Course Overview:

In this Pre-Calculus online course, students will understand and apply concepts, graphs and applications of a variety of families of functions, including polynomial, exponential, logarithmic, logistic and trigonometric. An emphasis will be placed on use of appropriate functions to model real world situations and solve problems that arise from those situations. A focus is also on graphing functions by hand and understanding and identifying the parts of a graph. A scientific and/or graphics calculator is recommended for work on assignments, and on examinations.

As the course progresses, students will cover the major units of Introductory Trigonometry and Graphs, Trigonometric Equations and Identities, Analytical Trigonometry, Sequences and Series, Conic Sections and an Introduction to Calculus. A focus is also on graphing functions by hand and understanding and identifying the parts of a graph.

Semester 1:  

In Semester A, the course focuses on foundational concepts in mathematics. Students learn that basic operations and transformations apply to all functions and that any type of equation can be simplified to a linear equation. Linear and quadratic equations have numerous practical applications, and there are similarities between equations and inequalities. Common graphs can be transformed using basic techniques, and there are various types of functions with both graphical and algebraic applications. Functions can be used to solve real-life problems, and polynomial equations can be solved using similar techniques as other types of equations. There are important theorems for solving polynomial equations, and rational functions involve vertical, horizontal, and slant asymptotes. Exponential and logarithmic equations are also related.

Semester 2: 

In Semester B, the course delves into additional mathematical concepts. Trigonometric functions are used to model real-world phenomena, and right triangle situations can be solved using trigonometric ratios. The Unit Circle is a useful tool for solving these problems. Numeric patterns can be represented with explicit or recursive functions, and formulas are used to find sums of numbers. The course explores the equations of conic sections, highlighting their similarities and differences, as well as their practical applications. Finally, the study of calculus emphasizes the importance of limit and continuity.

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