Course Title: Use technical mathematics (advanced)

Part B: Course Detail

Teaching Period: Term2 2013

Course Code: CIVE5674

Course Title: Use technical mathematics (advanced)

School: 130T Vocational Engineering

Campus: City Campus

Program: C6093 - Advanced Diploma of Engineering Design

Course Contact: Program Manager

Course Contact Phone: +61 3 9925 4468

Course Contact Email: engineering-tafe@rmit.edu.au


Name and Contact Details of All Other Relevant Staff

Program Manager
Mr. Ahmet Ertuncay
Tel. 9925 8375
Email: ahmet.ertuncay@rmit.edu.au

Ms. Annabelle Lopez
Tel. 9925 4823
Email: Annabelle.lopez@rmit.edu.au

Nominal Hours: 60

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

EDX130B Use technical mathematics (basic)

Course Description

This unit of competency deals with the skills and knowledge required to understand, solve and graph quadratic, exponential, logarithmic and trigonometric functions.


National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

EDX140B Use technical mathematics (advanced)

Element:

1. Determine non-linear laws by transforming them into linear form

Performance Criteria:

1.0 The different types of polynomials and their respective characteristics are identified,
1.1 Polynomial expressions are manipulated and simplified using addition, subtraction, multiplication and factoring in the correct order.
1.2 The distributive law is used in the manipulation and simplification of polynomial expressions.
1.3 Trinomials are factored using trial and error, the difference between two squares and other methods.
1.4 Quadratic equations are solved using the factoring and complete the square methods.
1.5 Quadratic equations are solved using the quadratic formula.
1.6 Rational binomial and trinomial algebraic expressions are manipulated and simplified
1.7 Quadratic equations are graphed and sketched in order to determine solutions to practical vocational problems.
 

Element:

10. Vocational mathematical problems are solved using the unit circle definitions of trigonometric functions, graphs of circular functions and real number angular measure.

Performance Criteria:

10.0 Trigonometric expressions are simplified using the addition formulae.
10.1 Trigonometric expressions are simplified using the double angle formulae.
10.2 Trigonometric expressions are simplified using the sum to product formulae.
10.3 Trigonometric expressions are simplified using the product to sum formulae.
10.4 Trigonometric expressions are manipulated using the trigonometric ratios.
10.5 Vocational problems are solved using trigonometric identities.
 

Element:

11. Vocational mathematics problems are solved by determining empirical laws for data related by either an exponential or a power law.

Performance Criteria:

11.0Graphs of quadratic functions can be sketched and interpreted.
11.1 The significance of the leading coefficient and the zeros can be shown.
11.2 Quadratic equations can be solved using the quadratic formula.
11.3 Simultaneous linear and quadratic equations can be solved algebraically and geometrically.
11.4 Verbally formulated problems involving quadratic and linear equations can be interpreted and solved.

Element:

12. Vocational mathematics problems are solved using Trigonometric identities.

Performance Criteria:

12.0Arithmetic and algebraic expression can be manipulated and simplified using the laws of indices and logarithms.
12.1 The graphs of simple exponential and logarithmic functions can be graphed to show the behaviour for large and small values.
12.2 Exponential and simple logarithmic equations can be solved using indices, logarithms, calculator and graphical techniques.
12.3 Logarithms can be converted between bases, especially 10 and base e.
12.4 Non-linear functions (including exponential) can be transformed to linear forms and the data plotted.
12.5 Lines of best fit can be drawn, data interpolated and constants estimated in suggested relationships.
12.6 Verbally formulated problems involving growth and decay and be interpreted and solved.
 

Element:

13. Vocational mathematics problems are solved using the sine and or the cosine rule.

Performance Criteria:

13,0 The graphs of simple trigonometric functions can be sketched showing the significance of amplitude, period and phase angle.
13.1 Trigonometric expressions can be simplified using trigonometric identities 
 

Element:

14. Vocational mathematics problems involving exponential and logarithmic functions are solved.

Performance Criteria:

14.0The basic operations can be performed on matrices up to 3 x 3.
14.1 Matrix equations and expressions can be manipulated.
14.2 Inverse and identity matrices up to 3 x 3 can be recognized and used to solve systems of linear equations.
14.3 Determinants up to 3 x 3 can be found and used to solve systems of linear equations. 
 

Element:

2. Graph exponential and logarithmic functions and solve exponential and logarithmic equations.

Performance Criteria:

2.0 Exponential expressions containing positive indices are simplified using the index laws.
2.1 Exponential problems containing negative, fractional and zero indices are simplified.
2.2 Expressions involving powers and roots are solved with a calculator.
2.3 Numerical and literal expressions are expanded and simplified.
2.4 Vocational formulae containing exponents are transposed.

Element:

3. Graph quadratic functions and solve quadratic equations

Performance Criteria:

3.0 Distinction can be made between a relation and a function
3.1 Given the equation of a function the graph can be sketched
3.2 Functions of the type y = mx+b, are solved
3.3 Calculations are performed using the typical functions of a graphics calculator
3.4 Quadratic functions are sketched from the defining rule and by completing the square, showing line of symmetry, x and y intercepts.
3.5 Quadratic equations are solved graphically by using a graphics calculator
3.6 Equations are determined from graphs using quadratic rules
3.7 Systems consisting of a quadratic and linear equation are solved analytically
3.8 Systems consisting of a quadratic and linear equation are solved graphically using a graphics calculator
3.9 Non-routine vocational problems are solved using simple algebraic functions and their graphs.

Element:

4. Graph trigonometric functions and solve trigonometric equations.

Performance Criteria:

4.0 Non linear data is transformed into linear data
4.1 The line of best fit (regression) is drawn
4.2 The corresponding non-linear formula is determined.

Element:

5. Solve practical problems using polynomials

Performance Criteria:

5.0 Algebraic expressions are simplified using indices.
5.1 Exponential equations are solved without using logarithms.
5.2 The meaning of a logarithm as an exponent is described
5.3 Change of base formula and a calculator is used to evaluate logarithms.
5.4 Logarithmic expressions are changed in their form
5.5 Exponential equations are solved using logarithms.
5.6 Formulae involving logarithmic and exponential forms are transposed.
5.7 The inverse of a function is defined.
5.8 Exponential and logarithmic functions are graphed.
5.9 The relationship between exponential and logarithmic functions is explained.
5.10 Non-routine vocational problems are solved using exponents and logarithms.

Element:

6. Solve vocational mathematical problems using simple algebraic functions and their graphs.

Performance Criteria:

6.0 Two simultaneous equations involving exponential, power and linear relationships are solved graphically.
6.1 Growth and decay problems are solved graphically.
 

Element:

7. Solve vocational mathematics problems using indices.

Performance Criteria:

7.0 Exponential and power equations are transposed into logarithmic form and plotted as linear graphs using log –log and semi-log scales.
7.1 The least squares regression line is determined for data related by exponential or power laws.
7.2 A graphics calculator is used to graph and determine the least squares regression line of exponential or power functions.
7.3 Empirical laws are determined for engineering data related by an exponential or power law.
 

Element:

8. Use matrix algebra and determinants to solve up to three linear equations in three unknowns.

Performance Criteria:

8.0 Sin, cos and tan functions are defined in terms of the unit circle.
8.1 Secant, cosecant and tangent are defined in terms of cosine, sine and tangent.
8.2 Angles are expressed as fractions and multiples.
8.3 A calculator is used to convert radians to degrees and degrees to radians.
8.4 The values of the six trigonometric functions for any angle given in degrees or radians are determined using a calculator.
8.5 A calculator is used to determine the measure of any angle in degrees, degrees minutes and seconds, or radians.
8.6 Angular displacement and angular velocity are calculated.
8.7 The area of a sector is calculated.
8.8 The graphs of y = sinx, y = cosx and y = tanx are sketched with x in degrees or radians.
8.9 A graphics calculator is used to sketch graphs of the form
y = asin(bx+c)
8.10 Trigonometric expressions are simplified using the properties and relationships of sine and cosine.
8.11 Vocational problems are solved using circular functions, the graphs of circular functions and the basic trig identities.
 

Element:

9. Vocational growth and decay problems are solved using graphical methods.

Performance Criteria:

9.0 Oblique triangles are solved using the sine rule.
9.1 Oblique triangles are solved using the cosine rule.
9.2 Vocational problems requiring the application of the sine and or the cosine rule are solved in two and three dimensions.
 

Learning Outcomes


.


Details of Learning Activities

You will participate in individual and team problem solving activities related to typical engineering workplace problems. These activities involve class participation (discussions and oral presentations), completion of all assigned work, prescribed exercises, homework, tutorials, application of theory to engineering problems and completion of calculations to industry standard as well as completion of all other assessments to a satisfactory standard.

Engineering employment requires the capacity to work effectively in teams, to communicate effectively in both oral and writing and to learn effectively. In order to prepare students for employment as graduates they will be provided a quality assured teaching and learning environment which is conductive to the development of adult learning. Adult learning is characterised by the students accepting responsibility for their own learning and actively participating in the learning process as individuals and as contributors to the teams. Adult learning is the hallmark of a professional. The specific responsibilities as adult learners in respect of this subject are:
. to be aware of and to observe the regulations related to plagiarism
. to submit (on time) all work for assessment as required
. to complete all pre-reading and preparatory work prior to the class for which it will be used
. to effectively use the academic staff resources provided (consultation time, tutors, e- mail etc)
. to participate as an effective and honest member of a learning team
. to contribute effectively to a group of peers in a climate of mutual respect and to question each other and the academic staff when uncertain.


Hence, you will participate in individual and team problem solving activities related to typical engineering workplace problems. These activities involve class participation, discussions, prescribed exercises, assignments and other self-directed student activities.

Lecture sessions are generally devoted to topic summaries and short quizzes whilst tutorial sessions are generally devoted to discussions (student queries) of assigned exercises and portfolio questions.

PLEASE NOTE, IN THIS COURSE, LEARNING GUIDE IS USED AS REFERENCE ONLY.

Learning and simulated work activities to demonstrate an understanding of typical problems encountered in meeting performance requirements and compliance standards are outlined below:

* Classroom tutorial activities are achieved to consolidate theories
*Practical Exercises This course requires that students demonstrate highly practical skills.
Underpinning knowledge is required before undertaking practical exercises.

Research activities to undertake investigative activities are undertaken. It is expected that students would require approximately 50% of course hours to be allocated for independent study to do project research and problem solving activities.

Assignment tasks involve applications of standards and codes whenever applicable and shall be as close as practicable to real work situations and include real work decisions by the learner.


Teaching Schedule

This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes. For absences due to public holidays and other class cancellations, the topics & assessment tasks will be shifted accordingly. As teaching schedule is currently on contingency mode, whilst flexibility is offered, self directed learning is much called for on the part of the students.

Week Number, Topic Delivered, Assessment Task
1 Introduction to course, course guide, assessment, topic breakdown, resources, OHS issues.
2 Course Summary OR otherwise, Introduction to course, course guide, assessment, topic breakdown, resources, OHS issues (for Late Starters)
3 Indices and Radicals/Polynomials Indices and Radicals – Quiz (Part of Option 1)
4 Polynomials/Functions & Graphs Polynomials – Quiz (Part of Option 1)
5 Functions & Graphs Functions & Graphs – Quiz (Part of Option 1)
6 Logarithmic Functions/Exponential Functions Logarithmic & Exponential Functions – Quiz (Part of Option 1)
7 Exponential Functions/Non Linear Empirical Equations
8 Non Linear Empirical Equations / Compound Interest, Exponential Growth and Decay
Non Linear Empirical Equations – Quiz (Part of Option 1)
9 Compound Interest, Exponential Growth and Decay
Compound Interest Exponential Growth & Decay – Quiz (Part of Option 1)
10 Determinants & Matrices Determinants & Matrices – Quiz (Part of Option 1)
11 Determinants & Matrices/Circular Functions
12 Circular Functions Circular Functions – Quiz (Part of Option 1)
13 Trigonometry of Oblique Triangles Trigonometry of Oblique Triangles – Quiz (Part of Option 1)
14 Trigonometry of Oblique Triangles/Trigonometric Identities Trigonometric Identities – Quiz (Part of Option 1)
15 Question & Answer Forum / Workshop – Feedback available Part 1 Portfolio of Assigned Questions (Option 2) due in
16 Question & Answer Forum / Workshop – Feedback available Part 2 Portfolio of Assigned Questions – Late Submissions with Penalty (Option 2) due in
17 All Deferred Assignments and Portfolios and other outstanding issues (special consideration) Deferred/ Alternative Assessments due in including those with Special Consideration
18 Feedback on Grades and Finalising Results

This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes. For absences due to public holidays and other class cancellations, the topics & assessment tasks will be shifted accordingly. As teaching schedule is currently on contingency mode, whilst flexibility is offered, self directed learning is much called for on the part of the students.


Learning Resources

Prescribed Texts

‘Mathematics for technicians’, by Blair Alldis 6th edition


References


Other Resources


Overview of Assessment

Assessment are conducted in both theoretical and practical aspects of the course according to the performance criteria set out in the National Training Package. Students are required to undertake summative assessments that bring together knowledge and skills. To successfully complete this course you will be required to demonstrate competency in each assessment tasks detailed under the Assessment Task Section.

Your assessment for this course will be marked using the following table:

NYC (<50%) Not Yet Competent

CAG (50-59%) Competent - Pass

CC (60-69%) Competent - Credit

CDI (70-79%) Competent - Distinction

CHD (80-100%) Competent - High Distinction


Assessment Tasks

The assessment is conducted in both theoretical and practical aspects of the course according to the performance criteria set in the National Training Package.
Assessment may incorporate a variety of methods including written/oral activities and demonstration of practical skills to the relevant industry standards.

Students are advised that they are likely to be asked to personally demonstrate their assessment work to their teacher to ensure that the relevant competency standards are being met. Students will be provided with feedback throughout the course to check their progress.

Feedback will be provided throughout the course. To successfully complete this course you will be required to demonstrate competency in each assessment task
detailed under Assessment Tasks section of Course Guide Part B (this document).

Assessment tasks have been designed to encourage life-long learning and self directed learning, encouraging students to ask questions and manage their time in order to progressively complete work throughout the semester. Individual as well as team activities will be demonstrated in preparation for work in industry where competing demands and adaptation to change characterise the work environment, and where communication, team work and organisation skills are of paramount importance.

Assessment details:

Choose one of Collection of Quizzes OR Collection of Exercises (Portfolio) – Student has a choice to either sit 10 quizzes (10 marks each for a total of 100 marks) or to complete a portfolio of evidence, being the assigned exercises for this course (worth 100 marks). Student chooses one of these options, but generally not both. Someone with good mathematics background from high school or VCE is expected to choose the quizzes whilst someone that had a break in his/her studies is expected to choose the portfolio.

Option 1: Collection of Quizzes – This is a collection of a student’s quizzes (10 quizzes altogether) where analysis and solution to practical application problems/questions in engineering where mathematics has been applied is demonstrated. This assessment focuses on the students’ ability to solve problems and provide logical solutions to practical exercises. These individual assessments collectively has a weighting of 100%, is closed book , and are all scheduled during lecture sessions (see teaching schedule).
Note: Allowed in assessment room are NON-programmable calculators, pens, rulers and bottle of water only.

Option 2: Portfolio of Evidence- This is the student’s mathematics exercise book, where he/she writes solutions to mathematical problems and other application questions, presented neatly with all working completed and all titles/headings included. This assessment focuses on the students’ ability to solve problems and provide logical solutions to practical exercises. Portfolio has a weighting of 100%, and is an individual assessment.
Note: Use exercise book with NO spirals.

NOTE: QUESTIONS ABOUT SPECIFIC ASSESSMENTS AND MARKS OBTAINED MAY NOT BE ENTERTAINED IF LATER THAN 1 WEEK AFTER RESULTS WERE COMMUNICATED TO STUDENTS

 Assessment requirements also include:

- attendance and satisfactory completion of prescribed practical exercises ,
- evidence of participation in and satisfactory completion of work simulation projects.
-satisfactory completion of class assignment work
-timely submission and standard presentation for all assessment material / documentation
This course is graded using the following course grades-

Grade Grade level Competency Level

CHD
Competent with High Distinction -The learner will confidently apply novel but relevant solutions to unfamiliar and complex tasks.

CDI
Competent with Distinction -The learner will confidently evaluate alternative solutions to an unfamiliar task or
problem and use the most appropriate solution.

CC
Competent with Credit -The learner will elegantly apply appropriate facts, rules and standard solutions to achieve an unfamiliar task or problem with
confidence.

CAG
Competency Achieved - Graded -The learner will be able to apply facts, rules
and standard solutions to achieve a predictable task or solve a problem.

NYC
Not Yet Competent
-Although the learner exhibits access to a limited range of facts and rules, the learner has difficulty applying these facts and rules to a familiar task.
DNS- Did Not Submit for Assessment

Students should be informed with the special consideration policy available at -

http://www.rmit.edu.au/browse;ID=qkssnx1c5r0y 


Assessment Matrix

Element Covered, Assessment Task, Proportion of Final Assessment. Approximate Time
1,2,3,4,5,6,7,8, 9, 10, 11, 12, 13 and 14 ------  Option 1: Collection of Quizzes -----100 % -------As per teaching schedule
1,2,3,4,5,6,7,8, 9, 10, 11, 12, 13 and 14 ------ Option 2: Portfolio of Evidence ------100 % ------- As per teaching schedule
NOTE: Student chooses one of above named assessment options, but NOT both
(for any changes, refer to online blackboard announcement)

Other Information

In this course, minimum student directed hours are 12 in addition to 48 scheduled teaching hours.
* Student directed hours involve completing activities such as reading online resources, assignments, report for practical work, and individual student-teacher course-related consultation.

Study and learning Support:

Study and Learning Centre (SLC) provides free learning and academic development advice to all RMIT students.
Services offered by SLC to support numeracy and literacy skills of the students are:

assignment writing, thesis writing and study skills advice
maths and science developmental support and advice
English language development

Please Refer http://www.rmit.edu.au/studyandlearningcentre to find more information about Study and learning Support

Disability Liaison Unit:

Students with disability or long-term medical condition should contact Disability Liaison Unit to seek advice and support to
complete their studies.

Please Refer http://www.rmit.edu.au/disability to find more information about services offered by Disability Liaison Unit

Late submission:

Students requiring extensions for 7 calendar days or less (from the original due date) must complete and lodge an Application
for Extension of Submittable Work (7 Calendar Days or less) form and lodge it with the Senior Educator/ Program Manager.
The application must be lodged no later than one working day before the official due date. The student will be notified within
no more than 2 working days of the date of lodgment as to whether the extension has been granted.

Students seeking an extension of more than 7 calendar days (from the original due date) must lodge an Application for Special
Consideration form under the provisions of the Special Consideration Policy, preferably prior to, but no later than 2 working days
after the official due date.

Assignments submitted late without approval of an extension will not be accepted or marked.

Special consideration:

Please Refer http://www.rmit.edu.au/browse;ID=riderwtscifm to find more information about special consideration


PLAGIARISM:
Plagiarism may occur in oral or written presentations. Plagiarism is the presentation of another person’s work, idea or creation as one’s own; without appropriate referencing. Plagiarism is not acceptable. The use of another person’s work or ideas must be acknowledged. Failure to do so may result in charges of academic misconduct, which may result in cancellation of results and exclusion from your course.
Please Refer: www.rmit.edu.au/academicintegrity to find more information about plagiarism
Other Information:
All email communications will be sent to your RMIT email address and you must regularly check your RMIT emails.

The underpinning knowledge and skills for this course are listed in the accreditation document and are available upon request from your instructor.

Course Overview: Access Course Overview