MAT 03: Intermediate Algebra – 0 credits, 4 hours

Course Coordinator: Professor Ron Forman

Course Description: MAT 03 prepares students for the study of pre-calculus and calculus. It is an intensive introduction to the concepts of College Algebra and Trigonometry, covering such topics as real numbers, polynomial operations, linear and quadratic equations, and trigonometric functions and equations. It will help students develop the skills to pass the Algebra II and Trigonometry Regents Exam and Parts III, IV and V of the CUNY Compass Assessment Test in Mathematics.

Catalog Description: MAT 03 prepares students for the study of pre-calculus and calculus. It is an intensive introduction to the concepts of college algebra and trigonometry, covering topics such as real numbers, polynomial operations, linear and quadratic equations, Gaussian elimination and trigonometric equations.. Upon completion of the course, students will have developed mathematics skills that can enhance their performance on the New York State Algebra II and Trigonometry Regents and on college placement tests in intermediate algebra and trigonometry. Students who pass the course and attend a CUNY college may be able to satisfy Parts 3, 4 and 5 of the university’s Compass Assessment Test by forwarding an official statement of their math courses to the college.

Explanation and Objectives: MAT 03 is designed to help students make a smooth transition from high school to college mathematics. This course focuses on the mathematical reasoning and numeracy skills required to meet college freshman-level mathematics coursework and testing requirements. Upon completion of the course, students will have developed mathematical skills that can enhance their performance on the N.Y. State Algebra II and Trigonometry Regents and college placement tests in intermediate algebra, such as the Compass Assessment Test in Mathematics, Parts III, IV and V.

Topical Course Outline: (Based on 56, 50-minute sessions) All lessons will include elements of mathematics skill development (i.e., application of appropriate formulas and use of mathematical vocabulary) and use of mathematical reasoning (exploring, developing and understanding mathematical ideas or inventing new ways to solve problems).

1. Inequalities: (3 sessions)
   Linear Inequalities, Inequalities Involving Absolute Values and Quadratic Inequalities.
2. Rational Expressions: (6 sessions)
   Addition, Subtraction, Multiplication and Division of Rational Expressions, Simplifying Complex Fractions, Fractional Equations.
3. Exponents: (2 sessions)
   Laws of Positive Integral Exponents, Zero and Negative Exponents, Rational Exponents.
4. Quadratic Equations: (7 sessions)
   Solving by Factoring, Solving by Completing the Square, Solving by Quadratic Formula, Verbal Problems Leading to a Quadratic Equation, Properties of the Roots of a Quadratic Equation.Graphing Quadratic Equations.
5. Radicals: (3 sessions)
   Simplification of Radicals, Addition and Subtraction of Expressions Containing Radicals, Multiplication and Division of Radicals, Equations with Radicals.
6. Complex Numbers: (2 sessions)
   Pure Imaginary Numbers, Addition, Subtraction, Division and Multiplication of Complex Numbers.
7. Functions: (3 sessions)
   Relations, Functional Notation, Inverses, Composition of two Functions.
8. Logarithms: (4 sessions)
   Scientific Notation, Exponential Functions, Using the Common Logarithm Table, Calculations Using Common Logarithms, Graphing Exponential and Logarithmic Functions.
9. Statistics and Probability: (8 sessions)
   Summation Symbol, Frequency Distributions, Measures of Central Tendency, Measures of Variance, Normal Distribution, Counting Problems, Addition and Subtraction Rules of Probability, Conditional Probability, Regression.
10. Trigonometry: (12 sessions)
    Trigonometry of Right Triangles, Solving Right Triangles, Law of Sines, Law of Cosines, Identities, Area of Triangles, Sum and Difference Formulas, Half Angle and Double Angle Formulas, First and Second Degree Trigonometric Equations, Verbal Problems, Force Problems, Vector Addition and Subtraction, Graphing Trigonometric Functions, Graphing Systems of Trigonometric Functions, Resolving Vectors, Unit Circle, Reference Angles, Inverse Trigonometric Functions.
11. Supplementary Topics, Testing and Review: (6 Sessions)
    At least three days at the end of the semester should be reserved for an intensive review for the Algebra II and Trigonometry Regents Exam. There should also be a review of topics covered on the CUNY Compass Exam.
12. Writing in Mathematics: (All Sessions)
    Discussion and practice of critical thinking and writing skills in mathematics needed to pass the Algebra II and Trigonometry Regents examination and CUNY Compass Exam.

Textbook: Bittinger, Ellenbogen & Johnson, Elementary and Intermediate Algebra Concepts and Applications, 3rd Edition 2001, (ISBN 0201719665) or suitable text book approved by course coordinator.

Methods of Teaching: Lectures with student participation supplemented by computer software. Mathematical concepts and procedures will be developed through examples, demonstrations and discussions, with an emphasis on explaining why and how a procedure works. Teachers will also encourage students to engage in creative mathematical work by asking them to develop procedures themselves based on what they have learned in previous lessons. Each week a cumulative review will be presented as a take-home or in-class assignment and at least one fifteen-minute quiz will be administered to assess progress and problems. Test-taking tips and strategies will be a part of each lesson. Actual Algebra II and Trigonometry Regents Exam questions will be used each day in class.

Assignments: Students will be given homework assignments each day. A large portion of each assignment will include questions similar to those on the Algebra II and Trigonometry Regents Exam and the CUNY Compass Exam.

Methods of Evaluation: Students will be evaluated in terms of their development toward being prepared for the Algebra II and Trigonometry Regents Exam and CUNY Compass Assessment Test. Progress will be evaluated throughout the semester using homework assignments, weekly exams and the final examination. Students will take the regularly scheduled Algebra II and Trigonometry Regents Exam administered by the high school at the end of the semester. However, the grade on the Regents exam will not be considered in the student’s final grade. There will be a Pre-Test and a Post-Test to evaluate student progress in the course.

Pre-requisites: Students in the third or fourth year of high school and fall into one of the following categories:

1. Students enrolled in an Algebra II and Trigonometry class who have been identified by the high school as being in need of extra assistance to pass the Algebra II and Trigonometry Regents Exam at the conclusion of the course.
2. Students who have taken and failed the Algebra II and Trigonometry Regents Exam for the first time with a grade of 64% or lower.
3. Students who will be sitting for the CUNY Compass Assessment Test during the semester.

Supplementary Resources:

1. Stigler, James W and Hiebert, James. “Understanding and Improving Classroom Mathematics Instruction,” Phi Delta Kappan, 1997, at http://www.pdkintl.org/kstg9709.htm
2. Sullivan, Algebra and Trigonometry (Fifth Edition), Prentice Hall Publisher, ISBN:0-13-080006-6
3. Weiss. Introductory Statistics (Fifth Edition), 1999, Addison-Wesley Publisher, ISBN: 0-201-88330-9
4. Student Resource Materials from the Kingsborough Community College Mathematics Skills Laboratory
5. Stand and Deliver – VHS
6. A Beautiful Mind – DVD