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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 3^{rd} 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 |