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Common Core Mathematics 9-12


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  • Topics

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