# Intermediate Algebra

MTH 119W## Course Description

Prerequisite: MATH LEVEL 5. Includes fundamental concepts of algebra and applications, equation solving, graphs, systems of linear equations, quadratic equations, algebraic fractions, exponents, radicals, functions, and logarithms. Credit may be earned in MTH 119 or MTH 119A, but not both. A GRAPHING CALCULATOR IS REQUIRED. (60-0)

## Outcomes and Objectives

### Students will develop their skills in recognizing, evaluating, and simplifying algebraic expressions.

#### Objectives:

- Add, subtract, multiply, and divide polynomial expressions.
- Factor a variety of polynomials. (Taking out a common factor, difference of squares, sum/difference of cubes, trinomials, and by grouping.)
- Reduce, add, subtract, multiply, and divide rational expressions.
- Convert between radical and exponential form.
- Simplify expressions using the rules of exponents (including negative and fractional exponents).
- Simplify expressions using the laws of logarithms.
- Convert between exponential and logarithmic form.
- Write complex numbers in a + bi form.
- Add, subtract, multiply, and divide complex numbers.

### Students will use a graphing calculator to evaluate and analyze linear, quadratic, square root, exponential, and logarithmic functions.

#### Objectives:

- Graph and linear, quadratic, square root, exponential, or logarithmic function.
- Create a table of input/output 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 solve a variety of equations, inequalities, and systems of equations.

#### Objectives:

- Solve a variety of polynomial, radical, rational, exponential, logarithmic, and absolute value equations.
- Solve equations symbolically, graphically, and numerically.
- Solve a variety of linear and absolute value inequalities.
- Solve inequalities symbolically and graphically.
- Use interval notation, relational symbols (< , >, , ), a 1-dimensional graph, or a verbal description to describe a set of numbers.
- Solve systems of equations algebraically, graphically and using TI-83 software (rref).

### Students can define, recognize, and understand concepts related to functions.

#### Objectives:

- State and explain the definition of a function.
- Identify several characteristics of functions.
- Identify or describe relationships between the numerical, graphical, and algebraic representations of a function.
- Evaluate, compose, and compute with functions.
- Identify examples of functions in the real world.
- Describe the relationships between a function and its inverse function.

### Students can recognize and understand concepts related to linear functions.

#### Objectives:

- Calculate the slope of a line in a variety of contexts.
- Identify the slope of a line as positive, negative, zero, or undefined.
- Interpret the slope of a line in an applied context.
- Calculate the y-intercept of a line in a variety of contexts.
- Interpret the y-intercept of a line in an applied context.
- Calculate the x-intercept of a line in a variety of contexts.
- Interpret the x-intercept of a line in an applied context.
- Calculate the equation of a line in a variety of contexts.
- Recognize a linear function and its corresponding graph.

### Students can recognize and understand concepts related to quadratic functions.

#### Objectives:

- Complete the square for a variety of quadratic expressions.
- Recognize a quadratic function and its corresponding parabolic graph.
- Determine the x and y coordinates of the maximum or minimum point of a parabola.

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

#### Objectives:

- Recognize an exponential function and its corresponding graph.
- Recognize a logarithmic function and its corresponding graph.
- Describe the inverse relationships between the logarithmic and exponential functions.
- Describe the growth and decay properties of exponential and logarithmic functions.

### Students will develop their skills in the construction and interpretation of Cartesian graphs.

#### Objectives:

- Construct the graph of a polynomial, absolute value, logarithmic, exponential, or radical function if given the corresponding equation.
- Construct a graph representing a given scenario.
- Identify an appropriate scale for both axes when constructing a graph.
- Approximate a curve of best fit if given a set of data.
- Describe trends in a set of data.
- Identify the x and y coordinates of maximums and minimums of a graph.
- Identify where a graph is increasing, decreasing, and constant.
- Approximate one coordinate of a point on a graph if given the other.
- Identify graphs as linear, quadratic, exponential, or logarithmic.

### 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 communicate effectively about mathematics.

#### Objectives:

- Orally describe solutions to problems using appropriate terminology.
- Provide complete written solutions to problems using appropriate terminology.
- Use appropriate vocabulary for the audience and purpose.
- Derive meaning from a reading.
- Articulate important ideas and conclusions in writing.