advertisement

Honors Algebra II/Trigonometry Course Syllabus 2002 – 2003 Ms. Zimmermann Course Description This year-long Honors Algebra II/Trigonometry course will focus on developing algebraic skills through understanding in the following key ways: writing algebraic expressions to represent problems described in words, given as diagrams, or based on data; understanding the relationships among equations, graphs, and solutions to equations; and knowing how and when to use algebraic or approximate methods to solve a variety of equations and combinations of equations or inequalities. The second semester of the course will focus on trigonometric functions, graphs, and identities. Students who successfully complete this course will be prepared to take Honors Pre-Calculus/Calculus A. Course Goals The content objectives for this course are aligned with the content standards for Algebra II, Trigonometry, and Probability and Statistics, as outlined in the Mathematics Content Standards for California Public Schools. [You can find a full copy of the text on the Internet at http://www.cde.ca.gov/board/. From there, click on the Mathematics (pdf) link.] We also have goals for developing students’ learning and problem solving strategies. These goals are in line with our Expected Schoolwide Learning Results (“ESLRs”), focusing especially on critical thinking and listening, problem solving, and effective communication. The cooperative learning that is integral to the CPM curriculum also promotes our citizenship ESLR. On completion of Honors Algebra II/Trigonometry, students should be able to use problem solving strategies in conjunction with a knowledge of the inter-connections among algebra, geometry, functions, and trigonometry to analyze problems and formulate appropriate solutions and to extend current knowledge by making new connections; visualize, express, interpret, and graph functions and their inverses (when they exist); solve equations and systems of equations; and connect right triangle definitions with the trigonometric functions. Required Materials Textbook: Notebook: Journal: Calculator: Other: Optional: College Preparatory Mathematics 3, Volumes 1 (Units 1 – 6) and 2 (Units 7 – 13) PreCalculus, Fifth Edition (Houghton Mifflin Company, Publishers) a two-inch three-ring binder (or a math section in a larger binder) with dividers, binder paper, and graph paper a spiral notebook with lined paper a TI-82 or T-83 (recommended) graphing calculator pencils, erasers, and pens in contrasting colors 3 x 5 index cards in assorted colors (optional) Course Overview Note: The topic description for each unit is followed by a list of the content standards addressed in that unit. Unit 1 1ST SEMESTER Sharpening Pencils Exploring Functions Introduction to the Graphing Calculator; Function Investigation; Gathering and Organizing Data; Linear and Quadratic Functions; Lines of Best Fit; Subproblems (Algebra II Standards 2.0 – 3,0, 7.0 – 8.0, 10.0, 15.0, 24.0 – 25.0) 12 days Course Overview (continued) Unit 2 The Bouncing Ball: Sequences Arithmetic and Geometric Sequences; Discrete and Continuous Functions; Systems of Equations; Arithmetic and Geometric Series (from Unit 13) 11 days (Algebra II Standards 2.0 – 3.0, 7.0 – 10.0, 12.0, 15.0, 22.0 – 25.0) Unit 3 Fast Cars and Depreciation: Exponential Functions Exponential Functions; Negative and Non-Integer Exponents; Radicals; Depreciation and Appreciation 11 days (Algebra II Standards 2.0 – 4.0, 7.0 – 8.0, 10.0, 12.0, 15.0, 22.0, 24.0 – 25.0) Unit 4 The Gateway Arch: Parabolas and Other Parent Graphs Stretching, Compressing, and Moving Parent Graphs; Vertex of a Parabola; Non-Functions 14 days (Algebra II Standards 1.0 – 4.0, 7.0 – 10.0, 12.0, 15.0 – 17.0, 22.0, 24.0 – 25.0) Unit 5 The Toy Factory: Linear Systems and Matrices More Systems of Equations; System of Inequalities; Three Equations and Three Variables; Matrices; Finding the Equation of a Parabola 13 days (Algebra II Standards 1.0 – 4.0, 7.0 – 10.0, 12.0, 15.0 – 17.0, 22.0, 24.0 – 25.0) Unit 6 The Case of the Cooling Corpse: Logarithms and Other Inverses Inverse Functions; Logarithms 13 days (Algebra II Standards 1.0 – 4.0, 7.0 – 17.0, 22.0, 24.0 – 25.0) Unit 7 At the County Fair: Polynomials and General Systems Graphs of Polynomial Functions; Finding Intersections of Non-Linear Functions; Complex Numbers; Polynomial Long Division (from Unit 13) and Sum and Difference of Cubes 10 days (Algebra II Standards 1.0 – 13.0, 15.0 – 17.0, 22.0, 24.0 – 25.0) Unit 8 2ND SEMESTER The Circle of Terror: Circular Functions Sine and Cosine Functions and Their Graphs; Radian Measure; Tangent Function 15 days (Algebra II Standards 1.0 – 3.0, 5.0 – 13.0, 15.0 – 16.0, 22.0, 24.0 – 25.0; Trigonometry Standards 1.0 – 5.0, 9.0, 12.0, 19.0) Unit 9 The Search for Sunken Treasure: More Triangles and Trigonometry Laws of Sines and Cosines; Inverse Trigonometric Functions 11 days (Algebra II Standards 1.0 – 3.0, 5.0 – 16.0, 22.0, 24.0 – 25.0; Trigonometry Standards 1.0 – 5.0, 7.0 – 9.0, 12.0 –14.0, 19.0) Units 10 – 13 More Algebra II Topics Probability; Permutations and Combinations; the Binomial Theorem; Mathematical Induction; More Complex Numbers 7 days (Algebra II Standards 5.0 – 6.0, 18.0 – 21.0; Probability & Statistics Standards 1.0 – 3.0) Selected Topics from PreCalculus, Fifth Edition Trigonometric Functions; Circular Functions and Inverses; Graphs of Circular Function Sinusoids; Graphs of Tangent, Cotangent, Secant, and Cosecant Functions; Trigonometric Identities and Equations; Composition of Ordinates; Rotary Motion; Triangle Problems (Trigonometry Standards 1.0 – 19.0) 11 weeks