# Advanced Algebra and Trig

Advanced Algebra/Trigonometry is the third, and final, Regents Math course. the one year course culminates with a regents Exam in June. Upon completion of this course, students have the option of moving on to other Elective and Advanced Placement math courses.

Algebra II/Trigonometry Curriculum

1. Equations and Inequalities

- Expressions and Formulas
- Properties of Real Numbers
- Solving Equations
- Solving Absolute Value Equations
- Solving Inequalities
- Solving Compound and Absolute Value Inequalities

2. Linear Relations and Functions

- Relations and Functions
- Linear Relations and Functions
- Rate of Change and Slope
- Writing Linear Equations
- Scatter Plots and Lines of Regression
- Special Functions
- Parent Functions and Transformations
- Graphing Linear and Absolute Value Inequalities

3. Systems of Equations and Inequalities

- Solving Systems of Equations by Graphing
- Solving Systems of Equations Algebraically
- Solving Systems of Inequations by Graphing
- Optimization with Linear Programming
- Systems of Equations in Three Variables

4. Quadratic Functions and Relations

- Graphing Quadratic Functions
- Solving Quadratic Equations by Graphing
- Solving Quadratic Equations by Factoring
- Complex Numbers
- Completing the Square
- The Quadratic Formula and the Discriminant
- Transformations with Quadratic Functions
- Quadratic Inequalities

5. Polynomials and Polynomial Functions

- Operations with Polynomials
- Dividing Polynomials
- Polynomial Functions
- Analyzing Graphs of Polynomial Functions
- Solving Polynomial Equations
- The Remainder and Factor Theorems
- Roots and Zeros
- Rational Zero Theorem

6. Inverses and Radical Functions and Relations

- Operations on Functions
- Inverse Functions and Relations
- Square Root Functions and Inequalities
- Operations with Radical Expressions
- Rational Exponents
- Solving Radical Equations and Inequalities

7. Exponential and Logarithmic Functions and Relations

- Graphing Exponential Functions
- Solving Exponential Equations and Inequalities
- Logarithms and Logarithmic Functions
- Solving Logarithmic Equations and Inequalities
- Properties of Logarithms
- Common Logarithms
- Base e and Natural Logarithms
- Using Exponential and Logarithmic Functions

8. Rational Functions and Relations

- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Graphing Reciprocal Functions
- Graphing Rational Functions
- Variation Functions
- Solving Rational Equations and Inequalitie

9. Sequences and Series

- Sequences as Functions
- Arithmetic Sequences and Series
- Geometric Sequences and Series
- Infinite Geometric Series
- Recursion and Iteration
- The Binomial Theorem
- Proof by Mathematical Induction

10. Probability and Statistics

- Experiments, Surveys, and Observational Studies
- Statistical Analysis
- Conditional Probability
- Probability Distributions
- The Normal Distribution
- Hypothesis Testing
- Binomial Distributions

11. Trigonometric Functions

- Trigonometric Functions in Right Triangles
- Angles and Angle Measure
- Trigonometric Functions of General Angles
- Law of Sines
- Law of Cosines
- Circular Functions
- Graphing Trigonometric Functions
- Translations of Trigonometric Graphs
- Inverse Trigonometric Functions

12. Trigonometric Identities and Equations

- Trigonometric Identities
- Verifying Trigonometric Identities
- Sum and Difference of Angles Identities
- Double-Angle and Half-Angle Identities
- Solving Trigonometric Equations