The high school standards specify the mathematics that all students should study in order to be college and career ready. The standards are listed in conceptual categories which portray a coherent view of high school mathematics:

Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability

The Real Number System

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

Quantities 

• Reason quantitatively and use units to solve problems

The Complex Number System 

• Perform arithmetic operations with complex numbers
• Represent complex numbers and their operations on the complex plane
• Use complex numbers in polynomial identities and equations

Vector and Matrix Quantities

• Represent and model with vector quantities.
• Perform operations on vectors.
• Perform operations on matrices and use matrices in applications.

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
• Understand the relationship between zeros and factors of polynomials
• Use polynomial identities to solve problems
• Rewrite rational expressions

Creating Equations

• Create equations that describe numbers or relationships

Reasoning with Equations and Inequalities

• 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

Interpreting 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

 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 

• Extend the domain of trigonometric functions using the unit circle
• Model periodic phenomena with trigonometric functions
• Prove and apply trigonometric identities

Congruence

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

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
• Apply trigonometry to general 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
• Visualize relationships between two-dimensional and three-dimensional objects

Modeling with Geometry 

• Apply geometric concepts in modeling situations

Interpreting Categorical and 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 and Justifying Conclusions

• Understand and evaluate random processes underlying statistical experiments
• Make inferences and justify conclusions from sample surveys, experiments and observational studies

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

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