Course Title: Apply mathematical techniques to scientific contexts

Part B: Course Detail

Teaching Period: Term2 2013

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=a sinbx and y=a cosbx, 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.
  • Puzzle extension questions.
  • Completion of a Theory Workbook.

Teaching Schedule



10th July


Linear Equations

11th July2.1Linear Graphs 
17th July2.1, 2.7Simultaneous Linear Equations 
18th July2.2, 2.4The Definition of a Function and Function Notation 
24th July2.1, 2.4Properties of Functions: shape, intercepts and asymptotes 
25th July2.1, 2.5Expanding and Factorizing Quadratics 
31st July2.1, 2.5Solving Quadratic Equations 
1st August2.3, 2.5Sketching and Drawing Quadratics 
7th August2.6Determining the Rule of a Quadratic from its Graph 
8th August2.1, 2.7Simultaneous Quadratic and LInear Equations 
14th August5.1Representations of Statistical Data 
15th August2.1 - 2.7ASSESSMENTQUIZ 1
21st August3.1Scatterplots and Curves of Best Fit 
22nd August3.2Linearizing Curves of Best Fit 
28th August5.2, 5.3, 5.6Frequency Curves and Percentiles 
29th August5.1, 5.4, 5.6Mean, Median and Mode, Stem and Leaf PlotsPROJECT set
2nd - 8th September Mid-Semester Break 
11th September5.1, 5.5, 5.6Interquartile Range and Box and Whisker Plots 
12th September5.1, 5.5, 5.6Variance and Standard Deviation 
18th September4.1, 4.2Index Laws and Solving Indicial Equations 
19th September4.3, 4.4Logarithm Laws and Solving Logarithmic Equations 
25th September4.6Graphing Exponential FunctionsPROJECT due
26th September4.6Graphing Logarithmic Functions 
2nd October4.5Applications of Exponential and Logarithmic Functions 
3rd October4.1 - 4.6ASSESSMENTQUIZ 2
9th October1.1, 1.2Converting Between Degrees and Radians and the Unit Circle 
10th October1.3Trigonometric Ratios 
16th October1.4, 1.5Sine Graphs and Their Transformations 
17th October1.4, 1.5Cosine Graphs and Their Transformations 
23rd October1.4Tangent Graphs 
24th October1.6Applications of Circular Functions 
30th OctoberAllRevision Class 
31st OctoberAllRevision Class 

Learning Resources

Prescribed Texts

Theory Workbook (Provided in Class)

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

Quiz One: This quiz is worth 20 per cent of your final mark and is sat within normal class time. It covers all aspects of linear and quadratic algebra, graphs, and function notation.

Project: The project is worth 20 per cent of the final mark and is to be completed outside of class. It assesses students ability to apply statistics in everyday life.

Quiz Two: This quiz is worth 20 per cent of the final mark and is sat within normal class hours. It covers all aspects of indices and logarithms.

Exam: The exam is worth 40 per cent of the final mark and is sat during the exam period at the end of the semester. It assesses everything learnt in this course, with slightly more detail being paid to circular functions.

Assessment Matrix

Other Information

Breakdown of Nominal Hours:

  • 48 hours in class
  • 22 hours expected outside of class
  • Total: 70 Hours

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