2/6/2016
X
DATE
REQUIRED COURSE
ELECTIVE COURSE
Math/Science
X
DIVISION
NEW COURSE
REVISION
LAKE LAND COLLEGE
Course Information Form
COURSE NUMBER
MAT140
SEM CR HRS 5
TITLE
LT HRS
5
Algebra with Trigonometry
LAB HRS
SOE HRS
ECH
5
(Assigned by Administration)
COURSE PCS#
Prerequisites: One year high school geometry (or MAT009) and MAT006 (or placement by
assessment) with grade of “C” or higher.
Catalog Description (40 Word Limit): A unified study of the algebraic and trigonometric concepts
needed for calculus. Credit not granted for both this course and College Algebra. A Graphing
calculator is required. Ask instructor for calculator recommendation.
List the Major Course Segments (Units)
Contact Lt Hrs
Graphing Basics
9
Linear and Quadratic Functions
6
Functions and Their Graphs
6
Polynomial and Rational Functions
9
Exponential and Logarithmic Functions
5
Systems of Equations
2
Basic Trigonometry
24
Analytic Trigonometry
9
Additional Topics
5
EVALUATION:
Textbook:
Quizzes
Lab Work
X
Exams
Projects
X
Oral Pres.
Comp Final
X
Contact Lab Hrs
Papers
Other
Title: Algebra and Trigonometry, PreCalc, Real Mathematics, Real People
Author: Larson
Publisher: Brooks/Cole Cengage Learning
Volume/Edition: 6th Edition
Copyright Date: 2012
Major Course Segment
Hours
Learning Outcomes
Graphing Basics
Rectangular Coordinate System
1
Demonstrate an understanding of the rectangular
coordinate system.
Graphs of Equations
2
Sketch the graph equations y = f(x) manually and
on graphing calculators.
Solving Equations
3
Use graphs to find zeros of an equation or
intersections of two equations, both manually and
on a graphing calculator.
Applications
1
Set up and solve word problems, especially
geometry, investment, motion, and mixture
problems.
Solving Inequalities
1
Solve inequalities.
Lines in the plane and slope
1
Understand slope of a line. Demonstrate an
understanding of forms of line equation: pointslope, slope-intercept, vertical line, general.
Demonstrate an understanding of parallel and
perpendicular lines.
Functions and Relations
2
Understand distinction between relation and
function. Find domain and range from graph or rule
of a relation.
Linear Functions
1
Graph linear functions. Understand direct variation.
Quadratic Functions and
Applications
3
Solve quadratic equations by either square root
property, completing the square, or quadratic
formula. Find vertex, axis of symmetry, and
intercepts of a quadratic function. Find maximum
or minimum of quadratic function both manually and
on a graphing calculator and apply to word
problems.
Characteristics of Equations
1
Understand characteristics of functions such as
increasing or decreasing, even or odd.
Standard Library of Functions
1
Recognize standard functions: identity, square,
square root, absolute value, etc.
Linear and Quadratic Functions
Functions and Their Graphs
Major Course Segment
Hours
Learning Outcomes
Graphing by Transformations
2
Graph a variety of functions by applying
transformations (shifts, stretches and shrinks,
reflections) to standard functions.
Composition of Functions
1
Form composite functions.
Mathematical Models
1
Form mathematical models by constructing and
analyzing functions.
Power Functions
1
Demonstrate an understanding of characteristics of
power functions f(x) = xn and apply transformations
to their graphs.
Polynomial Functions
1
Identify polynomials and their degrees and zeros.
Analyze graphs of polynomials.
Polynomial Division
1
Perform polynomial division by long or by synthetic
division.
Real Zeros of a Polynomial
2
Use remainder, factor, rational zeros,
boundedness, and intermediate value theorems to
analyze real zeros of a polynomial.
Complex Zeros and
Fundamental Theorem of
Algebra
2
Add, subtract, multiply, and divide complex
numbers. Find complex solutions of quadratic
equation with negative discriminate. Use conjugate
pairs theorem to find complex zeros of a
polynomial. Construct polynomial with specified
zeros.
Rational Functions
1
Find domain and analyze graph of a rational
function.
Polynomial Inequalities
1
Solve polynomial inequalities.
One-to-one and Inverse
Functions
1
Understand one-to-one functions. Find inverse of a
function.
Exponential Functions
1
Evaluate and graph exponential functions.
Logarithmic Functions
1
Understand connection between exponential and
logarithmic expressions. Be able to evaluate and
graph logarithmic equations.
Polynomial and Rational Functions
Exponential and Logarithmic
Functions
Major Course Segment
Hours
Learning Outcomes
Properties of Logarithms
1
Understand properties of logarithms. Use change
of base theorem for logarithmic bases other than 10
and e.
Logarithmic and Exponential
Equations
1
Solve logarithmic and exponential equations both
manually and on graphing calculators.
2
Solve 2 x 2 and 3 x 3 systems of linear equations
by substitution or elimination. Solve system of
equations on a graphing calculator.
Measures of Angles
2
Demonstrate a working knowledge of how to
describe an angle.
Converting degrees to Radians,
Radians to Degrees
1
Convert between radian and degree measure.
Basic and Co-function Identities
2
Demonstrate the ability to identify a unit circle and
its relationship to real numbers
Trigonometric Functions of
Acute Angles
3
Evaluate trigonometric functions of any angles.
Trigonometric Functions of a
Real Variable
2
Apply the fundamental trigonometric identities.
Graphs of Trigonometric
Functions, Amplitude,
Vertical Change, Variation
and periodicity
7
Demonstrate the ability to sketch the graphs of
trigonometric functions and translations of graphs of
sine and cosine functions.
Inverse Trigonometric Functions
4
Demonstrate the ability to evaluate the inverse
trigonometric functions and to evaluate the
compositions of trigonometric functions and inverse
trigonometric functions.
Right Triangle Trigonometric
Applications
3
Systems of Equations
Systems in Two or Three
Variables
Basic Trigonometry
Sketch and solve right triangle, using trigonometric
functions.
Major Course Segment
Hours
Learning Outcomes
Analytic Trigonometry
Basic Trigonometric Identities
2
Use Sum, Difference, DoubleAngle Half-angle Identities , to
verify Trigonometric Identities
4
Trigonometric Equations
3
Demonstrate the knowledge of how to use
fundamental trigonometric identities to evaluate
trigonometric functions. Simplify trigonometric
expressions, to verify trigonometric identities.
Demonstrate the ability to use sum and difference
formulas, double angle formulas and half-angle
identities to rewrite and evaluate trigonometric
functions.
Apply standard algebraic techniques and inverse
trigonometric functions to solve trigonometric
equations.
Additional Topics
Law of Sines and Cosines and
Applications
5
Demonstrate an understanding of the Law of Sines
and the Law of Cosines. Apply them to solve
oblique triangles and find the area of oblique
triangles.
Course Outcomes: At the successful completion of this course, students will be able to:

Graph equations, find intercepts of equations, and solve equations both algebraically and graphically.

Demonstrate an understanding of the characteristics of linear and quadratic functions.

Graph functions using transformations both algebraically and graphically.

Demonstrate an understanding of polynomial and rational functions.

Understand the properties of logarithms and use these properties to solve logarithmic and exponential
equations.

Demonstrate a working knowledge of how to describe an angle using radian and degree measure.

Demonstrate of working knowledge of how to evaluate trigonometric functions of any angle using both
the unit circle and right triangle method.

Demonstrate the ability to sketch the graphs and translations of the graphs of sine, cosine, tangent and
cotangent curves both manually and on calculator.

Demonstrate the knowledge of how to use fundamental trigonometric identities to evaluate
trigonometric functions, simplify trigonometric expressions, to verify trigonometric identities and solve
trigonometric equations.

Demonstrate an understanding of the Law of Sines and the Law of Cosines and apply them to solve
oblique triangles.