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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.


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.


  • the student should be able to:

  • Geometry/Trigonometry:

  • the student should be able to:
    1. Use radians to measure angles.
    2. Find reference angles for angles measured in degrees and radians.
    3. Find the trigonometric functions for a general angle.
    4. Use reciprocal, Pythagorean, and double angle trigonometric identities.
    5. Solve trigonometric equations.
    6. Perform operations on and factor trigonometric expressions.
    7. Use the distance and midpoint formulas.


  • the student should be able to:
    1. Identify and graph the following families of relations:

    1. Graph functions and relations by using various graphing techniques: symmetry,reflection, and translation. 
    2. 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
    • Determinants of 2x2 and 3x3 matrices
    • Cramer's Rule
    • Systems of linear inequalities
    • Systems involving second-degree equations
    • Applications
    X. Analytic Geometry 
    • Distance and midpoint formulas
    • Completing the square
    • Equations and graphs of general circles