Course Title: Use technical mathematics (advanced)

Part B: Course Detail

Teaching Period: Term1 2010

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

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. Solve practical problems using polynomials

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 mathematics problems are solved using Trigonometric identities.

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. Graph quadratic functions and solve quadratic equations

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

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. Graph trigonometric functions and solve trigonometric equations.

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

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. Solve vocational mathematics problems using indices.

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

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

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

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

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

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

Performance Criteria:

8.0 Sin, cos and tan 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 of .
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 rigonometric 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 mathematics problems are solved using the sine and or the cosine rule.

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


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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), prescribed exercises, homework, tutorials, application of theory to engineering problems and completion of calculations to industry standard, computer software application work in laboratory sessions (depending on availability of computer lab), tests and examination.


Teaching Schedule

This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes.
Week 1 - Indices and Radicals Part I
Week 2 - Indices and Radicals Part II
Week 3 - Polynomials
Week 4 - Polynomials/Functions and Graphs
Week 5 - Functions and Graphs
Week 6 - Test 1 (Assessment 1)
Week 7 - Logarithmic Functions
Week 8 - Exponential Functions
Week 9 - Non Linear Empirical Equations
Week 10 - Compound Interest, Exponential Growth and Decay
Week 11 - Test 2 (Assessment 2)
Week 12 - Circular Functions
Week 13 - Trigonometry of Oblique Triangles
Week 14 - Trigonometric Identities
Week 15 - Determinants and Matrices Part I
Week 16 - Determinants and Matrices Part II
Week 17 - (Optional: Vector/Frame Analysis)
Week 18 - Test 3 (Assessment 3)
This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes.


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

To be deemed competent students must demonstrate an understanding of all elements of a competency.
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.

Assessment details:
Assessment 1 – This is a written test (closed book) to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. This test will have a weighting of 30% of the final overall assessment mark.
Assessment 2 – This is a written test (closed book) to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. This test will have a weighting of 30% of the final overall assessment mark.
Assessment 3 – This is a written test (closed book) to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. This test will have a weighting of 40% of the final overall assessment mark.

Note: Students will not be entitled to any supplementary work. All assessments need to be passed.


Assessment Matrix

Other Information

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