Broward College Pre-Calculus Algebra & Trigonometry Course Outline

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1 Broward College Pre-Calculus Algebra & Trigonometry Course Outline LAST REVIEW: Academic Year NEXT REVIEW: Academic Year COMMON COURSE NUMBER: MAC 1147 INSTRUCTOR NAME: Freddy R. Matute, MBA CONTACT: TEXT BOOK:Algebraand Trigonometry by Swokowski& Cole, 12 th. Edition, 2005 CREDIT HOURS: 5 CONTACT HOURS BREAKDOWN: Lecture/Discussion 70 Contact Hours/Week 10H CALCULATOR: Scientific Calculator CATALOG COURSE DESCRIPTION: PREREQUISITE(S): MAC 1105 with a grade of B or better or permission of the Department Chair COREQUISITE(S): None This course is designed to satisfy the dual requirements of MAC 1114 and MAC 1140, thus preparing the student for the study of calculus. In this course the student will study various function families (e.g. polynomial, exponential, logarithmic, and trigonometric) from both analytic and graphical viewpoints, and will use them to model real-life situations. The student will be exposed to additional topics that will deepen their mathematical understanding, including systems, augmented matrices, sequences & series, and parametric functions. A graphing calculator may be required. Recommendation of the Mathematics Department or at least a grade of B in the prerequisite course is required. General Education Requirements Associate of Arts Degree (AA), meets Area(s): Area 5 General Education Requirements Associate in Science Degree (AS), meets Area(s): Area 4 General Education Requirements Associate in Applied Science Degree (AAS), meets Area(s): Area 4 UNIT TITLES 1. Polynomial, Rational, and other Algebraic Functions, with Their Properties and Graphs 2. Polynomial and Rational Equations 3. Exponential and Logarithmic Functions, with Their Properties and Graphs 4. Trigonometric Functions, with Their Properties and Graphs 5. Inverse Trigonometric Functions and Graphs 6. Trigonometric Identities and Equations 7. Triangle Trigonometry 8. Conic Sections 9. Polar -Defined Functions 10. Vectors and Parametric Equations 11. Sequences and Summations II. Units: Unit 1 Polynomial, Rational, and other Algebraic Functions, with Their Properties and Graphs

2 1.0 The students shall be able to recognize and graph polynomial, rational, and other algebraic functions, as well as write functions that satisfy specific characteristics. 1.1 Recognize and construct the graphs of polynomial functions. 1.2 Recognize and construct graphs of rational functions. 1.3 Define, graph, and write the equations of vertical, horizontal, and slant asymptotes. 1.4 Recognize and construct graphs of piecewise functions. 1.5 Create appropriate functions, from among the above-mentioned types, thatsatisfy specific given conditions. Unit 2 Polynomial and Rational Equations 2.0 The student shall be able to identify the zeros of polynomial functions, determine solutions to polynomial and rational equations, and formulate the partial fraction decomposition of rational expressions. 2.1 Determine the number of zeros of a polynomial and the multiplicity of each zero. 2.2 Read and apply the remainder theorem and the factor theorem. 2.3 Read and apply Descartes' rule of signs. 2.4 Read and apply the rational root theorem. 2.5 Perform synthetic division in applications involving polynomials. 2.6 Formulate and write the steps for the partial fraction decomposition of arational expression. Unit 3 Exponential and Logarithmic Functions, with Their Properties and Graphs 3.0 The student shall be able to recognize and graph exponential and logarithmic functions; solve exponential and logarithmic equations. 3.1 Read and apply the definitions and properties of exponents and logarithms. 3.2 Recognize and graph exponential and logarithmic functions. 3.3 Recognize and solve exponential and logarithmic equations with both exactand estimated (using a calculator) solutions with regard to populationgrowth, compound interest, carbon-14 dating, etc. 3.4 Read and solve applications of exponential and logarithmic functions such as exponential growth, decay such as population growth, compoundinterest, carbon-14 dating, etc and interpret results in context writing solutions in both exact and estimated (using a calculator) formats. Unit 4 Trigonometric Functions, with Their Properties and Graphs 4.0 The student shall be able to define, apply, and graph the trigonometric functions.

3 4.1 Solve problems involving degree and radian measure of angles as they relateto circular models in the physical world. 4.2 Define the sine, cosine, tangent, cotangent, secant, and cosecant functions of angles and of real numbers. 4.3 Know and apply the fundamental identities relating the functions. 4.4 Sketch the graphs of the six basic trigonometric functions and specify the intervals over which they increase or decrease. 4.5 Identify and use the domain, range, amplitude, period and phase shift to graph trigonometric functions. Unit 5 Inverse Trigonometric Functions and Graphs 5.0 The student shall be able to define, apply, and graph the inverse trigonometric functions. 5.1 Define and graph the inverse trigonometric functions. 5.2 Apply the definitions, methods of evaluating, and techniques of graphing the inverse trigonometric functions. Unit 6 Trigonometric Identities and Equations 6.0 The student shall be able to verify trigonometric identities and solve trigonometric equations. 6.1 Write the proof of trigonometric identities by using fundamental identities,addition-subtraction formulas, cofunction formulas, half-angle formulas, double-angle formulas, half-angle identities and product-to-sum and sum-to-product formulas. 6.2 Algebraically solve trigonometric equations, both with and without an interval specified. Unit 7 Triangle Trigonometry 7.0 The student shall be able to solve right and oblique triangles. 7.1 Solve a right triangle using the definitions of sine, cosine and tangent (along with cosecant, secant and cotangent). 7.2 Read and interpret a word problem and apply the Law of Sines and Law of Cosines. 7.3 Read and interpret real world problems such as navigational, angle ofelevation/depression, temperature, air flow, biorhythms, and time. Unit 8 Conic Sections 8.0 The student shall be able to graph conic sections.

4 8.1 Recognize, write the equations of, and graph conic sections such as parabolas, hyperbolas, ellipses, and circles. Unit 9 Polar -Defined Functions 9.0 The student shall be able to manipulate between polar and rectangular coordinates: 9.1 Plot points in polar coordinates on a polar plane. 9.2 Convert ordered pairs from rectangular to polar coordinates and vice-versa. 9.3 Convert equations in rectangular form to polar form and vice-versa. 9.4 Plot graphs of simple polar equations. Unit 10 Vectors and Parametric Equations 10.0 The students shall be able to manipulate 2-dimensional vectors; use vectors to solve applied problems; and work with parametric equations Interpret the various forms of vectors both geometrically and analytically as used in physics Perform operations of addition, subtraction, and scalar multiplication of vectors both geometrically and analytically Calculate the dot product of vectors, the scalar projection of a vector onto another vector, and the cosine of the angle between vectors Express vectors in trigonometric form Read, interpret, and solve applied problems using vectors as used inphysics. Unit 11 Sequences and Series, and the Binomial Theorem 11.0 The students shall be able to apply properties of sequences and series, and binomial theorem Perform operations on summations; determine sequences defined recursively; and determine the nthterm of an arithmetic or geometric sequence Compare the differences between arithmetic and geometric sequences 11.3 Determine the sum of the first n terms of an arithmetic or geometric sequence and also the sum of an infinite geometric series Apply the binomial theorem to expand powers of binomials; and write the kthterm of an indicated binomial expansion.

5 EVALUATION TESTS (70%): There will be three tests as follows: Test 1: Includes Chapters 2, 4 & 5 Test 2: Includes Chapters 6 & 7 Test 3: Includes Chapters & 11 Each test is graded on the basis of 80 points. These tests will be given in class. There are NO makeups on these tests. Students who miss a test are assigned a grade of zero for that test. Under very special circumstances when makeup tests are permitted it will be graded over 80% and it will not be the same given to the rest of the class. HOMEWORK (15%): There are exercises at the end of each of the sections, which you must satisfactorily complete as part of your course requirements. The main objective of these exercises is to provide you with "hand-on" conclusions for your analysis. QUIZZES (15%): There will be quizzes at the beginning of the class that will be graded by your instructor. The quizzes will be based on the material sent for homework. If you are late for the quiz or if you miss a class, you receive a grade of zero. FINAL GRADE Base on the average of your three tests including quizzes, homework and project: CLASS RULES AND REQUIREMENTS A B C D F Below NO cellphones are allowed in class. 2. NO food, drinks, or baseball caps are allowed in class. 3. If you miss a quiz, exam or paper due date you must bring a letter explaining the reason to the professor. The professor and the college director will sign the letter and it will be filed in your personal folder. A limit of three letters is allowed per year without further penalty. 4. Students who are absent more than two unexcused times per semester will receive a letter dropping for the course 5. Students who are absent more than three unexcused times per semester will receive an F for the course. 6. If a student is absent more than two classes consecutively they must present a letter explaining why and that letter will be filed in the student s folder. 7. Students who make-up quizzes, exams, mid-term or final exams will be allowed to take the exam over 80%. 8. Individual instructors will decide when make-up exams will be taken. 9. Students who cheat or plagiarize at any time will be subject to severe penalties up to, and excluding expulsion from the school. Dishonesty is not permitted; get used to it. 10. Read the sections of the textbook corresponding to the material covered in class, preferably before the class 11. Do all the homework problems assigned 12. Ask questions if you experience difficulty 13. Seek assistance if you need extra help

6 14. Consider forming study groups with your classmates 15. Consider visiting the Khan Academy site for extra help COURSE CALENDAR PRECALCULUS DATE TOPIC 8/29/2016 Introduction to class rules and policies; Read Sections 2.1, 2.3, 2.5 8/31/2016 Read Sections 2.6, 4.1, 4.2 and solve proposed exercises 9/2/2016 Read Sections 4.3, 4.4, 4.5 and solve proposed exercises 9/5/2016 Read Sections 5.1, 5.2, 5.3 and solve proposed exercises 9/7/2016 Read Sections 5.4, 5.5, 5.6 and solve proposed exercises 9/9/2016 Review Chapters 2, 4 & 5 9/12/2016 Test 1: Chapters 2, 4 & 5 9/14/2016 Read Sections 6.1, 6.2, 6.3 and solve proposed exercises 9/16/2016 Read Sections 6.4, 6.5, 6.6 and solve proposed exercises 9/19/2016 Read Sections 6.7, 7.1, 7.2 and solve proposed exercises 9/21/2016 Read Sections 7.3, 7.4, 7.5 and solve proposed exercises 9/23/2016 Read Sections 7.6, Review Chapters 6 & 7, (early class 4:00-7:00 pm ) Test 2: Chapter 6 & 7 (from 7:00-8:00 pm) 9/26/2016 Read Sections 8.1, 8.2 and solve proposed exercises 9/28/2016 Read Sections 8.3, 8.4, 8.5 and solve proposed exercises 9/30/2016 Read Sections 8.6, 11.1, 11.2 and solve proposed exercises 10/3/2016 Read Sections 11.3, 11.4, 11.5 and solve proposed exercises 10/5/2016 Read Sections 11.6, 10.1, 10.2 and solve proposed exercises 10/7/2016 Read Sections 10.3, 10.4, 10.5 and solve proposed exercises 10/10/2016 Review Chapters 8, 10 & 11 10/12/2016 Test 3: Chapter 8, 10 & 11

7 PROPOSED EXERCISES PRECALCULUS HOMEWORK Section Page Exercises

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