Math Ladder · High school · Grade 11

Algebra 2

Functions and their families: polynomial, rational, radical, exponential and logarithmic, plus complex numbers and sequences.

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67 topics in 7 units. Builds on Algebra 1 and Geometry. Leads to Precalculus and Trigonometry, Probability and Statistics and Discrete Math. It also opens the way to Physics 2 on the Physics Ladder, and General Chemistry 1 on the Chemistry Ladder. Not sure this is the right course? Find your rung.

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Unit 1 Functions and Their Graphs

9 topics

Combine, compose and invert functions, and use the graphs of the parent functions.

  1. Parent Functions
  2. Combining Transformations
  3. Even and Odd Functions
  4. Adding, Subtracting, Multiplying and Dividing Functions
  5. Composition of Functions
  6. Inverse Functions
  7. Checking Inverses by Composition
  8. Restricting a Domain for an Inverse
  9. Ramps: Building Bent-Line Graphs from ReLU

Unit 2 Quadratics and Complex Numbers

9 topics

Extend quadratics with complex numbers, inequalities and new systems.

  1. The Vertex Formula
  2. Writing Quadratics from Points
  3. The Imaginary Unit i
  4. Adding and Multiplying Complex Numbers
  5. Dividing Complex Numbers
  6. Quadratics with Complex Solutions
  7. Quadratic Inequalities
  8. Systems in Three Variables
  9. Nonlinear Systems

Unit 3 Polynomial Functions

16 topics

Divide and factor polynomials, find their zeros, and sketch their graphs.

  1. Seeing Structure in Expressions
  2. End Behavior of Polynomials
  3. Zeros and Multiplicity
  4. Polynomial Long Division
  5. Synthetic Division
  6. The Remainder and Factor Theorems
  7. Sums and Differences of Cubes
  8. Factoring Quadratic-Type Polynomials
  9. The Rational Root Theorem
  10. Solving Polynomial Equations
  11. The Fundamental Theorem of Algebra
  12. Writing a Polynomial from Its Zeros
  13. Sketching Polynomial Graphs
  14. Polynomial Identities
  15. The Binomial Theorem
  16. Polynomial and Rational Inequalities

Unit 4 Rational Expressions and Functions

10 topics

Simplify and combine rational expressions, solve rational equations, and graph rational functions.

  1. Simplifying Rational Expressions
  2. Multiplying and Dividing Rational Expressions
  3. Adding and Subtracting Rational Expressions
  4. Complex Fractions
  5. Rational Equations
  6. Work-Rate and Average-Cost Models
  7. Direct, Inverse and Joint Variation
  8. Asymptotes and Holes
  9. Graphing Rational Functions
  10. Slant Asymptotes

Unit 5 Radical Functions and Equations

4 topics

Work with nth roots, rationalize denominators, graph radical functions, and solve radical equations.

  1. nth Roots
  2. Simplifying and Rationalizing Radicals
  3. Square Root and Cube Root Functions
  4. Radical Equations

Unit 6 Exponential and Logarithmic Functions

14 topics

Use e and compound interest, understand logarithms, and solve exponential and log equations.

  1. Graphs of Exponential Functions
  2. Exponential Equations with a Common Base
  3. Compound Interest
  4. The Number e and Continuous Growth
  5. What a Logarithm Is
  6. Switching Between Log and Exponential Form
  7. Properties of Logarithms
  8. Change of Base
  9. Graphs of Logarithmic Functions
  10. Logarithmic Scales
  11. Solving Exponential Equations with Logs
  12. Solving Logarithmic Equations
  13. Exponential and Logarithmic Models
  14. Choosing a Function Model

Unit 7 Sequences and Series

5 topics

Write sequences recursively, use sigma notation, and sum arithmetic and geometric series.

  1. Recursive Formulas
  2. Sigma Notation
  3. Arithmetic Series
  4. Finite Geometric Series
  5. Infinite Geometric Series
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