MATH
1333 College Algebra
(3
credit hours/3 lecture hours)
Course Syllabus
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Course Description
(Prerequisite:
MATH 1023 or 19 on the ACT math exam, or at least 43 on Intermediate
Algebra and at least 38 on Numerical skills ASSET test, or at least 59 on the
COMPASS exam) The real number
system and fundamental operations, linear and quadratic equations, functions and
graphs, complex numbers, inequalities, and logarithms.
Rationale
Knowledge of the fundamental concepts of algebra is
necessary for the study of any of the other sciences as well as for using an
ever-increasing collection of software packages. It is a prerequisite for any in-depth study of statistics,
which can be applied at some level of field of endeavor.
General Course Goals
- The
student will be able to simplify algebraic expressions according to
mathematical conventions.
- The
student will be able to factor polynomials with integer coefficients (those
which are factorable over the set of integers).
- The
students will be able to solve any linear equation.
- The
student will be able to solve applied problems including ones involving
mixtures, distances, and simple geometric computations.
- The
student will be able to solve quadratic equations by factoring or using the
quadratic formula from memory. This
includes quadratic equations with complex solutions.
- The
student will be able to solve other equations involving radicals, absolute
values, and rational exponents.
- The
student will be able to perform the four fundamental operations with complex
number.
- The
student will be able to solve linear and quadratic inequalities and express
solutions in interval notation.
- The
student will understand the elements and purpose of the rectangular
coordinate system.
- The
student will be ale to graph linear and quadratic equations in tow variables
o the rectangular coordinate plane with an without the use of a graphing
utility.
- The
student will understand the concept of a function and to perform binary
operations on functions.
- The
student will be able to find the inverse of an invertible function.
- The
student will understand the language of variation.
- The
student will be able to find zeros of a polynomial function of a degree
greater than two performing synthetic division when necessary.
- The
student will understand and be able to graph (manually) the four conic
sections.
- The
student will understand and be able to simplify logarithmic expressions.
- The
student will be able to solve systems of equations by substitution, linear
combination, and matrix operations.
Grading
System
See
first day handout.
Policy
on Absences
See
Attendance as contained in the College Catalog.
Required
Text and Materials
Textbook;
Swokowski, Earl W. and Cole, Jeffery A.
Fundamental of College Algebra, Eleventh Edition.
Brooks/Cole Publishing Company. (ISBN 0-534-42086-9)
Solution Manual (ISBN 0-534-46459-9)
Materials:
Graphing Calculator (TI –83) and Grid paper
Learning
Objectives
Chapters
1 and 2:
Fundamental Algebra Concepts, Equations, and Inequalities
Goal:
The student will be able to solve linear equations, quadratic equations,
and inequalities; and solve equations and inequalities involving rational
expressions, absolute values, rational exponents, and radicals.
Objectives:
- The
student will be able to add, subtract, and multiply algebraic expressions
and give the expressions in the simplest form.
- The
student will be able to factor polynomials with integer coefficients.
- The
student will be able to add, subtract, multiply or divide rational
expressions and give the expressions in simplest form.
- The
student will be able to solve linear equations involving rational
expressions.
- The
student will be able to use the knowledge learned from studying equations to
solve applies problems involving rate-time-distance, mixture, area, simple
interest, and shared work relationships.
- The
student will be able to solve quadratic equations by the factoring method or
by using the quadratic formula (from memory).
- The
student will be able to add, subtract, multiply, and divide complex numbers
and express the result in the form ax + b.
- The
student will be able to solve equations involving absolute values, rational
exponents, and radicals.
- The
student will be able to solve linear and quadratic inequalities and express
solution in interval set notation
.
Chapter
3:
Functions and Graphs
Goal:
The student will be able to graph equations with or without a calculator
and to interpret, describe, and create graphs of functions.
Objectives:
- The
student will be able to name the components of the rectangular coordinate
system and to plot points on it.
- Given
two points on the rectangular coordinate plane, the student will be able,
using memorized formulas, to find the distance between the points and to
find the midpoint of the segment joining the two points.
- Given
an equation with two variables, the student will be able to plot selected
solutions to the equation and determine the shape of the graph.
- Given
the equation of a circle in general form, the student will be able to find
the center and radius of the circle by completing the square.
- Given
minimum information about a line (i.e., two points on the line, one point on
the line, the slope of the line, a point on the line, and the equation of a
parallel line, etc.), the student will be able to find the general form of
the equation of the line and graph it.
- Given
a graph, the student will be able to determine whether the graph is a
function.
- Given
the equation of a specific function, the student will be able to find the
function value corresponding to a specific value of the independent
variable.
- Given
the equation of a specific function f, the student will be able to
simplify the difference quotient ((f
+ h) - f(x))/h.
- Given
the graph of the function f(x), the student will be able to produce the
graph of the function cf(x), f(cx), f(x) + c, and f(x + c) for
any real number c.
- Given
a quadratic function, the student will be able to find the vertex of its
parabolic graph by the completing the square method and draw the graph of
the function.
- Given
two functions f and g, the student will be able to find the
equations of the functions f
+ g, f – g,
fg, and f/g
and state the domains of each function.
- Given
a function f, the student will be able to determine whether or not
the function is one – to – one.
- Given
a function f, the student will be able to determine whether the
function is even, odd, or neither.
Chapter
4:
Polynomial Functions, Rational Functions, and Conic Sections
Goal:
The student will be able to graph polynomial and rational functions with
or without the aid of a calculator.
Objectives:
- Given
a polynomial function of degree greater than two. The student will be able
to find zeros of the function by factoring and/or using the quadratic
formula.
- Given
a polynomial function of degree greater than two, the student will be able
to find all values of x
for which f(x) > 0.
- Given
polynomials f and p,
the student will be able to find polynomials q
and r (quotient and remainder) such that
f(x) = p(x)q(x) + r(x)
by long division.
- Given
a polynomial f, the
student will be able to divide f
by a binomial of the form x – c
by using synthetic
division.
- Given
a polynomial f of degree greater than two, the student will be able to
give the number of real zeros and the number of complex zeros that
f has.
- The
student will be able to find vertical and horizontal asymptotes to the graph
of a rational function.
- With
the aid of a graphing utility, the student will be able to produce the graph
of a rational function.
- Given
a rational function, the student will be able to determine the domain of a
rational function.
- Given
a statement of the form x varies directly as y or x varies
inversely as y, the student will be able to give an equation-relating
x, y, and a constant of proportionality k.
- Given
a solution to a statement of variation, the student will be able to
determine the values of the constant of proportionality k.
Chapter
5:
Exponential Functions
Goal:
The Student will be able to understand and manipulate exponential
logarithmic expressions.
Objectives:
- Given
the graph of a function f, the student will be able to draw the graph
of f inverse by
reflecting the graph of f
across the line y = x.
- Given
a one – to – one function f, the student will be able to derive
at its inverse.
- The
student will be able to graph an exponential function with or without the
aid of a graphing calculator.
- From
memory, the student will be able to give the approximate value of the number
e.
- Without
the aid of a calculator, the student will be able to determine the whole
number value of logarithmic expression.
- With
the aid of a calculator, the student will be able to determine the value of
any natural or common logarithm.
- The
student will be able to use laws of logarithms to simplify logarithmic
expressions.
Chapter
6:
Systems of Equations and Inequalities
Goal:
The students will be able to understand and solve systems of equations
and inequalities.
Objectives:
1.
The students will be able to solve
systems of equation by using the substitution method and the elimination method.
2.
The students will be able to solve
systems of linear equations in two variables and in more than two variables.
3.
The students will be able to solve
systems of inequalities.
4.
The students will be able to find
the inverse of a matrix.
Assignments
1.3
Algebraic Expressions
2.1
Equations
2.2
Applied Problems
2.3
Quadratic Equation
2.4
Complex Numbers
2.5
Other Types of Equations
2.6
Inequalities
2.7
More on Inequalities
Test
1
3.1
Rectangular Coordinate Systems
3.2
Graphs of Equations
3.3
Lines
3.4
Definition of Function
3.5
Graphs of Functions
3.6
Quadratic Functions
3.7
Operations on Functions
Test
2
4.1
Polynomial Functions of Degree Greater Than 2
4.2
Properties of Division
4.3
Zeros of Polynomials
4.4
Complex and Rational Zeros of Polynomials
4.5
Rational Functions
4.6
Variation
Test
3
5.1
Inverse
Functions
5.2
Exponential Functions
5.4
Logarithmic Functions
5.5
Properties of Logarithms
5.6
Exponential and Logarithmic Equations
Test
4
6.1
Systems
of Equations
6.2
Systems
of Linear Equations in Two Variables
6.3
Systems
of Inequalities
6.5
Systems
of Linear Equations in More than Two Variables
6.7
Inverse
of a Matrix
Test
5
Final
Exam – common comprehensive
College Algebra Math 1333
Textbook
Assignment
Sheet (Mrs. Scott)
Section
Textbook Page(s)
Problem Numbers
1.3
43 - 44
46, 50, 52, 56,
58, 72, 74, 78, 84, 86, 88,
92, 94
2.1
66 – 68
6, 8, 12, 14, 18, 20, 22, 32, 38, 40, 44,
60, 64,
66, 68, 70, 72
2.3
91
2, 6, 10, 12, 14, 16, 18, 20, 22, 24, 28,
30, 32, 34, 36
2.4
102 - 103
2, 4, 6, 10, 12, 16, 18, 20, 24, 26, 30,
32, 34,
36, 38, 40, 42, 44
2.5
109 – 110
2, 4, 8, 10, 12, 14, 20,
24, 34, 36,
52a, 52d,
54
2.6
119 – 120 2
– 22 even, 26, 28, 30, 32, 34, 48, 56,
58, 60, 64
2.7
127
2, 4, 6, 10, 12, 20, 22
3.1
141 – 142 2,
6, 12, 14, 24
3.2
156 – 157 4,5,
6, 9, 14, 17, 25, 26, 32, 34, 36,
38, 48,
50, 51, 57, 58
3.3
172 – 174 2,
4, 6, 16, 20, 24, 26, 30, 32, 36, 42, 44
3.4
190 – 192 2,
4, 6, 12, 38, 40, 42, 44, 46, 48
3.5
209
4, 6, 8, 10, 12, 14, 16, 34, 36, 38, 40
3.6
223 – 224 2,
4, 6, 8, 10, 14, 18, 20, 22, 30, 32
3.7
236 – 237 2,
4, 6, 10, 12, 14, 18, 22, 24, 30, 32
Test
2 (Chapter 3)
4.1
255 – 256 2,
4, 6, 8, 10, 14, 18, 20
4.2
265
2, 4, 6, 8,18, 20, 22, 24, 26, 28
4.3
277 – 278 2,
4, 6, 8, 10, 16, 17, 18, 19, 21
4.4
287
2 – 10 even
4.5
304 – 305 4,
12, 22, 30, 34, 36
4.6
312 – 313 2,
4, 6, 8, 10, 12, 16, 20
Test
3 (Chapter 4)
5.1
328
6 – 20 even, 26, 28, 30, 32, 34,40
5.2
339 - 340 1
– 10, 11(a, c, e, g), 14, 16, 18
5.4
365 – 366 2,
4, 12, 14, 16, 18, 19, 20, 22, 23, 24
5.5
376
2, 4, 5, 6, 10, 12, 18, 20, 22, 23
5.6
388
2 – 20 even,
Test 4 (Chapter 5)
_____________________________________________________________________________
6.1
406
2-14 even, 18, 20, 28, 30
6.2
416
2 – 20 even
6.3
424 – 425
2 – 20 even
6.5
449 – 450
2 – 22 even
6.7
466 – 467
2 – 12 even
Revised
January 2007
College Algebra Plato
Assignment
CHAPTER 1
Number of Mastery Tests
Exponents and Radicals
3
Factoring
3
Algebraic Fractions
3
Algebraic Operations
3
Rational Products and Quotients
2
Rational Sums and Differences
2
CHAPTER 2
Solving Equations
2
Word Problems
1
Quadratic Equations
2
Intervals, Distance, and Absolute Value
2
Inequalities
3
CHAPTER 3 & 4
Graphing
2
Lines and Slopes
2
Parallel and Perpendicular Lines, Advanced Algebra
3
Slope Intercept Form
3
Parabolas
2
Definition of Functions
2
Composite and Inverse Functions
4
Distance and Circles
3
Total Bonus Points 100
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