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NORTHVIEW HIGH SCHOOL SYLLABUS PreCalculus Semester Two Tina Ely [email protected] Room #1149 elymathpage.wordpress.com Matt Coty [email protected] Room #1152 Math CATS Hours: Tuesdays & Thursdays, 2:45-3:45 TEXTS: Foley, Gregory, Demana, Franklin, D., Waits, Bert K., and Kennedy, Daniel. Precalculus: Graphical, Numerical, Algebraic. Pearson, Addison Wesley, 2007, seventh edition. COURSE OVERVIEW: Precalculus is the preparation for calculus. The study of the topics, concepts, and procedures of precalculus deepens students’ understanding of algebra and extends their ability to apply algebra concepts and procedures at higher conceptual levels, as a tool, and in the study of other subjects. The theory and applications of trigonometry and functions are developed in depth. New mathematical tools, such as vectors, matrices, and polar coordinates, are introduced, with an eye toward modeling and solving real-world problems. REQUIREMENTS: Supplies needed 3-ring binder (Assignments should be done on loose leaf paper.) Paper and pencil Graphing calculator (TI-83 or TI-84 is recommended) Practice Students will have an assignment every class period. A schedule of assignments and tests will be provided. Students are responsible for assignments regardless of attendance. Each problem will be corrected, re-done when necessary, and kept in his/her notebook. Students should always try to do each problem on every assignment and to show all steps he/she took to get the answer. Keeping up with assignments is very important for having a successful year. GRADING POLICY: Your student will have a test or a quiz almost every week. You may refer to your student’s planner and see the school-wide grading systems for assigning letter and semester grades. This course will have a cumulative exam at the end of each semester. There are no retakes allowed for this course. ASSESSMENTS: Quizzes (1-2 per chapter): 100 points each Chapter Tests (4 or 5 per semester): 200 points each Exam (1 per semester) 20% of semester grade SCHEDULE: Chapter P P.1 P.2 P.3 P.4 P.5 P.6 P.7 Real Numbers Cartesian Coordinate Systems Linear Equations and Inequalities Lines in the Plane Solving Equations Graphically, Numerically, and Algebraically Complex Numbers Solving Inequalities Algebraically Chapter 1 1.1 Modeling and Equation Solving 1.2 Functions and Their Properties 1.3 Twelve Basic Functions 1.4 Building Functions from Functions 1.5 Parametric Relations and Inverses 1.6 Graphical Transformations 1.7 Modeling With Functions Chapter 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Linear and Quadratic Functions and Modeling Power Functions with Modeling Polynomial Functions of Higher Degree with Modeling Real Zeroes of Polynomial Functions Complex Zeroes and the Fundamental Theorem of Algebra Graphs of Rational Functions Solving Equations in One Variable Solving Inequalities in One Variable Chapter 3 3.1 3.2 3.3 3.4 3.5 3.6 Exponential and Logistic Functions Exponential and Logistic Modeling Logarithmic Functions and Their Graphs Properties of Logarithmic Functions Equation Solving and Modeling Mathematics of Finance Chapter 4 4.1 Angles and Their Measures 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Trigonometric Functions of Acute Angles Trigonometry Extended: The Circular Function Graphs of Sine and Cosine: Sinusoids Graphs of Tangent, Cotangent, Secant, and Cosecant Graphs of Composite Trigonometric Functions Inverse Trigonometric Functions Solving Problems with Trigonometry Review for the first semester exam and Exam Chapter 5 5.1 Fundamental Identities 5.2 Proving Trigonometric Identities 5.3 Sum and Difference Identities 5.4 Multiple Angle Identities 5.5 The Law of Sines 5.6 The Law of Cosines Chapter 6 6.1 Vectors in the Plane 6.2 Dot Products of Vectors 6.3 Parametric Equations and Motion 6.4 Polar Coordinates 6.5 Graphs of Polar Equations Chapter 7 7.1 Solving Systems of Two Equations 7.2 Matrix Algebra 7.3 Multivariate Linear Systems and Row Operations 7.4 Partial Fractions 7.5 Systems of Inequalities in Two Variables Chapter 8 8.1 Conic Sections and Parabolas 8.2 Ellipses 8.3 Hyperbolas Chapter 9 9.1 Basic Combinatorics 9.2 The Binomial Theorem 9.3 Probability Chapter 10 10.1 Limits and Motion: The Tangent Problem 10.2 Limits and Motion: The Area Problem 10.3 More on Limits