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MAT136 - Algebra 3 and Trigonometry
Catalog Description: Topics include absolute value equations and inequalities; solving systems of linear equations using determinants; review of rational exponents, radical expressions and complex numbers; quadratic equations and inequalities; solving equations reducible to quadratic form; quadratic, exponential and logarithmic functions and applications; graphs of functions; algebra of functions; inverse functions; conic sections; nonlinear systems of equations and inequalities; right triangle trigonometry; trigonometric functions and the unit circle. Not open to students with credit in MAT 140 or higher. Prerequisite: MAT 102 with a grade of ‘C’ or higher or by placement.
Lecture: 3 hrs.
Course Learning Outcomes (CLOs):
Upon successful completion of this course as documented through writing, objective testing, case studies, laboratory practice, and/or classroom discussion, the student will be able to:
1.Given a set of real numbers, display the set in set-builder notation, interval notation or by graphing the set on a real number line.
2.Given an absolute value linear equation or absolute value linear inequality, solve the equation or inequality.
3.Given a system of linear equations, correctly solve the system by the addition method or by using determinants.
4.Given two or more radical expressions, add, subtract, multiply or divide the expressions and write the answer in simplest form.
5.Given two complex numbers, add, subtract, multiply or divide the numbers and write the answer in the form a + bi.
6.Given an equation that reduces to a quadratic equation, correctly solve the equation by factoring, taking square roots, completing the square or using the quadratic formula.
7.Given a quadratic inequality or rational inequality, correctly solve the inequality.
8.Given a quadratic, cubic, absolute value or square root function, correctly graph the function.
9.Given two functions, add, subtract, multiply, divide or find the composition of the functions.
10.Given a 1 - 1 function, find its inverse.
11.Given an exponential expression, write it in logarithmic form, or vice versa.
12.Given an exponential or logarithmic function, correctly graph the function.
13.Given an exponential or logarithmic equation, correctly solve the equation.
14.Given the equation of one of the four basic conic sections (parabola, circle, ellipse or hyperbola), identify the type and graph the equation.
15.Given a system of nonlinear equations or inequalities, solve the system by substitution or graphing.*
16.Given an angle in degree or radian measure, convert between the two forms.
17.Given two sides of a right triangle or a point in the coordinate system, evaluate any of the six trigonometric functions for the corresponding angle.
18.Given the equation y = sinx or y = cosx, graph the equation.
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
I. INEQUALITIES AND ABSOLUTE VALUE
A. Sets, Set Builder Notation, Interval Notation, and Number Line Notation
B. First-degree Inequalities
C. Absolute Value Equations and Inequalities
II. SYSTEMS OF EQUATIONS
A. Solving Systems of Linear Equations by the Addition Method
B. Solving Systems of Linear Equations by Using Determinants
C. Application Problems
III. RADICAL EXPRESSIONS
A. Rational Exponents and Radical Expressions
B. Operations on Radical Expressions
C. Complex Numbers
D. Solving Equations Containing Radical Expressions
IV. QUADRATIC EQUATIONS
A. Solving Quadratic Equations by Factoring or by Taking Square Roots
B. Solving Quadratic Equations by Completing the Square
C. Solving Quadratic Equations by Using the Quadratic Formula
D. Solving Equations that are Reducible to Quadratic Equations
E. Quadratic Inequalities and Rational Inequalities
F. Applications of Quadratic Equations
A. Properties of Quadratic Functions
B. Graphs of Functions
C. Algebra of Functions
D. One-to-one and Inverse Functions
VI. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
A. Exponential Functions
B. Introduction to Logarithms
C. Graphs of Logarithmic Functions
D. Solving Exponential and Logarithmic Equations
E. Applications of Exponential and Logarithmic Functions
VII. CONIC SECTIONS
A. The Parabola
B. The Circle
C. The Ellipse and the Hyperbola
D. Solving Nonlinear Systems of Equations
E. Quadratic Inequalities and Systems of Inequalities
VIII. RIGHT ANGLE TRIGONOMETRY
A. Angles and Arcs
B. Trigonometric Functions of Acute Angles
C. Trigonometric Functions of any Angle
D. Graphs of y = sin x and y = cos x only (no transformations)
Effective Term: Fall 2012