Pre-Calculus Syllabus

Functions (2.1) The Graph of a Function (2.2) Properties of Functions (2.3) Linear Functions and Modeling (2.4) Library of Functions; Piecewise-defined Functions (2.5) Graphing Techniques: Transformations (2.6) Mathematical Models: Constructing Functions (2.7) Activities to Support Instruction: Symmetry Activity Use of TI-84+ to analyze collected data Data Analysis and Linear Modeling with Red Sox Data, Superbowl Data, Olympic Data Quadratic Modeling with Statue of Liberty problem Creative Function Project
Composite Functions (4.1) One-to-One Functions; Inverse Functions (4.2) Exponential Functions (4.3) Logarithmic Functions (4.4) Properties of Logarithms (4.5) Logarithmic and Exponential Equations (4.6) Compound Interest ; “e”(4.7) Exponential Growth and Decay; Newton’s Law of Cooling; Logistic Growth and Decay (4.8) Building Exponential, Logarithmic, and Logistic Models from Data (4.9) Activities to Support Instruction: Modeling and Analyzing with M&M Activity Definition of “e” Activity Comparison of Interest-Bearing Accounts Activity
Angles and Their Measure (5.1) Trigonometric Functions: Unit Circle Approach (5.2) Properties of the Trigonometric Functions (5.3) Graphs of the Sine and Cosine Functions (5.4) Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions (5.5) Phase Shift; Sinusoidal Curve Fitting (5.6) Activities to Support Instruction: Mnemonic Device for Values of Trig Functions Modeling and Analyzing with Ferris Wheel Problem Modeling and Analyzing with Donali National Park Daylight Hours problem Collecting Data, Modeling and Analyzing Sound Waves Activity
Inverse Sine, Cosine and Tangent Functions (6.1) Inverse Cosecant, Secant and Cotangent Functions (6.2) Trigonometric Identities and Proof (6.3) Sum and Difference Formulas and Their Derivations (6.4) Double-Angle and Half-Angle Formulas and Their Derivations (6.5) Product-to-Sum and Sum-to-Product Formulas (6.6) Basic Trigonometric Equations (6.7) Trigonometric Equations with Multiple Angles and Trig Functions (6.8) Activities to Support Instruction: Hexagon Mnemonic Device for Trig Identities
Right Triangle Trigonometry; Applications (7.1) Law of Sines and Derivation (7.2) Law of Cosines and Derivation (7.3) Area of a Triangle and Heron’s Formula Derivation (7.4)
Polar Coordinates (8.1) Polar Equations and Graphs (8.2) Complex Number Plane; Trig Form of a Complex Number; DeMoivre’s Theorem; Finding Powers and Roots (8.3) Euler’s Identity
Sequences; Sigma Notation; Explicit and Recursive Formulas (11.1) Arithmetic Sequences and Series (11.2) Geometric Sequences and Series (11.3) Harmonic Sequences Real World Applications Activities to Support Instruction: Fractal Project
Math Induction Proof (11.4) Binomial Theorem (11.5) Activities to Support Instruction: Pascal’s Triangle Activity
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