# Course Title: Use quadratic, exponential, logarithmic and trigonometric functions and matrices

## Part B: Course Detail

Teaching Period: Term1 2008

Course Code: CIVE5613

Course Title: Use quadratic, exponential, logarithmic and trigonometric functions and matrices

School: 130T Infra, Electrotec & Build Serv

Campus: City Campus

Program: C6066 - Advanced Diploma of Civil Engineering (Structural Design)

Course Contact : Tony Skinner Program Coordinator

Course Contact Phone: (03) 9925 4444

Course Contact Email:tony.skinner@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Program Coordinator:
Mr Tony Skinner
Tel. 9925 4444
Fax. 99254377
Email: tony.skinner@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

EDX130 – Use mathematics at technician level

Course Description

This unit covers the competency to understand, solve and graph quadratic, exponential, logarithmic and trigonometric functions with the aid of a graphics calculator.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: EDX100 Use quadratic, exponential, logarithmic and trigonometric functions and matrices Element: Determine non-linear laws by transforming them into linear form Performance Criteria: 1.1 Non linear data is transformed into linear data 1.2 The line of best fit (regression) is drawn 1.3 The corresponding non-linear formula is determined. Element: Graph exponential and logarithmic functions and solve exponential and logarithmic equations Performance Criteria: 2.0Arithmetic and algebraic expression can be manipulated and simplified using the laws of indices and logarithms. 2.1 The graphs of simple exponential and logarithmic functions can be graphed to show the behaviour for large and small values. 2.2 Exponential and simple logarithmic equations can be solved using indices, logarithms, calculator and graphical techniques. 2.3 Logarithms can be converted between bases, especially 10 and base e. 2.4 Non-linear functions (including exponential) can be transformed to linear forms and the data plotted. 2.5 Lines of best fit can be drawn, data interpolated and constants estimated in suggested relationships. 2.6 Verbally formulated problems involving growth and decay and be interpreted and solved. Element: Graph quadratic functions and solve quadratic equations Performance Criteria: 3.0 Graphs of quadratic functions can be sketched and interpreted. 3.1 The significance of the leading coefficient and the zeros can be shown. 3.2 Quadratic equations can be solved using the quadratic formula. 3.3 Simultaneous linear and quadratic equations can be solved algebraically and geometrically. 3.4 Verbally formulated problems involving quadratic and linear equations can be interpreted and solved. Element: Graph trigonometric functions and solve trigonometric equations. Performance Criteria: 4.0 The graphs of simple trigonometric functions can be sketched showing the significance of amplitude, period and phase angle. 4.1 Trigonometric expressions can be simplified using trigonometric identities Element: Solve practical problems using polynomials Performance Criteria: 5.1 The different types of polynomials and their respective characteristics are identified, 5.2 Polynomial expressions are manipulated and simplified using addition, subtraction, multiplication and factoring in the correct order. 5.3 The distributive law is used in the manipulation and simplification of polynomial expressions. 5.4 Trinomials are factored using trial and error, the difference between two squares and other methods. 5.5 Quadratic equations are solved using the factoring and complete the square methods. 5.6 Quadratic equations are solved using the quadratic formula. 5.7 Rational binomial and trinomial algebraic expressions are manipulated and simplified 5.8 Quadratic equations are graphed and sketched in order to determine solutions to practical vocational problems. Element: Solve vocational mathematical problems using simple algebraic functions and their graphs Performance Criteria: 6.0 Distinction can be made between a relation and a function 6.1 Given the equation of a function the graph can be sketched 6.2 Functions of the type y = mx+b, y = square root of y, y = a raised to x are solved 6.3 Calculations are performed using the typical functions of a graphics calculator 6.4 Quadratic functions are sketched from the defining rule and by completing the square, showing line of symmetry, x and y intercepts. 6.5 Quadratic equations are solved graphically by using a graphics calculator 6.6 Equations are determined from graphs using quadratic rules 6.7 Systems consisting of a quadratic and linear equation are solved analytically 6.8 Systems consisting of a quadratic and linear equation are solved graphically using a graphics calculator 6.9 Non-routine vocational problems are solved using simple algebraic functions and their graphs. Element: Solve vocational mathematics problems using indices Performance Criteria: 7.0 Exponential expressions containing positive indices are simplified using the index laws. 7.1 Exponential problems containing negative, fractional and zero indices are simplified. 7.2 Expressions involving powers and roots are solved with a calculator. 7.3 Numerical and literal expressions are expanded and simplified. 7.4 Vocational formulae containing exponents are transposed. Element: Use matrix algebra and determinants to solve up to three linear equations in three unknowns Performance Criteria: 8.0The basic operations can be performed on matrices up to 3 x 3. 8.1 Matrix equations and expressions can be manipulated. 8.2 Inverse and identity matrices up to 3 x 3 can be recognized and used to solve systems of linear equations. 8.3 Determinants up to 3 x 3 can be found and used to solve systems of linear equations. Element: Vocational growth and decay problems are solved using graphical methods Performance Criteria: 9.0 Two simultaneous equations involving exponential, power and linear relationships are solved graphically. 9.1 Growth and decay problems are solved graphically. Element: 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(theta), cos(theta), and tan(theta),  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 (pi). 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 using 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: Vocational mathematics problems are solved by determining empirical Performance Criteria: 9.0 Exponential and power equations are transposed into logarithmic form and plotted as linear graphs using log –log and semi-log scales. 9.1 The least squares regression line is determined for data related by exponential or power laws. 9.2 A graphics calculator is used to graph and determine the least squares regression line of exponential or power functions. 9.3 Empirical laws are determined for engineering data related by an exponential or power law. Element: 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: Vocational mathematics problems are solved using the sine and or the cosine rule Performance Criteria: 11.1 Oblique triangles are solved using the sine rule. 11.2 Oblique triangles are solved using the cosine rule. 11.3 Vocational problems requiring the application of the sine and or the cosine rule are solved in two and three dimensions. Element: Vocational mathematics problems involving exponential and logarithmic functions are solved Performance Criteria: 12.0 Algebraic expressions are simplified using indices. 12.1 Exponential equations are solved without using logarithms. 12.2 The meaning of a logarithm as an exponent is described 12.3 Change of base formula and a calculator is used to evaluate logarithms. 12.4 Logarithmic expressions are changed in their form 12.5 Exponential equations are solved using logarithms. 12.6 Formulae involving logarithmic and exponential forms are transposed. 12.7 The inverse of a function is defined. 12.8 Exponential and logarithmic functions are graphed. 12.9 The relationship between exponential and logarithmic functions is explained. 12.10 Non-routine vocational problems are solved using exponents and logarithms.

Learning Outcomes

• Solve practical problems using polynomials
• Solve vocational mathematics problems using indices
• Solve vocational mathematical problems using simple algebraic functions and their graphs
• Determine non-linear laws by transforming them into linear form
• Vocational mathematics problems involving exponential and logarithmic functions are solved
• Vocational growth and decay problems are solved using graphical methods
• Vocational mathematics problems are solved by determining empirical laws for data related by either an exponential or a power law
• Vocational mathematical problems are solved using the unit circle definitions of trigonometric functions, graphs of circular functions and real number angular measure.
• Vocational mathematics problems are solved using the sine and or the cosine rule.
• Vocational mathematics problems are solved using Trigonometric identities.
• Graph quadratic functions and solve quadratic equations.
• Graph exponential and logarithmic functions and solve exponential and logarithmic equations.
• Graph trigonometric functions and solve trigonometric equations.
• Use matrix algebra and determinants to solve up to three linear equations in three unknowns.

Details of Learning Activities

• Overview of engineering mathematical problems involving polynomials, functions and their graphs.
• Solve engineering mathematical problems involving nonlinear laws by transforming them into linear.
• Demonstrate with applications vocational growth and decay problems using graphical methods.
• Apply the sine and cosine rules to solve typical engineering workplace problems.

Participate in individual and team problem solving calculation activities completed to industry standard related to typical engineering problems requiring:
• manipulating and factorising of polynomial expressions
• solving quadratic equations by factorizing, formula and graphically
• expanding and simplifying expressions
• calculating with scientific and engineering notation
• transforming non-linear data to linear
• transposing and graphing logarithmic functions
• using logarithmic scales
• solving exponential and logarithmic equations
• manipulating trigonometric identities
• using inverse trigonometric rations
• applying radian and degree conversion and angular velocity
• applying sine and cosine rule
• graphing trigonometric functions
• manipulating and solving matrices up to 3 x 3

Teaching Schedule

See Online Learning Hub for details.

Learning Resources

Prescribed Texts

 1. ‘Mathematics for technicians’, by Blair Alldis

References

 Fitzgerald G. F, Peckham I.A, Mathematical Methods for Engineers and Scientists, third edition, 2002, Pearson Education Australia   Fitzgerald G. F, Tables, RMIT Notes in Mathematics, 1995.

Other Resources

Overview of Assessment

This unit will be assessed in the classroom environment using holistic assessment based on typical workplace activities. Assessment will comprise:
• Three to four tests to be given during the semester (3 x 33 1/3% or 4 x 25%)

Assessment Tasks

As per Assessment Matrix below

Assessment Matrix

 Element Covered Assessment Task Proportion of Final Assessment Submission Time 1,2,3,4 and 5 Test 1 33 1/3 % Week 6 6,7,8,9 and 10 Test 2 33 1/3 % Week 12 11,12,13 and14 Test 3 33 1/3 % Week 18

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