# Pre-Calculus Mathematics

MTH 151

## Course Description

Prerequisite: Any MTH 119 and MTH 121 with grades of "C" or better, or three years of high school college-preparatory mathematics including trigonometry. MTH 121 may be taken concurrently with instructor approval. Designed for students planning to take calculus. Includes a study of the elementary functions, equations and inequalities, systems of equations, review of trigonometry, and analytic geometry. A GRAPHING CALCULATOR IS REQUIRED. (60-0)

## Outcomes and Objectives

### Develop problem-solving and mathematical modeling skills.

#### Objectives:

• Solve application problems involving algebraic, trigonometric, exponential, and logarithmic functions.
• Use mathematical modeling to fit a curve of best fit to a set of real world data.

### Demonstrate a basic understanding of sequences and series. Objectives

#### Objectives:

• Identify and evaluate basic sequences, including arithmetic and geometric sequences.
• Identify and evaluate arithmetic and geometric series.
• Express series in summation notation.

### Demonstrate a conceptual understanding of a function.

#### Objectives:

• Recognize the multiple representations of a function.
• Translate between different representations of a function.

### Understand functions and functional notation.

#### Objectives:

• Identify the domain and range of a function.
• Add, subtract, multiply, divide, and compose functions. Identify their resulting domains.
• Describe the effect a horizontal or vertical shift of a function has on its graph and equation.
• Describe the effect a reflection of a function about an axis has on its graph and equation.
• Evaluate functions exactly and approximately.

### Demonstrate a conceptual understanding of an inverse function.

#### Objectives:

• Identify the algebraic and graphical relationship between a function and its inverse.
• Describe and compute the inverse of a one-to-one function.

### Understand the algebraic and geometric properties of linear, quadratic, polynomial, piecewise, rational, trigonometric and inverse trigonometric, and logarithmic and exponential functions.

#### Objectives:

• Identify the extreme values of these functions and their locations.
• Identify intervals in which these functions are increasing or decreasing.
• Describe the end behavior of these functions.
• Identify the x- and y-intercepts of the graphs of these functions.
• Identify the linear asymptotes of these functions.
• Sketch the graphs of these functions.

### Solve a variety of equations, inequalities, and systems of equations.

#### Objectives:

• Solve an n x n system of linear equations, n = 2, 3, or 4.
• Solve polynomial, trigonometric, logarithmic, and exponential equations.
• Solve polynomial and rational inequalities.
• Solve systems of nonlinear equations graphically and by substitution.

### Demonstrate an understanding of conic sections.

#### Objectives:

• Sketch the graph of a conic section given its equation or characteristics.
• Write the equation of a conic section in standard form given its graph or characteristics.
• Determine the characteristics of a conic section given its equation or graph.

### Demonstrate an understanding of parametric equations.

#### Objectives:

• Sketch graphs of parametric equations.
• Convert between parametric and rectangular equations.

### Demonstrate an understanding of polar equations and their graphs.

#### Objectives:

• Sketch polar graphs.
• Convert points and equations between rectangular and polar form.
• Identify symmetries in polar graphs.