Pre Calculus/Trigonometry

Third Draft - Updated 10/20/00

Prerequisite: 2nd year Algebra and Geometry.

First semester of this course focuses on the study of functions and their graphs. Polynomial, rational, exponential, logarithmic and trigonometric functions are covered. Second semester focuses on analytic trigonometry, vectors, matrices, determinants, systems of equations and inequalities, sequences, probability, statistics and analytic geometry.

1. The student understands and applies the concepts and procedures of mathematics.

• 1. understands how to solve equations both algebraically and graphically
• 2. learns to work with functions through graphing, combinatory, and inverse
• 3. solves higher order polynomials including rational and complex numbers
• 4. solves logarithmic and exponential functions
• 5. uses the trigonometric functions, modes, and their graphs
• 6. applies the law of sine and cosine to solve for triangular measurement
• 7. solves systems of equations with multiple variables
• 8. sets of systems of equations in matrices and used determinants and inverses
• 9. graphs conic sections: parabolas, ellipses, hyperbolas, and circles

2. The student uses mathematics to define and solve problems.

• 1. learns to set up problems in scatter plots and finds a best-fit line of regression
• 2. uses a graphing utility to solve complex problems
• 3. uses exponential, logarithmic, and Gaussian models to solve complex problems
• 4. sets up and solves problems with maximization or minimization concepts
• 5. develops a system of constraints
• 6. shows all steps when problem solving.

3. The student uses mathematical reasoning

• 1. interprets results from information gained in solving a problem
• 2. verifies results using a graphing utility to insure they are reasonable
• 3. verifies trigonometric identities and uses them to solve problems

4. The student communicates knowledge and understanding in both everyday and mathematical language.

• 1. organizes ideas and solutions in mathematical language that is appropriate for expressing conclusions
• 2. verbally communicates ideas and thoughts regarding specific topics of mathematics
• 3. explains important concepts to each other to aid in a higher level of understanding of mathematical concepts

5. The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

• 1. applies advanced mathematical capabilities to solve situations that occur in an everyday situation
• 2. uses mathematical application to other classroom work including presentations and problem solving
• 3. solves specific problems and develops an understanding as to how they may be used in real-life careers