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:
- graph and solve linear inequalities.
- graph systems of linear inequalities.
- solve equations and inequalities containing absolute values.
- solve and graph linear equations and systems of linear equations.
- create linear equations that pass through a given point and are parallel to a given line.
- create linear equations that pass through a given point and are perpendicular to a given line.
- simplify polynomial expressions.
- choose and apply appropriate techniques to factor a variety of polynomials.
- state whether a mathematical relation is a function and find its domain and range.
- construct the inverse of a given function.
- sketch graphs of basic exponential functions.
- utilize the properties of exponents to simplify exponential expressions and to solve exponential equations.
- sketch graphs of basic logarithmic functions.
- utilize the properties of logarithms to simplify logarithmic expressions and to solve logarithmic equations.
- simplify expressions containing radicals, using complex numbers where appropriate.
- solve quadratic equations for real and complex solutions.
- solve equations containing radicals.
- simplify rational expressions and solve rational equations for real and complex solutions.
- sketch graphs of basic conic sections.
- solve and graph systems of non-linear equations.
- develop an appropriate equation or system of equations and use the resulting equation(s) to solve application problems.
Course Topics The topics for this course are typically allocated as follows:
|5||Linear equations review and introduction to variation
Direct, inverse, and joint variation
|5||Linear inequalities in one variable and their number line graphs
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
|10||Solving and graphing systems of linear equations
Graphing systems of linear inequalities
Solving linear systems in three variables
|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
Introduction to and definition of a function
Types of functions
Domain and range
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
Logarithmic and exponential equations
|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
Completing the square
Graphs of quadratic equations
Simplifying rational expressions
|10||Conic sections and nonlinear systems of equations
Equations and graphs of parabolas, circles, ellipses, and hyperbolas
Solving and graphing nonlinear systems of equations
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