MTH 151 - Pre-Calculus Mathematics

1. Develop problem-solving and mathematical modeling skills.
   1. Solve application problems involving algebraic, trigonometric, exponential, and logarithmic functions.
   2. Use mathematical modeling to fit a curve of best fit to a set of real world data.
2. Demonstrate a conceptual understanding of a function.
   1. Recognize the multiple representations of a function.
   2. Translate between different representations of a function.
3. Understand functions and functional notation.
   1. Identify the domain and range of a function.
   2. Add, subtract, multiply, divide, and compose functions. Identify their resulting domains.
   3. Describe the effect a horizontal or vertical shift of a function has on its graph and equation.
   4. Describe the effect a reflection of a function about an axis has on its graph and equation.
   5. Evaluate functions exactly and approximately.
4. Demonstrate a conceptual understanding of an inverse function.
   1. Identify the algebraic and graphical relationship between a function and its inverse.
   2. Describe and compute the inverse of a one-to-one function.
5. Understand the algebraic and geometric properties of linear, quadratic, polynomial, piecewise, rational, trigonometric and inverse trigonometric, and logarithmic and exponential functions.
   1. Identify the extreme values of these functions and their locations.
   2. Identify intervals in which these functions are increasing or decreasing.
   3. Describe the end behavior of these functions.
   4. Identify the x- and y-intercepts of the graphs of these functions.
   5. Identify the linear asymptotes of these functions.
   6. Sketch the graphs of these functions.
6. Solve a variety of equations, inequalities, and systems of equations.
   1. Solve an n x n system of linear equations, n = 2, 3, or 4.
   2. Solve polynomial, trigonometric, logarithmic, and exponential equations.
   3. Solve polynomial and rational inequalities.
   4. Solve systems of nonlinear equations graphically and by substitution.
7. Demonstrate an understanding of conic sections.
   1. Sketch the graph of a conic section given its equation or characteristics.
   2. Write the equation of a conic section in standard form given its graph or characteristics.
   3. Determine the characteristics of a conic section given its equation or graph.
8. Demonstrate an understanding of parametric equations.
   1. Sketch graphs of parametric equations.
   2. Convert between parametric and rectangular equations.
9. Demonstrate an understanding of polar equations and their graphs.
   1. Sketch polar graphs.
   2. Convert points and equations between rectangular and polar form.
   3. Identify symmetries in polar graphs.
10. Demonstrate a basic understanding of sequences and series. Objectives
    1. Identify and evaluate basic sequences, including arithmetic and geometric sequences.
    2. Identify and evaluate arithmetic and geometric series.
    3. Express series in summation notation.
11. Communicate effectively about mathematics.