I. Course Description: Pre-calculus is a college-preparatory course intended for highly motivated students who have successfully completed Algebra I, Geometry, and Algebra II with Trigonometry. A variety of topics are reviewed and expanded upon, including trigonometry, complex numbers, function, graphing and logarithms. Many topics are combined to explore new areas such as polar coordinates, polar graphing, conic sections, vectors, matrices, polynomial theory and induction proofs. Graphing is studied in-depth to determine properties of functions. Many other areas are covered to give the college-bound student a basis for calculus. II. Course Objectives: Course objectives can be found at the Alabama Learning Exchange. http://alex.state.al.us/standardall.php?subject=ma2013&ccode=pre&summary=3 Upon completion of this course a student should be able to: Demonstrate a theoretical, operational, and graphic understanding of functions including polynomial, rational, exponential, logarithmic, and trigonometric. Apply algebraic skills to the formulation and solution of real world application problems. Represent equations and systems of equations graphically, and to integrate the algebraic and graphic interpretation of these concepts. Advance readily to higher level math classes Calculus. III. Classroom Expectations: A good classroom citizen does not inhibit the learning of others, actively engages in the learning process, and respects and follows the rules. In order to create a positive classroom environment, the following classroom rules that are (1) reasonable and necessary, (2) clear and understandable, (3) consistent with instructional goals, and (4) consistent with all school rules and policies will be followed by teacher and students. 1. Be polite and respect your classmates, your teacher, and your school by using appropriate language, by paying attention when others are speaking, by raising your hand to speak during class, and by helping your fellow students to learn and be successful we are all on this journey together. 2. Come to class on time with all materials and be in your assigned seat ready to work when the bell rings pencils are preferred by math teachers so please sharpen before the tardy bell rings. 3. Complete all assignments on time and to the best of your own abilities and show your work to receive credit remember that a good teacher serves as an expert guide, not a cart, as we explore important mathematical concepts. Page 1
Accommodations: Requests for accommodations for this course or any school event are welcomed from students and parents. Concerning laptop utilization: 1. Student laptops should not be hard wired to the network or have print capabilities. 2. Neither the teacher, nor the school is responsible for broken, stolen, or lost laptops or handheld devices. 3. Laptops and other electronic devices will be used at the individual discretion of the teacher for legitimate educational purposes only. IV. Grading Policy: Test grades will account for 70% of the 9-weeks grade, with the remaining 30% being determined by quiz/daily grades. The grading scale is as follows: A (90-100), B (80-89), C (70-79), D (65-69), and F (below 65). Grades will be a reflection of mastery of the standards. Make sure all absences are excused as class work can be made up and graded for excused absences only. The Final Exam counts for 1/5 of final grade. V. Make-up Test Policy: To be arranged by the student on the first day back to class. Makeup tests will be given before school in the computer lab next to the guidance office. VI. VII. Text and Other Required Reading: Materials and Supplies Needed: Blitzer: Precalculus, 4e Pencils, loose leaf paper, graph paper, and a scientific calculator. A graphing calculator is not required but I highly recommend a TI84 (this is the calculator used in the Calculus class and on AP exams). Each exam will have a calculator and non-calculator section. VIII. Unit Plans: We will cover eight units during our study of precalculus, after an initial review of important algebra topics. Units 1-4: Semester 1, Units 5-9: Semester 2. * The syllabus serves as a guide for both the teacher and student; however, during the term it may become necessary to make additions, deletions, or substitutions. Adequate notice will be provided to students of any necessary changes. Page 2
Units Essential Questions Academic Vocabulary What content is involved in the study of precalculus? Unit 1 Getting off to a good start Review the fundamental concepts of algebra Unit 2 Functions and Graphs Unit 3 Trigonometric Functions Unit 4 Analytic Trigonometry and Applications Unit 5 Polar Coordinates, Complex numbers, Vectors Do we have the necessary algebra prerequisite skills to begin our study of precalculus topics? How are zeroes and end behavior of polynomial functions related to the degree of the polynomial? How are logarithmic and exponential functions used to model real world problems? What type of real-world problems are modeled using trigonometry? How are graphic representations of trig functions useful in understanding real-life phenomena? How are algebraic and geometric concepts related to trigonometric identities and formulas? How is trigonometry used to solve real world problems involving measure? How are polar and rectangular graphing related? How are vectors used to solve real world problems involving motion? Algebraic Expressions Mathematical Models Sets Intersection/Union Real Numbers Exponents Scientific Notation Radicals/Rational Exponents Polynomials Inequalities Absolute Value Linear functions Quadratic functions Exponential functions Logarithmic functions Inverse functions Maximum, Minimum Roots/Zeroes Even/Odd functions Asymptotes Growth/Decay Models Unit Circle Standard Position Trigonometric Function Amplitude Period Phase Shift Radian/Degree Measure Inverse functions Domains/Ranges Identities - Tautologies Trigonometric Equations Angles of Elevation Angles of Depression Law of Sines Law of Cosines Herron s formula Polar coordinates Cartesian coordinates Complex number Polar form Vector Cross Product Page 3
Unit 6 Systems of Equations, Matrices Unit 7 Conic Sections, Parametric Equations Unit 8 Sequences, Probability Unit 9 Foundations for Calculus How can systems of equations be used to model real world problems? What does it mean to solve a system of equations algebraically and graphically? How can we use matrices to solve systems of equations? How are multiple representations of conic sections related and used to model real world situations? How are parametric equations and vectors used to solve real world problems? How are recursive relationships used to model and investigate long term behavior? How are median fit and least squares regression used to develop mathematical models? How is the concept of a limit applied in mathematics to function discontinuities? Why are limits important in the study of end behavior? Dot Product Linear Systems Non-linear systems Substitution Elimination Matrices Inconsistent/Dependent Matrix Inverses Determinants Matrix Operations Conic Section Parabola Hyperbola Ellipse Parametric equations three-dimensional coordinate systems Geometric Sequence Arithmetic Sequence Infinite sequence Convergence Sigma Notation Correlation Regression lines Residuals Outliers Limits Continuity Rate of Change Derivitives Page 4
Dear Parent/Guardian, I look forward to having a great year! I feel fortunate to have your son/daughter in my class this semester and hope that you will contact me should you have any concerns about the progress of your son/daughter or any aspect of the instruction. With your son/daughter, please read the attached policies, then sign and date this signature page and have your son/daughter return this form. Please provide a current email address and phone number at which I can contact you should the need arise. Please contact me at school with any concerns. Thank you, Bucky Garner Parent/Guardian Name (Print) Date Parent/Guardian Signature Date Email address (w) (h) Phone number (w) (h) (c) Page 5