Pre-Calculus Description
Pre-Calculus begins with a study of different number systems. The real and complex number systems are explored. Basic set theory is introduced and used to make logical arguments about number systems and their subsets. The concept of sets are connected to the mapping of set A, domain, to set B, range, through the use of functions. A library of basic functions is established and transformations and compositions are used to graph and analyze these functions. Math modeling is introduced and connected to equations in one and two variables, and functions. This leads to a discussion of the relationship between the function and its graph to include the ability to predict behavior. In contrast, an analysis of the general equation of the second degree leads to a thorough study of circles, parabolas, ellipses, and hyperbolas, which are not necessarily functions. Polynomial and rational functions, and their graphs, are then studied in depth. Exponential and logarithmic functions are further explored, including a study of the logistic growth function. The study of trigonometry is introduced through a review of right triangle trigonometry and applications of the law of sines and law of cosines in an applied context. Trigonometry functions are defined on the unit circle. Graphs of the trigonometric functions are investigated and plane transformations are applied. The model for harmonic motion is discussed as an application of trigonometric functions of a real number. Trigonometric equations are introduced, and methods of verifying trigonometric identities are explored. Trigonometric equations are solved and their solutions are connected to the graph of a function and the unit circle. Infinite series are reviewed, and summation notation is introduced to write partial sums. Methods of probability and statistics are reviewed. Pre-calculus ends with a discussion of vectors, polar equations, and parametric equations.
Units- Introduction to Mathematical Modeling
- The General Equation in the Second Degree
- Polynomial and Rational Functions
- Domain, Range, solutions and connection to Inverse Functions
- The Relationship between Exponential and Logarithmic Functions
- Analyzing Trigonometric Functions
- Introduction to Vectors, Polar, and Parametric Equations