Number and Quantity

The Real Number System

 Extend the properties of exponents to rational exponents.
 Use properties of rational and irrational numbers.

The Complex Number Systems

 Perform arithmetic operations with complex numbers.
 Use complex numbers in polynomial identities and equations.

Algebra

Seeing Structure in Expressions

 Interpret the structure of expressions.
 Write expressions in equivalent forms to solve problems.
Arithmetic with Polynomials and Rational Expressions
 Perform arithmetic operations on polynomials.

Creating Equations

 Create equations that describe numbers or relationships.

Reasoning with Equations and Inequalities

Solve equations and inequalities in one variable.

 Solve systems of equations.

Functions

Interpreting Functions

 Interpret functions that arise in applications in terms of the context.
 Analyze functions using different representations.

Building Functions

 Build a function that models a relationship between two quantities.
 Build new functions from existing functions.

Linear, Quadratic, and Exponential Models

 Construct and compare linear, quadratic, and exponential models and solve problems.
 Interpret expressions for functions in terms of the situation they model

Trigonometric Functions

 Prove and apply trigonometric identities.

Geometry

Congruence

 Prove geometric theorems.

Similarity, Right Triangles, and Trigonometry

 Understand similarity in terms of similarity transformations.

 Prove theorems involving similarity.

 Define trigonometric ratios and solve problems involving right triangles.

Circles

 Understand and apply theorems about circles.

 Find arc lengths and areas of sectors of circles.

Expressing Geometric Properties with Equations

 Translate between the geometric description and the equation for a conic section.

 Use coordinates to prove simple geometric theorems algebraically.

Geometric Measurement and Dimension

 Explain volume formulas and use them to solve problems.

Statistics and Probability

Conditional Probability and the Rules of Probability

 Understand independence and conditional probability and use them to interpret data.

 Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Using Probability to Make Decisions

 Use probability to evaluate outcomes of decisions