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# College Algebra and Trigonometry

 DESCRIPTION: An intermediate and advanced algebra course. Topics include quadratic equations, systems of linear equations, exponential and logarithmic functions; topics from trigonometry, including identities,equations and solutions of triangles. TEXT: Algebra with Trigonometry for College Students Jerome Kaufmann 3rd Edition CREDITS: 4 PREREQUISITES: MAT 1175/MA 175 Prepared by: Prof. H. Africk Prof. M. Harrow Spring 2008

A. Testing/ Assessment Guidelines:
The following exams should be scheduled:
1. A one-hour exam at the end of the First Quarter.
2. A one session exam at the end of the Second Quarter.
3. A one-hour exam at the end of the Third Quarter.
4. A one session Final Examination.

B. A scientific calculator is required.

Learning Outcomes
for
MAT 1275/ MA 275 College Algebra and Trigonometry

1. Students will be able to solve
• Linear and fractional equations.
• One-variable quadratic equations by factoring, completing the square, and the
quadratic formula.
• Radical and exponential equations.
• Systems of equations.

2. Students will be able to perform operations with and also simplify polynomial, rational,
radical, complex, exponential, and logarithmic expressions.

3. Students will be able to apply their knowledge of algebra and trigonometry to solve
verbal problems.

4. Students will be able to
• Solve problems involving right and oblique triangles.
• Perform calculations using sum, difference, double-angle, and half-angle formulas.
• Prove trigonometric identities.
• Solve trigonometric equations.

Attendance and Lateness Policy

The attendance and lateness policy is in accordance with the catalog (see page 30 of the catalog)
or at the instructor’s discretion.

New York City College of Technology Policy on Academic Integrity

Students and all others who work with information, ideas, texts, images, music, inventions, and
other intellectual property owe their audience and sources accuracy and honesty in using,
crediting, and citing sources. As a community of intellectual and professional workers, the
College recognizes its responsibility for providing instruction in information literacy and
academic integrity, offering models of good practice, and responding vigilantly and
appropriately to infractions of academic integrity. Accordingly, academic dishonesty is
prohibited in The City University of New York and at New York City College of Technology
and is punishable by penalties, including failing grades, suspension, and expulsion. The complete
text of the College policy on Academic Integrity may be found in the catalog.

 MAT 1275 College Algebra and Trigonometry Chapter Pages Homework I. Rational Expressions 2 sessions Adding and Subtracting Rational Expressions Chapter 4, Section 4.3 pages 168-175 p.175: 15-23, 27-39, 49-57 odd, 63 B. More on Rational Expressions and Complex Fractions Chapter 4, Section 4.4 pages 177-184 p.184: 1,5,9,11,13, 15,21, 37-49 odd C. Fractional Equations Chapter 4, Section 4.6 pages 191-195 p.197: 1-11, 21-31 odd D. More Fractional Equations and Applications Chapter 4, Section 4.7 pages 200-202 p.206: 1-11 odd II. Exponents and Radicals 3 1/2 sessions A. Using Integers as Exponents Chapter 5, Section 5.1 pages 214-218 p.219: 1,2,3,4, 15-25, 29-35, 43-69 odd B. Roots and Radicals Chapter 5, Section 5.2 pages 220-227 p.228: 1-15, 21-35, 39-59 odd C. Combining Radicals and Simplifying Radicals Containing Variables Chapter 5, Section 5.3 pages 229-233 (omit examples 3 and 5, 5e) p.233: 1-15, 21-35, 41-47, 65-71 odd D. Products and Quotients Involving Radicals Chapter 5, Section 5.4 pages 235-239 (omit example 2d) p.239: 1-9, 15-23, 31-35, 43-47, 53- 71 odd E. Equations Involving Radicals Chapter 5, Section 5.5 pages 241-244 (omit examples 5 and 6) p.244: 1-17 odd, 31-38 all F. The Merging of Exponents and Roots Chapter 5, Section 5.6 pages 245-249 p.249: 1-15, 31-35, 45-51, 59-73 odd First Examination 1/2 session III. Quadratic Equations 4 sessions A. Complex Numbers Chapter 6, Section 6.1 pages 261-268 p.268: 9-19, 27-37, 43-53, 61-79, 85- 91 odd B. Quadratic Equations Chapter 6, Section 6.2 pages 270-274 (omit example 2) p.277: 5-17, 37-45, 53,55,59,61 odd C. Completing the Square Chapter 6, Section 6.3 pages 278-281 p.281: 1-9, 15-23, 27-31 odd, 33-38 all, 39-51 odd D. The Quadratic Formula Chapter 6, Section 6.4 pages 282-289 (Derive the quadratic formula) p.289: 3-7, 11-23, 51-57 odd E. More Quadratic Equations and Applications Chapter 6, Section 6.5 pages 290-293 (omit example 4) p. 298: 1- 7, 21-29, 49,50,51,53 p. 309: 39,41 p. 149: 59,67 F. Graphing Parabolas Chapter 7, Section 7.4 pages 340-347 p.347: 1-7, 11-17, 23-27 odd G. More Parabolas Chapter 7, Section 7.5 pages 347-350 (omit example 5) p.354: 1-17 odd IV. Systems of Equations 4 sessions A. Systems of Two Linear Equations in Two Variables, The Substitution Method Chapter 11, Section 11.1 pages 516-522 (omit example 4 and problem 2) p.522: 11-15 odd, 19, 25-29 odd, 37,38,45,47,48 B. The Elimination-by-Addition Method Chapter 11, Section 11.2, pages 524-531 p.531: 1-9 odd, 15-27 odd p.64: 41,42,44,48 C. Systems of three Linear Equations in Three Variables Chapter 11, Section 11.3 pages 535-541 (omit examples 5, 6) HW p.542: 1-5, 11-17 odd D. Determinants and Cramer's Rule Chapter 12, Sections 12.3 and 12.4 pages 582-595 p.587: 21-35 odd, p.594: 11-29 odd E. System involving Nonlinear Equations Chapter 11, Section. 11.4 pages 544-547 (without graphing) p.551: 1-9 (part b) odd, 13 and 15 (part b), 39 Midterm Examination 1 session V. Basic Concepts of Trigonometry 5 sessions A. A Brief Review of Some Geometric Concepts Chapter 14, Section 14.1 pages 636-645 P.645: 27,30,33,35 B. Radian Measure Chapter 14, Section 14.2 pages 646-650 p.652: 1-23 odd C. Trigonometric Functions Chapter 14, Section 14.3 pages 654-663 p.663: 1-7, 17-21, 20,35, 39-47 odd D. Trigonometric Functions of Any Angle Chapter 14, Section 14.4 pages 665-674 p.674: 1-9, 13-21, 25-47, 51-63 odd E. Right Triangle Trigonometry Chapter 14, Section 14.5 pages 675-684 p.684: 1-11, 17-21, 27,28,30 F. Solving oblique Triangles - Law of Cosines Chapter 1.4, Section 14.6 pages 686-691 p.691: 1-15 odd G. Law of Sines Chapter 14, Section 14.7 pages 694-702 p.702: 1-11 odd, 15 VI. Trigonometric Identities and Equations 5 sessions A. Trigonometric Identities Chapter 16, Section 16.1 pages 746-753 p.753: 3-7, 13-17 odd, 25-33, 41-47, 51-55 odd B. Trigonometric Equations Chapter 16, Section 16.2 pages 755-759 p.759: 1-5, 6, 9-13, 17-29, 35-41, 53- 57, 65-69 odd Third Examination 1/2 session C. Sum and Difference Formula Chapter 16, Section 16.3 pages 760-768 (omit example 7) p.768: 1-19, 27-35 odd D. Multiple and Half-Angle Formulas Chapter 16, Section 16.4 pages 770-777 p.777: 1-3, 21-25, 29-35, 39-45, 49- 57 odd (Add problems like sin 2x = - 1/2, cos 3y = square root of (3) Tan A/2 = square root of ( 3) etc.) VII. Logarithmic Functions 2 sessions A. Exponents Chapter 10, Section 10.1 pages 467-473 (examples 1-5 only) p. 473 1-9, 13-25 odd B. Logarithms Chapter 10, Section 10.3 pages 485-492 p.492: 1-35, 41-65, 69-85 odd C. Logarithmic Functions Chapter 10, Section 10.4 pages 497-499 (omit natural logarithms) p.497: 1-19 all D. Exponential Equations Chapter 10, Section 10.5 pages 502-509 (examples 1, 11) p.509: 1-10, 43-47 E. Compound Interest 10.2 only ex 1, 10.5 ex 7 p.482: 3-9 odd, 25 p.509: 43-47 all Final Examination 1 session