Download College Algebra with Applications

College Algebra with Applications
Course Outcome Summary
Information
Course Number
10-804-195
Credits
3
Contact Hours
54
Development Date
02/23/2004
Types of Instruction
Type of Instruction
Contact Hours
Credits
Classroom Presentation
54
3
Totals
54
3
Competencies, Linked Exit Learning Outcomes, and
Performance Standards
1.
Apply mathematical problem solving skills
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
1.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
1.b.
by participating actively in class discussions and activities.
Performance will be successful when:
1.a.
you show work in a clear and logical manner.
1.b.
you verify solutions.
1.c.
you verify that the solution is within the stated range and reflect appropriate accuracy or
precision.
1.d.
you label solutions with appropriate units.
Learning objectives
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College Algebra with Applications
Outcome Summary
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What you will learn as you master the competency:
2.
a.
b.
Review the method of verifying the solution to equations
Predict that the solution to an equation is within a range
c.
Review the determination of appropriate units for solutions to equations
d.
Describe what is necessary to present clear and logical mathematical work
Use the fundamental concepts of algebra
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
2.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
2.b.
by participating actively in class discussions and activities.
Performance will be successful when:
2.a.
you apply properties of real numbers.
2.b.
you locate real numbers on the number line.
2.c.
you evaluate expressions using absolute value.
2.d.
2.e.
you relate absolute value to distances on the number line.
you represent absolute value expressions without the use of the absolute value.
2.f.
you model a problem situation algebraically.
2.g.
you apply positive integer exponents, negative integer exponents, and rational number
exponents to evaluation and simplification of expressions.
2.h.
you relate roots to rational number exponents.
2.i.
you define mononomial, binomial, trinomial, and polynomial.
2.j.
2.k.
you perform algebraic operations on polynomials.
you apply the binomial theorem to expand powers of binomials.
2.l.
you factor polynomials.
Learning objectives
What you will learn as you master the competency:
a.
Identify properties of real numbers
b.
Describe the evaluation of absolute numbers
c.
Define inequality symbols
d.
Identify the location of numbers on a number line
e.
Recognize algebraic expressions with one or more algebraic terms
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College Algebra with Applications
Outcome Summary
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3.
f.
Review the properties of exponents
g.
h.
Evaluate algebraic expressions
Describe the concept of factoring polynomials
i.
Describe the expansion of powers of binomial
Analyze the features of a graph of a given function or relation
Linked Core Abilities
*
Apply relevant technologies
Performance Standards
Competence will be demonstrated:
3.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
3.b.
by participating actively in class discussions and activities.
Performance will be successful when:
3.a.
3.b.
you use the Cartesian coordinate system.
you find distances in the Cartesian coordinate system.
3.c.
you use function notation correctly.
3.d.
you graph a relation or function in X and Y.
3.e.
3.f.
you differentiate between symmetry about the X-axis, the Y-axis, and the origin.
you determine the intercept of a graph.
3.g.
you apply the vertical line test to distinguish between a relation and a function.
3.h.
you define a relation or function.
3.i.
you determine the domain and range of a relation or function.
3.j.
you define a 1-1 function.
3.k.
you apply the horizontal line test for 1-1.
3.l.
you determine the inverse function of a 1-1 function.
3.m.
you specify the relation between the domain and the range of a function and its inverse.
Learning objectives
What you will learn as you master the competency:
a.
Describe the Cartesian coordinate system
b.
Describe the process of finding the distance between two points on a coordinate grid
c.
Define functional notation
d.
Distinguish between a function and relation
e.
Define the concept of symmetry around an axis
f.
Describe the vertical line test
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Outcome Summary
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4.
g.
Distinguish between the domain and range of a function
h.
i.
Define the inverse of a function
Explain the intercepts of a graph
Solve linear and quadratic equations and inequalities
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
4.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
4.b.
by participating actively in class discussions and activities.
Performance will be successful when:
4.a.
you define a linear function, a linear equation, and a linear inequality.
4.b.
4.c.
you define a solution of an equation.
you relate the solution of an equation to the X-intercept of a graph of the function and to
the root (or zero) of the function.
4.d.
you distinguish between an identity and a conditional equation.
4.e.
you define equivalent equations and inequalities.
4.f.
you solve linear equations and inequalities (with or without absolute values)
algebraically.
4.g.
you solve linear equations and inequalities (with or without absolute values) graphically.
4.h.
you define quadratic equations.
4.i.
you solve quadratic equations using: graphical methods, factoring, completing the
square, and the quadratic formula.
4.j.
you solve 2nd or higher order equations or inequalities algebraically or graphically.
4.k.
4.l.
you model a verbal problem with an algebraic representation and a graph.
you solve the algebraic representation of a verbal problem.
4.m.
you interpret the algebraic answer to a verbal problem in terms of the original problem.
4.n.
you use the equivalent interval notation, absolute value notation, and/or inequality
notation when writing solutions of inequalities.
Learning objectives
What you will learn as you master the competency:
a.
Describe the concept of linearity
b.
Relate the concept of the solution of an equation to the X intercept (or zero) of the
equation
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Outcome Summary
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5.
c.
Review the concept of solving linear equations and inequalities both algebraically and
graphically
d.
Describe the methods of solving quadratic equations
e.
Distinguish between linear and quadratic equations
f.
Relate the verbal expression of an applied problem to it's mathematical representation
g.
Describe the proper notation when solving inequalities
h.
Distinguish between an identity and conditional equation
Analyze the properties of linear and quadratic functions
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
5.a.
5.b.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
by participating actively in class discussions and activities.
Performance will be successful when:
5.a.
you determine slop, X-intercept, and Y-intercept.
5.b.
you relate slope to parallel and perpendicular lines.
5.c.
you use point-slope, slope-intercept, and standard forms of the equation of a line.
5.d.
you convert between point-slope, slope-intercept, and standard forms of the equation of
a line.
5.e.
you use the midpoint formula.
5.f.
you find the equation of a line that is parallel to or perpendicular to a given line through
a specified point.
5.g.
you find the equation of the perpendicular bisector of a given line segment.
5.h.
5.i.
you prove geometric theorems algebraically.
you graph quadratic functions.
5.j.
you apply the concepts of vertically stretching or shrinking or shrinking, reflecting, or
shifting a graph of a quadratic to transform the graph.
5.k.
you determine the sum, difference, product, and quotient of two functions.
5.l.
you determine the composition of two functions.
5.m.
you note that function composition is non-commutative.
5.n.
you apply geometric transformations as compositions.
5.o.
you determine the vortex, axis of symmetry, and direction from the standard form of a
quadratic function.
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Outcome Summary
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5.p.
you change the form of a quadratic function to a standard form.
5.q.
you find zeros of quadratic functions algebraically and graphically.
Learning objectives
What you will learn as you master the competency:
6.
a.
Define the slope, X and Y intercepts of a line
b.
c.
Describe the forms of an equation of a line
Describe the concept of parallel and perpendicular lines through their mathematical
expressions
d.
Describe the properties of functions
e.
Explain transformation of functions
f.
Review the concepts associated with quadratic equations
Use theories of equations to find the zeros of a polynomial function
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
6.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
6.b.
by participating actively in class discussions and activities.
Performance will be successful when:
6.a.
6.b.
6.c.
6.d.
you define the degree of a polynomial function.
you identify local maxima and minima of a polynomial function using graphical and
analytical methods.
you determine whether a function is increasing or decreasing on an interval.
6.e.
you apply the concepts of continuity, discontinuity, the intermediate value theorem, and
the bisection method of finding a zero to determine the features of a graph.
you determine the behavior of a polynomial function at the end points of its domain.
6.f.
you apply transformations to polynomial functions.
6.g.
you apply the remainder theorem, the factor theorem, the rational roots theorem,
synthetic division, the upper and lower bounds theorem, and Descartes' law of signs to
find zeros of a polynomial function.
you use the fundamental theorem of algebra to determine the number of roots of a
polynomial equation.
6.h.
6.i.
you use graphical methods to estimate the roots of a polynomial equation.
Learning objectives
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Outcome Summary
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What you will learn as you master the competency:
7.
a.
b.
Identify the degree of a polynomial
Describe the methods of finding the zeros of polynomial functions
c.
Define the properties of polynomial functions of higher degree
d.
Explain graphical aspects of polynomial functions
e.
Explain analytical aspects of polynomial functions
Determine complex solutions to polynomial equations
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
7.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
7.b.
by participating actively in class discussions and activities.
Performance will be successful when:
7.a.
you define the imaginary unit i.
7.b.
you define complex numbers and complex conjugates.
7.c.
you perform operations with complex numbers including addition, subtraction,
multiplication, and division.
7.d.
you apply the fundamental theorem of algebra and the linear factorization theorem to
determine solutions to polynomial equations.
7.e.
you find complex (non-real) solutions to polynomial equations.
Learning objectives
What you will learn as you master the competency:
8.
a.
Define the concept of a complex number including it's representation and conjugate
b.
Explain the process of performing arithmetic operations on complex numbers
c.
Describe the method of finding imaginary solutions to polynomial equations
d.
Describe the application of fundamental theorem of algebra to determine the solution to
polynomial equations
e.
Describe the application of the linear factorization theorem to determine the solution to
polynomial equations
Perform computations with rational functions
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Outcome Summary
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Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
8.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
8.b.
by participating actively in class discussions and activities.
Performance will be successful when:
8.a.
8.b.
you define a rational expression.
you recognize a rational expression.
8.c.
you simplify rational expressions.
8.d.
you add, subtract, multiply and divide rational expressions.
8.e.
8.f.
you simplify complex fractions.
you define a rational function and the domain of a rational function.
8.g.
you find vertical, horizontal, and oblique asymptotes.
8.h.
you discuss the properties of f(x) = 1/x, graph it and apply transformations to rational
functions.
8.i.
you determine the behavior of rational functions as the absolute value of the variables
becomes large.
8.j.
you identify removable discontinuities.
8.k.
you determine the end behavior for rational functions where the degree of the numerator
does not exceed the degree of the denominator.
8.l.
you graph rational functions.
8.m.
you solve rational functions algebraically and graphically.
8.n.
you discuss extraneous solutions.
Learning objectives
What you will learn as you master the competency:
9.
a.
Define a rational expression
b.
c.
Describe the process of simplifying a rational expression
Explain the performance of arithmetic operations on rational expressions
d.
Describe the process of finding asymptotes
e.
Describe the properties and behavior of rational functions and their transformations
f.
Discuss the process of graphing rational functions
g.
Describe the process of solving rational functions graphically
h.
Describe the process of solving rational functions algebraically
Perform computations with radical functions
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Outcome Summary
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Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
9.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
9.b.
by participating actively in class discussions and activities.
Performance will be successful when:
9.a.
you define radical, index, and radicand.
9.b.
you define principal square root, cube root, nth root.
9.c.
you determine the domain of radical expression.
9.d.
you solve radical equations algebraically and check for extraneous roots.
Learning objectives
What you will learn as you master the competency:
10.
a.
Define radical, index, and radicand
b.
c.
Define principal square root, cube root, nth root
Describe the process of determining the domain of radical expressions
d.
Describe the process of solving radical equations algebraically
e.
Explain the process of checking for extraneous roots in solving radical equations
Analyze exponential and logarithmic functions
Linked Core Abilities
*
Apply relevant technologies
Performance Standards
Competence will be demonstrated:
10.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
10.b.
by participating actively in class discussions and activities.
Performance will be successful when:
10.a. you define base and exponent.
10.b.
10.c.
you define the exponential function with base 10, base 2, fractional base, an arbitrary
base, and base e.
you graph the exponential function with base 10, base 2, fractional base, an arbitrary
base, and base e.
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10.d.
you apply transformations to exponential functions.
10.e.
you apply exponential functions to such problems as exponential growth and decay,
half-life, interest, annuities, and mortgages.
10.f.
you solve exponential equations algebraically and graphically.
10.g.
you define logarithmic functions with base a- also discuss possible values for the base.
10.h.
you define the common logarithmic function and the natural logarithmic function.
10.i.
you discuss the inverse relationship between the logarithmic function and the
exponential function (same base).
10.j.
you determine the domain and range of logarithmic functions.
10.k.
you produce the graph of a logarithmic function (with various bases) considering the
domain and the range.
10.l.
you solve exponential and logarithmic functions algebraically and graphically.
Learning objectives
What you will learn as you master the competency:
a.
Describe exponential functions of any base
b.
Describe the application of exponential and logarithmic functions
c.
Define the common logarithmic function and the natural logarithmic function
d.
e.
Discuss determining the domain and range of logarithmic functions
Discuss the inverse relationship between the logarithmic function and the exponential
function
Explain the solution of exponential and logarithmic functions algebraically and
graphically.
f.
11.
Solve non-linear systems of equations
Linked Core Abilities
*
Apply relevant technologies
Performance Standards
Competence will be demonstrated:
11.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
11.b.
by participating actively in class discussions and activities.
Performance will be successful when:
11.a. you solve a nonlinear system of equations algebraically.
11.b.
you use graphing calculator to solve non-linear systems of equation.
11.c.
you use nonlinear systems of equation to solve applied problems.
Learning objectives
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What you will learn as you master the competency:
12.
a.
b.
Describe the methods of solving a nonlinear system of equations algebraically
Discuss the use of a graphing calculator to solve non-linear systems of equation
c.
Explain the use of nonlinear systems of equations to solve applied problems
Solve systems of linear equations
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
12.a. by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
12.b. by participating actively in class discussions and activities.
Performance will be successful when:
12.a.
12.b.
you solve systems of linear equations in three or more variables algebraically.
you use the graphing calculator to solve systems of linear equations in three or more
variables.
12.c.
you use systems of three equations to solve applied problems.
Learning objectives
What you will learn as you master the competency:
13.
a.
Review thee solution of systems of linear equations in three or more variables
algebraically
b.
Describe the use of the graphing calculator to solve systems of linear equations in three
or more variables
c.
Describe the use of systems of three equations to solve applied problems
Perform basic operations with matrices
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
13.a.
13.b.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
by participating actively in class discussions and activities.
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Outcome Summary
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Performance will be successful when:
13.a. you add matrices.
13.b.
you subtract matrices.
13.c.
you multiply a matrix by a scaler.
13.d.
13.e.
you multiply matrices when possible.
you solve application problems using basic operations with matrices.
13.f.
you perform basic operations with matrices using the graphing calculator.
Learning objectives
What you will learn as you master the competency:
a.
Describe the process of adding and subtracting matrices
14.
b.
Describe the process of multiplying a scalar by a matrix
c.
Discuss the conditions under which it is possible to multiply matrices
d.
e.
Explain the process of multiplying matrices
Explain the use of a graphing calculator to perform matrix operations
f.
Discuss solving application problems using basic operations with matrices.
Use the inverse of a square matrix
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
14.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
14.b.
by participating actively in class discussions and activities.
Performance will be successful when:
14.a.
14.b.
you recognize the identity matrix of a square matrix.
you recognize when two square matrices are inverses of one another.
14.c.
you find the inverse of a square matrix, if it exists.
14.d.
you use inverses of matrices to solve systems of equations.
14.e.
you solve application problems involving matrix inverses.
14.f.
you use a graphing calculator to compute matrix inverses.
Learning objectives
What you will learn as you master the competency:
a.
Recognize the identity matrix of a square matrix
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15.
b.
Recognize when two square matrices are inverses of one another
c.
d.
Describe the steps to find the inverse of a square matrix, if it exists
Explain the use inverses of matrices to solve systems of equations
e.
Describe the solution of application problems involving matrix inverses
f.
Describe the use a graphing calculator to compute matrix inverses
Solve systems of equations using matrix equations
Linked Core Abilities
*
Apply relevant technologies
Performance Standards
Competence will be demonstrated:
15.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
15.b.
by participating actively in class discussions and activities.
Performance will be successful when:
15.a. you identify a matrix equation.
15.b.
you identify a matrix equation.
15.c.
you write a system of linear equations as a matrix equation.
15.d.
15.e.
you find the solution of a system of linear equations by using inverses of matrices.
you solve application problems using systems of linear equations and matrix equations.
Learning objectives
What you will learn as you master the competency:
a.
Identify a matrix equation
b.
Describe the writing of a system of linear equations as a matrix equation.
c.
Describe finding the solution of a system of linear equations by using inverses of
matrices
Discuss the solution of application problems using systems of linear equations and
matrix equations
d.
16.
Solve systems of linear inequalities
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
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16.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
16.b.
by participating actively in class discussions and activities.
Performance will be successful when:
16.a.
you graph linear inequalities algebraically.
16.b.
you graph systems of linear inequalities algebraically.
Learning objectives
What you will learn as you master the competency:
17.
a.
Explain the process of graphing linear inequalities algebraically
b.
Explain the process of graphing systems of linear inequalities algebraically
Produce the graph of a conic section
Linked Core Abilities
*
Apply relevant technologies
Performance Standards
Competence will be demonstrated:
17.a.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
17.b.
by participating actively in class discussions and activities.
Performance will be successful when:
17.a.
you distinguish between the type of conic sections produced when a quadratic
polynomial in two unknowns is graphed.
17.b.
you find the center and the semi-major and semi-minor axes given the polynomial form
of the equation of an ellipse.
17.c.
you find the center, the axes, and the asymptotes given the polynomial form of the
equation of a hyperbola.
17.d.
you find the center, the axis, and the directrix given the polynomial form of the equation
for a parabola.
17.e.
you sketch the graph of a conic section given its equation in polynomial form.
Learning objectives
What you will learn as you master the competency:
a.
Distinguish between the type of conic sections produced when a quadratic polynomial in
two unknowns is graphed
b.
Explain how to find the center and the semi-major and semi-minor axes given the
polynomial form of the equation of an ellipse
c.
Explain how to find the center, the axes, and the asymptotes given the polynomial form
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of the equation of a hyperbola
18.
d.
Explain how to find the center, the axis, and the directrix given the polynomial form of
the equation for a parabola
e.
Describe the process of sketching the graph of a conic section given its equation in
polynomial form
Solve problems involving sequences and series
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
18.a. by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
18.b.
by participating actively in class discussions and activities.
Performance will be successful when:
18.a.
18.b.
you find terms of sequences given the nth term.
you find a general term for a sequence.
18.c.
you convert between sigma notation and other notation for a series.
18.d.
you find the nth term of an arithmetic and geometric sequence.
18.e.
18.f.
you find the common difference of an arithmetic sequence.
you construct an arithmetic and geometric sequence.
18.g.
you find the common ratio of a geometric sequence.
18.h.
you find the sum of the first n terms of an arithmetic and geometric sequence.
18.i.
you find the sum of an infinite geometric series, if is exists.
Learning objectives
What you will learn as you master the competency:
a.
Describe the process of finding terms of sequences given the nth term
b.
Describe the process of finding a general term for a sequence
c.
Explain sigma notation and other notations and the conversion between them
d.
Describe the process of finding the nth term of an arithmetic and geometric sequence
e.
Describe the process of finding the common difference of an arithmetic sequence
f.
g.
Explain the construction of an arithmetic and geometric sequence
Describe the process of finding the common ratio of a geometric sequence
h.
Describe the process of finding the sum of the first n terms of an arithmetic and
geometric sequence
Describe the process of finding the sum of an infinite geometric series, if is exists
i.
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19.
Use the Binomial Theorem
Linked Core Abilities
*
Learn effectively
Performance Standards
Competence will be demonstrated:
19.a.
19.b.
by submitting all in-class and take home assignments with passing grades according to
the grading scale in the syllabus.
by participating actively in class discussions and activities.
Performance will be successful when:
19.a.
19.b.
you expand a power of a binomial using Pascal's triangle or factorial notation.
you find a specific term of binomial expansion.
Learning objectives
What you will learn as you master the competency:
a.
b.
Recognize Pascal's triangle
Explain the process of expanding a power of a binomial using Pascal's triangle or
factorial notation
c.
Define binomial expansion
d.
Describe the process of finding a specific term of binomial expansion.
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College Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\873994033.doc