MAT 136 -- Intermediate Algebra and Trigonometry ()
Prerequisite: MAT 096 --ElementaryAlgebra and Trigonometry
Informal description: This course the first step for peoplewho want to learn the algebra and trigonometry necessary for advanced mathematicalapplications and calculus. The course requires the use of a graphing calculator.
Courses this course is a prerequisite for:
Course Description: Rational exponents; synthetic division; rationalexpressions; completing the square; circles; complex numbers; quadraticformula; linear systems; inverse functions; graphs and propertiesof logarithms and exponential functions; reference angles; radian measure;graphs of sine, cosine, and tangent; basic trigonometric identities andequations; Law of Sines; Law of Cosines. 4 class hours.
Objectives:
The student should be able to: Perform skills in three categories: Algebra, Geometry/Trigonometry,Graphing and Graphing Calculator.
Note: Throughout the course the students are expected to solve appliedproblems related to the topics of the course.
Algebra:
the student should be able to:
Geometry/Trigonometry:
the student should be able to:
Use radians to measure angles.
Find reference angles for angles measured in degrees and radians.
Find the trigonometric functions for a general angle.
Use reciprocal, Pythagorean, and double angle trigonometric identities.
Solve trigonometric equations.
Perform operations on and factor trigonometric expressions.
Use the distance and midpoint formulas.
Graphing:
the student should be able to:
Identify and graph the following families of relations:
Graph functions and relations by using various graphing techniques: symmetry,reflection, and translation.
Graph inverse functions.
Graphing Calculator:
the student should be able to:
Course Outline
I. Polynomials and Factoring
Arithmetic operations and simplification using general factoring techniques
Long division of general polynomials
Synthetic division
II. Rational Expressions
Arithmetic operations and simplification of general rational expressions
III. Absolute Value Functions
Graphing techniques
Equations and inequalities involving absolute values of general expressions
Applications
IV. Exponents, Radicals, and Complex Numbers
Rational exponents and general radical expressions
Operations and simplification of radical expressions
Complex numbers
Operations and simplification of complex numbers
V. Equations and Inequalities
Linear equations and inequalities and their graphs
Quadratic formula, quadratic equations and inequalities and their graphs
Absolute value equations and their graphs
Rational equations
Equations involving rational exponents and radicals
Applications
VI. Functions and Graphs
Functional terminology and notation
Graphs of functions
Graphing techniques of symmetry
Reflection, translation, dilation and contraction
Functional operations, function composition, inverse functions and theirgraphs
VII. Exponential and Logarithmic Functions
Graphs and properties of exponential and logarithmic functions
VIII. Trigonometric Functions IX. Systems of Equations and Inequalities
Systems of linear equations in two and three variables