Course Title: Use a range of techniques to solve mathematical problems

Part B: Course Detail

Teaching Period: Term2 2018

Course Code: MATH7081

Course Title: Use a range of techniques to solve mathematical problems

School: 174T School of VE Engineering, Health & Science

Campus: City Campus

Program: C4386 - Certificate IV in Tertiary Preparation

Course Contact: Namrita Kaul

Course Contact Phone: +61 3 9925 4387

Course Contact Email:

Name and Contact Details of All Other Relevant Staff

Rauha Quazi

+61 3 9925 4277

Nominal Hours: 110

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites


Course Description

This unit describes the skills and knowledge to use a range of specialist techniques and concepts to solve mathematical problems.

National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

VU22074 Use a range of techniques to solve mathematical problems


1. Use ratio, proportion and percent to solve problems

Performance Criteria:

1.1 Determine a ratio from information in a practical problem and express it in simplest form 1.2 Divide a quantity into a given ratio 1.3 Convert between fractions, decimals and percent forms 1.4 Calculate a percentage increase or decrease of a quantity


2. Use trigonometry to determine lengths

Performance Criteria:

2.1 Use Pythagoras' Theorem to determine an unknown side of a right angled triangle 2.2 Use Pythagoras' Theorem and trigonometric ratios to find unknown side lengths and angles in triangles


3. Use indices to solve problems

Performance Criteria:

3.1 Evaluate index form expressions 3.2 Simplify exponential expressions using the first two index laws 3.3 Convert between decimal numbers and numbers expressed in Standard Notation 3.4 Perform calculations with numbers expressed in Standard Notation, using a calculator


4. Use measurements to solve mensuration problems in two and three dimensions

Performance Criteria:

4.1 Determine lengths and perimeters of rectangles, triangles, circles and simple combined shapes using appropriate and correct units 4.2 Determine areas of rectangles, triangles, circles and simple combined shapes using appropriate and correct units 4.3 Determine volumes of prisms and pyramids with rectangular, triangular and circular cross-sections and with simple combined shapes as cross sections using appropriate and correct units


5. Substitute into and transpose equations and formulae

Performance Criteria:

5.1 Substitute given values into equations and formulae 5.2 Write equations to solve problems 5.3 Transpose formulae 5.4 Solve linear equations


6. Solve problems by plotting points

Performance Criteria:

6.1 Plot given points and points determined from the general formula y = mx+c on the Cartesian plane 6.2 Determine the gradient of a straight line 6.3 Determine the equation of a straight line, where the equation has the general form y = mx+c, y = a and x = b 6.4 Use interpolation and extrapolation to make predictions from the line of best fit, noting limitations


7. Present and evaluate statistical information

Performance Criteria:

7.1 Collect, organise and graphically represent statistical data 7.2 Interpret and analyse statistical information


8. Identify connections between formulae and graphical representations

Performance Criteria:

8.1 Use graphical techniques to draw linear and non-linear graphs 8.2 Develop equations for given linear graphs, including lines of best fit


9. Use algebraic techniques to analyse and solve problems

Performance Criteria:

9.1 Develop formulae to describe relationships between variables and substitute into formulae to find particular values 9.2 Use a range of techniques to solve a range of algebraic problems and perform algebraic manipulations

Learning Outcomes

Details of Learning Activities

- discussion of mathematical concepts relevant to each topic
- discussion of the mathematical routines and procedures for solving problems related to each topic
- working independently or in groups in solving problems on exercise and work sheets
- working in groups to solve more challenging problems requiring interpretation and evaluation of results

Teaching Schedule


Week starting




2 July

Order of operation

Directed numbers

Different types of fractions



9 July

Convert between fractions, decimals and precent

Significant figures

Rounding of numbers



16 July

Index laws

Simplify expressions using index laws



23 July

Ratio and proportion

Percentage increase and decrease

Quiz 1


30 July

Introduction to basic algebra

Substitution and transposition



6 Aug

Simplify algebraic expressions

Algebric techniques to solve problems

Solving linear equations



13 Aug

Graphing Linear equations

Determining Linear equations

Quiz 2


20 Aug

Application of linear equations and graphs

Simple non-linear graphs and their equations




Semester break: 27 Aug – 31 Aug



3 Sept

Scatter plot

Line of best fit

Workbook due


10 Sept

Introduction to Statistics: Types of Data

Collecting and Representing Statistical Data



17 Sept

 Interpret and analyse statistical information: Mean, Median, Mode, 5-Figure summary

Assignment hand out


24 Sept

Data collection for assignment and working on assignment



1 Oct

Pythagoras Theorem

Trigonometric ratios and applications

Assignment due


8 Oct

Perimeter and area of basic shapes and combined shapes



15 Oct

Total surface area and volume of basic shapes and combined shapes



22 Oct




29 Oct

Exam week


Learning Resources

Prescribed Texts


Other Resources

Online Learning materials will be provided during the course via canvas.

A basic scientific calculator is needed to solve problems.

An exercise book to complete exercises.

Overview of Assessment

Assessment in this course may include:

Assessment Tasks


Topics covered



Assessment 1: Quiz 1

Number skills, fractions and decimals and percent, indices


Week 4

Assessment 2: Quiz 2

Ratio and proportion,

Percent increase/decrease,

Substitution and transposition,

Basic algebra, linear equations


Week 7

Assessment 3: Workbook

Fractions and decimals


Ratio and proportion

Percent increase/decrease

Substitution, transposition

Graphing and solving linear equations

Simple non-linear graphs and their equations


Week 9

Assessment 4: Assignment

Collecting and representing data

Analyse and describe statistical information


Week 13

Assessment 5: Exam

Scatter plot

Line of best fit


Trigonometry and geometry


Week 17

Assessment Matrix

Other Information

This course is graded in accordance with competency-based assessment, but which also utilise graded assessment
CHD Competent with High Distinction (80 – 100%)
CDI Competent with Distinction (70 – 79%)
CC Competent with Credit (60 – 69%)
CAG Competency Achieved – Graded (50 – 59%)
NYC Not Yet Competent
DNS Did Not Submit for assessment

  • To pass the course you need to pass, on average, each type of assessment (test, assignments etc.) For example, if there are two quizzes you need to have an average of 50% to pass and you also need to have passed the other assessment types. You can’t make up marks from one type of assessment to another (e.g. pass the quizzes but fail the assignment component).
  • Late work that is submitted without an application for an extension (see below) will not be corrected.
  • APPLICATION FOR EXTENSION OF TIME FOR SUBMISSION OF ASSESSABLE WORK - A student may apply for an extension of up to 7 days from the original due date. They must lodge the application form (available online at least 24 hours before the due date. Students requiring longer extensions must apply for SPECIAL CONSIDERATION.
  • For missed assessments such as quizzes and exam- you (& your doctor if you are sick) must fill out a special consideration form. This form must be lodged online with supporting evidence prior to, or within, five working days of the scheduled time of the assessment.

Plagiarism is the presentation of the work, idea or creation of another person as though it is your own. It is a form of cheating and is a very serious academic offence that may lead to expulsion from the University. Plagiarised material can be drawn from, and presented in, written, graphic and visual form, including electronic data and oral presentation. Plagiarism occurs when the origin of the material used is not appropriately cited. It also occurs through enabling plagiarism, which is the act of assisting or allowing another person to plagiarise or to copy your own work. Please make sure you consider this carefully in completing all your work and assessments in this course and if you are unsure about whether you might have plagiarised, seek help from your teacher. 

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