Description

MATH 115 is a preparation for Calculus, either MATH 220 (for which Math 113 is an alternate prerequisite) or MATH 140, with a focus on functions and graphs and algebraic techniques preparatory to calculus. The functions studied include polynomials, rational functions, exponential and logarithmic functions, and trigonometric functions.

(A graphing calculator such as the TI- 83, is required for Math 115. It is used in exploring the graphs of functions and equations and in solving problems.)

Prerequisites

Satisfactory score on Math Department placement exam, completion of the appropriate module of MATH 003, or completion of Math 113.

Topics

Algebra

Inequalities
Absolute value inequalities
Table of signs for polynomial and rational inequalities

Functions

Domain
Operations including compositions
Inverses
Graphs
Symmetry
Transformations: Shifts, reflections, stretching and shrinking

Quadratic functions and equations

Applications involving quadratic equations
Parabolas
Extreme value problems
Quadratic related equations including radical equations

Polynomials

Shape of graph
Writing polynomial functions with specific properties
Using a graphing calculator to draw complete graphs

Rational functions

Finding intercepts and asymptotes
Graphing with and without calculator

Conic sections

Standard equations for parabolas, circles, ellipses, and hyperbolas, shifts of conic sections
(if time allows)

Exponential and Logarithmic functions

Definition
Graphs
Exponent rules
Laws of logarithms
Exponential and logarithmic equations
Exponential growth and decay

Trigonometry

Angles
Radian and degree measurement of angles
Arc length and angular speed

Trigonometric functions

Circle, point, and right-triangle definitions of functions
Graphs of trig functions
Sinusoidal graphs

Solving triangles

Right triangles
Law of Cosines
Law of Sines

Trigonometric identities

Reciprocal identities
Pythagorean identities
Negative-angle identities
Periodicity identities
Sine and cosine addition and subtraction identities
Double-angle identities
Power-reducing identities

Trigonometric equations

Finding algebraic solutions
Finding calculator solutions