MTH 151 - Pre-Calculus Mathematics

Credits: 5
Instructional Contact Hours: 5

Designed for students planning to take calculus who have had previous experiences with trigonimetry or are concurrently taking MTH 121. Includes a study of the elementary functions, equations and inequalities, systems of equations, review of trigonometry, and analytic geometry. GRAPHING TECHNOLOGY IS REQUIRED.

Prerequisite(s): High school GPA of 3.0 or higher within the last ten years or completion of Guided Self-Placement (GSP) process.
Corequisite(s): None
Lecture Hours: 75 Lab Hours: 0
Meets MTA Requirement: Math
Pass/NoCredit: Yes

Outcomes and Objectives

1. Develop problem-solving skills.

A. Solve application problems involving a variety of functions including, algebraic, trigonometric, exponential, and logarithmic functions.

2. Develop mathematical modeling skills.

A. Use mathematical modeling to fit a curve of best fit to a set of real-world data.

3. Demonstrate an understanding of functions.

A. Recognize the multiple representations of a function.
B. Translate between different representations of a function.
C. Identify the domain and range of a function.
D. Perform the four basic operations on functions.
E. Compose functions.
F. Describe the effects a horizontal or a vertical shift of a function has on its graph and equation.
G. Describe the effect a reflection of a function about an axis has on its graph and equation.
H. Evaluate functions exactly and approximately.

4. Demonstrate a conceptual understanding of an inverse function.

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

5. Demonstrate an understanding of the geometric properties of functions.

A. Identify the extreme values of quadratic, polynomial, piecewise, rational, trigonometric, inverse trigonometric, logarithmic, or exponential functions and their locations.
B. Identify intervals in which linear, quadratic, polynomial, piecewise, rational, trigonometric, inverse trigonometric, logarithmic, or exponential functions are increasing or decreasing.
C. Describe the end behavior of linear, quadratic, polynomial, piecewise, rational, trigonometric, inverse trigonometric, logarithmic, or exponential functions.
D. Identify the x- and y-intercepts of the graphs of linear, quadratic, polynomial, piecewise, rational, trigonometric, inverse trigonometric, logarithmic, or exponential functions.
E. Identify the linear asymptotes of piecewise, rational, trigonometric, inverse trigonometric, logarithmic, or exponential functions.
F. Sketch the graphs of linear, quadratic, polynomial, piecewise, rational, trigonometric, inverse trigonometric, logarithmic, or exponential functions.

6. Solve a variety of equations.

A. Solve polynomial equations.
B. Solve trigonometric equations
C. Solve logarithmic equations.
D. Solve exponential equations.

7. Solve a variety of inequalities.

A. Solve polynomial inequalities
B. Solve rational inequalities.

8. Solve systems of equations.

A. Solve an n x n system of linear equations, n = 2, 3, or 4.
B. Solve systems of nonlinear equations graphically.
C. Solve systems of non-linear equations by substitution.
D. Solve systems of non-linear equations by elimination.

9. Demonstrate an understanding of conic sections.

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

10. Demonstrate an understanding of parametric equations.

A. Sketch graphs of parametric equations.
B. Convert between parametric and rectangular equations.

11. Demonstrate an understanding of trigonometric identities.

A. Re-write expressions using the fundamental, Pythagorean, or the double angle identities for sine and cosine.
B. Use the fundamental, Pythagorean, or the double angle identities for sine and cosine to solve trigonometric equations.
C. Re-write expressions involving compositions of trigonometric or inverse trigonometric identities into an algebraic form.

12. Demonstrate an understanding of the polar graphing system.

A. Sketch polar graphs.
B. Convert points and equations between rectangular and polar form.
C. Identify symmetries in polar graphs.

13. Demonstrate a basic understanding of sequences.

A. Identify basic sequences which include arithmetic and geometric sequences
B. Evaluate basic sequences which include arithmetic and geometric sequences.

14. Demonstrate a basic understanding of series.

A. Identify and evaluate arithmetic and geometric series.
B. Evaluate arithmetic and geometric series.
C. Express series in summation notation.

15. Communicate effectively about mathematics.