Course No: MTH111
Credits:
4
Date: June 2010
Course Title:
College Algebra
Institution:
Rogue Community College
Type of Course:
Transfer
Length of Course:
A minimum of forty (40) lecture hours for one term.
Prerequisites:
MTH95 or appropriate scores on RCC placement test.
Department Assignment:
Mathematics
Department Mission Relationship: MTH111 reinforces traditional mathematics concepts and
learning techniques with current graphic calculator technology emphasizing technical
reading/writing and creative thinking skills.
Course Description: First course in the transfer mathematics sequence for science,
mathematics, and engineering students, and for general education math credit. Course topics
include: polynomial and rational functions, exponential and logarithmic functions, and systems
of equations and inequalities.
Expected Outcomes:
Assessment Methods:
1. Use mathematical problem solving
techniques involving polynomial and rational
functions, exponential and logarithmic
functions, and systems of equations. These
techniques include data fitting and the use of
graphical, symbolic, and narrative, and tabulr
methods of analysis.
1. Criterion-referenced tests and quizzes for
specific vocabulary, skills, concepts, and daily
problem assignments.
ISLO: Expresses ideas clearly in oral, written and
visual work; Locates, organizes, analyzes, and interprets
data; Integrates previous and new learning, along with
practical skills, and solve problems; Uses numeracy
skills for interpretation, synthesis, and analysis of data.
Homework, tests, group work, class discussions, and
instructor observation.
2. Communicate mathematical thoughts
and ideas using verbal and written skills by
creating mathematical models of real world
situations.
2. Criterion-referenced tests and quizzes for
specific vocabulary, skills, concepts, daily
problem assignments, in-class observations,
and project completion and presentations.
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ISLO: Expresses ideas clearly in oral, written and
visual work; Locates, organizes, analyzes, and interprets
data; Uses numeracy skills for interpretation, synthesis,
and analysis of data.
Homework, tests, group work, class discussions, and
instructor observation.
3. Use inductive and deductive reasoning to
develop and verify mathematical arguments.
3. Criterion-referenced tests and quizzes for
specific vocabulary, skills, concepts, and daily
problem assignments.
ISLO: Envisions creative approaches to issues and
problems; Uses numeracy skills for interpretation,
synthesis, and analysis of data.
Homework, tests, group work, class discussions, and
instructor observation.
4. Participate in problem solving exercises.
4. Daily problem assignments, in-class
observations, and project completion and
presentations.
ISLO: Envisions creative approaches to issues and
problems; Integrates previous and new learning, along
with practical skills, and solve problems
Homework, tests, group work, class discussions, and
instructor observation.
5. Use appropriate technology to enhance
mathematical thinking and understanding and
to solve mathematical problems and judge the
reasonableness of their results.
5. Daily problem assignments, in-class
observations, and project completion and
presentations.
ISLO: Locates, organizes, analyzes, and interprets
data; Uses numeracy skills for interpretation, synthesis,
and analysis of data.
Homework, tests, group work, class discussions, and
instructor observation.
6. Complete assignments/projects that
encourage independent, nontrivial exploration
of situations best modeled by polynomial,
rational, exponential, logarithmic, or systems
of equations.
6. In-class observation, and project
completion and presentations.
ISLO: Internalizes and assimilates information into new
situations; Demonstrates ability to transfer learning in
familiar and unfamiliar contexts in order to complete
tasks
Homework, tests, group work, class discussions, and
instructor observation.
Typical Required and Recommended Text(s): Robert Blitzer, Pre-calculus, 4th edition,
Prentice Hall Publishing, 2010
Typical Required and Recommended Equipment and Materials: Graphing calculator (TI83, TI-83 Plus, or TI-84 Plus are recommended), graph paper, pencil, paper, and notebook.
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TYPICAL COURSE OUTLINE:
Functions and Graphs (approx. 25% of course)
Graphs and Graphing Utilities
Plot points in the rectangular coordinate system
Graph equations in the rectangular coordinate system
Interpret information about a graphing utility’s viewing rectangle or table
Use a graph to determine intercepts
Interpret information given by graphs
Basics of Functions and Their Graphs
Find the domain and range of a relation
Determine whether a relation is a function
Determine whether an equation represents a function
Evaluate a function
Graph functions by plotting points
Use the vertical line test to identify functions
Obtain information about a function from its graph
Identify the domain and range of a function from its graph
Identify intercepts from the function’s graph
Identify intervals on which a function increases, decreases or is constant
Use graphs to locate relative maxima or minima
Identify even or odd functions and recognize their symmetries
Understand and use piecewise functions
Find and simplify a function’s difference quotient
Linear Functions and Slope
Calculate a line’s slope
Write the point-slope form of the equation of a line
Write and graph the slope-intercept form of the equation of a line
Graph horizontal or vertical lines
Recognize and use the general form of a line’s equation
Use intercepts to graph the general form of a line’s equation
Model data with linear functions and make predictions
Find slopes of equations of parallel and perpendicular lines
Interpret slope as rate of change
Find a function’s average rate of change
Transformations of Functions
Recognize graphs of common functions
Use vertical shifts to graph functions
Use horizontal shifts to graph functions
Use reflections to graph functions
Use vertical stretching and shrinking to graph functions
Use horizontal stretching and shrinking to graph functions
Graph functions involving a sequence of transformations
Combinations of Functions; Composite Functions
Find the domain of a function
Combine functions using the algebra of functions, specifying domains
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Form composite functions
Determine domains for composite functions
Write functions as compositions
Inverse Functions
Verify inverse functions
Find the inverse of a function
Use the horizontal line test to determine if a function has an inverse function
Use the graph of a one to one function to graph its inverse function
Find the inverse of a function and graph both functions on the same axes
Distance and Midpoint Formulas; Circles
Find the distance between two points
Find the midpoint of a line segment
Write the standard form of a circle’s equation
Give the center and radius of a circle whose equation is in standard form
Convert the general form of a circle’s equation to standard form
Modeling with Functions
Construct functions from verbal descriptions
Construct functions from formulas (geometric, economic, banking, distance etc.)
Polynomial and Rational Functions (approx. 25% of course)
Complex Numbers
Add and subtract complex numbers
Multiply complex numbers
Divide complex numbers
Perform operations with square roots of negative numbers
Solve quadratic equations with complex imaginary solutions
Quadratic Functions and Their Graphs
Recognize characteristics of parabolas
Graph parabolas
Determine a quadratic function’s minimum or maximum value
Solve problems involving a quadratic function’s minimum or maximum value
Polynomial Functions and Their Graphs
Identify polynomial functions
Recognize characteristics of graphs of polynomial functions
Determine end behavior of polynomials
Use factoring to find zeros of polynomial functions
Identify zeros and their multiplicities
Use the Intermediate Value Theorem
Understand the relationship between degree and turning points
Graph polynomial functions
Dividing Polynomials; Remainder and Factor Theorems
Use long division to divide polynomials
Use synthetic division to divide polynomials
Evaluate a polynomial using the Remainder Theorem
Use the Factor Theorem to solve a polynomial equation
Zeros of Polynomial Functions
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Use the Rational Root Theorem to find possible rational zeros
Find zeros of a polynomial function
Solve polynomial equations
Use the Linear Factorization Theorem to find polynomials with given zeros
Use Descartes’ Rule of Signs
Rational Functions and Their Graphs
Find the domains of rational functions
Use arrow notation
Identify vertical asymptotes
Identify horizontal asymptotes
Use transformations to graph rational functions
Graph rational functions
Identify slant asymptotes
Solve applied problems involving rational functions
Polynomial and Rational Inequalities (minor importance)
Solve polynomial inequalities
Solve rational inequalities
Solve problems modeled by polynomial or rations inequalities
Modeling Using Variation
Solve direct variation problems
Solve inverse variation problems
Solve combined variation problems
Solve problems involving joint variation
Exponential and Logarithmic Functions (approx. 25% of course)
Exponential Functions
Evaluate exponential functions
Graph exponential functions
Evaluate functions with base e
Use compound interest formulas
Logarithmic functions
Change from logarithmic to exponential form
Change from exponential to logarithmic form
Evaluate logarithms
Use basic logarithmic properties
Graph logarithmic functions
Find the domain of a logarithmic function
Use common logarithms
Use natural logarithms
Properties of Logarithms
Use the product rule
Use the quotient rule
Use the power rule
Expand logarithmic expressions
Condense logarithmic expressions
Use the change-of-base property
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Exponential and Logarithmic Equations
Use like bases to solve exponential equations
Use logarithms to solve exponential equations
Use the definition of a logarithm to solve logarithmic equations
Use the one-to-one property of logarithms to solve logarithmic equations
Solve applied problems involving exponential and logarithmic equations
Exponential Growth and Decay; Modeling Data
Model exponential growth and decay
Use logistic growth models
Use Newton’s Law of Cooling
Choose an appropriate model for data
Express an exponential model in base e
Systems of Equations and Inequalities (approx. 25% of course)
Systems of Linear Equations in Two Variables
Decide whether an ordered pair is a solution of a linear system
Solve linear systems by substitution
Solve linear systems by addition
Identify systems that do not have exactly one ordered pair solution
Solve problems using systems of linear equations
Systems of Linear Equations in Three Variables
Verify the solution of a system of linear equations in three variables
Solve systems of linear equations in three variables
Solve problems using systems in three variables
Systems of Nonlinear Equations in Two Variables
Recognize systems of nonlinear equations in two variables
Solve nonlinear systems by substitution
Solve nonlinear systems by addition
Solve problems using systems of nonlinear equations
Systems of Inequalities
Graph a linear inequality in two variables
Graph a nonlinear inequality in two variables
Use mathematical models involving linear inequalities
Graph systems of inequalities
Linear Programming
Write an objective function describing a quantity that must be maximized or minimized
Use inequalities to describe limitation in a situation
Use linear programming to solve problems
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