 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

link to Algebra 2 Honors Homepage