Course Title: Apply mathematical techniques to scientific contexts

Part B: Course Detail

Teaching Period: Term1 2014

Course Code: MATH7064

Course Title: Apply mathematical techniques to scientific contexts

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C3305 - Certificate III in Science

Course Contact: Namrita Kaul

Course Contact Phone: +61 3 9925 4309

Course Contact Email:

Name and Contact Details of All Other Relevant Staff

Nominal Hours: 70

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

There are no pre-requisites for this unit.

Course Description

The purpose of this unit is to provide learners with knowledge and skills related to basic statistics, functions and their graphs, circular functions, exponents and logarithms.

National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

VU20934 Apply mathematical techniques to scientific contexts


1. Use unit circle definitions of trigonometric quantities, graphs of the three basic trigonometric functions and radian measure to solve mathematics problems.

Performance Criteria:

1.1: sinθ, cosθ and tanθ are defined in terms of the unit circle and symmetry properties are used to convert the function of a negative angle or an angle greater than 90° to the function of an acute angle.
1.2: Angles are converted between degrees and radian measure.
1.3: The value of the three basic trigonometric ratios of any angle given in degrees or radians is determined.
1.4: The graphs of y=sinx, y=cosx and y=tanx, where x is measured in degrees or radians are sketched.
1.5: The graphs of y=asinbx and y=acosbx, giving amplitude and wavelength are sketched.
1.6: Problems involving simple applications of circular functions are solved.


2. Use simple algebraic functions and their graphs to solve mathematics problems.

Performance Criteria:

2.1: Simple problems involving direct and inverse proportion are solved.
2.2: Given a graph, its general shape, rates of change, intercepts and asymptotes are described and its domain and range are given using set notation.
2.3: The graph of a quadratic function is sketched.
2.4: Given its graph, the set of co-ordinates which make up the relation or its equation determine whether a relation is a function.
2.5: Quadratic equations are solved both algebraically and graphically.
2.6: Equations are determined from graphs with known quadratic rules.
2.7: Simultaneous equations are solved algebraically and graphically.


3. Determine non-linear laws by transforming them into a linear form.

Performance Criteria:

3.1: A set of non-linear data is transformed to a linear form and the line of best fit is drawn.
3.2: The corresponding non-linear formula is determined.


4. Solve problems involving exponential and logarithmic functions.

Performance Criteria:

4.1: Exponential expressions are simplified using the laws of indices.
4.2: Exponential equations are solved without using logarithms.
4.3: Expressions are converted between exponential and logarithmic forms.
4.4: Logarithms are evaluated.
4.5: Applied problems are solved using logarithms and simple exponential equations.
4.6: Graphs of exponential functions are drawn


5. Collect and process numerical data to illustrate its statistical properties.

Performance Criteria:

5.1: Statistical data is presented using tables and graphs.
5.2: Using frequency distribution curves, determine numbers and/or percentage values which have a particular characteristic.
5.3: Using cumulative frequency curves, determine percentiles for data.
5.4: Measures of central tendency are determined for a given set of data giving limitation of their use in isolation.
5.5: Determine measures of spread giving limitation of their use in isolation.
5.6: Properties of statistical data are determined.

Learning Outcomes

Details of Learning Activities

  • Class discussions of mathematical theories and proofs.
  • Worksheets
  • Practice Exams
  • Exercises

Teaching Schedule

Week Starting Topic Activities
10th February

Fundamentals: BODMAS, Transposition, Fractions and Surds

Linear Equations


Exercise 1

Exercise 2.1

17th February

Linear Functions

Function and Set Notation

Exercise 2.2

Exercise 2.3

24th February

Quadratic Equations

Quadratic Functions

Exercise 2.4

Exercise 2.5

3rd March

Simultaneous Equations

Test 1: Linear and Quadratic Algebra [10%]

Exercise 2.6


10th March

Index Laws

Exponential Functions

Exercise 3.1

Exercise 3.2

17th March

Logarithm Laws

Logarithmic Functions

Exercise 3.3

Exercise 3.4

24th March

Test 2: Exponentials and Logarithms [10%]

Measures of Central Tendency



Exercise 4.1

31st March


Mid-Semester Exam: Fundamentals, Linear and Quadratic Algebra, Exponentials and Logarithms [30%]



7th April

Measures of Spread

Cumulative Frequency Tables and Graphs

Exercise 4.2

Exercise 4.3

14th April

Scatter Diagrams

Lines of Best Fit

Exercise 4.4

Exercise 4.5

28th April


Trigonometric Ratios

Exercise 4.6

Exercise 5.1

5th May

Degrees and Radians

The Unit Circle

Exercise 5.2

Exercise 5.3

12th May

Symmetry and the Unit Circle


Exercise 5.4


19th May

Test 3: Statistics, Trigonometry, The Unit Circle [10%]

Sine Graphs


Exercise 6.1

26th May

Cosine Graphs

Tangent Graphs

Exercise 6.2

Exercise 6.3

2nd June

Practice Exam




9th June


Final Exam: Focus on Statistics, Trigonometry, The Unit Circle and Circular Functions. [40%]



Learning Resources

Prescribed Texts

Scientific Calculator (not CAS or Graphing)

SUGGESTED: Blank A4 Binder Book for Exercises or Loose-Leaf Paper and a Folder.


COFFEY, D. et al. (2000) Heinemann Outcomes Mathematics 10: CSF 11 Edition. Port Melbourne: Heinemann.

HEFFERNAN, J., HODGSON, B. & PARKHURST, S. (1993) Mathematical Methods VCE Units 1 & 2. Milton: The Jacaranda Press.

IAMPOLSKY, I. et al. (2013) Maths Quest 11 Standard General Mathematics. Milton: John Wiley & Sons Australia Ltd.

NOLAN, J. et al. (2006) Maths Quest 12 Further Mathematics. Milton: John Wiley & Sons Australia Ltd.

NOLAN, J. et al. (2000) Maths Quest 11 Mathematical Methods. Milton: John Wiley & Sons Australia Ltd.

NOVAK, A. et al. (2013) Maths Quest 12 Further Mathematics. Milton: John Wiley & Sons Australia Ltd.

WILLIAMS, R. et al. (2013) Maths Quest 11 Mathematical Methods CAS. Milton: John Wiley & Sons Australia Ltd.

Other Resources

Overview of Assessment

Assessment may consist of written tests, in class activities, presentations & written reports.


Assessment Tasks

  • Three tests worth 10% each.
  • Mid Semester Exam worth 30%.
  • Final Exam worth 40%

Assessment Matrix

Other Information

Breakdown of Nominal Hours:

  • 48 hours in class
  • 22 hours expected outside of class
  • Total: 70 Hours
  • To pass the course you need to pass, on average, each type of assessment
  • 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
  • If you miss an assessment task due to unavoidable circumstances, you need to follow the procedure of special consideration and apply within the allowed time frame.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