Math 109: Precalculus

Catalog Information

Title

Precalculus

(Credit Hours:Lecture Hours:Lab Hours)

(1:1:0)

Offered

F, W (second block), Summer

Description

Functions, trigonometric functions, and their graphs, trigonometric identities, solving trigonometric equations, equations of lines, slope-intercept and point-slope form of a line, secant lines and average rates of change, rates of change in the sciences, graphical introduction to limits.

Prerequisites

Co-requisite of Math 110 or Completion of a high school algebra 2 or intermediate algebra.

Minimal learning outcomes

Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts.

1. Functions
   • Perform arithmetic operations on functions including function composition
   • Compute difference quotients of functions
   • Understand properties of the absolute value function
   • Solve equations and inequalities involving absolute values
2. Trigonometric functions
   • Know the definition of the six trigonometric functions and their relationship to right triangles
   • Graph the six trigonometric functions
   • Identify trigonometric functions from others using graphical transformations
   • Trigonometric identities
   • The unit circle
   • Solving equations involving trigonometric functions
   • Real-world setup of problems involving trigonometric functions
3. Equations of lines
   • Slope of the secant line between two distinct points
   • Slope as a rate
   • Slope-intercept form of a line
   • Point-slope form of a line
   • Real-world examples of rates as slopes of lines
4. Limits
   • Limits as instantaneous rates of change
   • Graphical interpretation of limits
   • Limits of difference quotients