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# College Algebra

## Description

Includes fundamental topics covered in Intermediate Algebra with a more careful look at the
mathematical details and a greater emphasis on the concept of function. Covers quadratic,
polynomial, rational, exponential and logarithmic functions, equations and inequalities; the use of
matrices and determinants in solving linear systems of equations, solving non-linear systems;
sequences and series.

## Target Population

College Transfer Students with clear knowledge of the content of Intermediate Algebra who wish
to prepare for more advanced mathematical courses at a college level.

## Types of Instruction

 Instruction Type Contact Hours Credits Lecture / Demonstration 68 3

## Textbooks

Current information is available each semester from syllabi filed in the Arts & Sciences office.

## Learner Supplies

A full-function scientific (or graphing) calculator, Compass & Protractor, Class Folder (8.5" x
11"). Manufacturer: Unspecified.

## Prerequisites

Intermediate Algebra (20-804-201) with a grade of C or better
OR Intermediate Algebra Parts 1 (20-804-202) and 2 (20-804-203) with a grade of C or better in
both parts
OR appropriate placement score

## Exit Learning Outcomes Core Abilities

A. Mathematics
B. Communication
C. Critical thinking

## Competencies

A. Apply mathematical problem solving skills

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
A.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
A.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
A.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
A.1. show work in a clear and logical manner
A.2. verify the solution
A.3. verify that the solution is within the stated range and reflects appropriate accuracy or precision
A.4. label solution with appropriate units

B. Apply concepts of real numbers
Mathematics
Communication
Competence will be demonstrated:
B.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
B.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
B.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
B.1. identify, define, and apply properties of the real numbers
B.2. locate the real numbers on the number line
B.3. identify, define, and evaluate expressions using the absolute value
B.4. define and relate absolute value to distances on the number line
B.5. represent absolute value expressions without the use of the absolute value

C. Use the fundamental concepts of algebra

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
C.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
C.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
C.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
C.1. model a problem situation algebraically
C.2. apply positive integer exponents, negative integer exponents, rational number exponents to evaluation or simplify expressions
C.3. relate roots to rational number exponents
C.4. define monomial , binonomial, trinomial , and polynomial
C.5. define coefficient , term, and factors of polynomials
C.6. add, subtract, multiply, and divide polynomials
C.7. apply the binomial theorem to expand powers of binomials
C.8. factor polynomials

D. Construct graphs using Cartesian coordinates and summarize the features of the
graph of a given function or relation

Mathematics
Critical thinking
Competence will be demonstrated:
D.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
D.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
D.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
D.1. use the Cartesian coordinate system
D.2. find distances in the Cartesian coordinate system
D.3. use function notation correctly
D.4. graph a relation or function in X and Y
D.5. differentiate between symmetry about the X-axis, the Y-axis, and the origin
D.6. determine the intercepts of a graph
D.7. apply the vertical line test to distinguish between a relation and a function
D.8. define a relation or function and determines its domain and range
D.9. define a 1-1 function and applies the horizontal line test to test for 1-1
D.10. determine the inverse function of a 1-1 function
D.11. specify the relation between the domain and range of a function and its inverse

E. Solve linear and quadratic equations and inequalities

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
E.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
E.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
E.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
E.1. define (and/or recognize) a linear function
E.2. define (and/or recognize) a linear equation
E.3. define (and/or recognize) a linear inequality
E.4. define a solution of an equation and relates it to the X-intercept of the graph of the function, and to the root (or zero) of the function
E.5. distinguish between an identity and a conditional equation
E.6. define equivalent equations and inequalities
E.7. solve linear equations and inequalities (with or without absolute values) algebraically
E.8. solve linear equations and inequalities (with or without absolute values) graphically
E.10. solve quadratic equations using graphical methods, factoring, completing the square, and the quadratic formula
E.11. solve 2nd or higher order equations or inequalities algebraically or graphically
E.12. model a verbal problem with an algebraic representation and a graph, solve the
algebraic representation, and interpret the algebraic answer in the words of the original problem
E.13. use the equivalent interval notation, absolute value notation, and / or inequality notation when writing solutions of inequalities

F. Determine the properties of and solve linear and quadratic functions

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
F.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
F.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
F.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
F.1. determine slope, X-intercept, and Y-intercept
F.2. relate slope to parallel and perpendicular lines
F.3. use point-slope, slope-intercept, standard forms of the equation of a line - converts between the forms
F.4. use the midpoint formula
F.5. find the equation of a line that is parallel to or perpendicular to a given line through a specified point
F.6. find the equation of the perpendicular bisector of a given line segment
F.7. prove geometric theorems algebraically
F.9. apply the concepts of vertically stretching or shrinking or shrinking, reflecting, or
shifting a graph of a quadratic to transform the graph
F.10. define and determine the sum, difference, product, and quotient of two functions
F.11. define and determine the composition of two functions - notes that function composition is non-commutative
F.12. apply geometric transformations as compositions
F.13. determine the vertex, axis of symmetry, and direction from the standard form of a quadratic function
F.14. change the form of a quadratic function to standard form
F.15. find zeros of quadratic functions algebraically and graphically

G. Summarize features of the graph and find the zeros of a polynomial function using the theory of equations
Mathematics
Critical thinking
Communication
Competence will be demonstrated:
G.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
G.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
G.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
G.1. define the degree of a polynomial function
G.2. define and identify local maxima and local minima of a polynomial function using graphical and analytical methods
G.3. determine whether a function is increasing or decreasing on an interval
G.4. 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
G.5. determine the behavior of a polynomial function at the end points of its domain
G.6. apply transformations to polynomial functions
G.7. 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
G.8. use the fundamental theorem of algebra to determine the number of roots of a polynomial equation
G.9. use graphical methods to estimate the roots of a polynomial equation

H. Determine all solutions to polynomial equations

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
H.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
H.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
H.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
H.1. define the imaginary unit i
H.2. define complex numbers and complex conjugates
H.3. perform operations with complex numbers including addition, subtraction, multiplication, and division
H.4. apply the fundamental theorem of algebra and the linear factorization theorem to
determine solutions to polynomial equations
H.5. find complex (non-real) solutions to polynomial equations

I. Perform computations with rational functions

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
I.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
I.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
I.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
I.1. define a rational expression
I.2. recognize a rational expression
I.3. simplify rational expressions
I.4. add, subtract, multiply and divide rational expressions
I.5. simplify complex fractions
I.6. define a rational function and the domain of a rational function
I.7. find vertical, horizontal and oblique asymptotes
I.8. discuss the properties of f(x) = 1/x, graphs it and applies transformations to rational functions
I.9. determine the behavior of rational functions as the absolute value of the variables becomes large
I.10. identify removable discontinuities
I.11. determine the end behavior for rational functions where the degree of the numerator does not exceed the degree of the denominator
I.12. determine the end behavior for rational functions where the degree of the numerator exceeds the degree of the denominator
I.13. graph rational functions
I.14. solve rational functions algebraically and graphically
I.15. discuss extraneous solutions

J. Perform computations with radical functions

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
J.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
J.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
J.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
J.2. define principal square root , cube root, nth root
J.3. determine the domain of a radical expression
J.4. solve radical equations algebraically and checks for extraneous roots

K. Analyze exponential and logarithmic functions - solve exponential and logarithmic equations
Mathematics
Critical thinking
Communication
Competence will be demonstrated:
K.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
K.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
K.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
K.1. define base and exponent
K.2. define and graph the exponential function with base 10, base 2, fractional base, an arbitrary base and base e
K.3. apply transformations to exponential functions
K.4. apply exponential functions to such problems as exponential growth and decay,
half-life, interest, annuities, and mortgages
K.5. solve exponential equations algebraically and graphically
K.6. define logarithmic functions with base a - discussing possible values for the base
K.7. define the common logarithmic function and the natural logarithmic function
K.8. explain the inverse relationship between the logarithmic function and the exponential function (same base)
K.9. determine the domain and range of logarithmic functions
K.10. produce the graph of a logarithmic function (with various bases) considering the domain and the range
K.11. solve exponential and logarithmic functions algebraically and graphically

L. Solve systems of linear equations: using matrix row operations, inverse
matrices, and Cramer's Rule - solve non-linear systems

Mathematics
Critical thinking
Communication
Competence will be demonstrated:
L.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
L.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
L.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
L.1. solve systems of linear equations using substitution
L.2. solve systems of linear equations using elimination
L.3. define an n x m matrix, a square matrix, and elements of the matrix
L.4. define the matrix form of a system of linear equations
L.5. define row echelon form and reduced row echelon form
L.6. perform row operations on a matrix
L.7. solve a system of equations by performing row operations to reduce the augmented matrix to echelon form
L.8. define an inconsistent system
L.10. define matrix multiplication, the multiplicative identity matrix, and the multiplicative inverse matrix
L.11. recognize that matrix multiplication is generally not commutative
L.12. define the determinant of a 2x2 matrix and the determinant of an arbitrary square matrix
L.13. calculate the value of the determinant of a 2x2 matrix and 3x3, 4x4, and n x n matrix
L.14. calculate the inverse of a 2x2, 3x3, and 4x4 matrix
L.15. solve a system of equations by applying the inverse matrix and matrix multiplication (2 equations in 2 unknowns, 3 equations in 3 unknowns)
L.16. state Cramer's Rule - using Cramer's Rule to solve systems of linear equations
L.17. solve non-linear systems of equations by substitution
L.18. solve non-linear systems by graphing methods

M. Produce the graph of a conic section

Mathematics
Critical thinking
Competence will be demonstrated:
M.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
M.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
M.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
M.1. distinguish between the type of conic sections produced when a quadratic
polynomial in two unknowns is graphed
M.2. find the center and the semi-major and semi-minor axes given the polynomial
form of the equation of an ellipse
M.3. find the center, the axes, and the asymptotes given the polynomial form of the
equation of a hyperbola
M.4. find the center, the axis, and the directrix given the polynomial form of the
equation for a parabola
M.5. sketch the graph of a conic section given its equation in polynomial form

N. Calculate the sum of a series

Mathematics
Critical thinking
Competence will be demonstrated:
N.1. by completing and submitting for evaluation all in-class and take-home quizzes,
according to the grading scale contained in the syllabus
N.2. by demonstrating correct and accurate use of the scientific calculator on all
assignments, quizzes, tests, projects, and laboratory work when appropriate
N.3. by active participation in class discussions and activities
Performance will be satisfactory when you:
N.1. define a sequence, a term, and a series
N.2. calculate the sum of a finite series
N.3. identify an arithmetic sequence and a geometric sequence
N.4. calculate the sum of a finite arithmetic series given the first term, common
difference, and the number of terms or the first term, the last term, and the number of terms
N.5. calculate the sum of a finite geometric series given the first term, the common
ratio, and the number of terms or given the first term, the nth term and the number of terms
N.6. calculate the sum of an infinite geometric sequence given the first term and the nth term
N.7. state the principal of mathematical induction
N.8. use the principal of mathematical induction to prove the formulas for the sums of special sequences

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