Course Title: Apply mathematical techniques to scientific contexts

Part B: Course Detail

Teaching Period: Term1 2015

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:

1.1: sin x, cos x and tan x 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 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= sin x, y= cos x and y= tan x, where is measured in degrees or radians are sketched.
1.5: the graphs of and y = a sin bx and y = a cos bx , giving amplitude and wavelength are sketched.
1.6: problems are solved using simple applications of circular functions.


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

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

  • discussions about the theory of mathematical concepts and their real world applications.
  • exercises to consolidate knowledge

Teaching Schedule

WeekUnit, Topic, Assessments
1Unit 1 – Algebra
Mon: Orientation (no class today)
Thur: 1.1 – Linear Equations
2Mon: 1.2 – Quadratic Equations
Thur: 1.3 – Simultaneous Linear and Quadratic Equations
3Mon: 1.4 – Cubic Equations
Unit 2 – Functions
Thur: 2.1 – Function and Set Notation
4Mon: 2.2 – Linear Functions
Thur: 2.3 – Quadratic Functions
5Mon: 2.4 – Cubic Functions
Thur: 2.5 – Linearizing Functions
6In Class Assignment 1: Algebra and Functions (20%)
7Unit 3 – Indices and Logarithms
Mon: 3.1 – Index Laws
Thur: 3.2 – Solving Indicial Equations
8Mon: 3.3 – Relationship Between Indices and Logarithms
Thur: 3.4 – Exponential Graphs

(Mid – Semester Break 4th April – 12th April)

9Mon: 3.5 – Applications of Exponentials and Logarithms
Thur: Quiz 1 – Indices and Logarithms (10%)
10Unit 4 – Statistics
Mon: 4.1 – Types of Data and Organising Data
Thur: 4.2 – Graphical Representations of Univariate Data
11Mon: 4.3 – Measures of Central Tendency
Thur: 4.4 – Measures of Spread
12In Class Assignment 2: Statistics (20%)
13Unit 5 – Circular Functions
Mon: 5.1 – The Unit Circle and Symmetry
Thur: 5.2 – Applications of the Unit Circle in Trigonometry
14Mon: 5.3 – Basic Graphs of Sine, Cosine, and Tangent Functions
Thur: 5.4 – Transformations of Sine and Cosine Functions
15Mon: 5.5 – Applications of Circular Functions
Thur: Quiz 2 – Circular Functions (10%)
16Mon and Thur: Revision of all topics.
17Exam Week
Thursday 11th June: Open Book Exam – All Topics (40%)

Learning Resources

Prescribed Texts


Other Resources

A scientific calculator is recommended for this course. Graphical calculators are not allowed.

Overview of Assessment

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


Assessment Tasks

  • In Class Assignment 1 (Algebra and Functions)  20%
  • Quiz 1 (Indices and Logarithms)  10%
  • In Class Assignment 2 (Statistics) 20%
  • Quiz 2 (Circular Functions) 10%
  • Final Exam   40%

Assessment Matrix

Other Information

This course is graded in accordance with competency-based assessment, but which also utilises graded assessment
CHD- Competent with High Distinction (80 – 100%)
CDI- Competent with Distinction (60 – 79%)
CC- Competent with Credit (50 – 59%)
CAG- Competency Achieved – Graded (0 – 49%)
NYC- Not Yet Competent
DNS- Did Not Submit for assessment

  • All assessment types must be passed (exams, prac, and assignments etc.). For example, if there are two tests you need to have an average of 50% to pass. You can’t make up marks from one type of assessment to another (e.g. pass the tests but fail the prac component).
  • Late work that is submitted without an application for an extension will not be corrected.
  • APPLICATION FOR 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 online at least 24 hours before the due date. The application is lodged with the School Admin Office on Level 6, Bdg 51, or emailed to the Coordinator (
  • Students requiring extensions longer than 7 days must apply for Special Consideration (see the ‘Help me’ link in blackboard, via myRMIT studies or 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 online with supporting evidence (e.g. medical certificate), prior to, or within, 48 hours of the scheduled time of examination.
  • 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.

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