Math111E - Intermediate Algebra

TEXT/INSTRUCTIONAL RESOURCES:

TEXT: Beginning & Intermediate Algebra , 2^nd Ed., by J.W. Hall & B.A. Mercer.
Supplements: DVD (on reserve in the Library); Math Lab (times TBA)

COURSE ORGANIZATION/CONTENT:

Unit 1 – Operations with Real Numbers:
1. Sets; Natural numbers and integers.
2. Rational; real numbers and complex numbers; Operations with real numbers.
3. Identify and apply formulas in problem solving.
4. Solve equations .

Unit 2 – Linear Equations & Patterns
1. Solving linear equations in one variable.
2. Recognize a function.
3. Graph functions, and determine its domain and range.
4. Find equations of lines and graph it.
5. Slope, intercepts and the distance formula.
6. Different forms of the linear equation.
7. Linear inequalities; Variation.

Unit 3 – Lines and Systems of Equations :
1. Solving systems by graphing and substitution.
2. Solving systems by elimination .
3. Solving systems of three equations

Unit 4 – Linear Inequalties and systems of inequalities:
1. Solving linear and absolute value inequalities.
Unit 5-6 – Exponents and operations with Polynomials:
1. Properties and classification of polynomials
2. Operations with polynomials.
3. Modeling with polynomial functions .

Unit 7 – Linear, absolute value and Quadratic Functions:
1. Completing the squares and quadratic formula.
2. Absolute value equations and inequalities.
3. Solving quadratic inequalities.
4. Graphing quadratic functions.
5. Solving equations quadratic in form, and with add ing-exponents/exponents-and-square-roots.html">complex roots .
6. Solving minimum and maximum problems.

Unit 8 – Rational Functions and Variation:
1. Properties and classification.
2. Operations with expressions. Complex fractions.
3. Solving equations with rational expressions.

Unit 9 – Exponents and Radicals:
1. Rational exponents.
2. Operations with radicals.
3. Solving equations with radicals, and with complex roots

Unit 10 – Exponential and logarithmic functions:
1. Exponential and logarithmic functions.
2. Properties of logarithms.
3. Equations with logarithms and exponentials.

Unit 11 – Selected Topics, Conic Sections:
1. Circles, parabolas, ellipses and hyperbolas .
2. Systems of quadratic equations.

SPECIFIC OUTCOMES:
Unit 1: - understand common notation; distinguish numbers.
- compute with decimals , fractions and signed numbers.
- classify equations and formulas.
- simplify equations and inequalities; rearrange formulas.
- demonstrate an ability to analyze an argument and identify the
basic assumptions of the word problem. Solve the problem.
- draw conclusions and write them in full sentences.

Unit 2: - solve linear equations/inequalities.
- understand linear equations.
- represent linear equations graphically, graph linear inequalities.
- find the slope and intercepts of a linear equation.
- compute the distance between two points on the Cartesian plane.
- write linear equations in different forms.
- distinguish relations and functions, classify functions.
- find the domain and range of a function.
- add, subtract, multiply and divide functions.

Unit 3: - classify systems of linear equations.
- solve linear systems by graphing, substitution, elimination, Cramer’s Rule and matrix method.

Unit 4-7: - factor and solve polynomial equations.
- Identify and apply factoring to solve equations
- solve quadratic equations using the method of completing squares and the quadratic formula.
- solve quadratic inequalities.
- find critical numbers of inequalities.

Unit 8: - classify rational expressions.
- add, subtract, multiply and divide rational expressions.
- solve equations with rational expressions.
- solve problems of direct, inverse, joint variation.

Unit 9: - write radicals as expressions with rational exponents and vice-versa.
- simplify radicals; add, subtract, multiply and divide radicals.
- solve equations with radicals.

Unit 10: - understand the relationship of the exponential and logarithmic functions.
- graph exponential and logarithmic functions.
- apply the logarithmic properties.
- solve equations with exponentials and logarithms.

Unit 11 - distinguish the circle, parabola, ellipse and hyperbola.
- graph circles, parabolas, ellipses and hyperbolas.
- solve systems of quadratic equations.

REQUIREMENTS: Prerequisites: Math 110 with a grade of “C” or better, or its equivalent.
Calculators: It is required to use graphing calculators for this class . TI-83 or
higher. Results obtained with the use of calculators must be analyzed its validity.
Students should interpret the answer and understand how it was obtained.

Attendance: Students are expected to attend every class session. It is the
responsibility of the student to confer with the teacher before anticipated or after
unavoidable absences. The responsibility of make-up work lies with the student.
Messages may be left in my office or calling me or the secretary at 263-2870.

 My expectations of you: I expect you to be in class, on time for every class
session. Usually the classes are going to be conducted in an interactive way and
therefore student’s participation is essential. I encourage you to form study
groups and come to my office or the Math Lab for help if needed or just to
discuss your work. ABSOLUTELY NO CELLULAR PHONES ARE AL LOWED
TO BE ON DURING THE CLASS.

ASSESSMENT OF ACADEMIC ACHIEVEMENT:
Journal: You need to write in a journal format, a report of everything that you did
relevant for this class. This report should contain, among other things, a list of all
the topics covered, which topics you understood well and which ones you didn’t
understand so well, the time you spent studying the subject, comments about the
class, etc. At least 4 of the journals have to have included a newspaper or
magazine article that deals with mathematics. The journals are due at the
beginning of the last class period, every other week.

Homework: I will assign problems at the end of every class session. I will
collect some of the assignments. It is essential that students do every problem
assigned.

Quizzes: There will be twelve short quizzes based on homework problems.
Only ten of them will be considered in computing the final grade for the course.
There is no make-up for quizzes.

Tests: There will be three one-hour tests. They will be comprehensive over the
material covered up until that point. They will be written so that the specific
outcomes are fulfilled.

Paper: learning math is like learning a foreign language. And to learn a foreign
language you need to be good at your mother language. Therefore, you will write
summaries, paraphrases, analyses and syntheses, responses, essays, etc. You will
also get lots of practice in conducting, writing, and documenting research. We hope that
through varied and constant writing experience, you will learn not only math but also
strategies for invention, narration, using the writing of others to inform an audience or
support a position, evaluating sources, collaboration, revision, editing, research, etc.
And we hope you will leave this course with renewed confidence in your mathematical
and writing abilities. You will write a major paper, which is going to be considered as
your fourth test in this course.

Final Exam: There will be a two-hour comprehensive final exam.

Grading/evaluation:

TENTATIVE SCHEDULE: