# Course Title: Apply mathematical techniques to scientific contexts

## Part B: Course Detail

Teaching Period: Term2 2013

Course Code: MATH7064

Course Title: Apply mathematical techniques to scientific contexts

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C3305 - Certificate III in Science

Course Contact: Namrita Kaul

Course Contact Phone: +61 3 9925 4309

Course Contact Email: namrita.kaul@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 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 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. 1.3 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=a sinbx and y=a cosbx, 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

Details of Learning Activities

• Class discussions of mathematical theories and proofs.
• Worksheets.
• Puzzle extension questions.
• Completion of a Theory Workbook.

Teaching Schedule

 Date Element Topic Assessment 10th July 2.1 Linear Equations 11th July 2.1 Linear Graphs 17th July 2.1, 2.7 Simultaneous Linear Equations 18th July 2.2, 2.4 The Definition of a Function and Function Notation 24th July 2.1, 2.4 Properties of Functions: shape, intercepts and asymptotes 25th July 2.1, 2.5 Expanding and Factorizing Quadratics 31st July 2.1, 2.5 Solving Quadratic Equations 1st August 2.3, 2.5 Sketching and Drawing Quadratics 7th August 2.6 Determining the Rule of a Quadratic from its Graph 8th August 2.1, 2.7 Simultaneous Quadratic and LInear Equations 14th August 5.1 Representations of Statistical Data 15th August 2.1 - 2.7 ASSESSMENT QUIZ 1 21st August 3.1 Scatterplots and Curves of Best Fit 22nd August 3.2 Linearizing Curves of Best Fit 28th August 5.2, 5.3, 5.6 Frequency Curves and Percentiles 29th August 5.1, 5.4, 5.6 Mean, Median and Mode, Stem and Leaf Plots PROJECT set 2nd - 8th September Mid-Semester Break 11th September 5.1, 5.5, 5.6 Interquartile Range and Box and Whisker Plots 12th September 5.1, 5.5, 5.6 Variance and Standard Deviation 18th September 4.1, 4.2 Index Laws and Solving Indicial Equations 19th September 4.3, 4.4 Logarithm Laws and Solving Logarithmic Equations 25th September 4.6 Graphing Exponential Functions PROJECT due 26th September 4.6 Graphing Logarithmic Functions 2nd October 4.5 Applications of Exponential and Logarithmic Functions 3rd October 4.1 - 4.6 ASSESSMENT QUIZ 2 9th October 1.1, 1.2 Converting Between Degrees and Radians and the Unit Circle 10th October 1.3 Trigonometric Ratios 16th October 1.4, 1.5 Sine Graphs and Their Transformations 17th October 1.4, 1.5 Cosine Graphs and Their Transformations 23rd October 1.4 Tangent Graphs 24th October 1.6 Applications of Circular Functions 30th October All Revision Class 31st October All Revision Class EXAM PERIOD EXAM EXAM

Learning Resources

Prescribed Texts

 Theory Workbook (Provided in Class) Scientific Calculator (not CAS or Graphing) SUGGESTED: Blank A4 Binder Book for Exercises or Loose-Leaf 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

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

Assessment Tasks

Quiz One: This quiz is worth 20 per cent of your final mark and is sat within normal class time. It covers all aspects of linear and quadratic algebra, graphs, and function notation.

Project: The project is worth 20 per cent of the final mark and is to be completed outside of class. It assesses students ability to apply statistics in everyday life.

Quiz Two: This quiz is worth 20 per cent of the final mark and is sat within normal class hours. It covers all aspects of indices and logarithms.

Exam: The exam is worth 40 per cent of the final mark and is sat during the exam period at the end of the semester. It assesses everything learnt in this course, with slightly more detail being paid to circular functions.

Assessment Matrix

Other Information

Breakdown of Nominal Hours:

• 48 hours in class
• 22 hours expected outside of class
• Total: 70 Hours

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.

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