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# SYLLABUS FOR COLLEGE ALGEBRA

Chapter One sections 1, 2, and 3: Equations and Inequalities ‐ Reviewed by students

• Solve linear equations.

• Solve rational equations.

• Recognize identities, conditional equations, and inconsistent equations.

• Solve applied problems using mathematical models.

• Solve a formula for a variable.

Chapter Two sections 3 and 4: Functions and Graphs ‐ Reviewed by students

• Recognize and use the forms of a line’s equation.

• Graph equations in the rectangular coordinate system.

• Graph horizontal or vertical lines.

• Use a graph to determine intercepts.

• Model data with linear functions and make predictions.

• Find slopes and equations of parallel and perpendicular lines.

• Find functions average rate of change.

Chapter 3.7: Modeling Using Variation ‐ Reviewed by students

• Solve problems involving direct, inverse, and joint variation.

Students should already understand the above objectives or should be able to review them within the
first week of the semester.

Course Objectives

Chapter One: Equations and Inequalities

• Perform operations with complex numbers and square root of negative numbers.

• Solve quadratic equations by factoring, by the square root property, by completing the square, by

• Use the discriminant to determine the number and type of solutions.

• Determine the most efficient method to use when solving a quadratic equation.

• Solve problems modeled by quadratic equations.

• Solve polynomial equations by factoring, solve radical equations, solve equations with rational
exponents, solve equations that are quadratic in form, and solve equations involving absolute value.

• Solve linear inequalities, absolute value inequalities, and graph the solution sets.

Chapter Two: Functions and Graphs

• Determine whether a relation is a function and whether an equation represents a function.

• Find the domain of a function and evaluate a function.

• Obtain information about a function from its graph.

• Graph functions by plotting points, involving a transformation, or a sequence of transformations.

• Evaluate piecewise functions.

• Identify intervals on which a function increases, decreases, or is constant.

• Identify even or odd functions and recognize their symmetries.

• Use transformations to graph functions and graph functions involving sequence of transformations.

• Combine functions using the algebra of functions.

• Form composite functions and determine domains for composite functions.

• Write functions as compositions.

• Verify inverse functions.

• Find the inverse of a function and graph both functions on the same axes.

• Use the horizontal line test to determine if a function has an inverse function.

• Use the graph of a one‐to‐one function to graph its inverse function.

• Find the distance between two points and the midpoint of a line segment.

• Use the general form and standard form of a circle’s equation.

Chapter Three: Polynomial and Rational Functions

• Recognize characteristics of parabolas and graph parabolas.

• Use factoring to find zeros of polynomial functions and identify the multiplicity of a zero.

• Understand the relationship between degree and turning points.

• Use long division and synthetic division to divide polynomials.

• Use the Rational Zero Theorem to find possible rational zeros.

• Find polynomials with given zeros.

• Identify vertical and horizontal asymptotes.

• Solve problems modeled by polynomial or rational inequalities.

Chapter Four: Exponential and Logarithmic Functions

• Evaluate and graph exponential functions and logarithmic functions.

• Change from logarithmic to exponential form and exponential to logarithmic form.

• Find the domain of a logarithmic function.

• Use properties of logarithms.

• Solve exponential and logarithmic equations.

• Solve applied problems involving exponential and logarithmic equations.

• Model data with exponential and logarithmic functions.

Chapter Five: Systems of Equations and Inequalities

• Solve linear systems and nonlinear systems by substitution and by addition.

• Solve systems of linear equations in three variables.

• Find partial fraction decomposition of a rational expression.

• Graph system of inequalities.

• Solve problems involving systems of inequalities.

Chapter Six: Matrices and Determinants – (Optional– as time permits)

• Use matrices and Gaussian elimination and Gauss‐Jordan elimination to solve systems.

• Apply Gaussian elimination to systems without unique solutions and with differing numbers
of variables and equations.

In the event that Chesapeake College needs to close for an extended period of time due to a flu
pandemic, severe weather event, or other emergency situation, consideration will be given to the timing
and duration of the closure as follows:

1. Closure during the semester for up to one week – there will be an opportunity to make up work
missed without significant alteration to the semester calendar.

2. Closure extending beyond one week (or in situations where classes are cancelled on the same
days/evenings over multiple weeks) – the College may extend the length of the semester.
Depending on the timing of the closure, scheduled breaks, end of semester dates, and/or the
processing of final grades might be impacted.

Students can acquire information about closures on the College website or by calling 410‐822‐5400 or
410‐228‐4360. Chesapeake College courses held at off campus sites will follow the protocol of the host
facility.