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Intermediate Algebra Syllabus

Course Title: Intermediate Algebra (3 credits)

Course #: MAT* 137


An extremely rigorous course in Intermediate Algebra intended for Math, Science,
Engineering, Nursing, Teacher Preparation, and Business majors or for those students
whose future coursework includes algebra-based courses such as upper-level Chemistry
or Calculus. It has a minimal review of Elementary Algebra. Those needing a more
extensive review of Elementary Algebra (due to a period of time elapsing since
completing that course) should retake MAT* 095 (Elementary Algebra Foundations);
those needing a more general Math course, or additional Math preparation after
completing Elementary Algebra (e.g. for those with a grade in the C range in MAT*
095 – Elementary Algebra Foundations), should strongly consider MAT* 135 (Topics
in Contemporary Math) prior to taking Intermediate Algebra.

Topics include: polynomial and rational expressions, exponents and radicals, complex
numbers, linear, quadratic, literal, absolute value, and radical equations, systems of
linear equations, linear and absolute value inequalities, graphing linear and quadratic
functions, functional notation, exponential and logarithmic functions, binomial
theorem, and applications.

This course counts as a Math elective towards graduation (but does not transfer as a
Math course to most 4-year colleges).


A grade of C- or better in MAT* 095 Elementary Algebra Foundations (B- or better
strongly recommended), or satisfactory grade on the Mathematics placement test (score
of 58 or better on Accuplacer Elementary Algebra test within the past 6 months).

A knowledge of the following topics is indicated by completion of the above required
1. Number system development (natural numbers, integers, rational numbers,
irrational numbers, real numbers).
2. Concepts of terms vs. factors, expressions vs. equations.
3. Computations with negative numbers (including absolute value).
4. Simplifying algebraic expressions.
5. Solving linear equations.
6. Computations with algebraic fraction expressions.
7. Solving algebraic fraction equations.
8. Solving and graphing linear inequalities.
9. Graphing linear equations (including “table of values” method).
10. Solving systems of linear equations in 2 variables.
11. Computations with polynomials (including “FOIL” technique).
12. Factoring polynomials (including greatest common factor, “factor by
grouping”, “ac method”, and difference of 2 squares).


13. Computations with integer exponents.
14. Simplifying square roots.
15. Solving quadratic equations (by factoring, “square root method”, and
quadratic formula).


1. To further develop individual responsibility and respect for rules and
regulations, and a more advanced ability to be organized and follow a
detailed regimen.
2. To further develop analytical reasoning and critical thinking skills that will
enhance more advanced problem solving capabilities.
3. To develop intermediate algebra skills that will allow the study of a variety
of more advanced Mathematical topics


Upon successful completion of this course each student must have demonstrated
understanding and competency in each of the following topics and techniques (thru inclass
testing of each individual student independently):

1. Understanding basic concepts of set theory (subset, intersection, union).
2. Understanding of number system development (natural numbers, integers,
rational numbers, irrational numbers, real numbers, complex numbers).
3. Doing computations with integers (including absolute value).
4. Simplifying algebraic expressions.
5. Solving linear equations (including word problem applications – consecutive
integer, rectangle perimeter, d=rt).
6. Solving and graphing linear inequalities.
7. Solving literal equations (i.e. equations in several variables).
8. Solving absolute value equations.
9. Solving and graphing absolute value inequalities.
10. Simplifying and doing computations with polynomials (including division of
11. Factoring polynomials (including greatest common factor, “factor by
grouping”, “ac method”, difference of 2 squares, sum and difference of 2
12. Simplifying and doing computations with algebraic fraction expressions
involving factoring (including complex fractions).
13. Solving algebraic fraction equations (including word problem applications –
reciprocals, work).
14. Simplifying and doing computations with integer exponents and rational
15. Simplifying and doing computations with radical expressions.
16. Solving radical equations.
17. Simplifying and doing computations with complex numbers.
18. Understanding functions (including domain & range, function notation).
19. Graphing linear and non-linear functions – using “table of values” (“pen &
paper”) method.
20. Understanding concept of slope (including slope formula, slope-intercept
form, point-slope form).


21. Graphing linear inequalities in 2 variables.
22. Understanding of variation (including word problem applications – falling
23. Graphing and studying parabolas (including “completing the square”
24. Solving quadratic equations (by factoring, “square root method”, and
quadratic formula – in radical, non-decimal, format) – including word
problem applications (rectangle area, triangle area, pythagorean theorem).
25. Solving equations in quadratic form.
26. Solving and graphing quadratic inequalities.
27. Solving systems of equations in 2 and 3 variables (by substitution and
elimination) – including word problem applications (coins, ticket sales).
28. Understanding inverse functions.
29. Graphing exponential functions and solving exponential equations.
30. Understanding logarithmic function and being able to interchange
exponential and logarithmic notation.
31. Solving logarithmic equations.
32. Understanding basic binomial expansion (binomial theorem, Pascal’s

College Policies

Plagiarism: Plagiarism and Academic Dishonesty are not tolerated at Northwestern Connecticut
Community College. Violators of this policy will be subject to sanction. Please refer to your “Student
Handbook” under “Policy on Student Rights”, the Section entitled “Student Discipline”, or the College
catalog for additional information.

Americans with Disabilities Act (ADA): The College will make reasonable accommodations for
persons with documented learning, physical, or psychiatric disabilities. Students should notify Roseann
Dennerlein, the Counselor for Students with Disabilities. She is located at Green Woods Hall, in the
Center for Student Development.

Class cancellation information: If snowy or icy driving conditions cause the postponement or
cancellation of classes, announcements will be made on local radio stations. Student may also call the
College directly at (860) 738-6464 to hear a recorded message concerning any inclement weather
closings. Students are urged to exercise their own judgment if road conditions in their localities are