MAT 187 - Precalculus

5 Contact Hours, 5 Credits
5 lecture periods 0 lab periods


College-level algebra and trigonometry. Includes functions, polynomial functions, rational functions,  exponential functions, logarithmic functions, trigonometric functions and identities and graphing  technology use.

Prerequisite(s): MAT 095  or MAT 097  or required score on the Mathematics assessment test.
Recommendation: This course is intended as an intensive accelerated preparation for students  who plan to continue to Calculus.
Information: For students needing MAT 220 : Calculus I, this requires algebra and trigonometry that can be met either by (a) taking both MAT 151  and MAT 189  or (b) taking the single, accelerated MAT 187. Graphing technology is required for this course and will be used extensively.

 
AGEC Gen-Ed:  QR
CTE Gen-Ed: M&S

1. Analyze functions by determining the domain, range, graph, zeros, asymptotes, and other properties.
2. Solve various types of equations, inequalities, and systems.
3. Solve problems involving real world applications.
4. Solve trigonometric equations and verify trigonometric identities.
5. Solve triangles and real world applications.

1. Quadratic Equations
   1. Quadratic-in-form equations
   2. Radical equations that lead to quadratics
   3. Equations with rational exponents
2. Functions
   1. Definition and Representation
      1. Numerical
      2. Graphical
      3. Algebraic
   2. Transformations and Symmetry
   3. Operations including Composition
   4. Average Rate of Change
   5. Inverse Functions
3. Polynomial Functions
   1. Graphs
      1. Zeros (real and complex)
      2. Relative max and mins
      3. End Behavior (use limits to describe)
   2. Equations and Inequalities
   3. Applications
4. Rational Functions
   1. Domain
   2. Graphs
      1. Intercepts
      2. Asymptotes (use limits to describe)
   3. Equations and Inequalities
   4. Applications
5. Exponential and Logarithmic Functions
   1. Exponential Functions
      1. Graphs (domain, range, intercepts and asymptote)
      2. Equations
      3. Applications
   2. Logarithmic Functions
      1. Graphs (domain, range, intercepts, and asymptotes)
      2. Properties of logarithms
      3. Equations
      4. Applications
6. Trigonometry
   1. Angle Measure
   2. Right Triangle Trigonometric Definition
   3. Unit Circle Trigonometric Definition
   4. Graphs of Trigonometric Functions
   5. Trigonometric Identities
      1. Basic, Pythagorean, and Reciprocal
      2. Double Angle
   6. Inverse Trigonometric Functions (arcsin, arccos, arctan)
   7. Trigonometric Equations
   8. Oblique Triangles
      1. Law of Sines
      2. Law of Cosines