Academic Standards

A2.N.CN.A: Perform arithmetic operations with complex numbers.

A2.N.CN.A.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.

Points in the Complex Plane

Roots of a Quadratic

A2.N.CN.B: Use complex numbers in quadratic equations.

A2.N.CN.B.3: Solve quadratic equations with real coefficients that have complex solutions.

Points in the Complex Plane

Roots of a Quadratic

A2.A.SSE.A: Interpret the structure of expressions.

A2.A.SSE.A.1: Use the structure of an expression to identify ways to rewrite it.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Expressions

A2.A.APR.A: Understand the relationship between zeros and factors of polynomials.

A2.A.APR.A.1: 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).

Dividing Polynomials Using Synthetic Division

A2.A.APR.A.2: 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.

Graphs of Polynomial Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

A2.A.APR.B: Use polynomial identities to solve problems.

A2.A.APR.B.3: Know and use polynomial identities to describe numerical relationships.

A2.A.CED.A: Create equations that describe numbers or relationships.

A2.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Exploring Linear Inequalities in One Variable

Geometric Sequences

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

A2.A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles

Solving Formulas for any Variable

A2.A.REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

A2.A.REI.A.1: Explain each step in solving an 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.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

A2.A.REI.A.2: Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.

A2.A.REI.B: Solve equations and inequalities in one variable.

A2.A.REI.B.3: Solve quadratic equations and inequalities in one variable.

A2.A.REI.B.3.a: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Points in the Complex Plane

Roots of a Quadratic

A2.A.REI.C: Solve systems of equations.

A2.A.REI.C.4: Write and solve a system of linear equations in context.

Cat and Mouse (Modeling with Linear Systems)

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

A2.A.REI.D: Represent and solve equations graphically.

A2.A.REI.D.6: 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 approximate solutions using technology.

Point-Slope Form of a Line

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Standard Form of a Line

A2.F.IF.A: Interpret functions that arise in applications in terms of the context.

A2.F.IF.A.1: 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.

Absolute Value with Linear Functions

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

A2.F.IF.A.2: 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.

Cat and Mouse (Modeling with Linear Systems)

Slope

A2.F.IF.B: Analyze functions using different representations.

A2.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.

A2.F.IF.B.3.a: Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

A2.F.IF.B.4: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

A2.F.IF.B.4.a: Know and use the properties of exponents to interpret expressions for exponential functions.

Compound Interest

Exponential Functions

A2.F.IF.B.5: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Polynomial Form

Quadratics in Vertex Form

A2.F.BF.A: Build a function that models a relationship between two quantities.

A2.F.BF.A.1: Write a function that describes a relationship between two quantities.

A2.F.BF.A.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

A2.F.BF.A.1.b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

A2.F.BF.A.2: Write arithmetic and geometric sequences with an explicit formula and use them to model situations.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

A2.F.BF.B: Build new functions from existing functions.

A2.F.BF.B.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.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

A2.F.BF.B.4: Find inverse functions.

A2.F.BF.B.4.a: Find the inverse of a function when the given function is one-to-one.

A2.F.LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.

A2.F.LE.A.1: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs.

Absolute Value with Linear Functions

Arithmetic Sequences

Arithmetic and Geometric Sequences

Compound Interest

Exponential Functions

Geometric Sequences

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

A2.F.LE.A.2: For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

A2.F.LE.B: Interpret expressions for functions in terms of the situation they model.

A2.F.LE.B.3: Interpret the parameters in a linear or exponential function in terms of a context.

Arithmetic Sequences

Compound Interest

Introduction to Exponential Functions

A2.F.TF.A: Extend the domain of trigonometric functions using the unit circle.

A2.F.TF.A.1: Understand and use radian measure of an angle.

A2.F.TF.A.1.b: Use the unit circle to find sin theta, cos theta, and tan theta when theta is a commonly recognized angle between theta and 2pi.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

A2.F.TF.A.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.

Cosine Function

Sine Function

Tangent Function

A2.F.TF.B: Prove and apply trigonometric identities.

A2.F.TF.B.3: Know and use trigonometric identities to find values of trig functions.

A2.F.TF.B.3.b: Given the quadrant of the angle, use the identity sin² theta + cos² theta = 1 to find sin theta given cos theta, or vice versa.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

A2.S.ID.A: Summarize, represent, and interpret data on a single count or measurement variable.

A2.S.ID.A.1: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.

Polling: City

Populations and Samples

Real-Time Histogram

A2.S.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.

A2.S.ID.B.2: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

A2.S.ID.B.2.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

Zap It! Game

A2.S.IC.A: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

A2.S.IC.A.1: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City

Polling: Neighborhood

A2.S.IC.A.2: Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context.

A2.S.CP.A: Understand independence and conditional probability and use them to interpret data.

A2.S.CP.A.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”).

Independent and Dependent Events

A2.S.CP.A.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.

Independent and Dependent Events

A2.S.CP.A.3: Know and 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.

Independent and Dependent Events

A2.S.CP.A.4: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

A2.S.CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

A2.S.CP.B.5: 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.

Independent and Dependent Events

Correlation last revised: 1/22/2020