Pre-calculus is a full-year, high school credit course that is intended for the student who has successfully mastered the core algebraic and conceptual geometric concepts covered in the prerequisite courses: Algebra I, Geometry, and Algebra II. The course primarily focuses on the skills and methods of analytic geometry and trigonometry while investigating further relationships in functions, probability, number theory, limits, and the introduction of derivatives.
- Relations and Functions: Student will examine functions, inverses of functions and combine functions to verify inverses, as well as distinguish between linear and quadratic functions.
- Functions: Student will solve polynomials using the quadratic theorem, remainder theorem and factor theorem, identify graphs of different polynomial equations and inequalities, and understand complex numbers.
- Trigonometric Functions: Student will identify and solve for missing components of trigonometric functions, calculating trigonometric values for different angles and relate degrees to radians, and radians to degrees.
- Circular Functions and their Graphs: Student will use parametric equations with trigonometric operations to model and solve problems, and calculate amplitude, period, and phase shift for graphed trigonometric functions.
- Identities and Functions of Multiple Angles: Student will simplify trigonometric expressions utilizing trigonometric identities, and double and half-angel formulas, and combine the identities and angle formulas learned in this unit to prove trigonometric relationships.
- Application of Trigonometric Functions: Student will solve problems using trigonometric functions andcombine trigonometric functions and vectors to solve incline plane problems and navigation problems.
- Inverse Trigonometric Functions and Polar Coordinates: Student will solve for unknowns using inverse trigonometric functions, recognize their graphs, and convert equations from Cartesian to polar coordinates, and from polar to Cartesian coordinates.
- Quadratic Equations: Student will identify properties and equations of circles, ellipses, parabolas and hyperbolas, and calculate point rotations and apply them to equations.
- Counting Principles: Student will distinguish between mutually exclusive, independent and dependent events, and between combination and permutation, and use the explicit formula and the recursive formula to find the nth term as well as the general term of an arithmetic sequence, or geometric sequence.
- Calculus: Student will solve functions involving numbers and conditions, understand limit notation, and evaluate limits using the limit theorems, and find the slope of curves, and calculate the angle between two curves.