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

Part B: Course Detail

Teaching Period: Term2 2014

Course Code: MATH5341

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

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C4327 - Certificate IV in Tertiary Preparation

Course Contact: Nancy Varughese

Course Contact Phone: +61 3 9925 4713

Course Contact Email:

Name and Contact Details of All Other Relevant Staff

Name: Clea Price
Office: 51.04.19

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

The purpose of this unit is to provide learners with the knowledge and skills to use a range of specialist techniques and concepts to solve mathematical problems.

National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

VU21058 Use a range of techniques to solve mathematical problems


1. Use ratio, proportion and percent to solve problems

Performance Criteria:

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


2. Use trigonometry to determine lengths and angles

Performance Criteria:

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


3. Use basic indices to solve problems.

Performance Criteria:

Evaluate simple index form expressions
Simplify simple exponential expressions using the first two index laws
Convert between decimal numbers and numbers expressed in Standard Notation
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:

Determine lengths and perimeters of rectangles, triangles, circles and simple combined shapes using appropriate and correct units
Determine areas of rectangles, triangles, circles and simple combined shapes using appropriate and correct units
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 simple equations and formulae.

Performance Criteria:

Substitute given values into simple equations and formulae
Write equations to solve simple problems
Transpose simple formulae
Solve simple linear equations


6. Solve problems by plotting points.

Performance Criteria:

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


7. Present and evaluate statistical information.

Performance Criteria:

Collect, organise and graphically represent statistical data
Interpret, analyse and describe statistical information


8. Identify connections between formulae and graphical representations.

Performance Criteria:

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


9. Use algebraic techniques to analyse and solve problems.

Performance Criteria:

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

Learning Outcomes

At the completion of this course, the student must be able to:
apply a wide range of strategies and techniques to solve mathematical problems including:
− using ratio, proportion and percent
− using trigonometry to determine lengths and angles
− using basic indices
− using measurements to solve mensuration problems in two and three dimensions
− substituting into and transposing simple equations and formulae
− solving problems by plotting points
− presenting and evaluating statistical information
− identifying connections between formulae and graphical representations
− using algebraic techniques to analyse and solve problems

Details of Learning Activities

Students are expected to participate actively in all learning activities that include:
- 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


Date Starts

Unit Topics Exercises/Assessment
1 7th July 1. Number Skills

Order of Operations

Exercise 1.1

Directed Numbers Exercise 1.2
2 14th July

2. Basic

Addition and Subtraction of Fractions Exercise 2.1
Multiplication and Division of Fractions Exercise 2.2
3 21st July Rounding to Decimal Places Exercise 2.3
Rounding to Significant Figures Exercise 2.4
4 28th July Decimal Calculations Exercise 2.5
Ratio and Proportion Exercise 2.6
5 4th August Percentages Exercise 2.7
Test One: Number Skills and Basic Calculations (15%)


 11th August
 3. Algebra
 Fundamental Algebra  Exercise 3.1
 Simplifying Algebraic Expressions  Exercise 3.2
 18th August
 Transposition and Substitution  Exercise 3.3
 Solving Linear Equations  Exercise 3.4
 25th August
 Graphing Linear Relations  Exercise 3.5
 Determining LInear Relations  Exercise 3.6
 1st September
4. Statistics  Test Two: Algebra (15%)

 Types of Data
Statistics Assignment Handed out in Class

 Exercise 4.1

 Representing Data Exercise 4.2
 Mean, Median and Mode Exercise 4.3

15th September Five Number Summaries and Boxplots Exercise 4.4
Scatterplots, Correlation and LInes of Best Fit Exercise 4.5
 29th September
 5. Indices
 Index Laws  Exercise 5.1
 Scientific Notation  Exercise 5.2
  Statistics Assignment Due Monday 29th September (20%)
 6th October
 6. Geometry
 Metric Conversion  Exercise 6.1
 Perimeter  Exercise 6.2
 13th October
 Area  Exercise 6.3
 Volume  Exercise 6.4
 20th October
 Pythagoras’ Theorem  Exercise 6.5
 Trigonometric Ratios  Exercise 6.6
16 27th October Test Three: Indices, Geometry and Trigonometry (15%)
Revision for Final Exam
 17  3rd November    EXAM WEEK: Final Exam (35%)

Learning Resources

Prescribed Texts


Croucher, J.S. (1998), Introductory Mathematics & Statistics for Business (3rd Edition). Australia: McGraw-Hill.


Washington, A. J. (1995), Basic Technical Mathematics with Calculus - Metric Version (6th Edition). USA: Addison-Wesley Publishing Company.


Hodgson, B., Karanikolas, N., Langsford-Willing, B. et al. (2010). Maths Quest 12 Mathematical Methods CAS: TI-Nspire 2.0 Edition. Australia: Jacaranda Wiley.


Nolan, J., Phillips, G., Novak, A. et al. (2006). Maths Quest 12: Further Mathematics, VCE Mathematics Units 3 and 4 (2nd Edition). Australia: Jacaranda Wiley.


Heffernan, J., Hodgson, B., & Parkhurst, S. (1993). Mathematical Methods VCE Units 1 & 2. Australia: Jacaranda.


Iampolsky, E., Williams, R., Nolan, J. et al. (2010). Maths Quest 11 Standard General Mathematics: TI-Nspire Edition. Australia: Jacaranda Wiley.


Williams, R., Karanikolas, N., Boucher, K. et al. (2010). Maths Quest 11 Mathematical Methods CAS (2nd Edition). Australia: Jacaranda Wiley.


Barnes, M., Bakogianis, R., Boucher, K. et al. (2013). Maths Quest 11 Advanced General Mathematics (2nd Edition). Australia: Jacaranda Wiley.


Other Resources

There are no prescribed texts for this course. Exercises and notes will be handed out each class and uploaded to blackboard.

Overview of Assessment

Assessment in this course will include:
Worksheets (ungraded)
Exercises (ungraded)
Quizzes (graded)
Assignment (graded)
Tests (graded)

Assessment Tasks

There are five (5) assessment tasks for this course:

  • Three tests worth 15% each for a total of 45%.
  • One take home assignment worth 20%.
  • One end of semester exam worth 35%

Assessment Matrix

Other Information

Classroom lessons 17 x 4 hours = 72 hours

Tutorials 17 x 1 hour = 17 hours
Work outside class on Exercises, Worksheets etc = 6 hours
Assignment work = 5 hours
Revision and preparation for assessment tasks = 10 hours

TOTAL 110 hours

Students who are absent on the day of an assessment task, whose performance in an assessment task has been severely affected by some unforeseen circumstance or who are unable to submit an assignment by the due date, need to apply for Special Consideration and apply within the allowed time frame

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 on the web ) at least the day before the due date. The application is lodged with the School Admin Office on Level 6, Bdg 51. Students requiring longer extensions must apply for Special Consideration (form available on the Web). For missed assessments such as exams- you (& your doctor if you are sick) must fill out a special consideration form. This form must be lodged at the HUB or online with supporting evidence (eg medical certificate), prior to, or within, 48 hours of the scheduled time of examination.

Late work that is submitted without an application for an extension will not be assessed.

Course Overview: Access Course Overview