Virginia

$Virginia flag$

Skills available for Virginia high school math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

Show alignments for:

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

Actions

Print standards

MA.CF Characteristics of Functions

MA.CF.1 The student will identify and analyze the properties of polynomial, rational, piecewise-defined, absolute value, radical, and step functions and sketch the graphs of the functions.
- MA.CF.1.a Use mathematical reasoning to identify polynomial, rational, piecewise-defined, absolute value, radical, and step functions, given an equation or graph.
- MA.CF.1.b Given multiple representations of a polynomial, rational, piecewise-defined, absolute value, radical, and step function, analyze: domain and range; roots (including complex roots); intercepts; symmetry (including even and odd functions); asymptotes (horizontal, vertical, and oblique/slant); points of discontinuity; intervals for which the function is increasing, decreasing or constant; end behavior; and relative and/or absolute maximum and minimum points.
- MA.CF.1.c Sketch the graph of a polynomial, rational, piecewise-defined, absolute value, radical, and step function.
MA.CF.2 The student will determine the limit of a function if it exists.
- MA.CF.2.a Verify estimates about the limit of a function using graphing technology.
- MA.CF.2.b Determine the limit of a function algebraically and verify with graphing technology.
- MA.CF.2.c Determine the limit of a function numerically and verify with graphing technology.
  - Find limits of polynomials and rational functions (PC-HH.10)
  - Find limits involving factorization and rationalization (PC-HH.11)
- MA.CF.2.d Use proper limit notation, including when describing the end behavior of a function.
  - Determine end behavior using graphs (PC-HH.5)
- MA.CF.2.e As the variable approaches a finite number,
  - MA.CF.2.e.i determine the limit of a function numerically by direct substitution;
    - Find limits of polynomials and rational functions (PC-HH.10)
  - MA.CF.2.e.ii determine the limit of a function using algebraic manipulation;
    - Find limits involving factorization and rationalization (PC-HH.11)
  - MA.CF.2.e.iii estimate the limit of a function using a table; and
  - MA.CF.2.e.iv determine the limit of a function from a given graph.
- MA.CF.2.f As the variable approaches positive or negative infinity, analyze the limit of a function to describe the end behavior.
  - Determine end behavior of polynomial and rational functions (PC)
MA.CF.3 The student will analyze and describe the continuity of functions.
- MA.CF.3.a Describe continuity of a function.
  - Identify graphs of continuous functions (PC-II.1)
- MA.CF.3.b Use mathematical notation to communicate and describe the continuity of functions including polynomial, rational, piecewise, absolute value, radical, and step function, using graphical and algebraic methods.
  - Determine continuity on an interval using graphs (PC-II.5)
  - Determine the continuity of a piecewise function at a point (C-E.6)
- MA.CF.3.c Prove continuity at a point, using the definition.
- MA.CF.3.d Classify types of discontinuity based on which condition of continuity is violated.
  - Find and analyze points of discontinuity using graphs (PC-II.4)

MA.FR Functional Relationships

MA.FR.1 The student will analyze compositions of functions to determine and verify inverses of functions.
- MA.FR.1.a Construct the composition of functions algebraically and graphically.
- MA.FR.1.b Determine the domain and range of composite functions algebraically and graphically.
- MA.FR.1.c Develop the inverse of a function algebraically and graphically.
- MA.FR.1.d Compare the domain and range of the inverse of a function with the original function, both algebraically and graphically.
- MA.FR.1.e Use mathematical reasoning to generalize and communicate the criteria for an inverse function to exist.
  - Check whether two rational functions are inverses (PC-G.3)
MA.FR.2 The student will analyze the characteristics of exponential and logarithmic functions, and sketch the graphs of the functions.
- MA.FR.2.a Generalize characteristics of exponential and logarithmic functions from an equation or a graph.
- MA.FR.2.b Define e and estimate its value.
  - Evaluate natural logarithms (A2-AA.5)
- MA.FR.2.c Convert between equations written in logarithmic and exponential form.
  - Convert between natural exponential and logarithmic form (A2-AA.2)
  - Convert between exponential and logarithmic form (PC-I.1)
- MA.FR.2.d Use laws of exponents and properties of logarithms to solve equations and simplify expressions.
- MA.FR.2.e Represent contextual problems, using exponential and logarithmic functions, to include common and natural logarithms.
- MA.FR.2.f Sketch the graph of exponential and logarithmic functions and identify asymptotes, end behavior, intercepts, domain, and range.
MA.FR.3 The student will analyze sequences and finite series, and model and solve problems in context using sequences and series.
- MA.FR.3.a Use and interpret the notation: ∑, n, n^th, and a_n.
- MA.FR.3.b Derive the formulas associated with arithmetic and geometric sequences and series.
- MA.FR.3.c Determine the n^th term, a_n, for an arithmetic or geometric sequence.
  - Find terms of a sequence (PC-AA.1)
  - Find terms of a recursive sequence (PC-AA.2)
- MA.FR.3.d Determine the sum, S_n, if it exists, of an arithmetic or geometric series.
- MA.FR.3.e Model and solve problems in context, using sequences and series.
  - Write a repeating decimal as a fraction (PC-BB.11)
- MA.FR.3.f Distinguish between a convergent and divergent series.
  - Convergent and divergent geometric series (PC-BB.9)
- MA.FR.3.g Describe convergent series in relation to the concept of a limit.
  - Find the value of an infinite geometric series (PC-BB.10)

MA.AG Analytic Geometry

MA.AG.1 The student will identify and analyze the properties of conic sections and sketch a graph given an equation.
- MA.AG.1.a Given a translation or rotation matrix, determine an equation for the transformed function or conic section.
- MA.AG.1.b Convert between standard and general forms of conic equations by completing the square.
- MA.AG.1.c Graph conic sections from equations written in general or standard form using transformations.
  - Graph parabolas (PC-U.3)
  - Graph circles (PC-U.6)
- MA.AG.1.d Identify characteristics of conic sections including center, vertices, axes, symmetry, foci, directrix, eccentricity, and asymptotes.
- MA.AG.1.e Represent applications of conic sections.
MA.AG.2 The student will use parametric equations to model and solve problems in context.
- MA.AG.2.a Graph and analyze parametric equations and use the graph to determine solutions.
- MA.AG.2.b Use parametric equations to model contextual problems, including motion over time.
MA.AG.3 The student will perform operations with vectors in the coordinate plane.
- MA.AG.3.a Use vector notation.
- MA.AG.3.b Perform the operations of addition, subtraction, and scalar multiplication, graphically and algebraically on vectors.
- MA.AG.3.c Find the dot (inner) product of two vectors and use it to determine the angle between two vectors.
- MA.AG.3.d Determine if two vectors are orthogonal.
- MA.AG.3.e Express complex numbers in vector notation.
  - Find the modulus and argument of a complex number (PC-X.1)
- MA.AG.3.f Verify properties of the dot product.
- MA.AG.3.g Determine the components of a vector.
  - Find the component form of a vector (PC-Y.2)
  - Find the component form of a three-dimensional vector (PC-Z.2)
- MA.AG.3.h Determine the norm (magnitude) of a vector.
  - Find the magnitude of a vector (PC-Y.1)
  - Find the magnitude of a three-dimensional vector (PC-Z.1)
- MA.AG.3.i Find a unit vector in the same direction of a given vector.
  - Find a unit vector (PC-Y.13)
  - Find a three-dimensional unit vector (PC-Z.5)
- MA.AG.3.j Apply vectors to problems in context.
MA.AG.4 The student will investigate and identify the characteristics of the graphs of polar equations.
- MA.AG.4.a Classify polar equations (rose, cardioid, limaçon, lemniscate, spiral, and circle), given the graph or the equation.
- MA.AG.4.b Determine the effects of changes in the parameters of polar equations on the graph, using graphing technology.
  - Match polar equations and graphs (PC-X.5)
- MA.AG.4.c Convert between polar and rectangular forms of coordinates.
- MA.AG.4.d Convert between complex numbers written in rectangular form and polar form.
- MA.AG.4.e Convert equations between polar and rectangular forms.
- MA.AG.4.f Determine and verify the intersection of the graphs of two polar equations, using graphing technology.
MA.AG.5 The student will use matrices to organize data and will add and subtract matrices, multiply matrices, multiply matrices by a scalar, and use matrices to solve systems of equations.
- MA.AG.5.a Multiply matrices by a scalar.
  - Multiply a matrix by a scalar (PC-Q.4)
- MA.AG.5.b Add, subtract, and multiply matrices.
- MA.AG.5.c Represent problems with a system of no more than three linear equations.
- MA.AG.5.d Express a system of linear equations as a matrix equation.
- MA.AG.5.e Solve a system of equations using matrices.
  - Solve a system of equations using augmented matrices (PC-N.8)
  - Solve a system of equations using augmented matrices: word problems (PC-N.9)
- MA.AG.5.f Determine the inverse of a two-by-two or three-by-three matrix using paper and pencil.
- MA.AG.5.g Verify two matrices are inverses using matrix multiplication.
  - Identify inverse matrices (PC-Q.14)
- MA.AG.5.h Verify the commutative and associative properties for matrix addition and multiplication.

Virginia

Show alignments for:

Actions

MA.CF Characteristics of Functions

MA.CF.1 The student will identify and analyze the properties of polynomial, rational, piecewise-defined, absolute value, radical, and step functions and sketch the graphs of the functions.

MA.CF.1.a Use mathematical reasoning to identify polynomial, rational, piecewise-defined, absolute value, radical, and step functions, given an equation or graph.

MA.CF.1.c Sketch the graph of a polynomial, rational, piecewise-defined, absolute value, radical, and step function.

MA.CF.2 The student will determine the limit of a function if it exists.

MA.CF.2.a Verify estimates about the limit of a function using graphing technology.

MA.CF.2.b Determine the limit of a function algebraically and verify with graphing technology.

MA.CF.2.c Determine the limit of a function numerically and verify with graphing technology.

MA.CF.2.d Use proper limit notation, including when describing the end behavior of a function.

MA.CF.2.e As the variable approaches a finite number,

MA.CF.2.e.i determine the limit of a function numerically by direct substitution;

MA.CF.2.e.ii determine the limit of a function using algebraic manipulation;

MA.CF.2.e.iii estimate the limit of a function using a table; and

MA.CF.2.e.iv determine the limit of a function from a given graph.

MA.CF.2.f As the variable approaches positive or negative infinity, analyze the limit of a function to describe the end behavior.

MA.CF.3 The student will analyze and describe the continuity of functions.

MA.CF.3.a Describe continuity of a function.

MA.CF.3.b Use mathematical notation to communicate and describe the continuity of functions including polynomial, rational, piecewise, absolute value, radical, and step function, using graphical and algebraic methods.

MA.CF.3.c Prove continuity at a point, using the definition.

MA.CF.3.d Classify types of discontinuity based on which condition of continuity is violated.

MA.FR Functional Relationships

MA.FR.1 The student will analyze compositions of functions to determine and verify inverses of functions.

MA.FR.1.a Construct the composition of functions algebraically and graphically.

MA.FR.1.b Determine the domain and range of composite functions algebraically and graphically.

MA.FR.1.c Develop the inverse of a function algebraically and graphically.

MA.FR.1.d Compare the domain and range of the inverse of a function with the original function, both algebraically and graphically.

MA.FR.1.e Use mathematical reasoning to generalize and communicate the criteria for an inverse function to exist.

MA.FR.2 The student will analyze the characteristics of exponential and logarithmic functions, and sketch the graphs of the functions.

MA.FR.2.a Generalize characteristics of exponential and logarithmic functions from an equation or a graph.

MA.FR.2.b Define e and estimate its value.

MA.FR.2.c Convert between equations written in logarithmic and exponential form.

MA.FR.2.d Use laws of exponents and properties of logarithms to solve equations and simplify expressions.

MA.FR.2.e Represent contextual problems, using exponential and logarithmic functions, to include common and natural logarithms.

MA.FR.2.f Sketch the graph of exponential and logarithmic functions and identify asymptotes, end behavior, intercepts, domain, and range.

MA.FR.3 The student will analyze sequences and finite series, and model and solve problems in context using sequences and series.

MA.FR.3.a Use and interpret the notation: ∑, n, nth, and an.

MA.FR.3.b Derive the formulas associated with arithmetic and geometric sequences and series.

MA.FR.3.c Determine the nth term, an, for an arithmetic or geometric sequence.

MA.FR.3.d Determine the sum, Sn, if it exists, of an arithmetic or geometric series.

MA.FR.3.e Model and solve problems in context, using sequences and series.

MA.FR.3.f Distinguish between a convergent and divergent series.

MA.FR.3.g Describe convergent series in relation to the concept of a limit.

MA.AG Analytic Geometry

MA.AG.1 The student will identify and analyze the properties of conic sections and sketch a graph given an equation.

MA.AG.1.a Given a translation or rotation matrix, determine an equation for the transformed function or conic section.

MA.AG.1.b Convert between standard and general forms of conic equations by completing the square.

MA.AG.1.c Graph conic sections from equations written in general or standard form using transformations.

MA.AG.1.d Identify characteristics of conic sections including center, vertices, axes, symmetry, foci, directrix, eccentricity, and asymptotes.

MA.AG.1.e Represent applications of conic sections.

MA.AG.2 The student will use parametric equations to model and solve problems in context.

MA.AG.2.a Graph and analyze parametric equations and use the graph to determine solutions.

MA.AG.2.b Use parametric equations to model contextual problems, including motion over time.

MA.AG.3 The student will perform operations with vectors in the coordinate plane.

MA.AG.3.a Use vector notation.

MA.AG.3.b Perform the operations of addition, subtraction, and scalar multiplication, graphically and algebraically on vectors.

MA.AG.3.c Find the dot (inner) product of two vectors and use it to determine the angle between two vectors.

MA.AG.3.d Determine if two vectors are orthogonal.

MA.AG.3.e Express complex numbers in vector notation.

MA.AG.3.f Verify properties of the dot product.

MA.AG.3.g Determine the components of a vector.

MA.AG.3.h Determine the norm (magnitude) of a vector.

MA.AG.3.i Find a unit vector in the same direction of a given vector.

MA.AG.3.j Apply vectors to problems in context.

MA.AG.4 The student will investigate and identify the characteristics of the graphs of polar equations.

MA.AG.4.a Classify polar equations (rose, cardioid, limaçon, lemniscate, spiral, and circle), given the graph or the equation.

MA.AG.4.b Determine the effects of changes in the parameters of polar equations on the graph, using graphing technology.

MA.AG.4.c Convert between polar and rectangular forms of coordinates.

MA.AG.4.d Convert between complex numbers written in rectangular form and polar form.

MA.AG.4.e Convert equations between polar and rectangular forms.

MA.AG.4.f Determine and verify the intersection of the graphs of two polar equations, using graphing technology.

MA.AG.5 The student will use matrices to organize data and will add and subtract matrices, multiply matrices, multiply matrices by a scalar, and use matrices to solve systems of equations.

MA.AG.5.a Multiply matrices by a scalar.

MA.AG.5.b Add, subtract, and multiply matrices.

MA.AG.5.c Represent problems with a system of no more than three linear equations.

MA.AG.5.d Express a system of linear equations as a matrix equation.

MA.AG.5.e Solve a system of equations using matrices.

MA.AG.5.f Determine the inverse of a two-by-two or three-by-three matrix using paper and pencil.

MA.FR.3.a Use and interpret the notation: ∑, n, n^th, and a_n.

MA.FR.3.c Determine the n^th term, a_n, for an arithmetic or geometric sequence.

MA.FR.3.d Determine the sum, S_n, if it exists, of an arithmetic or geometric series.