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Skills available for Virginia high school math standards

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Virginia Curriculum Framework: Algebra I Virginia Curriculum Framework: Algebra I
Virginia Curriculum Framework: Algebra II Virginia Curriculum Framework: Algebra II
Virginia Curriculum Framework: Algebra, Functions and Data Analysis Virginia Curriculum Framework: Algebra, Functions and Data Analysis
Virginia Curriculum Framework: Geometry Virginia Curriculum Framework: Geometry
Virginia Curriculum Framework: Mathematical Analysis Virginia Curriculum Framework: Mathematical Analysis
Virginia Curriculum Framework: Probability and Statistics Virginia Curriculum Framework: Probability and Statistics
Virginia Curriculum Framework: Trigonometry Virginia Curriculum Framework: Trigonometry
Virginia Standards of Learning (2016): Algebra I Virginia Standards of Learning (2016): Algebra I
Virginia Standards of Learning (2016): Algebra II Virginia Standards of Learning (2016): Algebra II
Virginia Standards of Learning (2016): Algebra, Functions and Data Analysis Virginia Standards of Learning (2016): Algebra, Functions and Data Analysis
Virginia Standards of Learning (2016): Geometry Virginia Standards of Learning (2016): Geometry
Virginia Standards of Learning (2016): Mathematical Analysis Virginia Standards of Learning (2016): Mathematical Analysis
Virginia Standards of Learning (2016): Probability and Statistics Virginia Standards of Learning (2016): Probability and Statistics
Virginia Standards of Learning (2016): Trigonometry Virginia Standards of Learning (2016): Trigonometry
Virginia College and Career Ready Performance Expectations Virginia College and Career Ready Performance Expectations
Virginia Standards of Learning (2023): Algebra 1 Virginia Standards of Learning (2023): Algebra 1
Virginia Standards of Learning (2023): Algebra 2 Virginia Standards of Learning (2023): Algebra 2
Virginia Standards of Learning (2023): Algebra, Functions and Data Analysis Virginia Standards of Learning (2023): Algebra, Functions and Data Analysis
Virginia Standards of Learning (2023): Discrete Mathematics Virginia Standards of Learning (2023): Discrete Mathematics
Virginia Standards of Learning (2023): Geometry Virginia Standards of Learning (2023): Geometry
Virginia Standards of Learning (2023): Mathematical Analysis Virginia Standards of Learning (2023): Mathematical Analysis
Virginia Standards of Learning (2023): Probability and Statistics Virginia Standards of Learning (2023): Probability and Statistics
Virginia Standards of Learning (2023): Trigonometry Virginia Standards of Learning (2023): Trigonometry

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A2.EO Expressions and Operations

A2.EO.1 The student will perform operations on and simplify rational expressions.
- A2.EO.1.a Add, subtract, multiply, or divide rational algebraic expressions, simplifying the result.
- A2.EO.1.b Justify and determine equivalent rational algebraic expressions with monomial and binomial factors. Algebraic expressions should be limited to linear and quadratic expressions.
  - Simplify rational expressions: linear and quadratic factors (A2)
- A2.EO.1.c Recognize a complex algebraic fraction and simplify it as a product or quotient of simple algebraic fractions.
  - Simplify complex fractions (A2-X.7)
- A2.EO.1.d Represent and demonstrate equivalence of rational expressions written in different forms.
  - Simplify rational expressions (A2-X.4)
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.2.c Convert between radical expressions and expressions containing rational exponents.
A2.EO.3 The student will perform operations on polynomial expressions in two or more variables 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.
  - Add and subtract polynomials (A2-L.2)
  - Multiply polynomials (A2-L.3)
- 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.
  - Divide polynomials using long division (A2-L.4)
  - Divide polynomials using synthetic division (A2-L.5)
- 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.
  - Powers of i (A2-K.8)
- A2.EO.4.b Identify equivalent radical expressions containing negative rational numbers and expressions in a + bi form.
  - Introduction to complex numbers (A2-K.1)
- A2.EO.4.c Apply properties to add, subtract, and multiply complex numbers.
  - Add and subtract complex numbers (A2-K.2)
  - Multiply complex numbers (A2-K.4)

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.a Create an absolute value equation in one variable to model a contextual situation.
  - Write absolute value equations from graphs (A2-G.3)
- A2.EI.1.b Solve an absolute value equation in one variable algebraically and verify the solution graphically.
  - Solve absolute value equations (A2-G.1)
  - Graph solutions to absolute value equations (A2-G.2)
- 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.
  - Solve absolute value inequalities (A2-G.4)
  - Graph solutions to absolute value inequalities (A2-G.5)
- 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.
  - Solve quadratic equations: word problems (A2-O.7)
- 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.
  - Solve quadratic inequalities (A2-O.10)
- 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.
  - Graph solutions to quadratic inequalities (A2-O.9)
A2.EI.3 The student will solve a system of equations in two variables containing a quadratic expression.
- A2.EI.3.a Create a linear-quadratic or quadratic-quadratic system of equations to model a contextual situation.
- A2.EI.3.b Determine the number of solutions to a linear-quadratic and quadratic-quadratic system of equations in two variables.
- A2.EI.3.c Solve a linear-quadratic and quadratic-quadratic system of equations algebraically and graphically, including situations in context.
- A2.EI.3.d Verify possible solution(s) to linear-quadratic or quadratic-quadratic system of 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.4 The student will represent, solve, and interpret the solution to an equation containing rational algebraic expressions.
- A2.EI.4.a Create an equation containing a rational expression to model a contextual situation.
- A2.EI.4.b Solve rational equations with real solutions containing factorable algebraic expressions algebraically and graphically. Algebraic expressions should be limited to linear and quadratic expressions.
  - Solve rational equations (A2-X.8)
- A2.EI.4.c Verify possible solution(s) to rational 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.4.d Justify why a possible solution to an equation containing a rational expression might be extraneous.
  - Solve rational equations (A2-X.8)
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.
  - Solve radical equations (A2-S.4)
- 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.5.c Justify why a possible solution to an equation with a square root might be extraneous.
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.
  - Write a quadratic function in factored form from its x-intercepts and another point (A2-N.12)
  - Write a polynomial from its roots (A2-Q.3)
- A2.EI.6.b Determine the number and type of solutions (real or imaginary) of a polynomial equation of degree three or higher.
  - Descartes' Rule of Signs (A2-Q.7)
  - Fundamental Theorem of Algebra (A2-Q.8)
- A2.EI.6.c Solve a polynomial equation over the set of complex numbers.
  - Solve polynomial equations (A2-Q.1)
  - Find the roots of factored polynomials (A2-Q.2)
- A2.EI.6.d Verify possible solution(s) to polynomial equations of degree three or higher algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions in context.
  - Match polynomials and graphs using zeros (A2-Q.10)

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.
  - Identify function types (A2)
- 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.
  - Linear functions over unit intervals (A2-D.4)
  - Exponential functions over unit intervals (A2-Z.6)
- A2.F.2.d Determine the location and value of absolute (global) maxima and absolute (global) minima of a function.
  - Find the maximum or minimum value of a quadratic function (A2)
- 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.
  - Match polynomials and graphs using end behavior (A2-Q.9)
- 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).
  - Rational functions: asymptotes and excluded values (A2-X.1)
- 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.F.2.j Graph the inverse of a function as a reflection over the line y = x.
  - Graphs of inverse functions (A2-V.)
- A2.F.2.k Determine the composition of two functions algebraically and graphically.

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.a Formulate investigative questions that require the collection or acquisition of a large set of univariate quantitative data or summary statistics of a large set of univariate quantitative data and investigate questions using a data cycle.
  - Experiment design (A2-RR.8)
- A2.ST.1.b Collect or acquire univariate data through research, or using surveys, observations, scientific experiments, polls, or questionnaires.
- A2.ST.1.c Examine the shape of a data set (skewed versus symmetric) that can be represented by a histogram, and sketch a smooth curve to model the distribution.
- A2.ST.1.d Identify the properties of a normal distribution.
  - Find values of normal variables (A2-QQ.5)
- 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.f Calculate and interpret the z-score for a value in a data set.
  - Find z-values (A2-QQ.4)
- A2.ST.1.g Compare two data points from two different distributions using z-scores.
- A2.ST.1.h Determine the solution to problems involving the relationship of the mean, standard deviation, and z-score of a data set represented by a smooth or normal curve.
  - Standard deviation of random variables (A2-PP.7)
  - Find probabilities using the normal distribution II (A2-QQ.3)
- A2.ST.1.i Apply the Empirical Rule to answer investigative questions.
  - Find probabilities using the normal distribution I (A2-QQ.2)
- 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.d Determine whether the relationship between two quantitative variables is best approximated by a linear, quadratic, exponential, or a combination of these functions.
  - Identify linear, quadratic, and exponential functions from tables (A2)
- 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.
  - Find the equation of a regression line (A2-SS.4)
  - Exponential regression (A2-SS.7)
- A2.ST.2.f Use the correlation coefficient to designate the goodness of fit of a linear function using technology.
  - Match correlation coefficients to scatter plots (A2-SS.2)
  - Calculate correlation coefficients (A2-SS.3)
- A2.ST.2.g Make predictions, decisions, and critical judgments using data, scatterplots, or the equation(s) of the mathematical model.
- A2.ST.2.h Evaluate the reasonableness of a mathematical model of a contextual situation.
  - Analyze a regression line of a data set (A2-SS.6)
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.
  - Combinations and permutations (A2-OO.3)
- A2.ST.3.b Calculate the number of permutations of n objects taken r at a time.
  - Combinations and permutations (A2-OO.3)
- A2.ST.3.c Calculate the number of combinations of n objects taken r at a time.
  - Combinations and permutations (A2-OO.3)
- A2.ST.3.d Use permutations and combinations as counting techniques to solve contextual problems.
  - Find probabilities using combinations and permutations (A2-OO.4)
  - Combinations and permutations: word problems (A2)
- A2.ST.3.e Calculate and verify permutations and combinations using technology.
  - Combinations and permutations (A2-OO.3)

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A2.EO Expressions and Operations

A2.EO.1 The student will perform operations on and simplify rational expressions.

A2.EO.1.a Add, subtract, multiply, or divide rational algebraic expressions, simplifying the result.

A2.EO.1.b Justify and determine equivalent rational algebraic expressions with monomial and binomial factors. Algebraic expressions should be limited to linear and quadratic expressions.

A2.EO.1.c Recognize a complex algebraic fraction and simplify it as a product or quotient of simple algebraic fractions.

A2.EO.1.d Represent and demonstrate equivalence of rational expressions written in different forms.

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.2.c Convert between radical expressions and expressions containing rational exponents.

A2.EO.3 The student will perform operations on polynomial expressions in two or more variables 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.a Create an absolute value equation in one variable to model a contextual situation.

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.3 The student will solve a system of equations in two variables containing a quadratic expression.

A2.EI.3.a Create a linear-quadratic or quadratic-quadratic system of equations to model a contextual situation.

A2.EI.3.b Determine the number of solutions to a linear-quadratic and quadratic-quadratic system of equations in two variables.

A2.EI.3.c Solve a linear-quadratic and quadratic-quadratic system of equations algebraically and graphically, including situations in context.

A2.EI.3.d Verify possible solution(s) to linear-quadratic or quadratic-quadratic system of 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.4 The student will represent, solve, and interpret the solution to an equation containing rational algebraic expressions.

A2.EI.4.a Create an equation containing a rational expression to model a contextual situation.

A2.EI.4.b Solve rational equations with real solutions containing factorable algebraic expressions algebraically and graphically. Algebraic expressions should be limited to linear and quadratic expressions.

A2.EI.4.c Verify possible solution(s) to rational 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.4.d Justify why a possible solution to an equation containing a rational expression might be extraneous.

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.5.c Justify why a possible solution to an equation with a square root might be extraneous.

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.EI.6.c Solve a polynomial equation over the set of complex numbers.

A2.EI.6.d Verify possible solution(s) to polynomial equations of degree three or higher algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions in context.

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.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.F.2.j Graph the inverse of a function as a reflection over the line y = x.

A2.F.2.k Determine the composition of two functions algebraically and graphically.

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.a Formulate investigative questions that require the collection or acquisition of a large set of univariate quantitative data or summary statistics of a large set of univariate quantitative data and investigate questions using a data cycle.

A2.ST.1.b Collect or acquire univariate data through research, or using surveys, observations, scientific experiments, polls, or questionnaires.

A2.ST.1.c Examine the shape of a data set (skewed versus symmetric) that can be represented by a histogram, and sketch a smooth curve to model the distribution.

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.f Calculate and interpret the z-score for a value in a data set.

A2.ST.1.g Compare two data points from two different distributions using z-scores.

A2.ST.1.h Determine the solution to problems involving the relationship of the mean, standard deviation, and z-score of a data set represented by a smooth or normal curve.