Algebra 2 builds on Algebra 1 concepts and introduces more advanced topics in functions, equations, and mathematical reasoning. Here are the key learning goals:
1. Expressions, Equations, and Inequalities
- Simplify and manipulate algebraic expressions, including polynomials and rational expressions.
- Solve linear, absolute value, and quadratic equations.
- Solve and graph linear and nonlinear inequalities, including absolute value and quadratic inequalities.
2. Functions and Their Properties
- Understand the concept of a function, domain, range, and function notation.
- Analyze key features of functions (intercepts, intervals of increase/decrease, maxima/minima).
- Perform operations on functions (addition, subtraction, multiplication, division, composition).
- Identify and apply inverse functions.
3. Polynomial and Rational Functions
- Perform polynomial operations (addition, subtraction, multiplication, division).
- Use factoring and the Remainder & Factor Theorems.
- Solve polynomial equations using factoring, synthetic division, and the Rational Root Theorem.
- Graph polynomial functions and analyze their end behavior.
- Simplify, multiply, divide, add, and subtract rational expressions.
- Solve rational equations and analyze their graphs, including asymptotes.
4. Exponential and Logarithmic Functions
- Understand and apply exponential growth and decay models.
- Convert between exponential and logarithmic forms.
- Apply logarithmic properties (product, quotient, power).
- Solve exponential and logarithmic equations.
- Use logarithmic scales in real-world contexts (e.g., pH, Richter scale).
5. Radical and Complex Numbers
- Simplify radical expressions and perform operations with radicals.
- Solve radical equations and check for extraneous solutions.
- Understand and perform operations with complex numbers.
- Solve quadratic equations with complex solutions.
6. Quadratic Functions and Conic Sections
- Graph and analyze quadratic functions using vertex form and standard form.
- Solve quadratic equations using factoring, completing the square, and the quadratic formula.
- Understand and analyze conic sections (parabolas, circles, ellipses, hyperbolas).
7. Systems of Equations and Matrices
- Solve systems of linear and nonlinear equations algebraically and graphically.
- Apply matrix operations (addition, subtraction, multiplication).
- Use determinants and inverses of matrices to solve systems of equations.
8. Sequences and Series
- Recognize and analyze arithmetic and geometric sequences.
- Use recursive and explicit formulas.
- Find sums of finite and infinite geometric series.
- Apply the Binomial Theorem.
9. Probability and Statistics
- Understand and apply the fundamental counting principle, permutations, and combinations.
- Calculate probabilities, including conditional probability and expected value.
- Analyze data sets using mean, median, standard deviation, and normal distribution.
10. Trigonometry and Periodic Functions
- Understand and use the unit circle.
- Define and evaluate trigonometric functions.
- Graph sine, cosine, and tangent functions and their transformations.
- Apply trigonometric identities and solve trigonometric equations.