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### AII-N Number and Quantity

- AII-N.RN The Real Number System
- Extend the properties of exponents to rational exponents.
- AII-N.RN.1 Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
- AII-N.RN.2 Convert between radical expressions and expressions with rational exponents using the properties of exponents.

- Extend the properties of exponents to rational exponents.
- AII-N.CN The Complex Number System
- Perform arithmetic operations with complex numbers.
- AII-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. - AII-N.CN.2 Use the relation
*i*² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

- AII-N.CN.1 Know there is a complex number

- Perform arithmetic operations with complex numbers.

### AII-A Algebra

- AII-A.SSE Seeing Structure in Expressions
- Interpret the structure of expressions.
- AII-A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.

- Write expressions in equivalent forms to reveal their characteristics.
- AII-A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- AII-A.SSE.3a Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.
- AII-A.SSE.3c Use the properties of exponents to rewrite exponential expressions.

- AII-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.
- AII-A.APR Arithmetic with Polynomials and Rational Expressions
- Understand the relationship between zeros and factors of polynomials.
- AII-A.APR.2 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*). - AII-A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.

- AII-A.APR.2 Apply the Remainder Theorem: For a polynomial
- Rewrite rational expressions.
- AII-A.APR.6 Rewrite 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*).

- AII-A.APR.6 Rewrite rational expressions in different forms: Write

- Understand the relationship between zeros and factors of polynomials.
- AII-A.CED Creating Equations
- Create equations that describe numbers or relationships.
- AII-A.CED.1 Create equations and inequalities in one variable to represent a real-world context.

- Create equations that describe numbers or relationships.
- AII-A.REI Reasoning with Equations and Inequalities
- Understand solving equations as a process of reasoning and explain the reasoning.
- AII-A.REI.1b Explain each step when solving rational or radical equations 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.
- AII-A.REI.2 Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.

- Solve equations and inequalities in one variable.
- AII-A.REI.4 Solve quadratic equations in one variable.
- AII-A.REI.4b Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in
*a + bi*form.

- AII-A.REI.4b Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in

- AII-A.REI.4 Solve quadratic equations in one variable.
- Solve systems of equations.
- AII-A.REI.7b Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

- Represent and solve equations and inequalities graphically.
- AII-A.REI.11 Given the equations
*y*=*f*(*x*) and*y*=*g*(*x*):- AII-A.REI.11.i recognize that each x-coordinate of the intersection(s) is the solution to the equation
*f*(*x*) =*g*(*x*); - AII-A.REI.11.ii find the solutions approximately using technology to graph the functions or make tables of values;
- AII-A.REI.11.iii find the solution of
*f*(*x*) <*g*(*x*) or*f*(*x*) ≤*g*(*x*) graphically; and - AII-A.REI.11.iv interpret the solution in context.

- AII-A.REI.11.i recognize that each x-coordinate of the intersection(s) is the solution to the equation

- AII-A.REI.11 Given the equations

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

### AII-F Functions

- AII-F.IF Interpreting Functions
- Understand the concept of a function and use function notation.
- AII-F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers.

- Interpret functions that arise in applications in terms of the context.
- AII-F.IF.4 For a function that models a relationship between two quantities:
- AII-F.IF.4.i interpret key features of graphs and tables in terms of the quantities; and
- AII-F.IF.4.ii sketch graphs showing key features given a verbal description of the relationship.

- AII-F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.

- AII-F.IF.4 For a function that models a relationship between two quantities:
- Analyze functions using different representations.
- AII-F.IF.7 Graph functions and show key features of the graph by hand and using technology when appropriate.
- AII-F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- AII-F.IF.7e Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.

- AII-F.IF.7 Graph functions and show key features of the graph by hand and using technology when appropriate.
- Analyze functions using different representations.
- AII-F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
- AII-F.IF.8b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.

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

- AII-F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.

- Understand the concept of a function and use function notation.
- AII-F.BF Building Functions
- Build a function that models a relationship between two quantities.
- AII-F.BF.1 Write a function that describes a relationship between two quantities.
- AII-F.BF.1a Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.
- AII-F.BF.1b Combine standard function types using arithmetic operations.

- AII-F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

- AII-F.BF.1 Write a function that describes a relationship between two quantities.
- Build new functions from existing functions.
- AII-F.BF.3b Using
*f*(*x*) +*k*,*k**f*(*x*),*f*(*k**x*), and*f*(*x*+*k*):- AII-F.BF.3b.i identify the effect on the graph when 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); - AII-F.BF.3b.ii find the value of
*k*given the graphs; - AII-F.BF.3b.iii write a new function using the value of
*k*; and - AII-F.BF.3b.iv use technology to experiment with cases and explore the effects on the graph.

- AII-F.BF.3b.i identify the effect on the graph when replacing
- AII-F.BF.4a Find the inverse of a one-to-one function both algebraically and graphically.
- AII-F.BF.5a Understand inverse relationships between exponents and logarithms algebraically and graphically.
- AII-F.BF.6 Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (sigma) notation.
- AII-F.BF.7 Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.

- AII-F.BF.3b Using

- Build a function that models a relationship between two quantities.
- AII-F.LE Linear, Quadratic, and Exponential Models
- Construct and compare linear, quadratic, and exponential models and solve problems.
- AII-F.LE.2 Construct a linear or exponential function symbolically given:
- AII-F.LE.2.i a graph;
- AII-F.LE.2.ii a description of the relationship; and
- AII-F.LE.2.iii two input-output pairs (include reading these from a table).

- AII-F.LE.4 Use logarithms to solve exponential equations, such as
*a**b*to the*c**t*power =*d*(where*a*,*b*,*c*, and*d*are real numbers and*b*> 0) and evaluate the logarithm using technology.

- AII-F.LE.2 Construct a linear or exponential function symbolically given:
- Interpret expressions for functions in terms of the situation they model.
- AII-F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

- Construct and compare linear, quadratic, and exponential models and solve problems.
- AII-F.TF Trigonometric Functions
- Extend the domain of trigonometric functions using the unit circle.
- AII-F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- AII-F.TF.2 Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
- AII-F.TF.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

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

- Prove and apply trigonometric identities.
- AII-F.TF.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.

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

### AII-S Statistics and Probability

- AII-S.ID Interpreting Categorical and Quantitative Data
- Summarize, represent, and interpret data on a single count or measurement variable.
- AII-S.ID.4a Recognize whether or not a normal curve is appropriate for a given data set.
- AII-S.ID.4b If appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.

- Summarize, represent, and interpret data on two categorical and quantitative variables.
- AII-S.ID.6 Represent bivariate data on a scatter plot, and describe how the variables’ values are related.
- AII-S.ID.6a Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.

- AII-S.ID.6 Represent bivariate data on a scatter plot, and describe how the variables’ values are related.

- Summarize, represent, and interpret data on a single count or measurement variable.
- AII-S.IC Making Inferences and Justifying Conclusions
- Understand and evaluate random processes underlying statistical experiments.
- AII-S.IC.2 Determine if a value for a sample proportion or sample mean is likely to occur based on a given simulation.

- Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
- AII-S.IC.3 Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.
- AII-S.IC.4 Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/- two standard deviations) and determine if a suggested parameter is plausible.
- AII-S.IC.6a Use the tools of statistics to draw conclusions from numerical summaries.
- AII-S.IC.6b Use the language of statistics to critique claims from informational texts. For example, causation vs correlation, bias, measures of center and spread.

- Understand and evaluate random processes underlying statistical experiments.
- AII-S.CP Conditional Probability and the Rules of Probability
- Understand independence and conditional probability and use them to interpret data.
- AII-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”).
- AII-S.CP.4 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 calculate conditional probabilities.

- Use the rules of probability to compute probabilities of compound events in a uniform probability model.
- AII-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.

- AII-S.CP.7 Apply the Addition Rule,

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