Course Description
Topics include sets, real numbers, factoring, functions, expressions (polynomial, rational, exponential, logarithmic, and radical), equations (linear, absolute value, rational, quadratic, exponential, logarithmic, and radical) and inequalities (linear and absolute value). Systems of three equations and complex numbers are introduced. Word problems are studied in detail. Skills for success in transfer-level mathematics courses are emphasized.
Prerequisite(s)
MATH 1414 with a grade of C or better or appropriate assessment score - Must be completed prior to taking this course.
At the end of this course, students will be able to:
- Find the domain of rational and radical functions.
- Solve and graph inequalities in two variables.
- Solve simple rational equations and identify extraneous solutions.
- Simplify radical and rational exponent expressions.
- Solve quadratic equations using the quadratic formula.
- Perform basic operations on exponential and logarithmic functions.
- Solve exponential and logarithmic equations including the natural logarithm and the exponent e.
- Solve application problems using a wide variety of techniques.
Topical Outline
1. Review of Factoring
2. Rational Expressions and Equations
2. Rational Expressions and Equations
a. Intro to rational expressions
b. Multiplication and division of rational expressions
c. Least Common Denominator
d. Addition and subtraction of rational expressions
e. Complex fractions
f. Rational equations
g. Applications using rational expressions and proportions
3. Relations and Functions
3. Relations and Functions
a. Intro to relations and functions
b. Graphs of functions
c. Algebra of functions and composition
d. Variation
4. More Equations and Inequalities
4. More Equations and Inequalities
a. Compound inequalities
b. Polynomial and rational inequalities
c. Absolute value equations and inequalities
d. Linear inequalities and systems of linear inequalities
e. 3 x 3 systems of equations
5. Radicals and Complex Numbers
a. Definition of an nth root
b. Rational exponents
c. Simplifying radical expressions
d. Addition, subtraction and multiplication of radicals
e. Division of radicals and rationalization
f. Solving radical equations
g. Complex numbers
6. Quadratic Equations and Functions
6. Quadratic Equations and Functions
a. Square root property and completing the square
b. Quadratic formula
c. Equations in quadratic form
d. Graphs of quadratic functions
e. Vertex of parabola: applications and modeling
7. Exponential and Logarithmic Functions and Applications
a. Inverse functions
b. Exponential functions
c. Logarithmic functions and their properties
d. The irrational number e and change of base
e. Logarithmic and exponential equations and applications