1. Number and Quantity

Students will be able to:
• Understand and perform arithmetic with complex numbers and interpret i2=−1.
• Perform operations (add, subtract, multiply, divide) on complex numbers.
• Understand the Fundamental Theorem of Algebra and its connection to solutions of polynomials.
• Use rational exponents and radical expressions.

2. Algebra: Expressions & Equations

Students will be able to:
• Simplify, manipulate, and evaluate polynomial expressions.
• Factor polynomials and solve polynomial equations.
• Rewrite expressions and solve rational and radical equations.
• Solve one-variable equations and inequalities, including absolute value.

3. Functions

Students will be able to:
• Understand function notation and representations (tables, graphs, equations).
• Analyze and interpret the behavior of functions across multiple types:

  • Polynomial functions (quadratic, cubic, higher degree)

  • Rational functions

  • Exponential and logarithmic functions

  • Piecewise, absolute value, and root functions
    • Evaluate and graph these functions using key features (intercepts, end behavior, asymptotes).

4. Building and Modeling with Functions

Students will be able to:
• Create functions to model real-world situations.
• Combine functions and explore transformations (translations, reflections, dilations).
• Interpret inverse functions and solve equations using inverses.
• Use functions to model growth/decay and other applied contexts.

5. Graphing and Solution Strategies

Students will be able to:
• Graph functions and identify key features using tables and technology.
• Explain solutions of equations in terms of graph intersections.
• Approximate solutions using numerical and graphical methods.
• Interpret rate of change and function behavior in context.

6. Statistics and Probability Connections

Students will be able to:
• Use statistical reasoning with functions and algebraic models.
• Interpret data summaries related to modeled relationships.
(Statistics may be integrated where appropriate as part of CCSS design.)

7. Mathematical Practice Skills

Across all content areas, students will:
✔ Make sense of problems and persevere in solving them
✔ Reason abstractly and quantitatively
✔ Construct viable arguments and critique others’ reasoning
✔ Model with mathematics
✔ Use appropriate tools strategically
✔ Attend to precision
✔ Look for structure and regularity in reasoning

Overall Summary

By the end of Algebra 2, students should be able to:

  • Work comfortably with complex numbers and polynomial systems.

  • Analyze multiple classes of functions (polynomial, rational, exponential, logarithmic, etc.) both algebraically and graphically.

  • Build and interpret mathematical models using functions.

  • Solve a broad range of equations and inequalities with understanding of underlying structures.

  • Apply algebra to real-world and contextual problems with clarity and precision.