Pre-Calculus

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.

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.