Algebra

College

Course Outline

 

Elementary Algebra:

Course Description:

This course includes the basic concepts typically introduced in high school algebra, including operations on polynomials, exponents, solving linear and quadratic equations, linear inequalities, word problems, factoring, rational expressions, and graphing linear equations.

Course Content:

This course will cover the following topics:

1)           Basic linear equations

a)           Solving basic linear equations

b)           Simplifying expressions to solve equations

c)           Introduction to problem solving

d)           Applications with linear models

e)           Formulas

f)            Solving linear inequalities

2)           Linear equations in two variables

a)           The rectangular coordinate system

b)           Graphing linear equations

c)           Slope of a Line

d)           Writing Equations of Lines

e)           Graphing linear inequalities

f)            Applications

3)           Polynomials and exponents

a)           Definition and properties of exponents

b)           Terminology for polynomials

c)           Addition, subtraction, multiplication, and division of polynomials

d)           Application of concepts using exponential expressions

e)           Scientific notation

4)           Factoring polynomials

a)           Greatest common factor

b)           Factor by grouping

c)           Factor simple trinomials

d)           Factor general trinomials

e)           Difference of squares

f)            Sum and difference of cubes

g)           Solve equations by factoring

5)           Rational expressions

a)           Fundamental properties of rational expressions

b)           Addition, subtraction, multiplication, and division of rational expressions

c)           Complex fractions

d)           Solving equations involving rational expressions

e)           Applications

 

Intermediate Algebra:

Course Description:

This course includes finding solutions to quadratic equations and inequalities, rational exponents and radicals, solving linear systems of equations and inequalities, functions, and application problems.

Course Content:

1)           Linear Equations and Inequalities in One Variable

a) Linear equations and inequalities

b) Compound inequalities

c) Absolute value equations and inequalities

 

2)           Rational exponents and radicals

a) Rational exponents

b) Radicals

c) Operations with radicals

d) Solve equations containing radicals

e) Complex numbers

 

3)           Quadratic equations

a) Solutions by factoring

b) Completing the square

c) The quadratic formula

d) Equations quadratic in form

e) Quadratic inequalities

f) Applications

 

4)           Systems of equations and inequalities

a) Systems of linear equations in two or more variables

i) By elimination

ii) By determinants (Cramer’s Rule)

b) Systems of linear inequalities

c) Applications

 

5)           Functions

a) Introduction to functions

i) Linear

ii) Quadratic

iii) Absolute Value

iv) Rational

v) Radical

b) Graphs of basic functions

c) Transformations

d) Algebra of functions

e) Inverse Functions

 

College Algebra:

Course Description:

This course is designed for students with a strong foundation in algebra. It includes the study of polynomial rational functions and inequalities, exponential and logarithmic functions, conics, systems of nonlinear equations and inequalities, and an introduction to sequences, series, and the Binomial Theorem. 

Course Content:

1) Functions

a) Function concept

b) Function notation

c) Operations with functions

d) Composition of functions

e) Inverses of functions

f) Graphs of function with transformations

g) Applications

2) Exponential and logarithmic functions

a) Exponential functions and graphs

b) Logarithmic functions and graphs

c) Properties of logarithms

d) Solving exponentials and logarithmic equations

e) Applications

3) Sequences and series

a) Sequences and series

b) Arithmetic sequences and series

c) Geometric sequences and series

d) Binomial expansion

e) Mathematical induction

f) Applications

4) Polynomial and rational functions

a) The Remainder and Factor Theorems

b) Synthetic division

c) Zeros of polynomials

d) Rational functions

e) Polynomial and rational inequalities

f) Applications

5) Conic sections and graphing

a) The circle

b) The parabola

c) The ellipse

d) The hyperbola

6) Systems of equations and inequalities

a) Systems of linear equations

b) Systems of linear inequalities

c) Systems of linear equations using matrices

d) Systems of nonlinear equations

e) Systems of nonlinear inequalities

f) Applications

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