This course provides a working knowledge of Precalculus and its applications. It begins with a review of algebraic operations. Emphasis is on solving and graphing equations that involve linear, polynomial, exponential, and logarithmic functions. Students learn to graph trigonometric and inverse trigonometric functions and learn to use the family of trigonometric identities. Other topics include conic sections, arithmetic and geometric sequences, and systems of equations.
After completing this course, you will be able to:
Perform operations on real numbers and polynomials.
Simplify algebraic, rational, and radical expressions.
Solve linear and quadratic equations and inequalities.
Solve word problems involving linear and quadratic equations and inequalities.
Solve polynomial, rational, and radical equations and applications.
Solve and graph linear, quadratic, absolute value, and piecewise-defined functions.
Perform operations with functions as well as find composition and inverse functions.
Graph quadratic, the square root, cubic, and cube root functions.
Graph and find zeroes of polynomial functions.
Graph quadratic functions by completing the square, using the vertex formula, and using transformations.
Solve and graph exponential and logarithmic equations.
Express angle measure in degrees or radians.
Evaluate and simplify trigonometric expressions.
Know the six trigonometric functions and how to evaluate those trigonometric functions using positions on the unit circle with respect to the right triangle.
Graph trigonometric and inverse trigonometric functions.
Use trigonometric functions to solve a right triangle and apply the Law of Sines and the Law of Cosines to solve triangles that are acute or obtuse.
Solve systems of linear equations and inequalities.
Model and solve applications using linear systems.
Evaluate and find partial sums of a series.
Evaluate and find sums of an arithmetic sequence and a geometric sequence.
Solve application problems involving arithmetic and geometric sequences and series.
Define, identify, and graph conic sections including circle, ellipse, parabola, and hyperbola.