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Pre-Calculus Mathematics

MTH 151

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.

Communicate effectively about mathematics.

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.