**ALGEBRA 2 Honors Syllabus** (correlated with: Algebra and Trigonometry Structure and Method Book 2, Brown, Dolciani, Sorgenfrey, and Kane; 2000 McDougal Littell)

Winter Term

**I. Probability**

- Randomness and Random Phenomena
- Using a Simulation Model to Study a Particular Situation: Simulation Component
- Language Relating to a Probability Experiment: Outcome, Trial, Event, Sample Space
- Definition of Probability
- Law of Large Numbers
- Complement Rule
- Mutually Exclusive (Disjoint) Events
- Addition Rule for Mutually Exclusive Events
- Venn Diagrams applied to Probability Problems
- Independent Events
- Multiplication Rule for Independent Events
- General Addition Rule for both Mutually Exclusive and Non-mutually Exclusive Events
- Conditional Probability: Dependent and Independent Events
- General Multiplication Rule for Dependent and Independent Events
- Probability Trees as Applied to Conditional Probability Problems
- Reverse Conditioning
- Expected Value and Variance of a Random Variable

Winter Break

**II. Polynomials**

- Polynomials (Basic definitions and properties, including definition of ODD and EVEN functions)
- Using Laws of Exponents
- Multiplying Polynomials

**III. Rational Expressions**

- Quotients of Monomials (Laws of exponents)
- Inequality, Set Builder, and Interval Notation
- Zero and Negative Exponents
- Scientific Notation and Significant Digits
- Applications of Functions to Geometry type problems involving Volume and Surface area.

**IV. Irrational and Complex Numbers, Root Function**

- Roots of Real Numbers
- The Square Root and Cube Root Function (basic properties and graph)
- Properties of Radicals
- Sums of Radicals
- Binomials Containing Radicals
- Equations Containing Radicals
- Rational and Irrational Numbers
- Arithmetic Mean and Geometric Mean (including Geometric Interpretation)
- The Imaginary Number i
- The Complex Numbers

**V. Variation and Polynomial Equations**

- Direct Variation and Proportion
- Inverse and Joint Variation
- Dividing Polynomials
- Synthetic Division
- Remainder and Factor Theorem
- Fundamental Theorem of Algebra
- Conjugate Root Theorem
- Descartes' Rule of Signs
- Rational Root Theorem
- Intermediate Value Theorem (Bracket and Halving Method)

**VI. Statistics (Univariate Data Analysis)**

- Categorial, and Quatitative Variables
- Graphical Displays: Frequency Tables, Contingency Tables, Bar Charts, Pie Charts, Segmented Bar Charts, Histograms, Stem and Leaf Plots. Dot Plots, Time Plots, Box Plots
- Distributions: Unimodal, Bi-modal, Multi-modal, Symmetric, Skewed, Uniform
- Measures of Center: Mean, and Median
- Measures of Spread: Sample Standard Deviation, Range, Interquartile Range
- Outliers and Outlier Criterion
- Numerical Display: Five Number Summary, Mean and Standard Deviation

Time Permitting:

- Sample Variance
- Using a Normal Model to Describe a Particular Population and Carry Out Probability Calculations Using the Normal Model