# Pre Calculus

## Course Description

In this 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.

Pre-Calculus Part B covers 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.

## Course Requirements

#### Grade Level

9-12

#### Materials

None

#### Duration

2 Semesters

#### Credit Value

1.0

#### Prerequisites

None

## Semester A

#### Enduring Understandings of this course:

- Basic operations and transformations apply to all functions.
- Any type of equation can be reduced to a simply linear equation.
- There are many applications that can be solved by using linear and quadratic equations.
- There are many similarities between equations and inequalities.
- All common graphs can be transformed using the same basic transformations.
- There are several types of functions.
- All functions have graphical and algebraic applications.
- Functions can be used to solve real-life problems.
- Polynomial functions can be solved using techniques similar to those of other types of equations.
- There are numerous theorems that can be useful when solving polynomial equations.
- The graphs of rational functions involve the use of vertical, horizontal and slant asymptotes.
- There is a relationship between exponential and logarithmic equations.

## Semester B

#### Enduring Understandings of this course:

- Graphs of trigonometric functions model various real-world phenomena.
- Many situations that involve right triangles can be solved using trigonometric ratio and the Unit Circle is a tool that can help solve those problems.
- Numeric patterns can be modeled with explicit or recursive functions.
- Sums of numbers can be found using a variety of formulas.
- The similarities and differences between the equations of conic sections as well as their practical real-world uses.
- Limit and continuity is essential to the study of calculus.