Course Title: Apply mathematical techniques to scientific contexts

Part B: Course Detail

Teaching Period: Term2 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: nancy.varughese@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Clea Price

51.04.19

clea.price@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

None

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 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. 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 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. 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

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

 Week Starting Unit Topic Assessments 1 6th July 1: Algebra Monday: Orientation (no class) Thursday: 1.1: Linear Equations 2 13th July Monday: 1.2: Quadratic Equations Thursday: 1.3: Simultaneous Quadratic and Linear Equations 3 20th July Monday: 1.4: Cubic Equations Thursday: 2.1: Function and Set Notation 2: Functions 4 27th July Monday: 2.2: Linear Functions Thursday: 2.3: Quadratic Functions 5 3rd August Monday: 2.4: Cubic Functions Thursday: 2.5: Linearizing Functions 6 10th August Assignment One Monday: Assignment One – Algebra and Functions (20%) Due 17th August Thursday: 3.1: Index Laws 3: Indices and Logarithms 7 17th August Monday: 3.2: Solving Indicial Equations Thursday: 3.3: The Relationship between Indices and Logarithms 8 24th August Monday: 3.4: Exponential Graphs Thursday: 3.5: Applications of Exponentials and Logarithms Mid Semester Break 9 7th September 4: Statistics Monday: 4.1: Classification and Organisation of Data Thursday: Quiz One – Indices and Logarithms (15%) 10 14th September Monday: 4.2: Representing Data Thursday: 4.3: Measures of Central Tendency – Ungrouped Data 11 21st September Monday: 4.4: Measures of Central Tendency – Grouped Data Thursday: 4.5: Measures of Dispersion 12 28th September Monday: Assignment Two – Statistics (20%) Due 5th October Thursday: 5.1: Radians and the Unit Circle 5: Circular Functions 13 5th October Monday & Thursday: 5.2: Unit Circle, Symmetry, Exact Values and Identities 14 12th October Monday: 5.3: Circular Functions Thursday: 5.3: Circular Functions, 5.4: Applications of Circular Functions 15 19th October Monday: Quiz Two – Circular Functions (15%) Thursday: Exam Revision Exam Revision 16 26th October Monday & Thursday: Exam Revision 17 2nd November Monday: Public Holiday – No Class Thursday: Final Exam (30%) EXAM

Learning Resources

Prescribed Texts

References

Other Resources

A scientific calculator is recommended for this course.

Overview of Assessment

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

•

·         Assignment 1 – Algebra and Functions (20%)

·         Quiz 1 – Indices and Logarithms (15%)

·         Assignment 2 – Statistics (20%)

·         Quiz 2 – Circular Functions (15%)

·         Final Exam – Algebra, Functions, Indices and Logarithms, Statistics and Circular Functions (30%)

Assessment Matrix

Other Information

·         This course is graded in accordance with competency-based assessment, but also utilises graded assessment:

o    CHD: Competent with High Distinction (80-100%)

o    CDI: Competent with Distinction (70-79%)

o    CC: Competent with Credit (60-69%)

o    CAG: Competency Achieved – Graded (50-59%)

o    NYC: Not Yet Competent (0-49%)

o    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.

Course Overview: Access Course Overview