This course will start with a review of basic algebra skills such as factoring,
solving linear equations and ... The access code is provided with the purchase of
a ... online access only and additional information can be found at Educo website
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LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING AND COMPUTER SCIENCE MAT 115 Syllabus: College Algebra and Trigonometry Catalog Description: 4 hrs Lecture, 3 Credits Prerequisite: MAT 096 or Placement This course will start with a review of basic algebra skills such as factoring, solving linear equations and inequalities and proceed to a study of polynomial, exponential, logarithmic, and trigonometric functions. These functions will be used in applications involving simple mathematical modeling where students will engage in inquiry activities aimed at improving critical-thinking skills. A graphing calculator is recommended. Instructional Objectives During this course, the instructor expects to: 1. To reinforce student's basic algebraic skills. 2. To introduce students to the concept of a function and its application in modeling. 3. To develop students’ problem-solving and critical thinking skills through inquiry learning and the use of technological tools. 4. To introduce students to the concepts and properties of quadratic, exponential, and logarithmic functions. 5. To introduce students to basic trigonometry. Performance Objectives: At the conclusion of this course, students will be able to: 1. To perform operations on polynomials, rational expressions, and radicals; to solve systems of linear equations graphically and algebraically. 2. To understand the concept of a function and its role in mathematical modeling of real-life problems. 3. To interpret and solve elementary word problems using technological tools. 4. To solve problems involving quadratic, exponential and logarithmic functions. 5. To parse and solve right-angle trigonometry problems.
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Textbook: College Algebra and Trigonometry by Man M. Sharma: EDUCO International, Inc: Second Edition Inquiry Problem Solving Competency: Students enrolled in MAT115 will be expected to deposit at least one inquiry learning project (see below) in their ePortfolios. Suitable examples of such projects can be found in the PQL Sampler or at the MEC website. Grading: Three (3) Tests ------------------------------------- 45% Three (3) Inquiry Learning Projects ------------ 15% Quizzes & Homework (online)------------------ 10% Final (Departmental)------------------------------- 30% Online access is required for quizzes, homework and tutorial. The access code is provided with the purchase of a new textbook along with instruction about online registration. Purchase of online access only and additional information can be found at the Educo website, www.educosoft.com Academic Integrity: This class will be conducted in compliance with LaGuardia Community College’s academic integrity policy. Sanctions for Academic Integrity Violations: Sanctions or penalties for violations of academic integrity are imposed by the faculty member teaching the course upon discovery of a violation. All cases of academic dishonesty are filed with the College Adjudicator, who maintains a record of academic integrity violations. The occurrence of a second or third offense of academic dishonesty may involve the imposition of a disciplinary sanction in addition to the academic sanction imposed by the instructor. Sanctions for violations of academic integrity include, but are not limited to, the following: failure of an exam, a grade of F on an essay or research paper, failure of a course project, failure of the course, suspension from the College or dismissal from the College IN Grade: The Incomplete grade may be awarded to students who have not completed all of the required course work but for whom there is a reasonable expectation of satisfactory completion. A student who is otherwise in good standing in a course – defined as complying with the college attendance policy and maintaining a passing average – but who has not completed at most two major assignments or examinations by the end of the course may request an IN grade. To be eligible a student must provide, before the instructor submits grades for the course, a documented reason, satisfactory to the instructor, for not having completed the assignments on time. (See catalog for more details). Attendance Policy: The maximum number of unexcused absences allowed is 15% of the total class meetings (about 7 hours). Unexcused absences beyond this maximum will result in a grade of WU or F. Department Contact Information: Main Office: E-223 Tel#: (718) 482-5710 Tutoring: Mathematics Learning Center, M-B44 2
Lesson
Topic
Section
1
Absolute value; solving absolute value equations and inequalities; comparing v-graphs and parabolas, i.e. y=abs(x) and y=x^2 Graphing linear equations; pointplotting; quadrants; intercepts Slope: parallel and perpendicular lines; graphs from a chart of values and using slope and yintercept Equation of a line: slopeintercept form; point-slope form, vertical and horizontal lines; parallel/perpendicular lines and conditions on slope Functions and relations; definitions; tabular functions; graphs; vertical line test; counterexamples; piecewise functions Functions: notation; domain and range; restricted values Difference quotient and average rate of change of a function Linear modeling: proportions and beyond—linear growth; supply and demand problems
1.3
Page 73-88
2.1
Page 95 -102
2.2
Page 106-120
Page 102-106: 1-15;17-27; 31-41; 43-53;59-73; 75-85 Page 112-114: 1-71
2.3
Page 106-120
Page 120-122: 1-71
2.4
Page 122-129
Page 129-131 1-31
2.4
Page 122-129
Page 129-131: 33-61
2 3
4
5
6 7 8,9
10
11
12
Inquiry Learning Project 1(addresses Inquiry Problem Solving Competency/writing ability) Solving systems of linear equations in two variables: graphical method; 3 solution types and graphical equivalents Solving systems of linear equations in two variables: algebraic method; e.g., addition/elimination or substitution
Page
2.4
Suggested Exercises-odd numbers Page 88-90: 23-45; 85-107; 109-131
Departmental Worksheet Departmental Worksheet
Project (linear modeling; e.g., comparison of different cell phone contracts, projected costs, best buy) 3.1
Page 145-153
Page 154-155: 1-7
3.1
Page 145-153
Page 154-155: 9-15
3
13
14 15
16 17
18 19 20
21
22 23
24
25
26 27 28 29
Solving systems of linear equations in two variables: application/word problems Review Test 1 Operations (+, -, x, ) on polynomials and special products; long division/synthetic division Quadratic functions; factoring trinomials of the form ax^2+bx+c Solving quadratic equations by factoring; zero property Solution by completing the square; square root property Solution by using the quadratic formula: formula derivation; solving applied problems Graphing quadratic functions: vertex and intercepts; condition for opening upward/downward Modeling involving quadratic functions; optimization Discussion of Inquiry Learning Project 2(addresses Inquiry Problem Solving Competency/writing ability)
3.1
Page 145-153
Page 154-155: 17-21
4.1
Page 205-215
4.3
Page 225-229
Instructor’s Material Instructor’s Test Page 215-217:29-39;41-49;65-81; 91-139 Page 230: 1-45
4.4
Page 232 – 247
Page 248-250: 29 - 277
5.1
Page 259-263
Page 263:1-23; 27-45; 47-63; 65-73
5.2
Page 264-271
5.3
Page 273-279
Page 272-273-273:1-21; 33-45; 73-103 Page 279-280:11-25;27-47
5.4
Page 281-288
Page 288: 1-39
5.7
Page 311-314
Page 315-317: 1-21
6.1 6.2
Page 327-335 Page 338-351
Project (e.g., quadratic growth of salary with time, beyond the vertex: consequences of retirement—fixed income; ageism resulting in salary decline) Page 336-337:1-27; 33-45;75-93 Page 352-353:33-57; 61-101
Rational expressions; arithmetic with rational expressions; simplification; rational functions (domain/excluded values) Solving equations containing rational expressions; application (word) problems Rational exponents; rational roots Solving equations with radicals Review Test 2
6.3
Page 354-357
Page 358:1-29; 47-57
7.4
Page 403-408
Page 408-409:1-43
7.6
Page 414-418
Page 419: 1-51 Instructor’s Material Instructor’s Test
4
30
Inverse functions: one-to-one function; horizontal line rule condition; finding inverses (linear and suitable odd power functions; rational functions where numerator and denominator are linear) 31 Exponential functions and their graphs; positive/negative exponents and graphical consequences 32 Modeling with exponential functions: calibrating exponential functions given (two-point) data 33 Meaning of the logarithm; (inverse) relation to exponential function 34 Properties of logarithms: reducing and expanding logarithmic expressions 35 Solving exponential equations: same and different bases 36 Solving logarithmic equations 37,38 Modeling with exponential functions: compound interest; growth and decay 39 Discussion of Inquiry Learning Project 3(addresses Inquiry Problem Solving Competency/writing ability) 40 Review 41 Test 3 42 Angles: unit circle and measurement (degrees/radians) 43 Trigonometric functions: definition of six basic ratios; 4545-90 and 30-60-90 right triangles; evaluation; Pythagorean identities 44 Right-triangle trigonometry: solving triangles 45
Right-triangle trigonometry: applications (angle of elevation and angle of depression)
8.1
Page 427-435
Page 435-436: 1-49
8.2
Page 437-441
Page 441-442: 1-31
Departmental Worksheet
8.3
Page 442-447
Page 447-448: 1-35
8.4
Page 448-452
Page 452-453: 1-29
8.5
Page 453-456
Page 456: 1-47
8.6 8.7
Page 457-460 Page 462-465
Page 461:1-67 Page 465: 1-27
Project (e.g., exponential growth as a function of time, projected values, maximum domain of the model)
9.1
Page 477-483
Instructor’s Material Instructor’s Test Page 484:1-27 Sections: A
9.1
Page 477-483
Page 484:29-53 Sections: B
9.2
Page 486-503
Page 504-505:1-13; 17-29
9.2
Page 486-503
Page 504-505: 39-47; 51-69
5
46,47 Graphs of the sine and cosine functions: amplitude and period and phase shift 48 Review for Final Exam Cumulative Departmental Final
10.1
Page 513-531
Page 532-533: 6 -19; 43 - 47
Departmental Review Given during Finals Week
Revised 9/5/2015
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