**Number and Quantity** |

| Extend the properties of exponents to rational
exponents |

| Use properties of rational and irrational numbers. |

| Reason quantitatively and use units to solve problems. |

| Perform arithmetic operations with complex numbers. |

| Represent complex numbers and their operations on the complex
plane. |

| Use complex numbers in polynomial identities and equations. |

| Represent and model with vector quantities. |

| Perform operations on vectors. |

| Perform operations on matrices and use matrices in applications. |

**Algebra** |

| Interpret the structure of expressions |

| Write expressions in equivalent forms to solve problems |

| Perform arithmetic operations on polynomials |

| Understand the relationship between zeros and factors of polynomials |

| Use polynomial identities to solve problems |

| Rewrite rational expressions |

| Create equations that describe numbers or relationships |

| Understand solving equations as a process of reasoning and explain the reasoning |

| Solve equations and inequalities in one variable |

| Solve systems of equations |

| Represent and solve equations and inequalities graphically |

**Functions** |

| Understand the concept of a function and use function notation |

| Interpret functions that arise in applications in terms of the context |

| Analyze functions using different representations |

| Build a function that models a relationship between two quantities |

| Build new functions from existing functions |

| Construct and compare linear, quadratic, and exponential models and solve problems |

| Interpret expressions for functions in terms of the situation they model |

| Extend the domain of trigonometric functions using the unit circle |

| Model periodic phenomena with trigonometric functions |

| Prove and apply trigonometric identities |

**Geometry** |

| Experiment with transformations in the plane |

| Understand congruence in terms of rigid motions |

| Prove geometric theorems |

| Make geometric constructions |

| Understand similarity in terms of similarity transformations |

| Prove theorems involving similarity |

| Define trigonometric ratios and solve problems involving right
triangles |

| Apply trigonometry to general triangles |

| Understand and apply theorems about circles |

| Find arc lengths and areas of sectors of circles |

| Translate between the geometric description and the equation for a conic section |

| Use coordinates to prove simple geometric theorems algebraically |

| Explain volume formulas and use them to solve problems |

| Visualize relationships between two-dimensional and three-dimensional objects |

| Apply geometric concepts in modeling situations |

**Statistics and Probability** |

| Summarize, represent, and interpret data on a single count or
measurement variable |

| Summarize, represent, and interpret data on two categorical and quantitative variables |

| Interpret linear models |

| Understand and evaluate random processes underlying statistical experiments |

| Make inferences and justify conclusions from sample surveys, experiments, and observational studies |

| 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 |

| Calculate expected values and use them to solve problems |

| Use probability to evaluate outcomes of decisions |