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

Actions

Print standards

9-12. Students will apply algebraic, geometric, and statistical concepts and the relationships among them to solve problems, model relations, and make decisions using data and situations within and outside of mathematics. In accomplishing this goal, students will develop and enhance a repertoire of skills and strategies for solving a variety of problem types.

9-12.1 Solve practical problems involving rational numbers (including numbers in scientific notation), percents, ratios, and proportions.
9-12.2 Collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems using mathematical models. Mathematical models will include polynomial, exponential, and logarithmic functions.
9-12.3 Use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include
- 9-12.3.a investigating and using formulas for finding distance, midpoint, and slope;
- 9-12.3.b applying slope to verify and determine whether lines are parallel or perpendicular;
- 9-12.3.c investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and
- 9-12.3.d determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.
9-12.4 Verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems.
9-12.5 Solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.
9-12.6 Use formulas for surface area and volume of three-dimensional objects to solve real-world problems.
9-12.7 Use similar geometric objects in two- or three-dimensions to
- 9-12.7.a compare ratios between side lengths, perimeters, areas, and volumes;
- 9-12.7.b determine how changes in one or more dimensions of an object affect area and/or volume of the object;
- 9-12.7.c determine how changes in area and/or volume of an object affect one or more dimensions of the object; and
- 9-12.7.d solve real-world problems about similar geometric objects.
9-12.8 Compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features.
9-12.9 Design and conduct an experiment/survey. Key concepts include
- 9-12.9.a sample size;
- 9-12.9.b sampling technique;
- 9-12.9.c controlling sources of bias and experimental error;
- 9-12.9.d data collection; and
- 9-12.9.e data analysis and reporting.
9-12.10 Investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include ∑ and an.
9-12.11 Use angles, arcs, chords, tangents, and secants to
- 9-12.11.a investigate, verify, and apply properties of circles;
- 9-12.11.b solve real-world problems involving properties of circles; and
- 9-12.11.c find arc lengths and areas of sectors in circles.

9-12. Students will be able to recognize, use, and interpret various functions and their representations, including verbal descriptions, tables, equations, and graphs to make predictions and analyze relationships in solving complex, real-world mathematical problems.

9-12.12 Transfer between and analyze multiple representations of functions, including algebraic formulas, graphs, tables, and words. Select and use appropriate representations for analysis, interpretation, and prediction.
9-12.13 Investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.
9-12.14 Recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and convert between graphic and symbolic forms of functions. Use a transformational approach to graphing. Use graphing calculators as a tool to investigate the shapes and behaviors of these functions.
9-12.15 Use knowledge of transformations to write an equation, given the graph of a function (linear, quadratic, exponential, and logarithmic).
9-12.16 Investigate and analyze functions (linear, quadratic, exponential, and logarithmic families) algebraically and graphically. Key concepts include
9-12.17 Determine optimal values in problem situations by identifying constraints and using linear programming techniques.

9-12. Students will be able to perform and justify steps in mathematical procedures and calculations and graph and solve a range of equations types. Students will reason from a variety of representations such as graphs, tables, and charts and will use displays of univariate data to identify and interpret patterns. Students will be able to calculate probabilities and analyze distributions of data to make decisions.

9-12.18 Given rational, radical, or polynomial expressions,
9-12.19 Graph linear equations and linear inequalities in two variables, including
- 9-12.19.a determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line; describing slope as rate of change and determine if it is positive, negative, zero, or undefined; and
- 9-12.19.b writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.
9-12.20 Given a point other than the origin on the terminal side of an angle, use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant, and cosecant of the angle in standard position. Relate trigonometric functions defined on the unit circle to trigonometric functions defined in right triangles.
9-12.21 Given the coordinates of the center of a circle and a point on the circle, write the equation of the circle.
9-12.22 Analyze graphical displays of univariate data, including dotplots, stemplots, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Use appropriate technology to create graphical displays.
9-12.23 Analyze the normal distribution. Key concepts include
- 9-12.23.a characteristics of normally distributed data;
- 9-12.23.b percentiles;
- 9-12.23.c normalizing data, using z-scores; and
- 9-12.23.d area under the standard normal curve and probability.
9-12.24 Describe orally and in writing the relationships between the subsets of the real number system.
9-12.25 Perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and identify field properties that are valid for the complex numbers.
9-12.26 Solve, algebraically and graphically,
9-12.27 Given one of the six trigonometric functions in standard form,
- 9-12.27.a state the domain and the range of the function;
- 9-12.27.b determine the amplitude, period, phase shift, vertical shift, and asymptotes;
- 9-12.27.c sketch the graph of the function by using transformations for at least a two-period interval; and
- 9-12.27.d investigate the effect of changing the parameters in a trigonometric function on the graph of the function.
9-12.28 Find, without the aid of a calculator, the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. This includes converting angle measures from radians to degrees and vice versa.
9-12.29 Investigate and identify the characteristics of conic section equations in (h, k) and standard forms. Use transformations in the coordinate plane to graph conic sections.
9-12.30 Using two-way tables, analyze categorical data to describe patterns and departure from patterns and to find marginal frequency and relative frequencies, including conditional frequencies.
- Find probabilities using two-way frequency tables (PC-X.5)
- Find conditional probabilities using two-way frequency tables (PC-X.9)
9-12.31 Calculate probabilities. Key concepts include
- 9-12.31.a conditional probability;
- 9-12.31.b dependent and independent events;
- 9-12.31.c addition and multiplication rules;
- 9-12.31.d counting techniques (permutations and combinations); and
- 9-12.31.e Law of Large Numbers.

9-12. Students will recognize verification and proof as fundamental aspects of mathematical reasoning. Students will integrate and apply inductive and deductive reasoning skills to make, test, and evaluate mathematical statements. This applies equally through simple mathematical calculations, in geometric applications, and more abstract statistical and algebraic processes. Students will use logical reasoning to analyze an argument and to determine whether conclusions are valid.

9-12.32 Use the relationships between angles formed by two lines cut by a transversal to
- 9-12.32.a determine whether two lines are parallel;
  - Identify parallel, intersecting, and skew lines and planes (G-D.1)
- 9-12.32.b verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and
  - Proofs involving parallel lines I (G-D.7)
  - Proofs involving parallel lines II (G-D.8)
- 9-12.32.c solve real-world problems involving angles formed when parallel lines are cut by a transversal.
  - Transversals: name angle pairs (G-D.3)
  - Transversals of parallel lines: find angle measures (G-D.4)
9-12.33 Given information in the form of a figure or statement, prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.
9-12.34 Given information in the form of a figure or statement, prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs.
- Prove similarity statements (G-P.14)
9-12.35 Construct and justify the constructions of
- 9-12.35.a a line segment congruent to a given line segment;
- 9-12.35.b the perpendicular bisector of a line segment;
  - Construct the midpoint or perpendicular bisector of a segment (G-B.15)
- 9-12.35.c a perpendicular to a given line from a point not on the line;
  - Construct a perpendicular line (G-D.2)
- 9-12.35.d a perpendicular to a given line at a given point on the line;
  - Construct a perpendicular line (G-D.2)
- 9-12.35.e the bisector of a given angle,
  - Construct an angle bisector (G-C.7)
- 9-12.35.f an angle congruent to a given angle; and
  - Construct a congruent angle (G-C.8)
- 9-12.35.g a line parallel to a given line through a point not on the given line.
  - Construct parallel lines (G-D.6)
9-12.36 Verify basic trigonometric identities and make substitutions, using the basic identities.

Virginia

Show alignments for:

Actions

9-12.1 Solve practical problems involving rational numbers (including numbers in scientific notation), percents, ratios, and proportions.

9-12.2 Collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems using mathematical models. Mathematical models will include polynomial, exponential, and logarithmic functions.

9-12.3 Use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include

9-12.3.a investigating and using formulas for finding distance, midpoint, and slope;

9-12.3.b applying slope to verify and determine whether lines are parallel or perpendicular;

9-12.3.c investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and

9-12.3.d determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

9-12.4 Verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems.

9-12.5 Solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.

9-12.6 Use formulas for surface area and volume of three-dimensional objects to solve real-world problems.

9-12.7 Use similar geometric objects in two- or three-dimensions to

9-12.7.a compare ratios between side lengths, perimeters, areas, and volumes;

9-12.7.b determine how changes in one or more dimensions of an object affect area and/or volume of the object;

9-12.7.c determine how changes in area and/or volume of an object affect one or more dimensions of the object; and

9-12.7.d solve real-world problems about similar geometric objects.

9-12.8 Compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features.

9-12.9 Design and conduct an experiment/survey. Key concepts include

9-12.9.a sample size;

9-12.9.b sampling technique;

9-12.9.c controlling sources of bias and experimental error;

9-12.9.d data collection; and

9-12.9.e data analysis and reporting.

9-12.10 Investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include ∑ and an.

9-12.11 Use angles, arcs, chords, tangents, and secants to

9-12.11.a investigate, verify, and apply properties of circles;

9-12.11.b solve real-world problems involving properties of circles; and

9-12.11.c find arc lengths and areas of sectors in circles.

9-12. Students will be able to recognize, use, and interpret various functions and their representations, including verbal descriptions, tables, equations, and graphs to make predictions and analyze relationships in solving complex, real-world mathematical problems.

9-12.12 Transfer between and analyze multiple representations of functions, including algebraic formulas, graphs, tables, and words. Select and use appropriate representations for analysis, interpretation, and prediction.

9-12.13 Investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.

9-12.15 Use knowledge of transformations to write an equation, given the graph of a function (linear, quadratic, exponential, and logarithmic).

9-12.16 Investigate and analyze functions (linear, quadratic, exponential, and logarithmic families) algebraically and graphically. Key concepts include

9-12.16.a continuity;

9-12.16.b local and absolute maxima and minima;

9-12.16.c domain and range, including limited and discontinuous domains and ranges;

9-12.16.d zeros;

9-12.16.e x- and y-intercepts;

9-12.16.f intervals in which a function is increasing or decreasing;

9-12.16.g asymptotes;

9-12.16.h end behavior;

9-12.16.i inverse of a function;

9-12.16.j composition of multiple functions;

9-12.16.k finding the values of a function for elements in its domain; and

9-12.16.l making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

9-12.17 Determine optimal values in problem situations by identifying constraints and using linear programming techniques.

9-12.18 Given rational, radical, or polynomial expressions,

9-12.18.a add, subtract, multiply, divide, and simplify rational algebraic expressions;

9-12.18.b add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents;

9-12.18.c write radical expressions as expressions containing rational exponents and vice versa; and

9-12.18.d factor polynomials completely.

9-12.19 Graph linear equations and linear inequalities in two variables, including

9-12.19.a determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line; describing slope as rate of change and determine if it is positive, negative, zero, or undefined; and

9-12.19.b writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

9-12.21 Given the coordinates of the center of a circle and a point on the circle, write the equation of the circle.

9-12.22 Analyze graphical displays of univariate data, including dotplots, stemplots, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Use appropriate technology to create graphical displays.

9-12.23 Analyze the normal distribution. Key concepts include

9-12.23.a characteristics of normally distributed data;

9-12.23.b percentiles;

9-12.23.c normalizing data, using z-scores; and

9-12.23.d area under the standard normal curve and probability.

9-12.24 Describe orally and in writing the relationships between the subsets of the real number system.

9-12.25 Perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and identify field properties that are valid for the complex numbers.

9-12.26 Solve, algebraically and graphically,

9-12.26.a absolute value equations and inequalities;

9-12.26.b quadratic equations over the set of complex numbers;

9-12.26.c equations containing rational algebraic expressions; and

9-12.26.d equations containing radical expressions.

9-12.27 Given one of the six trigonometric functions in standard form,

9-12.27.a state the domain and the range of the function;

9-12.27.b determine the amplitude, period, phase shift, vertical shift, and asymptotes;

9-12.27.c sketch the graph of the function by using transformations for at least a two-period interval; and

9-12.27.d investigate the effect of changing the parameters in a trigonometric function on the graph of the function.

9-12.28 Find, without the aid of a calculator, the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. This includes converting angle measures from radians to degrees and vice versa.

9-12.29 Investigate and identify the characteristics of conic section equations in (h, k) and standard forms. Use transformations in the coordinate plane to graph conic sections.

9-12.30 Using two-way tables, analyze categorical data to describe patterns and departure from patterns and to find marginal frequency and relative frequencies, including conditional frequencies.

9-12.31 Calculate probabilities. Key concepts include

9-12.31.a conditional probability;