MATH 115 (Pre-Calculus)
| 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. |
| 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
(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.
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| TEXT |
Text(s)
typically used in this course |
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