### AII-N: Number and Quantity

#### AII-N.RN: The Real Number System

1.1.1: 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.CN: The Complex Number System

1.2.1: Perform arithmetic operations with complex numbers.

AII-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.

AII-N.CN.2: Use the relation ??² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

### AII-A: Algebra

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

2.1.1: Interpret the structure of expressions.

AII-A.SSE.2: Recognize and use the structure of an expression to identify ways to rewrite it.

2.1.2: 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.3.a: Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.

AII-A.SSE.3.c: Use the properties of exponents to rewrite exponential expressions.

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

2.2.1: 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.CED: Creating Equations

2.3.1: Create equations that describe numbers or relationships.

AII-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.

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

2.4.1: 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.

2.4.2: Solve equations and inequalities in one variable.

AII-A.REI.4: Solve quadratic equations in one variable.

AII-A.REI.4.b.i: inspection, Write complex solutions in ?? + ???? form.

AII-A.REI.4.b.ii: taking square roots, Write complex solutions in a + bi form.

AII-A.REI.4.b.iii: factoring, Write complex solutions in a + bi form.

AII-A.REI.4.b.iv: completing the square, Write complex solutions in a + bi form.

AII-A.REI.4.b.v: the quadratic formula, and Write complex solutions in a + bi form.

AII-A.REI.4.b.vi: graphing. Write complex solutions in a + bi form.

2.4.4: 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-F: Functions

#### AII-F.IF: Interpreting Functions

3.1.1: 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.

3.1.2: 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.

3.1.3: 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.7.c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

AII-F.IF.7.e: Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.

3.1.4: 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.8.b: 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.BF: Building Functions

3.2.1: 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.1.a: Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.

AII-F.BF.1.b: 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.

3.2.2: Build new functions from existing functions.

AII-F.BF.3b: Using f(x) + k, k f(x), f(kx), 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(kx), and f(x + k) for specific values of k (both positive and negative); Include recognizing even and odd functions from their graphs.

AII-F.BF.3b.ii: find the value of k given the graphs; Include recognizing even and odd functions from their graphs.

AII-F.BF.3b.iv: use technology to experiment with cases and explore the effects on the graph. Include recognizing even and odd functions from their graphs.

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.7: Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.

#### AII-F.LE: Linear, Quadratic, and Exponential Models

3.3.1: 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 ab to the a power = d (where a, b, c, and d are real numbers and b > 0) and evaluate the logarithm using technology.

3.3.2: 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.

#### AII-F.TF: Trigonometric Functions

3.4.1: 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.

3.4.2: 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.

3.4.3: Prove and apply trigonometric identities.

AII-F.TF.8: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 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.

### AII-S: Statistics and Probability

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

4.1.1: 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.

4.1.2: 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.6.a: Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.

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

4.2.1: 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.

4.2.2: 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.CP: Conditional Probability and the Rules of Probability

4.3.1: 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.

Correlation last revised: 9/15/2020

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