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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:
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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
- 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
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How can Algebrator Help YOU?
- It solves any problem from your textbook
- It gives you all the steps, not just solutions - just like a teacher!
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- When you don't understand a step, it gives you an explanation
- You get your homework done in minutes, and you learn algebra
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simplification of algebraic expressions
(operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
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factoring and expanding expressions
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finding LCM and GCF
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operations with complex numbers (simplifying, rationalizing complex denominators...)
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solving linear, quadratic and many other equations
and inequalities (including basic logarithmic and exponential equations)
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solving a system of two and three linear equations
(including Cramer's rule)
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graphing curves
(lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
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graphing general functions
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operations with functions
(composition, inverse, range, domain...)
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simplifying logarithms
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basic geometry and trigonometry
(similarity, calculating trig functions, right triangle...)
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arithmetic and other pre-algebra
topics (ratios, proportions, measurements...)
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NEW! Linear Algebra
(operations with matrices, inverse matrix, determinants...)
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