#### N.CN: The Complex Number System

N.CN.1: Know there is a complex number i such that i² = ?1, and every complex number has the form a + bi with a and b real.

N.CN.4: Extend polynomial identities to the complex numbers.

### A: Algebra

#### A.SSE: Seeing Structure in Expressions

A.SSE.6: Interpret expressions that represent a quantity in terms of its context.

A.SSE.6.a: Interpret parts of an expression, such as terms, factors, and coefficients.

#### A.APR: Arithmetic with Polynomials and Rational Expressions

A.APR.9: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

A.APR.10: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x ? a is p(a), so p(a) = 0 if and only if (x ? a) is a factor of p(x).

A.APR.11: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

#### A.CED: Creating Equations

A.CED.16: Create equations and inequalities in one variable and use them to solve problems.

A.CED.17: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.18: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A.CED.19: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

#### A.REI: Reasoning with Equations and Inequalities

A.REI.21: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

### F: Functions

#### F.IF: Interpreting Functions

F.IF.22: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.23: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.24: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F.IF.25: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.25.a: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.25.b: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.IF.25.c: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.IF.27: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

#### F.BF: Building Functions

F.BF.28: Write a function that describes a relationship between two quantities.

F.BF.28.a: Combine standard function types using arithmetic operations.

F.BF.29: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

F.BF.30: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

#### F.TF: Trigonometric Functions

F.TF.33: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

F.TF.34: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

F.TF.35: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

F.TF.36: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

### S: Statistics and Probability

#### S.ID: Interpreting Categorical and Quantitative Data

S.ID.37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

#### S.IC: Making Inferences and Justifying Conclusions

S.IC.38: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S.IC.40: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

S.IC.41: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S.IC.42: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

S.IC.43: Evaluate reports based on data.

#### S.MD: Using Probability to Make Decisions

S.MD.44: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

S.MD.45: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Correlation last revised: 3/17/2015

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