Course Title: Apply mathematical techniques to scientific contexts
Part B: Course Detail
Teaching Period: Term1 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: nancy.varughese@rmit.edu.au
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 nonclassroom activities.
Prerequisites and Corequisites
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 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.
1.5 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 coordinates 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 nonlinear laws by transforming them into a linear form 
Performance Criteria: 
3.1: A set of nonlinear data is transformed into a linear form and the line of best fit is drawn. 3.2: The corresponding nonlinear 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
 Class discussions of mathematical theories and proofs.
 Worksheets
 Practice Exams
 Exercises
Teaching Schedule
Week Starting  Topic  Activities 
10th February 
Induction Linear Equations 
Exercise 2.1 
17th February 
Linear Functions Function and Set Notation 
Exercise 2.2 Exercise 2.3 
24th February 
Quadratic Equations Quadratic Functions 
Exercise 2.4 Exercise 2.5 
3rd March 
Simultaneous Equations Test 1: Linear and Quadratic Algebra [10%] 
Exercise 2.6

10th March 
Index Laws Exponential Functions 
Exercise 3.1 Exercise 3.2 
17th March 
Logarithm Laws Logarithmic Functions 
Exercise 3.3 Exercise 3.4 
24th March 
Test 2: Exponentials and Logarithms [10%] Measures of Central Tendency 
Exercise 4.1 
31st March 
Revision MidSemester Exam: Fundamentals, Linear and Quadratic Algebra, Exponentials and Logarithms [30%] 
Worksheets

7th April 
Measures of Spread Cumulative Frequency Tables and Graphs 
Exercise 4.2 Exercise 4.3 
14th April 
Scatter Diagrams Lines of Best Fit 
Exercise 4.4 Exercise 4.5 
21st April  MID SEMESTER BREAK  
28th April 
Correlation Trigonometric Ratios 
Exercise 4.6 Exercise 5.1 
5th May 
Degrees and Radians The Unit Circle 
Exercise 5.2 Exercise 5.3 
12th May 
Symmetry and the Unit Circle Revision 
Exercise 5.4 Worksheets 
19th May 
Test 3: Statistics, Trigonometry, The Unit Circle [10%] Sine Graphs 
Exercise 6.1 
26th May 
Cosine Graphs Tangent Graphs 
Exercise 6.2 Exercise 6.3 
2nd June 
Practice Exam Revision 
Worksheets 
9th June 
Revision Final Exam: Focus on Statistics, Trigonometry, The Unit Circle and Circular Functions. [40%] 
Worksheets

Learning Resources
Prescribed Texts
Scientific Calculator (not CAS or Graphing)  
SUGGESTED: Blank A4 Binder Book for Exercises or LooseLeaf Paper and a Folder. 
References
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
Assessments for this course may include the following:
assignments, quizzes and written exams
Assessment Tasks
 Three tests worth 10% each.
 Mid Semester Exam worth 30%.
 Final Exam worth 40%
Assessment Matrix
Other Information
Breakdown of Nominal Hours:
 48 hours in class
 22 hours expected outside of class
 Total: 70 Hours
Students who are absent on the day of an assessment task, whose performance in an assessment task has been severely affected by some unforeseen circumstance or who are unable to submit an assignment by the due date, need to apply for Special Consideration and apply within the allowed time frame
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 http://mams.rmit.edu.au/seca86tti4g4z.pdf ) 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
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