Course Title: Use technical mathematics (advanced)

Part B: Course Detail

Teaching Period: Term1 2015

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. +61 3 9925 8375
Email: ahmet.ertuncay@rmit.edu.au

Ms. Annabelle Lopez
Tel. +61 3 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:

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

Performance Criteria:

01.0 The different types of polynomials and their respective characteristics are identified.
01.1 Polynomial expressions are manipulated and simplified using addition, subtraction, multiplication and factoring in the correct order.
01.2 The distributive law is used in the manipulation and simplification of polynomial expressions.
01.3 Trinomials are factored using trial and error, the difference between two squares and other methods.
01.4 Quadratic equations are solved using the factoring and complete the square methods.
01.5 Quadratic equations are solved using the quadratic formula.
01.6 Rational binomial and trinomial algebraic expressions are manipulated and simplified.
01.7 Quadratic equations are graphed and sketched in order to determine solutions to practical vocational problems.

Element:

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

Performance Criteria:

02.0 Exponential expressions containing positive indices are simplified using the index laws.
02.1 Exponential problems containing negative, fractional and zero indices are simplified.
02.2 Expressions involving powers and roots are solved with a calculator.
02.3 Numerical and literal expressions are expanded and simplified.
02.4 Vocational formulae containing exponents are transposed.

Element:

03. Graph quadratic functions and solve quadratic equations.

Performance Criteria:

03.0 Distinction can be made between a relation and a function.
03.1 Given the equation of a function the graph can be sketched.
03.2 Functions of the type y = mx+b, are solved.
03.3 Calculations are performed using the typical functions of a graphics calculator.
03.4 Quadratic functions are sketched from the defining rule and by completing the square, showing line of symmetry, x and y intercepts.
03.5 Quadratic equations are solved graphically by using a graphics calculator.
03.6 Equations are determined from graphs using quadratic rules.
03.7 Systems consisting of a quadratic and linear equation are solved analytically.
03.8 Systems consisting of a quadratic and linear equation are solved graphically using a graphics calculator.
03.9 Non-routine vocational problems are solved using simple algebraic functions and their graphs.

Element:

04. Graph trigonometric functions and solve trigonometric equations.

Performance Criteria:

04.0 Non linear data is transformed into linear data.
04.1 The line of best fit (regression) is drawn.
04.2 The corresponding non-linear formula is determined.

Element:

05. Solve practical problems using polynomials.

Performance Criteria:

05.0 Algebraic expressions are simplified using indices.
05.1 Exponential equations are solved without using logarithms.
05.2 The meaning of a logarithm as an exponent is described.
05.3 Change of base formula and a calculator is used to evaluate logarithms.
05.4 Logarithmic expressions are changed in their form.
05.5 Exponential equations are solved using logarithms.
05.6 Formulae involving logarithmic and exponential forms are transposed.
05.7 The inverse of a function is defined.
05.8 Exponential and logarithmic functions are graphed.
05.9 The relationship between exponential and logarithmic functions is explained.
05.10 Non-routine vocational problems are solved using exponents and logarithms.

Element:

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

Performance Criteria:

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

Element:

07. Solve vocational mathematics problems using indices.

Performance Criteria:

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

Element:

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

Performance Criteria:

08.0 Sin, cos and tan functions are defined in terms of the unit circle.
08.1 Secant, cosecant and tangent are defined in terms of cosine, sine and tangent.
08.2 Angles are expressed as fractions and multiples.
08.3 A calculator is used to convert radians to degrees and degrees to radians.
08.4 The values of the six trigonometric functions for any angle given in degrees or radians are determined using a calculator.
08.5 A calculator is used to determine the measure of any angle in degrees, degrees minutes and seconds, or radians.
08.6 Angular displacement and angular velocity are calculated.
08.7 The area of a sector is calculated.
08.8 The graphs of y = sinx, y = cosx and y = tanx are sketched with x in degrees or radians.
08.9 A graphics calculator is used to sketch graphs of the form y = asin(bx+c)
08.10 Trigonometric expressions are simplified using the properties and relationships of sine and cosine.
08.11 Vocational problems are solved using circular functions, the graphs of circular functions and the basic trig identities.

Element:

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

Performance Criteria:

09.0 Oblique triangles are solved using the sine rule.
09.1 Oblique triangles are solved using the cosine rule.
09.2 Vocational problems requiring the application of the sine and or the cosine rule are solved in two and three dimensions.

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.


Learning Outcomes


.


Details of Learning Activities

You will involve in the following learning activities to meet requirements for this course,

  • Lectures
  • Tutorials


Teaching Schedule

 The proposed teaching schedule for this competency is detailed below:

Week    Topics DeliveredElement / Performance Criteria
1Introduction to the competency
Revision of Pre Requisite course
Assignment (part A) handed out (worth 5% of total mark) due date end of week 4.
 1.0,1.1,1.2,1.3
2Indices and Radicals1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7
3Polynomials 2.0, 2.1, 2.2, 2.3, 2.4
4Polynomials/Functions and Graphs3.0,  3.1, 3.2, 3.3, 3.4
5Functions and Graphs
Assignment  handed out (worth 15% of total marks, due date end of
week 16).

 3.5, 3.6, 3.7, 3.8, 3.9

4.0, 4.1, 4.2

6Logarithmic Functions 5.0,5.1, 5.2, 5.3, 5.4, 5.5
7Exponential Functions 5.6, 5.7, 5.8, 5.9, 5.10
8Practice test and revision

 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2.0, 2.1, 2.2, 2.3, 2.4,3.0, 3.1, 3.2, 3.3, 3.4,3.5, 3.6, 3.7, 3.8, 3.9
4.0, 4.1, 4.2,5.0,5.1, 5.2, 5.3, 5.4, 5.5
5.6, 5.7, 5.8, 5.9, 5.10

9Closed book Test (worth 40% of total mark)1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2.0, 2.1, 2.2, 2.3, 2.4,3.0, 3.1, 3.2, 3.3, 3.4,3.5, 3.6, 3.7, 3.8, 3.9
4.0, 4.1, 4.2,5.0,5.1, 5.2, 5.3, 5.4, 5.5
5.6, 5.7, 5.8, 5.9, 5.10
10Non Linear Empirical Equations6.0,6.1, 7.0,7.1, 7.2, 7.3
11Compound Interest, Exponential Growth and Decay) 9.0,9.1, 9.2
12Determinants and Matrices8.0, 8.1, 8.2, 8.3, 8.4, 8.5
14.0,14.1, 14.2, 14.3
 
13Determinants and Matrices (cont.)  8.1, 8.2, 8.3, 8.4, 8.5
14.1, 14.2, 14.3
14Circular Functions
Trigonometry of Oblique Triangles
 10.0,10.1, 10.2, 10.3, 10.4, 10.5
11.0,11.1, 11.2, 11.3, 11.4
 
15Trigonometric Identities12.0, 12.1, 12.2, 12.3, 12.4, 12.5,12.6
13.0,13.1, 13.2
 
16Practice Exam and revision6.0,6.1, 7.0,7.1, 7.2, 7.3,8.0, 8.1, 8.2, 8.3, 8.4, 8.5
8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 9.0,9.1, 9.2
 10.0,10.1, 10.2, 10.3, 10.4, 10.5
11.0,11.1, 11.2, 11.3, 11.4,12.0, 12.1, 12.2, 12.3, 12.4, 12.5,12.6
13.0,13.1, 13.2
 
17 - 18Closed book Exam
(worth 40% of total mark)
6.0,6.1, 7.0,7.1, 7.2, 7.3,8.0, 8.1, 8.2, 8.3, 8.4, 8.5
8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 9.0,9.1, 9.2
10.0,10.1, 10.2, 10.3, 10.4, 10.5
11.0,11.1, 11.2, 11.3, 11.4,12.0, 12.1, 12.2, 12.3, 12.4, 12.5,12.6
13.0,13.1, 13.2
 


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

  • Assignments, 20%
  • Test, 40%
  • Exam , 40%


Assessment Matrix

Assessment vs EDX140B Elements & Performance Criteria.

         EDX140B Elements & Performance Criteria
Assessments 1.01.11.21.31.41.51.61.72.02.12.22.32.43.03.13.23.33.43.53.63.73.83.94.04.14.25.0 5.15.25.3
Assignments x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
Test x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
Exam                              


 

         EDX140B Elements & Performance Criteria                   
Assessments5.45.55.65.75.85.95.10 6.06.17.07.17.27.3 8.08.18.28.38.48.58.68.78.88.98.10 8.119.09.1
Assignments x x x x x x x x x x x x x x x x x x x x x x x x x x x
Test x x x x x x x                    
Exam        x x x x x x x x x x x x x x x x x x  x

 

 



 

         EDX140B Elements & Performance Criteria                  
Assessments 9.210.010.110.210.310.410.5 11.011.111.211.311.412.012.112.212.312.412.512.6 13.013.114.014.114.214.3 
Assignments x x x x x x x x x x x x x x x x x x x x x x x
Test                         
Exam x x x x x x x x x x x x x x x x x x x x x x x x x

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:

Credit Transfer and/or Recognition of Prior Learning (RPL):

You may be eligible for credit towards courses in your program if you have already met the learning/competency outcomes through previous learning and/or industry experience. To be eligible for credit towards a course, you must demonstrate that you have already completed learning and/or gained industry experience that is:

• Relevant
• Current
• Satisfies the learning/competency outcomes of the course

Please refer to http://www.rmit.edu.au/students/enrolment/credit to find more information about credit transfer and RPL.

Study and Learning Support:

Study and Learning Centre (SLC) provides free learning and academic development advice to you. Services offered by SLC to support your numeracy and literacy skills are:

• Assignment writing, thesis writing and study skills advice
• Maths and science developmental support and advice
• English language development

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

Disability Liaison Unit:

If you are suffering from long-term medical condition or disability, you should contact Disability Liaison Unit to seek advice and support to complete your studies.

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

Late Submission:

If you require an Extension of Submittable Work (assignments, reports or project work etc.) for seven calendar days or less (from the original due date) and have valid reasons, you must complete 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. You will be notified within no more than two working days of the date of lodgement as to whether the extension has been granted.

If you seek an Extension of Submittable Work for more than seven calendar days (from the original due date), you must lodge an Application for Special Consideration form under the provisions of the Special Consideration Policy, preferably prior to, but no later than two working days after the official due date.

Submittable Work (assignments, reports or project work etc.) submitted late without approval of an extension will not be accepted or marked.

Special Consideration:

Please refer to http://www.rmit.edu.au/students/specialconsideration to find more information about special consideration.

Plagiarism:

Plagiarism is a form of cheating and it is very serious academic offence that may lead to expulsion from the university.

Please refer to http://www.rmit.edu.au/academicintegrity to find more information about plagiarism.

Email Communication:

All email communications will be sent to your RMIT email address and you must regularly check your RMIT emails.

Course Overview: Access Course Overview