Pre-calculus – mth225 (4 credits)
This course prepares students for success in calculus. A brief review of college algebra topics is presented including linear, polynomial, radical, rational and absolute value, functions, and equations. Students also examine systems of equations, exponential, logarithmic, and trigonometric functions as well as analytic geometry. In addition, students are introduced to sequences and series.
Rational, Logarithmic, and Exponential Functions
- Identify the vertical, horizontal, and slant asymptotes of a rational function.
- Solve exponential and logarithmic functions.
- Analyze the relationship between exponential and logarithmic functions.
- Analyze graphs of exponential and logarithmic functions.
- Apply exponential and logarithmic functions to real-world problems.
- Determine the domain of a rational function.
Trigonometric Equations, Law of Sines, Law of Cosines, and Polar Coordinates
- Convert coordinates between polar and rectangular.
- Convert equations between polar and rectangular.
- Solve trigonometric equations.
- Solve oblique triangles using the laws of sines and cosines.
Systems of Equations
- Calculate solutions using Gaussian elimination.
- Calculate solutions using inverse matrices.
Solve systems of linear equations in two variables.
- Solve systems of linear equations in three variables.
- Calculate solutions using Cramer’s rule.
Precalculus Content Review
- Review all topics and objectives from Weeks One through Six.
Trigonometric Functions and Identities
- Analyze values of inverse trigonometric functions.
- Convert angle measures between degrees and radians.
- Construct the unit circle.
- Use the unit circle to find the values of trigonometric functions.
- Apply trigonometric functions to solve right triangles.
- Describe the graphs of trigonometric functions.
- Manipulate trigonometric identities.
Conic Sections, Sequences, and Series
- Solve geometric sequences and series.
- Differentiate among the equations for conic sections.
- Examine how transformations affect conic sections.
- Use sequence and summation notation.
- Solve arithmetic series.
Introduction to Functions
- Analyze graphs of functions including inverse functions.
- Graph functions including inverse functions.
Use different methods to find the roots of polynomials.
- Apply the fundamental theorem of algebra.
- Apply the use of functions to real-world situations.
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