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Math 120 - Intermediate Algebra

Description: This course extends and reviews the concepts of elementary algebra while incorporating applications and problem-solving skills. Reviewed and extended topics include linear and quadratic equations and their graphs, linear inequalities, systems of linear equations, exponents, factoring polynomials, rational expressions, and radicals. New topics include absolute value equations and inequalities, graphs of absolute value functions, equations of parallel and perpendicular lines, graphs of linear inequalities, graphs of systems of linear inequalities, functions, function notation, domain and range, inverse functions, exponential and logarithmic functions and their graphs, quadratic and polynomial functions and their graphs, an introduction to the complex number system, finding the real and complex solutions for a variety of equations, an introduction to conic sections, and nonlinear systems of equations and their graphs.

Learning Outcomes and Objectives Upon completion of this course, the student will be able to:


 Course Topics The topics for this course are typically allocated as follows:

Lec Topic
5 Linear equations review and introduction to variation 
Formulas 
Direct, inverse, and joint variation 
Applications
5 Linear inequalities in one variable and their number line graphs 
Compound inequalities 
Absolute value equations 
Absolute value inequalities
8 Rectangular coordinate system 
Graphs of linear equations in two variables 
Slope of a line 
Parallel and perpendicular lines 
Finding equations of lines, including parallel and perpendicular lines 
Graphs of linear inequalities in two variables 
Applications
10 Solving and graphing systems of linear equations 
Graphing systems of linear inequalities 
Solving linear systems in three variables 
Applications
11 Exponents and radicals 
Introduction to rational exponents 
Simplifying expressions with rational exponents 
Simplifying radical expressions 
Solving radical equations 
Introduction to the complex number system 
Simplifying radicals and expressions using complex numbers
6 Functions 
Introduction to and definition of a function 
Function notation 
Types of functions 
Domain and range 
Inverse functions 
Graphing a function and its inverse
11 Exponential and logarithmic functions 
Introduction to exponential functions and their graphs 
Introduction to inverse exponentials: logarithms 
Graphs of logarithms 
Properties of logarithms 
Natural logarithms 
Logarithmic and exponential equations 
Applications
11 Solving quadratic equations and equations in quadratic form for real and complex solutions 
Factoring: greatest common factor, grouping, difference of two squares, sum and difference of two cubes, trinomials, and higher degree polynomials in quadratic form 
Square-root property 
Completing the square 
Quadratic formula 
Graphs of quadratic equations 
Applications
8 Rational expressions 
Simplifying rational expressions 
Complex fractions 
Rational equations 
Applications
10 Conic sections and nonlinear systems of equations 
Equations and graphs of parabolas, circles, ellipses, and hyperbolas 
Solving and graphing nonlinear systems of equations 
Applications
5 Optional topics 
Synthetic division, the discriminant, determinants, Cramer's Rule, Gaussian method for solving systems, the Binomial Theorem, sequences and series, graphing polynomial functions, graphing root functions, graphing rational functions, second degree inequalities, systems of second degree inequalities, and rational inequalities