ALGEBRA 2 Honors Syllabus (correlated with: Algebra and Trigonometry Structure and Method Book 2, Brown, Dolciani, Sorgenfrey, and Kane; 2000 McDougal Littell)
Spring Term
I. Exponential Functions
- Rational Exponents
- Real Number Exponents
- Exponential Functions defined Explicitly and Recursively
- Modeling Involving Exponential Growth and Decay Models
- Financial Math Models (Annuities, etc..) Involving Exponential Functions
- Logistic Growth Models
II. Logarithmic Functions
- Composition and Inverses of Functions
- Logarithmic Functions
- Laws of Logarithms
- Models Involving Logarithmic Functions
- The Natural Logarithm Function
III. Sequences and Series
- Sequences Defined both Explicitly and Recursively
- Arithmetic Sequences
- Geometric Sequences
- Series and Sigma Notation
- Sums of Arithmetic and Finite Geometric Sequences
IV. Trigonometric Functions in Context of Triangle Trigonometry
- Angles and Degree Measure
- Trigonometric Functions of Acute Angles
- Trigonometric Functions of General Angles
- Values of Trigonometric Functions
- Solving Right Triangles
- The Law of Cosines
- Area of a Triangle Formula and Hero's Formula
- Law of Sines (Including Ambiguos Case of Law of Sines)
- Solving General Triangles
V. Trigonometric Functions, Graphs, and Identities
- Radian Measure and the Wrapping Function
- Circular Functions
- Periodicity and Symmetry
- Graphs of Sine and Cosine Function
- Graphs of Tangent, Cotangent, Secant, and Cosecant
- Basic Identities: Reciprocal, Cofunction, Pythagorean and Related Identities
- Trigonometric Addition Formulae (Sin(sum/difference), Cos(sum/difference), Tan(sum/difference))
- Double-Angle and Half-Angle Formulae for Sine, Cosine, and Tangent
- Inverse Sine, Cosine, and Tangent Functions
- Further work with Trigonometric Equations
Time Permitting:
VI. Vectors
- Graphical Representation of a Vector
- Operations with Vectors: Addition, Subtraction, and Scalar Multiplication
- Algebraic Operations Involving Vectors (Vector Addition, Subtraction, and Scalar Multiplication)
- Parametric Equations and Vectors
VI. Counting Methods
- Fundamental Counting Principles
- Combinations
- Powers of Binomials
- Binomial Expansion
- Binomial Expansion Applied to Binomial Probability Model
- Permutations