Math 110A
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Degree Applicable
Course ID 010235
Glendale Community College
November 2015
COURSE OUTLINE
Math 110A
Precalculus I
Catalog Statement
Mathematics 110A is the first of two courses that prepares students for calculus. Topics include
first and second-degree equations and inequalities, the study of functions and their graphs
(polynomial, absolute value, radical, rational, exponential, logarithmic), and remainder and
factor theorems. Additional topics include a review of geometry, followed by an introduction to
trigonometric functions, solving right triangles, elementary trigonometric identities, inverse
trigonometric functions, and solving triangles using the Laws of Sines and the Law of Cosines.
Total Lecture Units: 3.0
Total Laboratory Units: 0.5
Total Course Units: 3.5
Total Lecture Hours: 48.0
Total Laboratory Hours: 24.0
Total Laboratory Hours To Be Arranged: 0.0
Total Faculty Contact Hours: 72.0
Prerequisite: MATH 101 OR MATH 120 OR MATH 220B
Note: A maximum of 3 units may be earned from the combination of MATH 110A and MATH
100. No credit will be given for MATH 110A if a student has successfully completed MATH
110 OR MATH 100 and MATH 102.
Course Entry Expectations
Prior to enrolling in the course, the student should be able to:
 solve absolute value equations and inequalities;
 solve linear equations and inequalities;
 perform polynomial operations;
 perform operations on radical and rational expressions;
 solve equations with radical and rational expressions;
 solve a quadratic equation using various methods;
 find the equation of a line;
 solve a system of linear equations in two or three unknowns;
 solve a non-linear system algebraically;
 find the inverse of a function;
 use the three properties of logarithms to simplify logarithmic expressions;
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solve exponential and logarithmic equations;
graph exponential and logarithmic functions;
graph the three basic conic sections;
find the nth term of a geometric series and arithmetic series;
divide synthetically.
Course Exit Standards
Upon successful completion of the required coursework, the student will be able to:
 solve equations including rational, linear, polynomial, exponential, absolute value,
radical, and logarithmic;
 apply functions to model real world applications;
 solve linear, non-linear, and absolute value inequalities;
 graph the following types of functions and relations: polynomial, rational, exponential,
and logarithm;
 apply transformations to the graphs of functions and relations;
 Recognize the relationship between functions and their inverses graphically and
algebraically;
 solve exponential and logarithmic equations;
 apply the Fundamental Theorem of Algebra and related theorems to find the roots of a
polynomial;
 apply the basic definitions of trigonometry to solve right triangle application problems;
 evaluate a trigonometric function at an angle whose measure is given in degrees and
radians;
 apply the laws of sines and cosines to solve application problems.
Course Content
Total Faculty Contact Hours = 72.0
Basic Concepts ( 4 lecture hours, 2 lab hours)
Real numbers
Exponents and radicals
Algebraic expressions
Rational expressions
Equations and Inequalities (7 lecture hours, 3 lab hours)
First degree equations
Quadratic equations
Complex numbers
Other types of equations (rational, radical, absolute value)
Linear and absolute value inequalities
Quadratic and other non-linear inequalities
Applications
Functions and Their Graphs (7 lecture hours, 3 lab hours)
Cartesian coordinate system
Function (linear, polynomial, rational, radical, absolute value) definition, evaluation,
domain and range
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Graphs of functions (linear, quadratic, rational, radical, absolute value) including vertices,
asymptotic behavior and intercepts
Transformations of functions (linear, quadratic, rational, radical, absolute value)
Quadratic functions
Algebra of functions
One-to-one functions and inverses
Polynomial Functions (7 lecture hours, 3 lab hours)
The Remainder Theorem and the Factor Theorem
Synthetic division
The Fundamental Theorem of Algebra
Rational roots
Graphing polynomial functions
Rational functions
Exponential and Logarithmic Functions (6 lecture hours, 3 lab hours)
Exponential functions
Logarithmic functions
Transformations of exponential and logarithmic functions
Properties of logarithms
Exponential and logarithmic equations
Common and natural logarithms
Applications
Geometry Review (5 lecture hours, 3 lab hours)
Properties of angles
Triangles properties
Circles
Polygons and solids
Trigonometric Functions (7 lecture hours, 3 lab hours)
Definition of the six trigonometric functions of a right triangle
Definition of the six trigonometric functions of any angle on the rectangular coordinate
system
Inverse trigonometric functions
Right triangle trigonometry and applications
Radian Measure (2 lecture hours, 2 lab hours)
Radian measure
Definition of the six trigonometric functions on the unit circle (Optional)
Linear and angular velocity
Oblique Triangles (3 lecture hours, 2 lab hours)
The Law of Cosines
The Law of Sines
Areas of triangles
Methods of Instruction
The following methods of instruction may be used in this course:
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lecture and discussion;
graphing calculator or computer demonstrations;
individual or group guided activities.
Out of Class Assignments
The following out of class assignments may be used in this course:
 homework (e.g. problems sets related to course content);
 group assignments and projects (e.g. group project to solve a “challenging” application
problem from the textbook);
 graphing calculator and/or computer assignments (e.g. explore of the effects of changes
in the form of a polynomial function to the shape of its graph).
Methods of Evaluation
The following methods of evaluation may be used in this course:
 quizzes;
 four to seven chapter examinations are required;
 participation in lab activities;
 a two-hour and twenty-minute comprehensive final examination is required.
Textbooks
Stewart, James. Precalculus. Custom Edition for GCC .4rd ed. Mason: Cengage Learning, 2011.
Print.
12th Grade Textbook Reading Level. ISBN #1305071743
Tussy, Alan S, and R. David Gustafson. Basic Geometry for College Students. Belmont:
Brooks/Cole/Cengage, 2010. Print.
11th Grade Textbook Reading Level. ISBN # 0-495-82948-X.
Student Learning Outcomes
Upon successful completion of the required coursework, the student will be able to:
 solve algebraic equations and inequalities;
 graph various functions and relations;
 find the roots of a polynomial;
 use trigonometric identities and formulas;
 use trigonometry to solve application problems;
 demonstrate the knowledge of complex numbers.