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### N Number and Quantity

- N-RN The Real Number System
- N-RN.A Extend the properties of exponents to rational exponents
- N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
- N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

- N-RN.B Use properties of rational and irrational numbers
- N-RN.3 Explain why:
- N-RN.3a the sum or product of two rational numbers is rational;
- N-RN.3b the sum of a rational number and an irrational number is irrational; and
- N-RN.3c the product of a nonzero rational number and an irrational number is irrational.

- N-RN.3 Explain why:

- N-RN.A Extend the properties of exponents to rational exponents
- N-Q Quantities
- N-Q.A Reason quantitatively and use units to solve problems
- N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.

- N-Q.A Reason quantitatively and use units to solve problems
- N-CN The Complex Number System
- N-CN.A Perform arithmetic operations with complex numbers
- N-CN.1 Know there is a complex number
*i*such that*i*² = –1, and every complex number has the form*a*+*b**i*with*a*and*b*real. - N-CN.2 Use the relation
*i*² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

- N-CN.1 Know there is a complex number
- N-CN.B Use complex numbers in polynomial identities and equations
- N-CN.7 Solve quadratic equations with real coefficients that have complex solutions.

- N-CN.A Perform arithmetic operations with complex numbers

### A Algebra

- A-SSE Seeing Structure in Expressions
- A-SSE.A Interpret the structure of expressions
- A-SSE.1 Interpret expressions that represent a quantity in terms of its context.
- A-SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.

- A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

- A-SSE.1 Interpret expressions that represent a quantity in terms of its context.
- A-SSE.B Write expressions in equivalent forms to solve problems
- A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- A-SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
- A-SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

- A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

- A-SSE.A Interpret the structure of expressions
- A-APR Arithmetic with Polynomials and Rational Expressions
- A-APR.A Perform arithmetic operations on polynomials
- A-APR.1 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.A Perform arithmetic operations on polynomials
- A-CED Creating Equations
- A-CED.A Create equations that describe numbers or relationships
- A-CED.1 Create equations and inequalities in one variable and use them to solve problems.
- A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- A-CED.3 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.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

- A-CED.A Create equations that describe numbers or relationships
- A-REI Reasoning with Equations and Inequalities
- A-REI.A Understand solving equations as a process of reasoning and explain the reasoning
- A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

- A-REI.B Solve equations and inequalities in one variable
- A-REI.4 Solve quadratic equations in one variable.
- A-REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.
- A-REI.4b Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions.

- A-REI.4 Solve quadratic equations in one variable.
- A-REI.C Solve systems of equations
- A-REI.6 Solve systems of linear equations algebraically, exactly, approximately, and graphically while focusing on pairs of linear equations in two variables.
- A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

- A-REI.A Understand solving equations as a process of reasoning and explain the reasoning

### F Functions

- F-IF Interpreting Functions
- F-IF.A Interpret functions that arise in applications in terms of the context
- F-IF.4 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.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
- F-IF.5 For example, if the function
*h*(*n*) gives the number of person-hours it takes to assemble*n*engines in a factory, then the positive integers would be an appropriate domain for the function.

- F-IF.5 For example, if the function
- F-IF.6 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.B Analyze functions using different representations
- F-IF.7 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.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
- F-IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

- F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- F-IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
- F-IF.8b Use the properties of exponents to interpret expressions for exponential functions.

- F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

- F-IF.7 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.A Interpret functions that arise in applications in terms of the context
- F-BF Building Functions
- F-BF.A Build a function that models a relationship between two quantities
- F-BF.1 Write a function that describes a relationship between two quantities.
- F-BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.
- F-BF.1b Combine standard function types using arithmetic operations.

- F-BF.1 Write a function that describes a relationship between two quantities.
- F-BF.B Build new functions from existing functions
- F-BF.3 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.A Build a function that models a relationship between two quantities

### G Geometry

- G-SRT Similarity, Right Triangles, and Trigonometry
- G-SRT.A Understand similarity in terms of similarity transformations
- G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
- G-SRT.1a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- G-SRT.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

- G-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
- G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

- G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
- G-SRT.B Prove theorems using similarity
- G-SRT.4 Prove theorems about triangles.
- G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

- G-SRT.C Define trigonometric ratios and solve problems involving right triangles
- G-SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- G-SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
- G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

- G-SRT.A Understand similarity in terms of similarity transformations
- G-GMD Geometric Measurement and Dimension
- G-GMD.A Explain volume formulas and use them to solve problems
- G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
- G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

- G-GMD.A Explain volume formulas and use them to solve problems

### S Statistics and Probability

- S-ID Interpreting Categorical and Quantitative Data
- S-ID.A Summarize, represent, and interpret data on two categorical and quantitative variables
- S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S-ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
- S-ID.6b Informally assess the fit of a function by plotting and analyzing residuals.

- S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

- S-ID.A Summarize, represent, and interpret data on two categorical and quantitative variables
- S-CP Conditional Probability and the Rules of Probability
- S-CP.A Understand independence and conditional probability and use them to interpret data
- S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
- S-CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
- S-CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
- S-CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
- S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

- S-CP.B Use the rules of probability to compute probabilities of compound events in a uniform probability model
- S-CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
- S-CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

- S-CP.A Understand independence and conditional probability and use them to interpret data