# College Algebra

MTH 122W## Course Description

Prerequisite: MATH LEVEL 6. Reviews the mechanics of basic Algebra and solidifies understanding by using algebraic techniques, constructing mathematical models, solving problems and interpreting results. Includes: algebraic expressions; equations and inequalities; functions, inverse functions, and graphs; polynomial and rational functions; radical functions; exponential and logarithmic functions; matrices and determinants; systems of equations and inequalities; complex numbers; sequences and series. A GRAPHING CALCULATOR IS REQUIRED. (60-0)

## Outcomes and Objectives

### Students will recognize and understand notation describing sets of real numbers.

#### Objectives:

- Understand set and interval notation .
- Apply the operations of intersection and union.

### Students can work with complex numbers.

#### Objectives:

- Define numbers in the form a + bi.
- Add, subtract, multiply, and divide complex numbers.
- Solve quadratic equations with complex solutions.

### Students can work with sequences and series.

#### Objectives:

- Find the terms of an arithmetic and geometric sequence.
- Find the sum of an arithmetic and geometric series.
- Apply the Binomial Theorem.

### Students can communicate effectively about mathematics in writing.

#### Objectives:

- Provide complete written solutions to problems using appropriate terminology.
- Articulate important ideas and conclusions in writing.

### Students will develop their problem-solving and mathematical modeling skills.

#### Objectives:

- Solve real world problems involving linear equations, quadratic equations, exponential equations, logarithmic equations, rational equations, and systems of equations.
- Use mathematical modeling to solve real world problems.
- Clarify and analyze the meanings of words, phrases and statements.
- Learn the meanings of relevant symbols used in the discipline and ways to use them.
- Transfer problem solving strategies for use in new contexts.
- Organize and present information or data in tables, charts, and graphs.
- Use symbol systems to raise questions about models and proposed answers to problems.
- identify, state and clarify arguments or reasoning, including those codified by systems of symbols.
- Generate and assess solutions to problems.

### Students will use graphing calculator technology to evaluate and analyze solutions to various functions.

#### Objectives:

- Graph linear, quadratic, radical, polynomial, exponential, or logarithmic function.
- Create a table of input/out pairs for any given function.
- Determine an appropriate window to obtain a complete graph of a linear, quadratic, square root, exponential, or logarithmic function.
- Find the intersection of any two functions
- Evaluate any numerical expression involving linear, quadratic, rational, square root, exponential, or logarithmic functions.

### Students can perform operations on polynomial functions.

#### Objectives:

- Apply properties of positive integral exponents.
- Perform addition, subtraction, multiplication and division of polynomial functions.
- Perform synthetic division.
- Factor polynomials.
- Reduce rational expression to simplest form.
- Add, subtract, multiply and divide rational expressions (including complex fractions).

### Students can perform operations on radical functions.

#### Objectives:

- Apply the properties of rational exponents.
- Add, subtract, multiply and divide radicals, expressing solutions in simplest form.

### Students can recognize, graph and solve problems relating to linear functions.

#### Objectives:

- Graph ordered pairs of any relation and identify whether or not it is a function.
- Graph any linear function.
- Find the distance between any two points in the plane.
- Find the slope of a line.
- Find the equation of a line, given information.
- Solve and graph a linear inequality.
- Solve absolute value equations and inequalities.

### Students will be able to graph any polynomial function

#### Objectives:

- Determine intercepts, axis of symmetry and maximum or minimum of a quadratic.
- Graph any quadratic function.
- Use synthetic division to identify zeros and graph any polynomial function.

### Students can solve nonlinear equations and inequalities involving a function of one variable.

#### Objectives:

- Solve quadratic equations by factoring, the quadratic formula, and graphing.
- Solve equations involving radicals.
- Solve polynomial equations symbolically (using synthetic division).
- Solve polynomial equations of degree greater than 2 using tables and graphs.
- Solve quadratic inequalities.
- Set up and solve application problems .

### Students can recognize and understand concepts related to logarithmic and exponential functions.

#### Objectives:

- Recognize an exponential or logarithmic function and its graph.
- Solve exponential or logarithmic equations.

### Students can solve systems of equations and inequalities.

#### Objectives:

- Solve systems of 2 and 3 linear equations.
- Solve linear programming problems.
- Solve systems of inequalities graphically.
- Set up and solve application problems.

### Students can work with matrices and determinants.

#### Objectives:

- Apply basic operations to matrices.
- Evaluate determinants.
- Solve systems of equations by matrix methods.