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

Part B: Course Detail

Teaching Period: Term1 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

 Teacher: David Thomas

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 Section C: Unit Information
22219VIC Certificate III in Science and 22220VIC Certificate IV in Science
© State of Victoria
Version 1 2013
Page 36
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


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


WeekWeek beginningTopicsExercises
110 FebInduction
Number Skills – Order of Operations
Number Skills – Directed Numbers
1.1, 1.2
217 FebFractions2.1a, 2.1b
324 FebDecimal Places and Significant Figures
2.2, 2.3
43 MarchRatio and Proportion
Test 1: Number Skills and Fractions
510 MarchPercentages
2.5, 3.1
617 MarchScientific Notation
Introductory Algebra and Simplifying Algebraic Expressions
3.2, 4.1
724 MarchTest 2: Fractions, Decimals, Percentages, Ratios, Indices and Scientific Notation
Solving Linear Equations
831 MarchRevision
Mid-Semester Exam
97 AprilSolving Worded Linear Equations4.2b
1014 AprilTransposition and Substitution4.3
1128 AprilStatistics: Univariate Data5.1a, 5.1b
125 MayStatistics: Univariate Data
Statistics: Bivariate Data
5.1c, 5.2
1312 MayLinear Relations4.4a, 4.4b
1419 MayTest 3: Algebra, Univariate Data, Linear Relations.
Metric Conversion and Perimeter
1526 MayVolume & Pythagoras’ Theorem6.2b, 6.3
162 JuneTrigonometric Ratios6.4
179 JuneRevision &
Final Exam

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

3 Tests, 10% each = 30%

Mid-Semester Exam = 20%

Statistics Assignment =15%

Final Exam = 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 corrected

Course Overview: Access Course Overview