplication and division of fractions.

fractions_image

Fractions in other forms - Decimals (print handout)

This 11 minute video covers:

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages
  • rates.

decimals-image

Algebra

Algebraic relationships (print handout)

This 9 minute video introduces:

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

Introduction to Algebra: Relationships in words video

Rearranging equations (print handout)

This 12 minute video covers:

  •  substituting values into equations
  • rearranging equations
  • including a range of examples.

Substituting and rearranging equations video

Inequalities (print Handout)

This 12 minute video covers graphing inequalities and rearranging inequalities.

Inequalities video

Index laws (print handout)

This 17 minute video introduces:

  • Power (or index) notation
  • Power (or index) rules
  • using power (or index) rules to simply expressions.

index laws image

Graphing and Geometry

Geometry (print handout)

This 7 minute video covers common shapes and their characteristics.

geometry-image

Pythagoras' Theorem (print handout)

This 4 minute video covers using Pythagoras’ Theorem.

pythagoras-image

Relationships as graphs (print handout)

This 7 minute video covers the Cartesian co-ordinate system and drawing graphs.

relationships as graphs image

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.

gradient image

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).

linear-image

Exponential graphs (print handout)

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

exp-graph-image

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

Success in Maths for IT

Students studying IT require a sound knowledge of mathematics.

To assist you if you have had bad experiences at school, not enough exposure to mathematics or the exposure was a number of years ago we have developed a series of videos.

These videos are based on the materials that is assumed in MAT1101 (found in the appendix of your study material (USQ username and password required)).

To view files click on the topic you wish to refresh. A copy of presentation is available for you to download (Printable Handout).

Index Laws (printable handout)

This 17 minute video introduces:

  • Power (or index) notation
  • Power (or index) rules
  • Using power (or index) rules to simplify expressions.


Index Laws video link

Expanding Brackets (printable handout)

This 19 minute video covers:

  • Distributive Law
  • Expanding brackets (single, double and triple)
  • Common expansions to get to know

Expanding brackets video

Factorising quadratic expressions (printable handout)

This 13 minute video covers:

  • Simple factorisation (adding one set of brackets)
  • Factorising quadratic expressions

factorising quadratic expressions video

Solving quadratic equations using factorisation  (printable handout)

This 7 minute video covers:

  • Quadratic equations
  • solving quadratic equations using factorisation

Solving quadratic equations using factorisation video

Solving quadratic equations using the quadratic formula (printable handout)

This 12 minute video covers:

  • Quadratic equations
  • The quadratic equation
  • Using the quadratic equation 
  • finding the number of solutions a quadratic equations will have.

Solving quadratic equations using the quadratic formula video

Solving simultaneous equations (using the substitution method) (printable handout)

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

solving simultaneous equations using substitution video

Solving simultaneous equations (using the elimination method) (printable handout)

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

solving simultaneous equations using elimination video

Fractions (printable handout)

This 16 minute video covers

  • Equivalent fractions
  • Mixed number and improper fractions
  • Addition, subtraction, multiplication and division of fractions.

Algebraic fractions (printable handout)

This 11 minute  video steps though cancelling when there is algebraic terms in both the numerator and the denominator.

cancelling with algebraic fractions video


Success in Maths for Statistics

Statistics require a basic knowledge of arithmetic, algebra and graphing.

Current students can complete an online readiness testing in mathematics (UConnect username and password required) to self assess knowledge and help to decide the level of support required in these areas. It should take about half an hour to complete.

The refreshment materials provide a review of basic math's skills with full worked examples and activities (with answers).

Success in Maths for Statistics online workshops include topics of formulas, arithmetic, calculator, graphing and basic statistics.

Module 1: Arithmetic

This 16 minute video includes information on:

  • useful keys on the calculator
  • order of operations
  • calculating percentages.
 

Module 2: Algebra

This 19 minute video includes:

  • use of mathematical formulae
  • rearranging and solving equations
  • develop and solve equations relating to practical situations.

SIMS2-image

Module 3: Graphing

This 19 minute video includes:

  • representing relationships as graphs
  • drawing graphs
  • the linear function
  • applications of graphs in statistics
  • demonstration with the SPSS package.

SIMS3-image

Module 4: Statistics

This 12 minute video includes:

  • organisation and display of data
  • the analysis of data
  • calculating summary statistics

SIMS4-image

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

Maths Topics

Mathematics is often a part of university study, so it is important to develop the mathematical skills necessary for study within most disciplines. Resources are available for students who have maths anxiety or for students who are studying mathematics off-campus. Assistance is also available with using calculators.

Current students can access online readiness testing and refreshment materials to  prepare for the maths required in their programs.  There are also a range of video snippets which compliment these materials for courses such as nursing, economics, statistics and engineering.

A range of downloadable print materials for a range of maths topics are available to assist you to improve your prerequisite mathematics skills, as well as additional online maths and sciences resources. Activities and fully worked solutions are included for topics from arithmetic through to introductory calculus.

Arithmetic

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.

More than just numbers (Level A)

  • Our number system (including whole numbers, place value & estimation)
  • Working with numbers (including power notation and the square root)
  • Calculations involving negative numbers
  • Order of calculations
  • Fractions (including equivalent fractions, mixed numbers and improper fractions, calculating with fractions, addition and subtraction of fractions, multiplication of fractions and division of fractions)
  • Decimals (including converting between decimals and fractions)

A2-image

The Power of Numbers (Level A)

  • Power notation
  • Calculating with powers including multiplying powers, dividing powers, negative indices, the zero index, adding and subtracting powers, special powers, fractional indices, finding a power of a power and finding a power of a product) 
  • Common applications of powers (including scientific notation, the metric system, converting between units)

Comparing numbers (Level A)

  • Comparing quantities of subtraction 
  • Comparing quantities by division (including percentages)
  • Ratios (including ratios in squares, rectangles, circles & triangles) 
  • Rates 

Video based materials

You can also watch some video snippets for some of arithmetic concepts

Calculating with negative numbers (print handout)

This 10 minute video covers how to calculate with negative numbers.

Calculating with negative numbers video

Order of operations (print handout)

This 6 minute video covers the importance of the order of operations with examples

order of operations

Fractions (print handout)

This 16 minute video covers:

  • Equivalent fractions 
  • Mixed number and improper fractions 
  • Addition, subtraction, multiplication and division.

Fractions video

Decimals: Fractions in other forms (print handout)

This 11 minute video covers:

  • the link between fractions and decimals
  • converting between fractions and decimals
  • percentages, including percentage increase and decrease
  • rates.

Image to play the video: Decimals: Fractions in other forms.

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

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

A5-image

Generalising numbers - Algebra (Level A)

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

A7-image

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

A8-image

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)

B3-image

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

B4-image

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)

C3-image

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)

D2-image

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.

Introduction to Algebra: relationships in words video

Substituting and rearranging equations (print handout)

This 12 minute video covers

  • substituting values into equations
  • rearranging equations.

Substituting and 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.

Expanding brackets video

Algebra: factorising quadratic expressions (print handout)

This 13 minute video covers 

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

Factorising quadratics video

Solving quadratic equations using factorisation (print handout)

This 7 minute video covers

  • quadratic equations
  • solving quadratic equations using factorisation.

Solving quadratic equations using factorisation video

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 quadratic equations using the quadratic formula video

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 substitution method)

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).

Solving simultaneous equations (using the elimination method)



Inequalities (print handout)

This 12 minute video covers graphing inequalities and rearranging inequalities.

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.

Cancelling with Algebraic fractions video

Videos for Graphing

Geometry (print handout)

This 7 minute video covers common shapes and their characteristics.

Image for Geometry video

Pythagoras' Theorem (print handout)

This 4 minute video covers using Pythagoras' Theorem.

Image to play the video for Pythagoras' Theorem

Relationships as graphs (print handout)

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

Video to play the video for Relationships as 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.

Image to play the video: 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).

image to play the video: The linear equation

Exponential graphs (print handout)

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

Introduction to exponentials video

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.

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.

completing the square image

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.

graphing_a_straight_line

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

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    

generaliseing numbers - graphs

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    

exponential and logarithmic functions

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)    

functions and relations

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)

algebra and geometry

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.

Click on this image to play the video for index laws.

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.

logs

Solving equations using logarithms (printable handout)

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

solving eqns using logs

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

Trigonometry

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.

Comparing numbers (part of module only)

  • Comparing quantities of subtraction
  • Comparing quantities by division (including percentages)
  • Ratios (including ratios in squares, rectangles, circles & triangles)
  • Rates

comparing numbers

Trigonometry (Level B)

  • Sine (including the sine ratio, the sine function, the inverse of the sine function, degrees, minutes and seconds, amplitude and period)
  • Cosine (including the cosine ratio, the cosine function, the inverse of the cosine function, amplitude and period)
  • Tangent (including the tangent ratio, the tangent function, the inverse of the tangent function, amplitude and period)

Trigonometry Level B

Trigonometric functions (Level C)

  • Radian measure (including what are radians, converting from degrees to radians, converting from radians to degrees, using radians measure in real world applications)
  • Graphs of sine, cosine, and tangent functions
  • Modelling using trigonometric functions (including amplitude, vertical shift, the period of trigonometric functions, the phase of trigonometric functions)
  • Inverse functions
  • Solving trigonometric equations

Trigonometric Functions

Trigonometry (Level D)

  • Radian Measure
  • Polar Co-Ordinates
  • Trigonometric Identities and Multiple Angle Formulae
  • Solving Trigonometric Equation
  • Periodicity
  • Amplitude
  • Triangle Solution
  • Compound Angles
  • Solving Equations Involving Trigonometric Functions

Trigonometry Level D

Video based materials

Introduction to trigonometry (printable handout)

This 20 minute video introduces:

  • labeling triangles for trigonometry
  • Pythagoras' Theorem
  • trigonometric ratios
  • worked examples using trigonometric ratios

trig intro

Solution to triangles - using the Sine and Cosine Rules

This 18 minute video shows how to use the sine and cosine rules (that is, when you do not have right angled triangles.

solution of triangles

Using Trigonometric identities

This 11 minute video has a number of worked examples of how to use the trigonometric identities.

trig identities

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

Matrices, vectors and discrete maths

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.

Matrices (Level B)

  • What are matrices (including: tables to matrices, defining a matrix, and matrix equality)
  • Calculating with matrices (including: addition, subtraction and multiplication)
  • Some special matrices (including: the identity matrix and the inverse matrix)
  • Solving matrix equations
  • Real world problems

Matrices B

Analytical geometry (Level C)

  • Describing points in space (including: rectangular coordinates, polar coordinates, and vectors)
  • Describing straight lines (including: equations of a straight line, distance between points and mid-point of a line)
  • Describing other curves (including circles)
  • Transformations (including: transforming points, straight lines, parabolas, circles and other curves)

C5

Matrices (Level D)

  • Matrix representation of data
  • Addition and subtraction of matrices
  • Multiplication of a matrix by a scalar
  • Multiplication of a matrix by a vector
  • Multiplication of two matrices
  • Special matrices
  • Linear equations in matrix form
  • Solution of a system of linear equations by row reduction
  • Solution of linear equations using the inverse of the coefficient matrix
  • Inverse matrices
  • Determinant of a square matrix

Matrices D

Discrete Mathematics (Level D)

  • Factorials
  • Binomial theorem
  • Sequence and series
  • Mathematical induction

Discrete-maths

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

Calculus

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.

Differentiation – looking at change (Level C)

  • Rate of change – the problem of the curve
  • Instantaneous rate of change and the derivative function
  • Shortcuts for differentiation (including: polynomial and other power functions, exponential functions, logarithmic functions, trigonometric functions, and where the derivative cannot be found)
  • Some applications of differential calculus (including: displacement-velocity-acceleration: when derivatives are meaningful in their own right, twists and turns, and optimization)

c6-differentiation

Integration – looking at change (Level C)

  • Area under the curve
  • The definite integral
  • The antiderivative
  • Steps in integration (including: using standard rules of integration, integrals of functions with constant multiples, and integrals of sum and difference functions)
  • More areas
  • Applications of integral calculus

C7-integration

Differentiation

  • Derivatives
  • Gradient functions
  • Differentiability
  • Derivatives of simple functions
  • Practical interpretations of the derivative
  • Simple applications of the derivative
  • The product rule
  • The quotient rule
  • The chain rule
  • Stationary points
  • Curve sketching
  • Maximum / minimum problems
  • Newton-Raphson method for finding roots
  • Solutions to exercise sets

D5-differentiation

Integration

  • Integration of basic functions
  • Integration by guess and check
  • Integration by substitution
  • Definite integration
  • Trapezoidal Rule
  • Simpson’s Rule

D6-integration

Videos:

Chain and Product rules:

This video shows worked examples for how to use the chain and product rules for differentiating functions.

chain-product-rules

Integration by Substitution:

This video shows worked examples of how to use the integration by substitution technique.

int-sub

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

Statistics

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.

Dealing with data (Level A)

  • Collecting data
  • Organising and displaying data from tables
  • Organising and displaying raw data (including: frequency distribution tables and grouped frequency distribution tables, frequency histograms, and stem-and-leaf plots)
  • Analysing data (including: measuring the centre and spread of data)
  • Data with two variables.

dealing with data

Statistics and probability (Level B)

  • Collecting data (including: how data are displayed and exploring single variable data sets)
  • Take your chances – probability (including: experimental probabilities, theoretical probabilities, and probability in practice)
  • Describing single data sets (including: the centre and spread of a data set)
  • Describing bivariate data sets

statisitics and probability

You can also get assistance with Statistics by having a look at the Success in Maths for Statistics program.

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

Mastering the calculator

A series of booklets for Sharp and Casio calculators are available to assist USQ students to learn how to use their calculator effectively.

The instructions in these booklets explain how to perform basic calculations.

Sharp

Sharp EL531LH

Sharp EL531RH

Sharp EL531WH

Sharp EL556L

Sharp EL-531XH


 

Casio

Casio fx82AU

Casio fx82AU PLUS

Casio fx100AU

Casio fx100AU PLUS


Casio fx82LB

Casio fx82MS

Casio fx82TL

Casio fx100S

Texas Instruments

TI 30XIIB