Course Description
Expands upon the topics of Algebra I including rational expressions, radicals
and exponents, quadratic equations, systems of equations, and applications.
Develops the mathematical proficiency necessary for selected curriculum
entrance. Credits not applicable toward graduation. Lecture 4 hours per week.
General Course Purpose
The purpose of this course is to (a) develop competency in the basic algebraic
skills necessary to succeed in 100-level math courses; this is the second half
of the Algebra I-II sequence and (b) develop skills in the oral and written use
of algebraic terminology. The use of current technology is strongly encouraged.
Entry Level Competencies
Prerequisites are a satisfactory score on an appropriate proficiency examination
and Algebra I or equivalent .
Course Objectives
Upon completion of the course, the student will be able to:
A. operate with integral and rational exponents,
B. operate with radical expressions ,
C. solve rational , radical and non- factorable quadratic equations in one
variable,
D. solve quadratic inequalities in one variable ,
E. write and graph linear equations in two variables using slope and intercept
concepts,
F. understand function concepts,
G. solve systems of linear equations,
H. work with common logarithms and their applications,
I. work with complex numbers ,
J. solve application problems.
Major Topics To Be Included
A. Review of number systems
1. Types of numbers
2. Properties of the real number system
3. Laws of signs
B. Algebraic expressions
1. Review polynomials
2. Factoring:
a. review Algebra I techniques
b. sum and difference of two cubes
c. expressions reducible to factorable quadratic by substitution and
grouping
3. Rational expressions
a. review rational expressions,
b. review arithmetic operations,
c. complex fractions.
C. Exponents and radicals
1. Laws of exponents
2. Negative and fractional exponents
3. Review scientific notation
4. Radical expressions using exponents; incorporate variables
5. Simplification and operations
6. Complex numbers
a. Definition
b. Arithmetic with complex numbers
D. Solution of equations in one variable
1. Review of linear and quadratic (factorable)
2. Completing the square
3. Quadratic formula
4. Rational
5. Absolute value (linear)
6. Radical equations
7. Literal equations (e.g., solve 1/f = 1/p + 1/q for q)
8. Application problems throughout *
E. Inequalities in one variable
1. Review of linear inequalities
2. Factorable, quadratic and rational
3. Graphing
4. Absolute value
F. Equations in two variables
1. Linear
a. slope, intercepts, slopes of parallel and perpendicular lines
b. finding equations, given point-slope, two points
c. graphing
2. Linear inequalities
3. Quadratic: graphing parabolas of the form y = ax^2 + bx + c
4. Solution of systems of linear equations
a. 2 x 2
b. 3 x 3
5. Application problems throughout *
G. Introduction to functions
1. Definition and terminology
2. Domain and range
3. Computing functional values
4. Graphic recognition of functions (linear, quadratic, absolute value,
square root )
H. Logarithms
1. Definition
2. Use of log button and its inverse on calculator
3. Properties: product, quotient and power rules
4. Graph of log10 x (Light treatment unless time permits otherwise)
5. Logarithmic and exponential equations
[* When possible,] I include problems that will help
students to remember basic geometric facts: perimeter, area, and volume
formulas; angle relationships in triangles; angles formed with intersecting
lines; angles formed with parallel lines cut by a transversal; similar and
congruent triangles; Pythagorean Theorem.
Extra Topics (optional)
A. Using graphic calculators
1. Graphing equations
2. Finding intercepts
3. Finding points of intersection
4. Use of appropriate windows
