Algebra 2

1. Polynomial and Rational Expressions

  • Simplify polynomials: Operations with polynomials, factoring, and solving quadratic equations.

  • Rational expressions: Simplifying, adding, subtracting, multiplying, and dividing rational expressions.

2. Quadratic Functions and Equations

  • Solve quadratic equations: Using various methods like factoring, completing the square, and the quadratic formula.

  • Graphing quadratic functions: Identifying key features such as the vertex, axis of symmetry, and x-intercepts.

3. Functions

  • Function notation: Interpreting and using function notation, finding values of functions.

  • Types of functions: Linear, quadratic, absolute value, square root, exponential, and logarithmic functions.

  • Composition of functions: Understanding the combination of two functions, f(g(x))f(g(x))f(g(x)).

4. Systems of Equations and Inequalities

  • Solving systems of linear equations: Using substitution, elimination, and graphical methods.

  • Solving systems of non-linear equations: Working with systems involving quadratics or other non-linear functions.

5. Exponents and Logarithms

  • Laws of exponents: Simplifying expressions involving exponents.

  • Exponential functions: Solving equations involving exponential growth and decay.

  • Logarithmic functions: Understanding the relationship between logarithms and exponents, solving logarithmic equations.

6. Radical Functions and Rational Exponents

  • Simplifying radical expressions: Using properties of square roots and cube roots.

  • Rational exponents: Expressing roots as exponents and simplifying expressions involving rational exponents.

7. Sequences and Series

  • Arithmetic and geometric sequences: Identifying patterns, finding terms, and using formulas for nth terms.

  • Series: Sum of arithmetic and geometric series.

8. Probability and Statistics

  • Probability: Using counting principles, permutations, and combinations.

  • Data analysis: Analyzing data sets using mean, median, mode, standard deviation, and interpreting statistical data.

9. Conic Sections

  • Circles, ellipses, parabolas, and hyperbolas: Graphing and writing equations of conic sections, understanding their properties.

10. Matrices

  • Operations with matrices: Adding, subtracting, and multiplying matrices.

  • Solving systems using matrices: Using matrix methods for solving systems of linear equations.

11. Advanced Topics in Functions

  • Polynomial functions: Analyzing higher-degree polynomials, graphing, and finding roots.

  • Rational functions: Identifying asymptotes and analyzing the behavior of rational functions.