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### N Number and Quantity

- N.RN The Real Number System
- 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.

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

- Extend the properties of exponents to rational exponents.
- N.CN The Complex Number System
- 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
- Use complex numbers in polynomial identities and equations.
- N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.
- N.CN.8 Extend polynomial identities to the complex numbers.
- N.CN.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

- Perform arithmetic operations with complex numbers.

### A Algebra

- A.SSE Seeing Structure in Expressions
- Interpret the structure of expressions.
- A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
- A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.
- 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.
- 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.3c Use the properties of exponents to transform expressions for exponential functions.

- A.SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula 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.

- Interpret the structure of expressions.
- A.APR Arithmetic with Polynomials and Rational Expressions
- Perform arithmetic operations on polynomials.
- A.APR.1 Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- A.APR.1b Extend to polynomial expressions beyond those expressions that simplify to forms that are linear or quadratic.

- A.APR.1 Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- Understand the relationship between zeros and factors of polynomials.
- A.APR.2 Understand and apply the Remainder Theorem: For a polynomial
*p*(*x*) and a number*a*, the remainder on division by*x*–*a*is*p*(*a*). In particular,*p*(*a*) = 0 if and only if (*x*–*a*) is a factor of*p*(*x*). - A.APR.3 Identify zeros of polynomials, when factoring is reasonable, and use the zeros to construct a rough graph of the function defined by the polynomial.

- A.APR.2 Understand and apply the Remainder Theorem: For a polynomial
- Use polynomial identities to solve problems.
- A.APR.4 Prove polynomial identities and use them to describe numerical relationships.
- A.APR.5 Know and apply the Binomial Theorem for the expansion of (
*x*+*y*)^{n}in powers of*x*and*y*for a positive integer*n*, where*x*and*y*are any numbers.

- Rewrite rational expressions.
- A.APR.6 Rewrite simple rational expressions in different forms; write
*a*(*x*)/b(*x*) in the form*q*(*x*) +*r*(*x*)/b(*x*), where*a*(*x*), b(*x*),*q*(*x*), and*r*(*x*) are polynomials with the degree of*r*(*x*) less than the degree of b(*x*), using inspection, long division, or, for the more complicated examples, a computer algebra system. - A.APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

- A.APR.6 Rewrite simple rational expressions in different forms; write

- Perform arithmetic operations on polynomials.
- A.CED Creating Equations
- 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.1c Extend to include more complicated function situations with the option to solve with technology.

- 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.2c Extend to include more complicated function situations with the option to graph with technology.

- 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.3a While functions will often be linear, exponential, or quadratic, the types of problems should draw from more complicated situations.

- A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- A.CED.4d While functions will often be linear, exponential, or quadratic, the types of problems should draw from more complicated situations.

- A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

- Create equations that describe numbers or relationships.
- A.REI Reasoning with Equations and Inequalities
- Understand solving equations as a process of reasoning and explain the reasoning.
- A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

- Solve systems of equations.
- A.REI.6 Solve systems of linear equations algebraically and graphically.
- A.REI.6b Extend to include solving systems of linear equations in three variables, but only algebraically.

- A.REI.6 Solve systems of linear equations algebraically and graphically.
- Represent and solve equations and inequalities graphically.
- A.REI.11 Explain why the
*x*-coordinates of the points where the graphs of the equation*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, making tables of values, or finding successive approximations.

- A.REI.11 Explain why the

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

### F Functions

- F.IF Interpreting Functions
- 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.5c Emphasize the selection of a type of function for a model based on behavior of data and context.

- 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.

- Analyze functions using different representations.
- F.IF.7 Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.
- F.IF.7c Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F.IF.7d Graph polynomial functions, identifying zeros, when factoring is reasonable, and indicating end behavior.
- F.IF.7f Graph exponential functions, indicating intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
- F.IF.7g Graph rational functions, identifying zeros and asymptotes when factoring is reasonable, and indicating end behavior.
- F.IF.7h Graph logarithmic functions, indicating intercepts and end behavior.

- 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 indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.

- Interpret functions that arise in applications in terms of the context.
- F.BF Building Functions
- 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.1b Combine standard function types using arithmetic operations.

- F.BF.1 Write a function that describes a relationship between two quantities.
- 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*(*k**x*), 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them. - F.BF.4 Find inverse functions.
- F.BF.4b Read values of an inverse function from a graph or a table, given that the function has an inverse.
- F.BF.4c Verify by composition that one function is the inverse of another.
- F.BF.4d Find the inverse of a function algebraically, given that the function has an inverse.

- F.BF.3 Identify the effect on the graph of replacing

- Build a function that models a relationship between two quantities.
- F.LE Linear, Quadratic, and Exponential Models
- Construct and compare linear, quadratic, and exponential models, and solve problems.
- F.LE.4 For exponential models, express as a logarithm the solution to
*a*b to the*c**t*power =*d*where*a*,*c*, and*d*are numbers and the base b is 2, 10, or*e*; evaluate the logarithm using technology.

- F.LE.4 For exponential models, express as a logarithm the solution to

- Construct and compare linear, quadratic, and exponential models, and solve problems.
- F.TF Trigonometric Functions
- Extend the domain of trigonometric functions using the unit circle.
- F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- F.TF.2 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.

- Model periodic phenomena with trigonometric functions.
- F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

- Prove and apply trigonometric identities.
- F.TF.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1, and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

- Extend the domain of trigonometric functions using the unit circle.

### G Geometry

- G.SRT Similarity, Right Triangles, and Trigonometry
- Define trigonometric ratios, and solve problems involving right triangles.
- G.SRT.8 Solve problems involving right triangles.

- Apply trigonometry to general triangles.
- G.SRT.9 Derive the formula
*A*= ½*a*b sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. - G.SRT.10 Explain proofs of the Laws of Sines and Cosines and use the Laws to solve problems.
- G.SRT.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles, e.g., surveying problems, resultant forces.

- G.SRT.9 Derive the formula

- Define trigonometric ratios, and solve problems involving right triangles.
- G.C Circles
- Find arc lengths and areas of sectors of circles.
- G.C.6 Derive formulas that relate degrees and radians, and convert between the two.

- Find arc lengths and areas of sectors of circles.

### S Statistics and Probability

- S.ID Interpreting Categorical and Quantitative Data
- Summarize, represent, and interpret data on a single count or measurement variable.
- S.ID.4 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.

- 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 discussing residuals.

- S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- Interpret linear models.
- S.ID.9 Distinguish between correlation and causation.

- Summarize, represent, and interpret data on a single count or measurement variable.
- S.IC Making Inferences and Justifying Conclusions
- Understand and evaluate random processes underlying statistical experiments.
- S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
- S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

- Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
- S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
- S.IC.4 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.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between sample statistics are statistically significant.
- S.IC.6 Evaluate reports based on data.

- Understand and evaluate random processes underlying statistical experiments.