Description
A review of polynomials, exponents, and radicals; solutions to equations and
inequalities in one and two
variables . Topics covered include exponential, logarithmic, and quadratic
functions; roots of
polynomials; graphs of various functions and conic sections; solutions of
systems of linear equations.
Recommend completion of two years of high school algebra.
Textbooks
Beecher/Penna/Bittinger College Algebra 3rd Ed. Pearson Addison
Wesley 2008. Required
Supplies
Scientific Calculator; TI-83 or TI-84 recommended
Competencies and Performance Standards
1. Simplify algebraic expressions .
Learning objectives
What you will learn as you master the competency:
a. Apply the rules for simplifying polynomial expressions.
b. Apply the rules for simplifying rational expressions.
c. Apply the rules for simplifying radical expressions .
Performance Standards
Competence will be demonstrated:
On assigned activities.
On written exams.
On a two hour cumulative final exam.
Criteria - Performance will be satisfactory when:
You can demonstrate the ability to simplify a variety of algebraic expressions.
2. Apply algebraic techniques to the solution of word problems.
Learning objectives
What you will learn as you master the competency:
a. Solve linear equations and inequalities.
b. Solve nonlinear inequalities.
c. Solve absolute value equations and inequalities.
d. Solve polynomial equations by factoring .
e. Solve quadratic equations by the quadratic formula.
f. Solve radical equations.
g. Solve rational equations.
h. Solve exponential and logarithmic equations.
i. Solve systems of equations in two or more variables.
j. Translate a word problem into an algebraic equation or equations.
Performance Standards
Competence will be demonstrated:
On assigned activities.
On written exams.
On a two hour cumulative final exam.
Criteria - Performance will be satisfactory when:
You can demonstrate the ability to solve a variety of algebraic equations and
inequalities.
You can demonstrate the ability to translate word problems into algebraic
equations.
3. Analyze relations, functions and their graphs.
Learning objectives
What you will learn as you master the competency:
a. Distinguish between functions and non-functions.
b. Determine the domain and range of functions and non-functions.
c. Use function notation.
d. Determine the inverse of a function.
e. Perform the basic operations with functions : addition, subtraction,
multiplication, division and
composition.
f. Sketch the graphs of a variety of basic algebraic functions.
Performance Standards
Competence will be demonstrated:
With relations expressed a variety of forms such as, tables, graphs, equations,
sets of ordered pairs
, verbal descriptions.
On assigned activities.
On written exams.
On a two hour cumulative final exam.
Criteria - Performance will be satisfactory when:
You can demonstrate the ability to distinguish between functions and
non-functions.
You can determine the domain range and inverse of a relation.
You can read and write using function notation correctly.
You can perform the basic operations of addition, subtraction , multiplication,
and composition with
functions.
You can sketch the graph of some basic algebraic functions.
4. Examine polynomial and rational functions in detail.
Learning objectives
What you will learn as you master the competency:
a. Determine slope and intercepts of a linear function.
b. Graph linear functions.
c. Write the equation of a linear function.
d. Determine the coordinates of the vertex , and the intercepts of a quadratic
function.
e. Graph quadratic functions.
f. Determine the zeros, and the y- intercept of higher degree polynomial
functions.
g. Graph higher degree polynomial functions.
h. Determine the asymptotes, and the intercepts of rational functions.
i. Graph rational functions.
Performance Standards
Competence will be demonstrated:
On assigned activities.
On written exams.
On a two hour cumulative final exam.
Criteria - Performance will be satisfactory when:
You can identify the slope and intercepts, and sketches the graph of any linear
function.
You can identify the vertex and intercepts , and sketches the graph of any
quadratic function.
You can identify the zeros and y -intercept, and sketches the graph of higher
degree polynomials.
You can identify the asymptotes and intercepts, and sketches the graph of
rational functions.
5. Analyze the properties, graphs, and applications of
exponential and logarithmic functions..
Learning objectives
What you will learn as you master the competency:
a. Simplify exponential and logarithmic expressions.
b. Solve exponential and logarithmic equations.
c. Sketch the graphs of exponential and logarithmic functions.
d. Apply exponential and logarithmic functions in various applications.
Performance Standards
Competence will be demonstrated:
On assigned activities.
On written exams.
On a two hour cumulative final exam.
Criteria - Performance will be satisfactory when:
You can simplify exponential and logarithmic expressions
You can solve exponential and logarithmic equations
You can sketch the graphs of exponential and logarithmic functions
You can correctly model real world situations with exponential or logarithmic
functions
6. Examine the equations and graphs of conic sections
in detail.
Learning objectives
What you will learn as you master the competency:
a. Identify the various conic sections from equations written in general form.
b. Convert the general form of the equation of a conic section into the standard
form.
c. Determine the radius and center of a circle.
d. Graph a circle.
e. Write the equation of a circle.
f. Determine the center, foci, vertices, major axis, and minor axis, of an
ellipse.
g. Graph an ellipse.
h. Write the equation of an ellipse.
i. Determine the center, foci, vertices, orientation, and asymptotes of a
hyperbola .
j. Graph a hyperbola.
k. Write the equation of a hyperbola.
l Determine the vertex, focus, directrix, and orientation
of a parabola .
m. Graph a parabola.
n. Write the equation of a parabola.
o. Determine the conic section from a general equation
Performance Standards
Competence will be demonstrated:
On assigned activities.
On written exams.
On a two hour cumulative final exam.
Criteria - Performance will be satisfactory when:
You can identify the conic section from an equation written in general form
You can write the equation of a conic section in standard form
You can identify the relevant features and sketches the graph of any conic
section
7. Apply systems of equations and matrices
Learning objectives
What you will learn as you master the competency:
a. Solve systems of equations using a specified method such as: graphing,
substitution , elimination,
Row-Echelon, Gaussian, Gauss-Jordon, Matrix Inverse or Cramer's Rule.
b. Perform basic operations with matrices
c. Sketch the graph of a system of linear inequalities
d. Solve a system of linear inequalities
Performance Standards
You will demonstrate your competence:
On assigned activities
On written exams
On a two hour cumulative exam
Your performance will be successful when:
You can solve a system of equations in two variables by the following methods:
graphing,
substitution, and elimination .
You can solve a system of equations in two and three variables by the following
methods:
Gaussian Elimination, Row-Echelon Form, Gaussian Elimination, Row-Echelon Form,
Matrix
Inverse and Cramer's Rule.
You can perform matrix operations such as: adding, subtracting, multiplying
scaler multiplication,
the identity of a matrice and calculate the inverse matrice for a 2x2 and a 3x3
matrice.
You can graph the solution of systems of linear inequalities.
You can find the best solution to a system of linear inequalities.
You can find the partial fraction decomposition of a rational expression.
Types of Instruction
Classroom Presentation
Grading Information
Grading Rationale
Each instructor has the flexibility to develop evaluative procedures within the
following parameters.
1. Written Exams must represent at least 60% of the final course grade.
2. Final Exam must represent at least 20% of the final course grade.
3. The Post Test is to be embedded in the final exam and must represent at least
10% of the final
course grade.
4. Other Activities may represent at most 10% of the final course grade.
Grading Scale
A 90%-100%
B 80%-89%
C 70%-79%
D 60%-69%
F Below 60%
