NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York

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1 NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York DEPARTMENT: Mathematics COURSE: MAT 1175/ MA 175 TITLE: DESCRIPTION TEXTS: Fundamentals of Mathematics Topics include linear and quadratic functins, intermediate algebra, plane geometry and trigonometry of the right triangle. 1) Intermediate. Martin-Gay, K.E. (2003) New York: Prentice Hall 2) Elementary College. Africk, H. (1997). Thomson Learning CREDITS: 4 PREREQUISITES: CUNY proficiency in math or MAT 0630/MA 630 or MAT 0650/MA 650 or MAT 0670/MA 670 Prepared by: Prof. M.E. Rojas Revised by: Prof. N. Benakli Prof. S. Han Prof. J. Liou-Mark Prof. A. Taraporevala Fall 2004 A. Testing Guidelines: The following exams should be scheduled: i. A one-hour exam at the end of the First Quarter ii. A one-session exam at the end of the Second Quarter iii. A one-hour exam at the end of the Third Quarter iv. A one-session Final Examination B. A scientific calculator with trigonometric functions is required.

2 Learning Outcomes for MAT 1175/ MA 175 Fundamentals of Mathematics 1. Students will be able to simplify exponents and use scientific notation. 2. Students will be able to Combine and factor polynomials. Combine and simplify rational and radical expressions. 3. Students will be able to solve Linear and quadratic equations. Systems of linear equations in two variables. Equations involving rational and radical expressions. 4. Students will be able to Identify lines and angles. Apply theorems and solve problems associated with parallel and perpendicular lines. Apply the SAS, SSS, ASA and AAS Theorems to congruent triangles. Apply the AA Theorem to similar triangles. Solve problems related to a parallelogram. Apply the Pythagorean Theorem. Solve special right triangles.

3 Mathematics Department Policy on Lateness/Absence A student may be absent during the semester without penalty for 10% of the class instructional sessions. Therefore, If the class meets: The allowable absence is: 1 time per week 2 absences per semester 2 times per week 3 absences per semester Students who have been excessively absent and failed the course at the end of the semester will receive either the WU grade if they have attended the course at least once. This includes students who stop attending without officially withdrawing from the course. the WN grade if they have never attended the course. In credit bearing courses, the WU and WN grades count as an F in the computation of the GPA. While WU and WN grades in non-credit developmental courses do not count in the GPA, the WU grade does count toward the limit of 2 attempts for a developmental course. The official Mathematics Department policy is that two latenesses (this includes arriving late or leaving early) is equivalent to one absence. Every withdrawal (official or unofficial) can affect a student s financial aid status, because withdrawal from a course will change the number of credits or equated credits that are counted toward financial aid. 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.

4 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: Note: The problems in the algebra text followed by a (G) require some basic geometry (area, perimeter, circumference, Pythagorean theorem) Session Section Homework (A-E) Exponents & Scientific Notation (pp ) 1.7 (A-C) More Work with Exponents & Scientific Notation (pp ) 3.1 (C-D) Graphing Linear Equations (pp ) 4.1 (A-B) Solving Systems of Linear Equations in Two Variables (pp ) 4.1 (C-D) Solving Systems of Linear Equations in Two Variables (pp ) 4.3 (A) Systems of Linear Equations & Problem Solving (Optional) (pp ) 5.1 (A-E) Adding & Subtracting Polynomials (pp ) 5.2 (A-D) Multiplying Polynomials (pp ) 5.3 (A-B) Dividing Polynomials (pp ) 5.4 (A-B) The Greatest Common Factor & Factoring by Grouping (pp ) p. 55: 1-9 odd, 15, 19, 23, odd, 37, 41, odd, 57, 59, odd, 87, odd, 103 p. 63: 3-15 odd, odd, odd, 69, odd p. 179: odd p. 269: 1-13 odd p. 269: odd, odd, odd p. 289: (Optional) 1, 3, 7, 9, 11, 13 p. 333: odd, odd, 45, 47, odd, odd (optional), 75 (optional), 77 (optional) p. 345: 1-11 odd, 19, 21, 29, 31, odd, 63, 65, 85 (G), 87 (G) p. 355: 1-5 odd, 7-10 all, odd, 47 (G), 49 (G) p. 363: 1-17 odd, odd

5 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: (A-B) Factoring Trinomials (pp ) 5.6 (A-B) Factoring by Special Products (pp ) 5.7 (A-B) Solving Equations by Factoring & Solving Problems (pp ) p. 373: 1-7 all odd, odd, odd, odd p. 381: 1-5 odd, odd, 63 (G), 64 (G) p. 393: 1-13 odd, odd, 51 (G), 53 (G), 61 (G) 10 First Examination (A-D) Multiplying & Dividing Rational Expression (pp ) 6.2 (A-C) Adding & Subtracting Rational Expressions (pp ) 2.1 (D) Linear Equations in One Variable (pp ) 6.4 (A) Solving Equations Containing Rational Expressions (pp ) 7.1 (A-B) Radical Expressions (pp ) 7.3 (A-C) Simplifying Radical Expressions (pp ) 7.4 (A-B) Adding, Subtracting, & Multiplying Radical Expressions (pp ) 7.5 (A-B) Rationalizing Numerators & Denominators of Radical Expression (pp ) 7.6 (A-B) Radical Equations & Problem Solving (pp ) p. 431: 3-9 odd, odd, odd, odd, 51 (G), 52 (G), p. 441: 5-9 odd, odd, odd, 11 (G), 12 (G) p. 88: odd, 47, 69, 70 p. 457: 1-7 odd, odd, odd p. 509: 7, 9, odd, 75 p. 525: 1, 7, 8, 13, 15, 25, 27, 31, 35, 37, 39, 45, 47, 48, 53, 55, 59, 60, 65, 66 p. 533: 1-6 all, 17, 21, 22, all, odd, 57-67odd, 45 (G), 46 (G), 85 (G) p. 543: 1, 3, 7, 11, 17, odd, 79 p. 555: 1-9 odd, 15, 17, odd, 28, all, odd (G), 59 (G), 61 (G)

6 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: (A) Solving Quadratic Equations (pp ) 8.2 (A,C) Solving Quadratic Equations by Using the Quadratic Formula (pp ) p. 595: 1-13 odd, 23 p. 605: 1-11 odd, 21, 23, 27, 33, 41, 51 (G), 52 (G), 58 (G) 18 Midterm Examination Lines: pp. 1-6: Ex. A-D 1.2 Angles pp. 8-13: Ex. A-C 1.3 Angle Classifications: pp.17-24: Ex. A-F 1.4 Parallel Lines: pp : Ex. A-E 1.5 Triangles: pp : Ex. A-F 2.1 The Congruence Statement: pp : Ex. A-C 2.2 The SAS Theorem: pp : Ex. A-C 2.3 The ASA and AAS Theorem: pp : Ex. A-D 2.5 Isosceles Triangles: pp : Ex. A-D 2.6 The SSS Theorem: pp : Ex. A, B 3.1 Parallelograms: pp : Ex. A-G 4.1 Proportions: pp : Ex. A, B 4.2 Similar Triangles: pp : Ex. A-H 4.4 Pythagorean Theorem: pp : Ex. A-D 4.5 Special Right Triangles: pp : Ex. A-D Page 7: 1-5 odd Page 14: 1-27 odd Page 26: 1-25 odd Page 42: 1-25 odd Page 55: 1-25 odd Page 71: 1-9 odd Page 81: 1-23 odd Page 93: 1-21 odd Page 111: 1-13 odd Page 118: 1-7 odd Page 139: 1-17 odd Page 161: 1-11 odd Page 173: 1-21 odd Page 192: 1-15 odd Page 207: 1-19 odd

7 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: 26 Third Examination The Trigonometric Functions: pp : Ex. A-G 5.2 Solution of Right Triangles: pp : Ex. A-G 6.1 The Area of a Rectangle and Square: pp : Ex. A-D 6.2 The Area of a Parallelogram: pp : Ex. A-E 6.3 The Area of a Triangle: pp : Ex. A-D 7.5 Circumference of a Circle: pp : Ex. A, D 7.6 Area of a Circle: pp. 342: Ex. A Page 223: 1-19 odd Page 234: 11-41odd Page 242: 1-5 odd Page 249: 1-17 odd Page 258: 1-13 odd Page 265: 1-23 odd Page 339: 1-5 odd, odd Page 348: 1-9 odd 29 Review for Final 30 Final Examination

8 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: Note: The problems in the algebra text followed by a (G) require some basic geometry (area, perimeter, circumference, Pythagorean theorem) Section 1.6 (A-E) Exponents & Scientific Notation (pp ) 1.7 (A-C) More Work with Exponents & Scientific Notation (pp ) 3.1 (C-D) Graphing Linear Equations (pp ) 4.1 (A-B) Solving Systems of Linear Equations in Two Variables (pp ) 4.1 (C-D) Solving Systems of Linear Equations in Two Variables (pp ) 4.3 (A) Systems of Linear Equations & Problem Solving (Optional) (pp ) 5.1 (A-E) Adding & Subtracting Polynomials (pp ) 5.2 (A-D) Multiplying Polynomials (pp ) 5.3 (A-B) Dividing Polynomials (pp ) 5.4 (A-B) The Greatest Common Factor & Factoring by Grouping (pp ) 5.5 (A-B) Factoring Trinomials (pp ) Homework p. 55: 1-9 odd, 15, 19, 23, odd, 37, 41, odd, 57,59, odd, 87, odd, 103 p. 63: 3-15 odd, odd, odd, 69, odd p. 179: odd p. 269: 1-13 odd p. 269: odd, odd, odd p. 289: (Optional) 1, 3, 7, 9, 11, 13 p. 333: odd, odd, 45, 47, odd, odd (optional), 75 (optional), 77 (optional) p. 345: 1-11 odd, 19, 21, 29, 31, odd, 63, 65, 85 (G), 87 (G) p. 355: 1-5 odd, 7-10 all, odd, 47 (G), 49 (G) p. 363: 1-17 odd, odd p. 373: 1-7 all, 9-13 odd, odd, odd, odd

9 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: Section 5.6 (A-B) Factoring by Special Products (pp ) 5.7 (A-B) Solving Equations by Factoring & Solving Problems (pp ) 6.1 (A-D) Multiplying & Dividing Rational Expression (pp ) 6.2 (A-C) Adding & Subtracting Rational Expressions (pp ) 2.1 (D) Linear Equations in One Variable (pp ) 6.4 (A) Solving Equations Containing Rational Expressions (pp ) 7.1 (A-B) Radical Expressions (pp ) 7.3 (A-C) Simplifying Radical Expressions (pp ) 7.4 (A-B) Adding, Subtracting, & Multiplying Radical Expressions (pp ) 7.5 (A-B) Rationalizing Numerators & Denominators of Radical Expression (pp ) 7.6 (A-B) Radical Equations & Problem Solving (pp ) Homework p. 381: 1-5 odd, odd, 63 (G), 64 (G) p. 393: 1-13 odd, odd, 51 (G), 53 (G), 61 (G) p. 431: 3-9 odd, odd, odd, odd, 51 (G), 52 (G), p. 441: 5-9 odd, odd, odd, 11 (G), 12 (G) p. 88: odd, 47, 69, 70 p. 457: 1-7 odd, odd, odd p. 509: 7, 9, odd, 75 p. 525: 1, 7, 8, 13, 15, 25, 27, 31, 35, 37, 39, 45, 47, 48, 53, 55, 59, 60, 65, 66 p. 533: 1-6 all, 17, 21, 22, all, odd, 57-67odd, 45 (G), 46 (G), 85 (G) p. 543: 1, 3, 7, 11, 17, odd, 79 p. 555: 1-9 odd, 15, 17, odd, 28, all, odd (G), 59 (G), 61 (G)

10 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: Section 8.1 (A) Solving Quadratic Equations (pp ) 8.2 (A,C) Solving Quadratic Equations by Using the Quadratic Formula (pp ) 1.1 Lines: pp. 1-6: Ex. A-D 1.2 Angles pp. 8-13: Ex. A-C 1.3 Angle Classifications: pp.17-24: Ex. A-F 1.4 Parallel Lines: pp : Ex. A-E 1.5 Triangles: pp : Ex. A-F 2.1 The Congruence Statement: pp : Ex. A-C 2.2 The SAS Theorem: pp : Ex. A-C 2.3 The ASA and AAS Theorem: pp : Ex. A-D 2.5 Isosceles Triangles: pp : Ex. A-D 2.6 The SSS Theorem: pp : Ex. A, B p. 595: 1-13 odd, 23 Homework p. 605: 1-11 odd, 21, 23, 27, 33, 41, 51 (G), 52 (G), 58 (G) Page 7: 1-5 odd Page 14: 1-27 odd Page 26: 1-25 odd Page 42: 1-25 odd Page 55: 1-25 odd Page 71: 1-9 odd Page 81: 1-23 odd Page 93: 1-21 odd Page 111: 1-13 odd Page 118: 1-7 odd

11 Text: Martin-Gay, K. E. (2003). Intermediate, 2 nd edition. Prentice-Hall: New York Africk, H. (1997). Elementary College. Thomson Learning: Section 3.1 Parallelograms: pp : Ex. A-G 4.1 Proportions: pp : Ex. A, B 4.2 Similar Triangles: pp : Ex. A-H 4.4 Pythagorean Theorem: pp : Ex. A-D 4.5 Special Right Triangles: pp : Ex. A-D 5.1 The Trigonometric Functions: pp : Ex. A-G 5.2 Solution of Right Triangles: pp : Ex. A-G 6.1 The Area of a Rectangle and Square: pp : Ex. A-D 6.2 The Area of a Parallelogram: pp : Ex. A-E 6.3 The Area of a Triangle: pp : Ex. A-D 7.5 Circumference of a Circle: pp : Ex. A, D 7.6 Area of a Circle: pp. 342: Ex. A Page 139: 1-17 odd Page 161: 1-11 odd Page 173: 1-21 odd Page 192: 1-15 odd Page 207: 1-19 odd Page 223: 1-19 odd Homework Page 234: 11-41odd Page 242: 1-5 odd Page 249: 1-17 odd Page 258: 1-13 odd Page 265: 1-23 odd Page 339: 1-5 odd, odd Page 348: 1-9 odd