MATH Precalculus (Revised August 2014)

Transcription

1 MATH 41 - Precalculus (Revised August 014) Course Description: Precalculus. Topics include elementary teory of functions and equations, analytic geometry, vectors, introductory logic, matematical induction, sequences and finite series. 4 credits. (4 lecture) Prerequisites: Mat 114: Pass wit a C or better. Mat 116: Pass wit a C or better. Course Intent: Tis course is intended primarily to prepare students for calculus. It can also be used for general matematics credit. Student Learning Outcomes 1. Te student will represent and manipulate algebraic and trigonometric functions and relations algebraically, grapically, and numerically, including partial fraction decomposition and finding zeroes of functions.. Te student will engage in algebraic and trigonometric problem solving and modeling.. Te student will syntesize algebraic and trigonometric facts and laws into proofs. 4. Te student will analyze and manipulate equations between various two dimensional systems suc as rectangular, polar, vector representations, conic systems and axes manipulations, as well as solving equations in tese systems. 5. Te student will investigate and perform summations and predictions on geometric, algebraic, and binomial sequences and series. Course Objectives: Upon completion of tis course, a student sould be able to: 1. Develop and use various problem-solving tecniques.. Recognize functions as ordered pairs.. Determine te grap of an algebraic equation or function. 4. Develop partial fraction decomposition. 5. Find te zeros of real functions 6. Utilize te six basic trigonometric functions. 7. Verify various trigonometric identities. 8. Apply te Law of sines and te Law of cosines for various types of situations. 9. Find te powers and roots of complex numbers using DeMoivre s Teorem. 10. Understand basic vectors ( dimensional).

2 11. Convert points in a rectangular coordinate system to polar coordinates. 1. Recognize algebraic formulas relating to circles, parabolas, ellipses, and yperbolas. 1. Use translation of axes, rotation of axes, and polar equations of conics. 14. Recognize te use of aritmetic and geometric sequences. 15. Use summation notation to represent a series. 16. Understand and use te Binomial teorem. 17. Understand matematical induction. 18. Understand te basic concepts of limits. Course Outline: Instructors may find it preferable to cover te course topics in te order listed below. However, te instructor may coose to organize topics in any order, but all material must be covered. APPROXIMATE TIME TEXT REFERENCE Unit I Factoring wit negative rational exponents Section: Addendum 1 Difference Quotient Section: Addendum Partial Fractions Section: 7. ( ours) Review Topics include te following: Graps and graping utilities, lines in te plane, slope, functions, polynomial functions of iger degree, syntetic division, real zeros of polynomial functions, and te intermediate value teorem. Required topics are: Factoring wit negative rational exponents, finding te difference quotient, and partial fraction decomposition. Unit II Trigonometry (review) Sections: {4., } Analytic Trigonometry (review) Sections: {5.1 5.} Analytic Trigonometry Sections: 5.4, 5.5 {7 ours} (4 ours) Tis unit contains Trigonometric Functions, te unit circle, graps of te trigonometric functions, inverse trigonometric functions, verifying identities, sum and difference formulas, double angle and alf-angle formulas, sum-to-product and product-to-sum formulas, and solving trigonometric equations. Unit III Applications of Trigonometry Sections: Capter 6 (1 ours) Tis unit includes Law of Sines, Law of Cosines, Polar coordinates, graps of Polar equations, DeMoivre s Teorem, vectors, and te dot product. Unit IV Conic Sections and Analytic Geometry Sections: Capter 9 (15 ours) Topics include te ellipse, te yperbola, te parabola, rotation of axes, parametric equations, and conic sections in polar coordinates.

3 Unit V Sequences, Induction, and Probability Sections: (14 ours) Tis unit contains Sequences and summation notation, aritmetic sequences, Geometric Sequences and Series, Matematical Induction, and Te Binomial Teorem. Unit VI Introduction to Calculus Sections: (10 ours) Tis unit contains an introduction to limits using tables and properties, continuity, and an introduction to derivatives. Textbook: Precalculus, Robert Blitzer, 5e, 01, Pearson Prentice Hall Suggested Metods: It is elpful to begin eac class wit questions concerning te material discussed and te assigned omework problems. In presenting new material, it is suggested tat an explanation be followed by students working examples in class. Students sould be encouraged to work te review exercises at te end of eac capter. Also, tey sould be encouraged to visit te Academic Support Center at teir respective colleges Departmental Policies: 1. Eac instructor must cover all course topics by te end of te semester. Te final exam is compreensive and questions on it can deal wit any of te course objectives.. Eac student sould receive a copy of te instructor s student syllabus for te course during te first week of class. Te syllabus sould also be available online.. A minimum of tree in class tests and a compreensive final examination must be given. Te final examination must be taken by all students. 4. All major tests sould be announced at least one week or te equivalent in advance. 5. Te final exam must count between 5 percent and 40 percent of te final grade. 6. Te final course average will be used in te usual manner (A = ; B = 80-89; C = 70-79; D = 60-69; F = below 60). 7. An open book or a take ome major test may be given at te discretion of te instructor. 8. Any review seet sould be compreensive and te student sould not feel tat classroom notes, omework, and test may be ignored in favor of te review seet for any examination.

4 Resource Materials: Any student enrolled in Mat 41 at HCCS as access to te Academic Support Center were tey may get additional elp in understanding te teory or improving teir skill. Te Center is staffed wit matematics faculty and student assistants, and offers tutorial elp. A Capter Tests preparation video CD comes wit te text. A Student s Solution Manual and MyMatLab are also available. Americans Wit Disabilities Act (ADA): Any student wit a documented disability (e.g. pysical, learning, psyciatric, vision, earing, etc.) wo needs to arrange accommodations must contact te Disability Services Office at teir respective college at te beginning of eac semester. Faculty are autorized to provide only te accommodations requested by te Disability Support Services Office. Academic Honesty: At Houston Community College, academic integrity is expected of all its members and stakeolders. Academic disonesty includes, but is not limited to, te willful attempt to misrepresent one s work, ceat, plagiarize, or impede oter students scolastic progress. Scolastic disonesty is treated wit te utmost seriousness by te instructor and te College. Please refer to te Student Handbook for specific information related to professional conduct and scolastic disonesty.

5 Addendum 1 Factoring wit negative rational exponents p. 67 Example 1 Exercises: p. 69 #9 101 Suggested supplementary problems Factor: x 4x 1 4x Factor: x 4 x 5x 4 5. Factor: 4x 5 4x 7x Factor: 5x x 1 65x x Factor: 87x x 5 47x x 5

6 Addendum Difference Quotient Te difference quotient is basically te slope formula but used wit nonlinear functions. Since a nonlinear function does not ave a slope in te traditional sense, we cannot refer to tis as te slope of te curve. Te formula for te difference quotient is: f x f x Example 1 Letf x x 4, find te difference quotient. Solution: f x x x x 4 f x f x x x x x x x x f x f x x x x 4 4 remember to square te binomial be careful wen subtracting Exercises Find te difference quotient for eac function. f x x f x x x 4 g x x. f x x x 4. g x x 4x 8 5.