Gizmos for Virginia - Mathematics: Algebra 2 (Standards of Learning adopted 2023)

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

A2.EO: : Expressions and Operations

A2.EO.2: : The student will perform operations on and simplify radical expressions.

A2.EO.2.a: : Simplify and determine equivalent radical expressions that include numeric and algebraic radicands.

A2.EO.2.b: : Add, subtract, multiply, and divide radical expressions that include numeric and algebraic radicands, simplifying the result. Simplification may include rationalizing the denominator.

A2.EO.3: : The student will perform operations on polynomial expressions and factor polynomial expressions in one and two variables.

A2.EO.3.a: : Determine sums, differences, and products of polynomials in one and two variables.

A2.EO.3.b: : Factor polynomials completely in one and two variables with no more than four terms over the set of integers.

A2.EO.3.c: : Determine the quotient of polynomials in one and two variables, using monomial, binomial, and factorable trinomial divisors.

A2.EO.3.d: : Represent and demonstrate equality of polynomial expressions written in different forms and verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials.

A2.EO.4: : The student will perform operations on complex numbers.

A2.EO.4.a: : Explain the meaning of i.

A2.EO.4.b: : Identify equivalent radical expressions containing negative rational numbers and expressions in a + bi form.

A2.EO.4.c: : Apply properties to add, subtract, and multiply complex numbers.

A2.EI: : Equations and Inequalities

A2.EI.1: : The student will represent, solve, and interpret the solution to absolute value equations and inequalities in one variable.

A2.EI.1.b: : Solve an absolute value equation in one variable algebraically and verify the solution graphically.

A2.EI.1.c: : Create an absolute value inequality in one variable to model a contextual situation.

A2.EI.1.d: : Solve an absolute value inequality in one variable and represent the solution set using set notation, interval notation, and using a number line.

A2.EI.1.e: : Verify possible solution(s) to absolute value equations and inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.

A2.EI.2: : The student will represent, solve, and interpret the solution to quadratic equations in one variable over the set of complex numbers and solve quadratic inequalities in one variable.

A2.EI.2.a: : Create a quadratic equation or inequality in one variable to model a contextual situation.

A2.EI.2.b: : Solve a quadratic equation in one variable over the set of complex numbers algebraically.

A2.EI.2.c: : Determine the solution to a quadratic inequality in one variable over the set of real numbers algebraically.

A2.EI.2.d: : Verify possible solution(s) to quadratic equations or inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.

A2.EI.5: : The student will represent, solve, and interpret the solution to an equation containing a radical expression.

A2.EI.5.a: : Solve an equation containing no more than one radical expression algebraically and graphically.

A2.EI.5.b: : Verify possible solution(s) to radical equations algebraically, graphically, and with technology, to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.

A2.EI.6: : The student will represent, solve, and interpret the solution to a polynomial equation.

A2.EI.6.a: : Determine a factored form of a polynomial equation, of degree three or higher, given its zeros or the x-intercepts of the graph of its related function.

A2.EI.6.b: : Determine the number and type of solutions (real or imaginary) of a polynomial equation of degree three or higher.

A2.F: : Functions

A2.F.1: : The student will investigate, analyze, and compare square root, cube root, rational, exponential, and logarithmic function families, algebraically and graphically, using transformations.

A2.F.1.a: : Distinguish between the graphs of parent functions for square root, cube root, rational, exponential, and logarithmic function families.

A2.F.1.b: : Write the equation of a square root, cube root, rational, exponential, and logarithmic function, given a graph, using transformations of the parent function, including f(x) + k; f(kx); f(x + k); and kf(x), where k is limited to rational values. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation.

A2.F.1.c: : Graph a square root, cube root, rational, exponential, and logarithmic function, given the equation, using transformations of the parent function including f(x) + k; f(kx); f(x + k); and kf(x), where k is limited to rational values. Use technology to verify transformations of the functions.

A2.F.1.d: : Determine when two variables are directly proportional, inversely proportional, or neither, given a table of values. Write an equation and create a graph to represent a direct or inverse variation, including situations in context.

A2.F.1.e: : Compare and contrast the graphs, tables, and equations of square root, cube root, rational, exponential, and logarithmic functions.

A2.F.2: : The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2.a: : Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.

A2.F.2.b: : Compare and contrast the characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions.

A2.F.2.c: : Determine the intervals on which the graph of a function is increasing, decreasing, or constant.

A2.F.2.d: : Determine the location and value of absolute (global) maxima and absolute (global) minima of a function.

A2.F.2.e: : Determine the location and value of relative (local) maxima or relative (local) minima of a function.

A2.F.2.f: : For any value, x, in the domain of f, determine f(x) using a graph or equation. Explain the meaning of x and f(x) in context, where applicable.

A2.F.2.g: : Describe the end behavior of a function.

A2.F.2.h: : Determine the equations of any vertical and horizontal asymptotes of a function using a graph or equation (rational, exponential, and logarithmic).

A2.F.2.i: : Determine the inverse of a function algebraically and graphically, given the equation of a linear or quadratic function (linear, quadratic, and square root). Justify and explain why two functions are inverses of each other.

A2.ST: : Statistics

A2.ST.1: : The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on univariate quantitative data represented by a smooth curve, including a normal curve.

A2.ST.1.d: : Identify the properties of a normal distribution.

A2.ST.1.e: : Describe and interpret a data distribution represented by a smooth curve by analyzing measures of center, measures of spread, and shape of the curve.

A2.ST.1.j: : Compare multiple data distributions using measures of center, measures of spread, and shape of the distributions.

A2.ST.2: : The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear, quadratic, exponential, or a combination of these functions.

A2.ST.2.a: : Formulate investigative questions that require the collection or acquisition of bivariate data and investigate questions using a data cycle.

A2.ST.2.b: : Collect or acquire bivariate data through research, or using surveys, observations, scientific experiments, polls, or questionnaires.

A2.ST.2.c: : Represent bivariate data with a scatterplot using technology.

A2.ST.2.e: : Determine the equation(s) of the function(s) that best models the relationship between two variables using technology. Curves of best fit may include a combination of linear, quadratic, or exponential (piecewise-defined) functions.

A2.ST.2.f: : Use the correlation coefficient to designate the goodness of fit of a linear function using technology.

A2.ST.2.g: : Make predictions, decisions, and critical judgments using data, scatterplots, or the equation(s) of the mathematical model.

A2.ST.3: : The student will compute and distinguish between permutations and combinations.

A2.ST.3.a: : Compare and contrast permutations and combinations to count the number of ways that events can occur.

A2.ST.3.b: : Calculate the number of permutations of n objects taken r at a time.

A2.ST.3.c: : Calculate the number of combinations of n objects taken r at a time.

A2.ST.3.d: : Use permutations and combinations as counting techniques to solve contextual problems.

A2.ST.3.e: : Calculate and verify permutations and combinations using technology.

Correlation last revised: 4/9/2024

Virginia - Mathematics: Algebra 2

Standards of Learning | Adopted: 2023

A2.EO: : Expressions and Operations

A2.EI: : Equations and Inequalities

A2.F: : Functions

A2.ST: : Statistics