# Course Title: Apply mathematical techniques to scientific contexts

## Part B: Course Detail

Teaching Period: Term1 2017

Course Code: MATH7064

Course Title: Apply mathematical techniques to scientific contexts

School: 174T School of VE Engineering, Health & Science

Campus: City Campus

Program: C4386 - Certificate IV in Tertiary Preparation

Course Contact: Dinah Van Ruyven

Course Contact Phone: +61 3 9925 4287

Course Contact Email: dinah.vanruyven@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Iain McKenzie

51.07.05

9925 4723 (On Campus Extension 54723)

iain.mckenzie@rmit.edu.au

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 Element: 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 sinx, cosx and tanx 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 angle1.2 Angles are converted between degrees and radian measure1.3 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 x is measured in degrees or radians are sketched1.5  The graphs of y= a sin bx and y =a cos bx, giving amplitude and wavelength are sketched   1.6  Problems involving simple applications of circular functions are solved Element: 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. Element: 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. Element: 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 forms4.4 Logarithms are evaluated.4.5 Applied problems are solved using logarithms and simple exponential equations.4.6 Graphs of exponential functions are drawn. Element: 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

Please refer to the Elements of Competency.

Details of Learning Activities

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

Teaching Schedule

 Week Week Beginning Date Unit Topic Assessments 1 6th February 1: Algebra 1.1 Linear Equations 1.2 Quadratic Equations 2 13th February 1.2 Quadratic Equations (cont) 1.3 Simultaneous Quadratic and Linear Equations 3 20th February 1.4 Cubic Equations 4 27th February 2: Functions 2.1 Function and Set Notation 2.2 Linear Functions 2.3 Quadratic Functions 2.4 Cubic Functions 5 6th March 2.4 Cubic Functions (cont) 2.5 Linearizing Functions Assignment 1 Assignment 1 Algebra and Functions (20%) Due Wednesday 15th March 6 13th March 3: Indices and Logarithms 3.1 Index Laws 3.2 Solve Indicial Equations Assignment 1(Algebra and Functions) Due Wednesday 15th March 3.3 The Relationship Between Indices and Logarithms 7 20th March 3.4 Exponential Graphs 3.5 Applications of Exponentials and Logarithms 8 27th March Revision – Indices & Logarithms Quiz 1 – Indices and Logarithms Quiz 1 – Indices and Logarithms (15%) 9 3rd April 4: Statistics 4.1 Classification and Organisation of Data 4.2 Representing Data 10 10th April 17th April 4.3 Measures of Central Tendency – Ungrouped Data 4.4 Measures of Central Tendency – Grouped Data 11 24th April 4.5 Measures of Dispersion Assignment 2 Assignment 2 – Statistics (20%) Started in Class – Due Wednesday 10th May 12 1st May 5: Circular Functions 5.1 Radians and the Unit Circle 5.2 Unit Circle, Symmetry, Exact Values and Identities 13 8th May 5.3 Circular Functions Assignment 2 – Statistics (20%) Due Wednesday 10th May 5.4 Applications of Circular Functions 14 15th May Circular Functions Practice – online Revision Quiz 5.4 Applications of Circular Functions 15 22nd May 5.4 Applications of Circular Functions(cont) Online Quiz review Quiz 2 Circular Functions (15%) Quiz 2 16 29th May Revision Exam Revision Exam Revision 17 (Exam Week) 5th June Exam Final Exam (30%)

Learning Resources

Prescribed Texts

References

Other Resources

A scientific calculator is recommended for this course.

Overview of Assessment

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

 Assessment 1: Assignment 1 (20%) Assessment 2: Quiz 1 (15%) Assessment 3: Assignment 2 (20%) Assessment 4: Quiz 2 (15%) Assessment 5: Exam (30%)

To be deemed competent you must demonstrate an understanding of all aspects required of the competency. Assessment methods have been designed to measure your achievement of each competency in a flexible manner over multiple tasks.

Assessment Mapping Matrix

 Element/ Performance Criteria Covered Assign 1 Quiz 1 Assign 2 Quiz 2 Exam 1.1 X X 1.2 X X 1.3 X X 1.4 X 1.5 X 1.6 X X 2.1 X 2.2 X 2.3 X X 2.4 X 2.5 X X 2.6 X 2.7 X X 3.1 X 3.2 X 4.1 X X 4.2 X 4.3 X X 4.4 X 4.5 X X 4.6 X X 5.1 X 5.2 X 5.3 X 5.4 X 5.5 X 5.6 X

 Assessment Topic/Details Assignment 1 Assignment 1 - Algebra and Functions (20%)   Submit at office Level 6 Building 51 Quiz 1 Quiz 1 – Indices and Logarithms (15%) Assignment 2 Assignment 2 – Statistics (20%)   Submit at office Level 6 Building 51 Quiz 2 Quiz 2 Circular Functions (15%) EXAM Final Exam (30%)

Assessment Matrix

Other Information

This course is graded in accordance with competency-based assessment, but also utilises graded assessment
CHD: Competent with High Distinction (80-100%)
CDI: Competent with Distinction (70-79%)
CC: Competent with Credit (60-69%)
CAG: Competency Achieved – Graded (50-59%)
NYC: Not Yet Competent (0-49%)
DNS: Did Not Submit for Assessment

Late work that is submitted without an application for an extension will not be corrected.

APPLICATION FOR EXTENSION OF TIME FOR SUBMISSION FOR ASSESSABLE WORK:

o    A student may apply for an extension of up to 7 days from the original due date.

o    They must lodge the application form (available online http://www1.rmit.edu.au/students/assessment/extension) at least 24 hours before the due date.

o    The application is lodged with the School Admin Office on Level 6, Bdg 51, or emailed to the Coordinator (nancy.varughese@rmit.edu.au).

o    Students requiring extensions longer than 7 days must apply for Special Consideration (see the “Help Me” link in blackboard, via myRMIT studies or http://www1.rmit.edu.au/students/specialconsideration).

§  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 (eg. 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 procedures of special consideration and apply within the allowed time frame.

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