912.HSN Number and Quantity

912.HSNCN The Complex Number System

912.HSNCN.A Perform arithmetic operations with complex numbers.

912.HSNCN.A.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

912.HSNCN.B Represent complex numbers and their operations on the complex plane.

912.HSNCN.B.4 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

912.HSNCN.B.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

912.HSNCN.B.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

912.HSNVM Vector and Matrix Quantities

912.HSNVM.A Represent and model with vector quantities.

912.HSNVM.A.1 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, v, v, v).

912.HSNVM.A.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

912.HSNVM.A.3 Solve problems involving velocity and other quantities that can be represented by vectors.

912.HSNVM.B Perform operations on vectors.

912.HSNVM.B.4 Add and subtract vectors.

912.HSNVM.B.4a Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

912.HSNVM.B.4b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

912.HSNVM.B.4c Understand vector subtraction v  w as v + (w), where w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise.

912.HSNVM.B.5 Multiply a vector by a scalar.

912.HSNVM.B.5a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(v_{x}, v_{y}) = (cv_{x}, cv_{y}).

912.HSNVM.B.5b Compute the magnitude of a scalar multiple cv using cv = c·v. Compute the direction of cv knowing that when cv is not equal to 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

912.HSNVM.C Perform operations on matrices and use matrices in applications.

912.HSNVM.C.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

912.HSNVM.C.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

912.HSNVM.C.8 Add, subtract, and multiply matrices of appropriate dimensions.

912.HSNVM.C.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

912.HSNVM.C.10 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

912.HSNVM.C.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

912.HSNVM.C.12 Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
912.HSA Algebra

912.HSAREI Reasoning with Equations and Inequalities

912.HSAREI.C Solve systems of equations

912.HSAREI.C.8 Represent a system of linear equations as a single matrix equation in a vector variable.

912.HSAREI.C.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
912.HSF Functions

912.HSFIF Interpreting Functions

912.HSFIF.C Analyze functions using different representations

912.HSFIF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

912.HSFIF.C.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

912.HSFBF Building Functions

912.HSFBF.A Build a function that models a relationship between two quantities

912.HSFBF.A.1 Write a function that describes a relationship between two quantities.

912.HSFBF.A.1c Compose functions.

912.HSFBF.B Build new functions from existing functions

912.HSFBF.B.4 Find inverse functions.

912.HSFBF.B.4b Verify by composition that one function is the inverse of another.

912.HSFBF.B.4c Read values of an inverse function from a graph or a table, given that the function has an inverse.

912.HSFBF.B.4d Produce an invertible function from a noninvertible function by restricting the domain.

912.HSFBF.B.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

912.HSFTF Trigonometric Functions

912.HSFTF.A Extend the domain of trigonometric functions using the unit circle

912.HSFTF.A.3 Use special triangles to determine geometrically the values of sine, cosine, and tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π  x, π + x, and 2π  x in terms of their values for x, where x is any real number.

912.HSFTF.A.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

912.HSFTF.B Model periodic phenomena with trigonometric functions

912.HSFTF.B.6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

912.HSFTF.B.7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

912.HSFTF.C Prove and apply trigonometric identities

912.HSFTF.C.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
912.HSG Geometry

912.HSGGPE Expressing Geometric Properties with Equations

912.HSGGPE.A Translate between the geometric description and the equation for a conic section

912.HSGGPE.A.3 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

912.HSGGMD Geometric Measurement and Dimension

912.HSGGMD.A Explain volume formulas and use them to solve problems

912.HSGGMD.A.2 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
912.HSS Statistics and Probability

912.HSSMD Using Probability to Make Decisions

912.HSSMD.A Calculate expected values and use them to solve problems

912.HSSMD.A.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

912.HSSMD.A.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

912.HSSMD.A.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

912.HSSMD.A.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

912.HSSMD.B Use probability to evaluate outcomes of decisions

912.HSSMD.B.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

912.HSSMD.B.5a Find the expected payoff for a game of chance.

912.HSSMD.B.5b Evaluate and compare strategies on the basis of expected values.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.