Course Title: Apply mathematical techniques to scientific contexts

Part B: Course Detail

Teaching Period: Term2 2014

Course Code: MATH7064

Course Title: Apply mathematical techniques to scientific contexts

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: 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


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:

Sine cosine and tangent 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 degrees to the function of an acute angle.

Angles are converted between degrees and radian measure.

The value of the three basic trigonometric ratios of any angle given in degrees or radians is determined.

The graphs of y=sinx, y=cosx and y=tanx, where x is measured in degrees or radians are sketched.

The graphs of y=asinbx and y=acosbx, giving amplitude and wavelength are sketched.

Problems involving simple applications of circular functions are solved.


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

Performance Criteria:

Simple problems involving direct and inverse proportion are solved.

Given a graph, its general shape, rates of change, intercepts and asymptotes are described and its domain and range are given using set notation.

The graph of a quadratic function is sketched.

Given its graph, the set of coordinates which make up the relation or its equation determine whether a relation is a function.

Quadratic equations are solved both algebraically and graphically.

Equations are determined from graphs with known quadratic rules.

Simultaneous equations are solved algebraically and graphically.


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

Performance Criteria:

A set of non-linear data is transformed to a linear form and the line of best fit is drawn.

The corresponding non-linear formula is determined.


4 Solve problems involving exponential and logarithmic functions

Performance Criteria:

Exponential expressions are simplified using the laws of indices.

Exponential equations are solved without using logarithms.

Expressions are converted between exponential and logarithmic forms.

Logarithms are evaluated.

Applied problems are solved using logarithms and simple exponential equations.

Graphs of exponential functions are drawn.


5 Collect and process numerical data to illustrate its statistical properties

Performance Criteria:

Statistical data is presented using tables and graphs.

Using frequency distribution vurves, determine numbers and/or percentage values which have a particular characteristic.

Using cumulative frequency curves, determine percentiles for data.

Measures of central tendency are determined for a given set of data given limitation of their use in isolation.

Determine measures of spread giving limitaion of their use in isolation.

Properties of statistical data are determined.

Learning Outcomes

By the end of this course, students will be able to:

  • Understand technical mathematical terminology.
  • Apply mathematical logic to a scientific context.
  • Use a scientific calculator for complex calculations.

Details of Learning Activities

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

Teaching Schedule

WeekStart Date                           TopicExercisesEXAM WEEK: Final Exam (40%)
17th July1. Basic Maths

Basic Mathematics



2. AlgebraLinear Equations2.1
214th JulyGraphing Linear Functions2.2
Function and Set Notation2.3
321st JulyQuadratic Equations - Expanding, Factorizing and Solving2.4
Graphing Quadratic Functions2.5
428th JulySimultaneous Equations2.6
Test One: Basic Maths and Algebra (15%)
54th August3. Indices and LogarithmsIndex Laws and Solving Indicial Equations3.1
Graphing Exponential Functions3.2
611th AugustLogarithm Laws and Solving Logarithmic Equations3.3
Graphing Logarithmic Functions3.4
718th AugustTest Two: Indices and Logarithms (15%)
 4. Statistics
Representing Data4.1
825th AugustMeasures of Central Tendency4.2
Cumulative Frequency Tables and Graphs4.3
Mid-Semester Break 1st September - 5th September     
8th September 
 4. Statistics
Measures of Dispersion4.4
Test Three: Statistics (15%)
15th September 
5. Trigonometry 
Pythagoras’ Theorem and Trigonometric Ratios5.3
Applications of Trigonometry5.4
 22nd September
Degrees, Minutes and Seconds 5.1 
 Conversion between Degrees and Radians 5.2
1229th SeptemberThe Unit Circle5.5
Unit Circle Symmetry5.6
136th OctoberExact Values5.7
Trigonometric Identities5.8
1413th October6. Circular FunctionsSine and Cosine Graphs6.1
Tangent Graphs6.2
1520th OctoberApplications of Circular Functions6.3
Test Four: Trigonometry and Circular Functions (15%)
1627th OctoberREVISION WEEK
173rd November

Learning Resources

Prescribed Texts

Scientific Calculator (not CAS or Graphing)

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


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


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


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


Heffernan, J. et al. (1993). Mathematical Methods VCE Units 1 & 2. Australia: The Jacaranda Press


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


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


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


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


Other Resources

Overview of Assessment

Assessments for this course may include the following:
assignments, quizzes and written exams


Assessment Tasks

  • Test One: Basic Mathematics and Algebra
  • Test Two: Indices and Logarithms
  • Test Three: Statistics
  • Test Four: Trigonometry and Circular Functions
  • Exam: All Topics.

Assessment Matrix

Other Information


  • 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