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

Part B: Course Detail

Teaching Period: Term2 2013

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

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:

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 and angles

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 right-angled triangles


3. Use basic indices to solve problems.

Performance Criteria:

3.1 Evaluate simple index form expressions
3.2 Simplify simple 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
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 simple equations and formulae.

Performance Criteria:

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


6. Solve problems by plotting points.

Performance Criteria:

6.1 Plot given points and points determined from the general formula y = mx 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, 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, analyse and describe statistical information


8. Identify connections between formulae and graphical representations.

Performance Criteria:

8.1 Use graphical techniques to draw linear and simple nonlinear 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
9.2 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

Week beginning Topic/Assessment                                                                     Exercises                                                                                                             

Induction and Numeracy Assessment
Number Skills -Order of operations
                           - Directed number

Order of operations Exercise
Directed number Exercise
15/7 Calculations involving fractions Fractions Exercise 1.

Word problems involving fractions

Decimal places and significant figures
Calculations involving decimals

Fractions Exercise 2.

Decimal places and significant figures Exercise
Decimals Exercise


 Ratio and proportion

Ratio and proportion Exercise 1.
Ratio and proportion Exercise 2.
5/8 Introduction to percentages
Calculations involving percentages
Introduction to algebra
Percentages Exercise
Basic Albegra Exercise 1.

Simplifying algebraic expressions
Working with indices

Basic Albegra Exercise 2.
Basic Albegra Exercise 3.
Indices Exercises


Scientific notation
Solving linear equations

Scientific notation Exercise
Linear Equations Exercise 0.
Linear Equations Exercise 1.



2/9  Solving linear equations Linear Equations Exercise 2.
Linear Equations Exercise 3.
9/9 Working with formulae
Formulae Exercise 1.
Formulae Exercise 2.
Formulae Exercise 3.
16/9 Metric conversion
Calculating perimeter
Calculating area
Metric Conversion Exercise
Perimeter Exercise 1.
Perimeter Exercise 2.
Area Exercise 1.
Area Exercise 2.
30/9 Calculating volume
Calculations involving the Theorem of Pythagoras
QUIZ 3. 
Volume Exercise
Theorem of Pythagoras Exercise 1.
Theorem of Pythagoras Exercise 1.
7/10 Introduction to trigonometric ratios
Calculations involving trigonometric ratios
Trigonometric Ratios Exercise 1
Trigonometric Ratios Exercise 2
14/10 Calculations involving trigonometric ratios
Analysis of univariate data

Trigonometric Ratios Exercise 3.
Statistics Exercise 1.
Statistics Exercise 2.

21/10 Further analysis of univariate data
Introduction to linear relations 
Working with linear relations
Linear Relations Exercise 1.
Linear Relations Exercise 2.
Linear Relations Exercise 3.
28/10  Analysis of bivariate data Statistics Exercise 3.
4/11  Revision

Learning Resources

Prescribed Texts


Any Year 10 or Year 11 Mathematics textbook.
MATHEMATICS for Biology/Pathology Technicians by Carly Marshall and Sue van Megen

0 7035 8505 0

Other Resources

Students are required to purchase:

-  a scientific calculator for use in class and when completing assessment tasks

- lined exercise book in which to complete Exercises

- binder with plastic sleeves for storing Exercises and Worksheets

- writing materials.

Overview of Assessment

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

Assessment Tasks

4 Quizzes(best 3 results of 4 quizzes) 20% 
 Statistics Assignment 15%
 Mid-semester Test 25%
 Final Test 40%

Assessment Matrix

Other Information

1. Breakdown of nominal hours:
    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

2.Note: This course will contribute to your grade average result in the Certificate IV in Tertiary Preparation (Science) qualification. Please note that you must achieve a CREDIT average across the program to be granted a guaranteed pathway in the following programs.
Diploma of Nursing (subject to passing the VETASSESS)
Diploma of Laboratory Technology (Biotechnology)
Diploma of Technology (Pathology Testing)
Diploma of Conservation and Land Management
Diploma of Dental Technology.

Course Overview: Access Course Overview