High School Mathematics

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

Quantities

  • 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.
  • 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.
  • 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.
  • Experiment with transformations in the plane
  • Understand congruence in terms of rigid motions
  • Prove geometric theorems
  • Make geometric constructions

Similarity, Right Triangles, & Trigonometry

  • 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.

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 Measures & Dimension

  • Explain volume formulas and use them to solve problems
  • Visualize relationships between two-dimensional and three-dimensional objects
  • Apply geometric concepts in modeling situations

Interpreting Categorical & Quantitative Data

  • 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

Making Inferences & Justifying Conclusions

  • Understand and evaluate random processes underlying statistical experiments
  • Make inferences and justify conclusions from sample surveys, experiments, and observational studies
  • Conditional Probability & the Rules of Probability
  • Use the rules of probability to compute probabilities of compound events.

Using Probability to Make Decisions

  • Calculate expected values and use them to solve problems
  • Use probability to evaluate outcomes of decisions