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Intermediate Algebra and Trigonometry

Course Description:

This course is an intermediate algebra and trigonometry course. It includes such topics such
as arithmetic with integers, algebraic representation, operations with polynomials , solving
linear equations , solving systems of two linear equations in two variables, exponents and
radicals, factoring, graphing linear equations, and the Pythagorean theorem.


MAT 012 or MAT 051 or the equivalent

Student Learning Outcomes: The students should be able to:

• compute the sum, difference, product and quotient of polynomials.
simplify expressions involving exponents and scientific notation.
• factor trinomials, difference of two squares, sum and difference of two cubes , and
higher-degree polynomials.
• factor using grouping and greatest common factors .
• solve linear equations, absolute value equations and inequalities.
• solve polynomial equations by factoring.
• solve quadratic equations using factoring and the quadratic equation.
• solve systems of linear equations using elimination, substitution and graphing .
• graph linear equations and inequalities in one and two variables.
• find the slope and intercepts of a line.
• find the slopes of parallel and perpendicular lines.
• find the equation of a line in slope-intercept and point-slope form.
• simplify algebraic expressions using integer and rational exponents .
• simplify and perform operations (addition, subtraction, multiplication, division) with
• rationalize a denominator involving a radical.
• simplify rational algebraic expressions using factoring.
• add, subtract, multiply , and divide rational algebraic expressions.
• simplify complex algebraic fractions.
• add, subtract, multiply and divide complex numbers.
• rationalize the denominator of the quotient of complex numbers.
• solve rational and radical equations.
• graph and find the equation of an equation's inverse.
• graph exponential and logarithmic equations .
• use the properties of exponentials and logarithms to solve equations.
convert angle measurements between degrees and radians.
• for a given angle, find the exact or approximate measure of its reference, coterminal,
complementary and supplementary angles.
• for a given angle, find the six exact or approximate trigonometric values.
• graph trigonometric equations.
• use identities to find trigonometric values.
• solve application problems using right triangle trigonometry, the law of sines and
the law of cosines.

Required Text and Readings:

Algebra with Trigonometry for College Students, 5th Edition, Charles McKeague, Saunders
College Publishing, 2002

Evaluation and Requirements of Students:

The final grade in this course will be a letter grade (A- F). At the beginning of the
semester, the instructor will advise the student of the determination of the final grade
which will be based on a mandatory final examination worth at least 30% of the final grade
and any other criteria specified by the instructor. The other criteria could include but is not
limited to class work, examinations, quizzes, and projects. Students can obtain copies of a
practice departmental final exam in the Math Lab (room S511) or from their instructor.
Students are required to attend all scheduled classes. The college's attendance policy, as
stated in the catalog, gives instructors the option of assigning a failing grade to students
who are excessively absent.

Outline of Topics Text Pages Pages in Text
Exponents and Scientific Notation 38
Polynomials, Sums, Differences and Products 49
Factoring 61
Special Factoring 70
Equations and Inequalities in One Variable  
Linear and Quadratic Equations in One Variable 101
Formulas 112
Applications 126
Linear Inequalities in One Variable 143
Equations with Absolute Value 154
Inequalities Involving Absolute Value 159
Equations and Inequalities Two Variables  
Paired Data and the Rectangular Coordinate System 178
The Slope of a Line 192
The Equation of a Line 202
Rational Expressions and Rational Functions  
Basic Properties and Reducing to lowest terms 347
Division of Polynomials 360
Multiplication and Division of Rational Expressions 371
Addition and Subtraction of Rational Expressions 380
Complex Fractions 389
Equations Involving Rational Expressions 394
Applications 405
Rational Exponents and Roots  
Rational Exponents 426
More Expressions Involving Rational Exponents 438
Simplified Form for Radicals 445
Addition and Subtraction of Radical Expressions 457
Multiplication and Division of Radical Expressions 461
Equations with Radicals 468
Complex Numbers 478
Quadratic Functions  
Completing the Square 493
The Quadratic Formula 505
Systems of Linear Equations and Inequalities  
Systems of Linear Equations in Ttio Variables 276
Applications 312
Exponential and Logarithmic Functions Fxponential Functions  
The Inverse of a Function  
Logarithms Are Exponents  
Properties of Logarithms  
Introduction to Trigonometry  
Degrees, Radians, and Special Triangles  
Trigonometric Functions  
Trigonometric Functions and Calculators  
Introduction to Identities  
Right Triangle Trigonometry  
The Law of Sines  
The Law of Cosines  

College Attendance Policy:
1. Absences

At BMCC, the maximum number of absences is limited to one more hour than the number of
hours a class meets in one week. For this course, you are allowed five hours of absence (not
five days). In the case of excessive absence, the instructor has the option to lower the grade or
assign an "F", "R", or "WU" grade.

2. Class Attendance

If you do not attend class at least once in the first three weeks of the course and once in the
fourth or fifth weeks, the Office of the Registrar is required to assign a grade of "WU".
Attendance in both regular and remedial courses is mandated by policy of the City University
of New York. Instructors are required by New York State law to keep an official record of
class attendance.

3. Lateness

Classes begin promptly at the times indicated in the Schedule of Classes. Arrival in classes
after the scheduled starting time constitutes lateness. Latecomers may, at the discretion of the
instructor, incur an official absence.

Academic Adjustments for Students with Disabilities:

Students with disabilities who require reasonable accommodations or academic adjustments for
this course must contact the Office of Services for Students with Disabilities. BMCC is
committed to providing equal access to all programs and curricula to all students.
BMCC Policy on Plagiarism and Academic Integrity Statement:

Plagiarism is the presentation of someone else's ideas, words or artistic, scientific, or technical
work as one's own creation. Using the idea or work of another is permissible only when the
original author is identified. Paraphrasing and summarizing, as well as direct quotations
require citations to the original source. Plagiarism may be intentional or unintentional. Lack of
dishonest intent does not necessarily absolve a student of responsibility for plagiarism.
Students who are unsure how and when to provide documentation are advised to consult with
their instructors. The library has guides designed to help students to appropriately identify a
cited work. For further information on integrity and behavior, please consult the college bulletin (also
available online).

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