WV--College- and Career-Readiness Standards

PRR.M.A2HS.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

PRR.M.A2HS.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

PRR.M.A2HS.3: Solve quadratic equations with real coefficients that have complex solutions. Instructional Note: Limit to polynomials with real coefficients.

Points in the Complex Plane

Roots of a Quadratic

PRR.M.A2HS.6: Interpret expressions that represent a quantity in terms of its context.

PRR.M.A2HS.6.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest

Exponential Growth and Decay

Unit Conversions

PRR.M.A2HS.6.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Compound Interest

Exponential Growth and Decay

Translating and Scaling Functions

Using Algebraic Expressions

PRR.M.A2HS.7: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II

Factoring Special Products

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

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

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations II

PRR.M.A2HS.9: 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.

PRR.M.A2HS.10: 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

Polynomials and Linear Factors

PRR.M.A2HS.11: 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.

Polynomials and Linear Factors

Quadratics in Factored Form

PRR.M.A2HS.13: 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, with coefficients determined for example by Pascal’s Triangle.

PRR.M.A2HS.16: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Instructional Note: Extend to simple rational and radical equations.

PRR.M.A2HS.17: 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 solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.

Cat and Mouse (Modeling with Linear Systems)

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

PRR.M.A2HS.18: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Absolute Value with Linear Functions

Exponential Functions

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Roots of a Quadratic

Zap It! Game

TF.M.A2HS.21: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

TF.M.A2HS.22: 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.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

MF.M.A2HS.23: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Compound Interest

Exploring Linear Inequalities in One Variable

Exponential Growth and Decay

Geometric Sequences

Modeling and Solving Two-Step Equations

Quadratic Inequalities

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

MF.M.A2HS.24: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

2D Collisions

Air Track

Compound Interest

Determining a Spring Constant

Golf Range

Points, Lines, and Equations

Slope-Intercept Form of a Line

MF.M.A2HS.25: 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.)

Linear Inequalities in Two Variables

Linear Programming

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

MF.M.A2HS.26: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.) While functions will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Algebra I.

Area of Triangles

Solving Formulas for any Variable

MF.M.A2HS.27: 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Roots of a Quadratic

Slope-Intercept Form of a Line

Translating and Scaling Sine and Cosine Functions

MF.M.A2HS.28: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (e.g., 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.)

General Form of a Rational Function

Introduction to Functions

Logarithmic Functions

Radical Functions

Rational Functions

MF.M.A2HS.29: 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.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

MF.M.A2HS.30: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

MF.M.A2HS.30.a: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions

Radical Functions

MF.M.A2HS.30.b: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function

Exponential Functions

Exponential Growth and Decay

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

MF.M.A2HS.32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.)

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Polynomial Form

Quadratics in Vertex Form

MF.M.A2HS.33: Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. (e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.)

Addition and Subtraction of Functions

Points, Lines, and Equations

MF.M.A2HS.34: 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Quadratics in Vertex Form

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

MF.M.A2HS.35: Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. (e.g., f(x) = 2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1.)

MF.M.A2HS.36: For exponential models, express as a logarithm the solution to a b 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.

Compound Interest

Logarithmic Functions

ICD.M.A2HS.39: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. (e.g., A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?)

Polling: City

Polling: Neighborhood

Populations and Samples

ICD.M.A2HS.41: 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.

Estimating Population Size

Polling: City

Polling: Neighborhood

ICD.M.A2HS.42: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Real-Time Histogram

Sight vs. Sound Reactions

ICD.M.A2HS.44: Use probabilities to make fair decisions (e.g., drawing by lots or using a random number generator).

Lucky Duck (Expected Value)

Probability Simulations

Theoretical and Experimental Probability

ICD.M.A2HS.45: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, and/or pulling a hockey goalie at the end of a game).

Estimating Population Size

Probability Simulations

Theoretical and Experimental Probability

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.