School District of the Chathams

Transcription

1 School District of the Chathams Curriculum Profile Program of Study: High School Mathematics Curriculum Course Title: Honors Precalculus Grade Level: Grade 11 I. Course Description Honors Precalculus is designed to cover mathematical concepts deemed important and necessary as stipulated by the New Jersey Core Curriculum Content Standards for high school students. The curriculum is designed to provide opportunities for students to engage in meaningful, substantial and appropriate mathematical content that develops an understanding and command of mathematics and fosters affective and intellectual growth. In particular, the course develops the mathematical prerequisites for advancing to study the calculus. II. Course Objectives and Alignment with NJCCCS Objectives as noted in the unit plans from NJCCS Standards 4.1, 4.2, 4.3, 4.4, and 4.5. III. Topical Outline Unit 1 Review of Relations and Functions Unit 2 Exponential and Logarithmic Functions

2 Unit 3 Trigonometric Functions Unit 4 Polar Coordinates Unit 5 Vectors Unit 6 Conics Unit 7 Limits and a Preview of Calculus Unit 8 Sequences Unit 9 Systems of Equations Unit 10 Data Analysis IV. Skills Function Analysis Polynomials, Conics, Absolute Value, Logarithms, Exponentials, Power Functions, Rational Functions, Trigonometric Functions Graphing Finding Local Maxima, Minima Finding x-intercepts and y-intercepts Symmetry, Even/Odd, Roots, End Behavior Finding Inverses Transformations Asymptotes, Holes Solving Equalities and Inequalities Exponential and Logarithmic Functions Logarithmic and Exponentials Functions Laws of Logarithms and Exponents

3 Solving Log and Exponential Equations Trigonometric Functions Conversion between DMS and Radians The Six Trigonometric Functions Transformations and Analysis of Amplitude, Period, Frequency Inverse Trigonometric Functions Pythagorean Identities and Trigonometric Formulas (Sum, Difference, Double-Angle, Half-Angle, etc.) Right Triangles, Law of Sines, Law of Cosines Polar Coordinates Conversion between Rectangular and Polar Coordinates and Equations Graphing Polar Equations Products and Quotients of Polar Complex Numbers DeMoivre s Theorem, Euler s Theorem, Finding Complex Roots Vectors 2D-Vectors Geometric Vectors Properties of Vectors Unit Vectors, Position Vectors, Parallel and Orthogonal Vectors, Projections Scalar, Dot and Cross Products 3D Vectors, Direction Angles

4 Conics Geometric and Algebraic Interpretations Properties of Parabolas, Ellipses, Hyperbolas Identifying Conics Polar Equations for Conics Parametric Equations Projectile Motion Limits, Preview of Calculus Finding One-Sided and Two-Sided Limits Continuity Tangent to a Curve, Derivatives Area under a Curve, Integrals Sequences Sequence, Term, Recursive Sequence, Sigma Notation Arithmetic Sequence and Series Geometric Sequence and Series Direct, Indirect and Induction Proof Techniques Binomial Theorem Systems of Equations Graphing, Substitution, Elimination and Matrix Solution Methods for Linear and Nonlinear Systems

5 Partial Fraction Decomposition Linear Programming Data Analysis One-Variable Statistics, Central Tendency Spread, Outliers, Histograms Scatterplots, Regression, Curve Fitting Using Excel and Graphing Calculators for Data Analysis V. Methods of Instruction and Sample Activities Large Group Instruction Cooperative Peer Group Individual and Group Projects Calculator and Computer Applications Individualized Instruction Differentiated Instruction VI. Instructional Materials Precalculus, Sixth Edition, by Michael Sullivan, Prentice Hall. Supplementary Materials Manipulatives (conic sections, vertical protractors, etc.) Calculators

6 Computers with Excel, Geometer s Sketchpad Teacher Generated Materials VII. Student Outcomes and Methods of Assessment A. Class Participation and Preparation B. Assessments: Written, Speaking, Projects, Demonstrations C. Timeliness and Quality of Homework