Standards are in bold, followed by a list of the IXL math skills that are aligned to that standards. Students can practice these skills online at www.ixl.com.
Standards: Virginia Standards of Learning
A.EO Expressions and Operations
A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.
A.2.b adding, subtracting, multiplying, and dividing polynomials; and
Polynomial vocabulary (A1-Z.1)
Model polynomials with algebra tiles (A1-Z.2)
Add and subtract polynomials using algebra tiles (A1-Z.3)
Add and subtract polynomials (A1-Z.4)
Add polynomials to find perimeter (A1-Z.5)
Multiply a polynomial by a monomial (A1-Z.6)
Multiply two polynomials using algebra tiles (A1-Z.7)
Multiply two binomials (A1-Z.8)
Multiply two binomials: special cases (A1-Z.9)
Multiply polynomials (A1-Z.10)
A.2.c factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.
GCF of monomials (A1-AA.1)
Factor out a monomial (A1-AA.2)
Factor quadratics using algebra tiles (A1-AA.3)
Factor quadratics with leading coefficient 1 (A1-AA.4)
Factor quadratics with other leading coefficients (A1-AA.5)
Factor quadratics: special cases (A1-AA.6)
Factor by grouping (A1-AA.7)
Factor polynomials (A1-AA.8)
Solve a quadratic equation by factoring (G-A.9)
A.3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form.
A.4 Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. The student will solve multistep linear and quadratic equations in two variables, including
A.4.a solving literal equations (formulas) for a given variable;
Rearrange multi-variable equations (A1-I.8)
Model and solve equations using algebra tiles (A1-J.1)
Write and solve equations that represent diagrams (A1-J.2)
Solve one-step linear equations (A1-J.3)
Solve two-step linear equations (A1-J.4)
Solve advanced linear equations (A1-J.5)
Solve equations with variables on both sides (A1-J.6)
Find the number of solutions (A1-J.7)
Solve linear equations: word problems (A1-J.9)
Solve linear equations: mixed review (A1-J.10)
Linear equations: solve for y (A1-S.11)
A.4.b justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;
Properties of addition and multiplication (A1-H.1)
Distributive property (A1-H.2)
Simplify variable expressions using properties (A1-H.3)
Properties of equality (A1-H.4)
Identify equivalent linear expressions (A1-I.3)
A.4.c solving quadratic equations algebraically and graphically;
Characteristics of quadratic functions (A1-BB.1)
Solve a quadratic equation using square roots (A1-BB.5)
Solve a quadratic equation using the zero product property (A1-BB.6)
Solve a quadratic equation by factoring (A1-BB.7)
Complete the square (A1-BB.8)
Solve a quadratic equation by completing the square (A1-BB.9)
Solve a quadratic equation using the quadratic formula (A1-BB.10)
Using the discriminant (A1-BB.11)
A.4.d solving multistep linear equations algebraically and graphically;
Solve two-step linear equations (A1-J.4)
Solve advanced linear equations (A1-J.5)
Solve equations with variables on both sides (A1-J.6)
Create equations with no solutions or infinitely many solutions (A1-J.8)
Solve linear equations: mixed review (A1-J.10)
Linear equations: solve for y (A1-S.11)
A.4.e solving systems of two linear equations in two variables algebraically and graphically; and
Solve a system of equations by graphing (A1-U.2)
Solve a system of equations using substitution (A1-U.8)
Solve a system of equations using elimination (A1-U.10)
Solve a system of equations using any method (A1-U.14)
A.4.f solving real-world problems involving equations and systems of equations.
Solve proportions: word problems (A1-C.6)
Solve linear equations: word problems (A1-J.9)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Write linear functions to solve word problems (A1-S.12)
Exponential growth and decay: word problems (A1-X.5)
A.5 The student will solve multistep linear inequalities in two variables, including
A.5.a solving multistep linear inequalities algebraically and graphically;
Does (x, y) satisfy the inequality? (A1-T.1)
Linear inequalities: solve for y (A1-T.2)
A.5.b justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets;
Graph inequalities (A1-K.1)
Write inequalities from graphs (A1-K.2)
Identify solutions to inequalities (A1-K.3)
Solve one-step linear inequalities: addition and subtraction (A1-K.4)
Solve one-step linear inequalities: multiplication and division (A1-K.5)
Solve one-step linear inequalities (A1-K.6)
Graph solutions to one-step linear inequalities (A1-K.7)
Solve two-step linear inequalities (A1-K.8)
Graph solutions to two-step linear inequalities (A1-K.9)
Solve advanced linear inequalities (A1-K.10)
Graph solutions to advanced linear inequalities (A1-K.11)
Graph compound inequalities (A1-K.12)
Write compound inequalities from graphs (A1-K.13)
Solve compound inequalities (A1-K.14)
Graph solutions to compound inequalities (A1-K.15)
Solve absolute value equations (A1-L.1)
Graph solutions to absolute value equations (A1-L.2)
Solve absolute value inequalities (A1-L.3)
Graph solutions to absolute value inequalities (A1-L.4)
A.5.c solving real-world problems involving inequalities; and
Linear inequalities: word problems (A1-T.4)
A.5.d solving systems of inequalities.
Is (x, y) a solution to the system of inequalities? (A1-T.5)
Solve systems of linear inequalities by graphing (A1-T.6)
A.6 The student will graph linear equations and linear inequalities in two variables, including
A.6.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. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and
Find the constant of variation (A1-R.2)
Find the slope of a graph (A1-S.2)
Find the slope from two points (A1-S.3)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
A.6.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.
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation (A1-S.8)
Write equations in standard form (A1-S.15)
Point-slope form: write an equation (A1-S.21)
Point-slope form: write an equation from a graph (A1-S.22)
A.F Functions
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
A.7.a determining whether a relation is a function;
Identify functions (A1-Q.4)
Identify functions: vertical line test (A1-Q.5)
A.7.b domain and range;
Domain and range of relations (A1-Q.2)
A.7.c zeros of a function;
Solve a quadratic equation by factoring (A1-BB.7)
A.7.d x- and y-intercepts;
Slope-intercept form: find the slope and y-intercept (A1-S.5)
Standard form: find x- and y-intercepts (A1-S.16)
A.7.e finding the values of a function for elements in its domain; and
Find values using function graphs (A1-Q.6)
Evaluate a function (A1-Q.7)
Evaluate a function: plug in an expression (A1-Q.8)
Complete a function table from a graph (A1-Q.9)
Complete a function table from an equation (A1-Q.10)
A.7.f making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.
Complete a function table from a graph (A1-Q.9)
Graph a proportional relationship (A1-R.3)
Write direct variation equations (A1-R.4)
Write and solve direct variation equations (A1-R.5)
Identify direct variation and inverse variation (A1-R.6)
Write inverse variation equations (A1-R.7)
Write and solve inverse variation equations (A1-R.8)
Slope-intercept form: graph an equation (A1-S.6)
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation (A1-S.8)
Slope-intercept form: write an equation from a table (A1-S.9)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Write linear functions to solve word problems (A1-S.12)
Complete a table and graph a linear function (A1-S.13)
Compare linear functions: graphs, tables, and equations (A1-S.14)
Standard form: find x- and y-intercepts (A1-S.16)
Standard form: graph an equation (A1-S.17)
Point-slope form: graph an equation (A1-S.20)
Point-slope form: write an equation (A1-S.21)
Point-slope form: write an equation from a graph (A1-S.22)
Slopes of parallel and perpendicular lines (A1-S.23)
Write an equation for a parallel or perpendicular line (A1-S.24)
Match quadratic functions and graphs (A1-BB.12)
A.8 The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.
Write direct variation equations (A1-R.4)
Write and solve direct variation equations (A1-R.5)
Identify direct variation and inverse variation (A1-R.6)
Write inverse variation equations (A1-R.7)
Write and solve inverse variation equations (A1-R.8)
A.S Statistics
A.9 The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores.
Mean, median, mode, and range (A1-KK.2)
Quartiles (A1-KK.3)
Mean absolute deviation (A1-KK.6)
Variance and standard deviation (A1-KK.7)
A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.
Interpret box-and-whisker plots (A1-N.5)
A.11 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.
Identify an outlier (A1-KK.4)
Identify an outlier and describe the effect of removing it (A1-KK.5)
Interpret a scatter plot (A1-KK.8)
Outliers in scatter plots (A1-KK.9)
Scatter plots: line of best fit (A1-KK.12)
Find the equation of a regression line (A1-KK.13)
Interpret regression lines (A1-KK.14)
Analyze a regression line of a data set (A1-KK.15)
9-12.MA Mathematical Analysis
9-12.MA.1 The student will investigate and identify the characteristics of polynomial and rational functions and use these to sketch the graphs of the functions. This will include determining zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Graphing utilities will be used to investigate and verify these characteristics.
Find the maximum or minimum value of a quadratic function (PC-C.1)
Characteristics of quadratic functions (PC-C.2)
Graph a quadratic function (PC-C.3)
Match quadratic functions and graphs (PC-C.4)
Solve a quadratic equation by factoring (PC-C.6)
Find the roots of factored polynomials (PC-D.4)
Write a polynomial from its roots (PC-D.5)
Rational root theorem (PC-D.6)
Conjugate root theorems (PC-D.8)
Descartes' Rule of Signs (PC-D.9)
Match polynomials and graphs (PC-D.11)
Solve equations with sums and differences of cubes (PC-D.13)
Rational functions: asymptotes and excluded values (PC-E.1)
9-12.MA.2 The student will apply compositions of functions and inverses of functions to real-world situations. Analytical methods and graphing utilities will be used to investigate and verify the domain and range of resulting functions.
9-12.MA.3 The student will investigate and describe the continuity of functions, using graphs and algebraic methods.
Identify graphs of continuous functions (C-I.1)
Determine continuity using graphs (C-I.2)
Determine one-sided continuity using graphs (C-I.3)
Determine the continuity of a piecewise defined function at a point (C-I.6)
9-12.MA.4 The student will expand binomials having positive integral exponents through the use of the Binomial Theorem, the formula for combinations, and Pascal's Triangle.
Pascal's triangle (PC-D.16)
Pascal's triangle and the Binomial Theorem (PC-D.17)
Binomial Theorem I (PC-D.18)
Binomial Theorem II (PC-D.19)
9-12.MA.5 The student will find the sum (sigma notation included) of finite and infinite convergent series, which will lead to an intuitive approach to a limit.
Identify arithmetic and geometric series (PC-W.9)
Introduction to sigma notation (PC-W.10)
Find the sum of a finite arithmetic or geometric series (PC-W.11)
Introduction to partial sums (PC-W.12)
Partial sums of arithmetic series (PC-W.13)
Partial sums of geometric series (PC-W.14)
Partial sums: mixed review (PC-W.15)
Convergent and divergent geometric series (PC-W.16)
Find the value of an infinite geometric series (PC-W.17)
9-12.MA.6 The student will use mathematical induction to prove formulas and mathematical statements.
9-12.MA.7 The student will find the limit of an algebraic function, if it exists, as the variable approaches either a finite number or infinity. A graphing utility will be used to verify intuitive reasoning, algebraic methods, and numerical substitution.
Find limits of polynomials and rational functions (C-F.5)
Find limits involving factorization and rationalization (C-F.6)
Determine end behavior of polynomial and rational functions (C-G.3)
Find the limit at a vertical asymptote of a rational function I (C-H.1)
Find the limit at a vertical asymptote of a rational function II (C-H.2)
9-12.MA.8 The student will investigate and identify the characteristics of conic section equations in (h, k) and standard forms. Transformations in the coordinate plane will be used to graph conic sections.
Find properties of parabolas (PC-P.1)
Write equations of parabolas in vertex form (PC-P.2)
Graph parabolas (PC-P.3)
Find properties of circles (PC-P.4)
Write equations of circles in standard form (PC-P.5)
Graph circles (PC-P.6)
Find properties of ellipses (PC-P.7)
Find the eccentricity of an ellipse (PC-P.8)
Write equations of ellipses in standard form (PC-P.9)
Find properties of hyperbolas (PC-P.10)
Find the eccentricity of a hyperbola (PC-P.11)
Write equations of hyperbolas in standard form (PC-P.12)
Convert equations of conic sections from general to standard form (PC-P.13)
9-12.MA.9 The student will investigate and identify the characteristics of exponential and logarithmic functions in order to graph these functions and solve equations and real-world problems. This will include the role of e, natural and common logarithms, laws of exponents and logarithms, and the solution of logarithmic and exponential equations.
Domain and range of exponential and logarithmic functions (PC-F.1)
Convert between exponential and logarithmic form (PC-F.2)
Solve exponential equations using factoring (PC-F.3)
Evaluate logarithms (PC-F.4)
Change of base formula (PC-F.5)
Product property of logarithms (PC-F.6)
Quotient property of logarithms (PC-F.7)
Power property of logarithms (PC-F.8)
Evaluate logarithms using properties (PC-F.9)
Solve exponential equations using logarithms (PC-F.10)
Solve logarithmic equations with one logarithm (PC-F.11)
Solve logarithmic equations with multiple logarithms (PC-F.12)
Exponential functions over unit intervals (PC-F.13)
Describe linear and exponential growth and decay (PC-F.15)
Exponential growth and decay: word problems (PC-F.16)
Compound interest: word problems (PC-F.17)
9-12.MA.10 The student will investigate and identify the characteristics of the graphs of polar equations, using graphing utilities. This will include classification of polar equations, the effects of changes in the parameters in polar equations, conversion of complex numbers from rectangular form to polar form and vice versa, and the intersection of the graphs of polar equations.
Convert complex numbers from rectangular to polar form (PC-T.2)
Convert complex numbers from polar to rectangular form (PC-T.3)
Convert complex numbers between rectangular and polar form (PC-T.4)
Match polar equations and graphs (PC-T.5)
9-12.MA.11 The student will perform operations with vectors in the coordinate plane and solve real-world problems, using vectors. This will include the following topics: operations of addition, subtraction, scalar multiplication, and inner (dot) product; norm of a vector; unit vector; graphing; properties; simple proofs; complex numbers (as vectors); and perpendicular components.
Find the magnitude of a vector (PC-U.1)
Find the component form of a vector (PC-U.2)
Find the direction angle of a vector (PC-U.3)
Find the component form of a vector from its magnitude and direction angle (PC-U.4)
Graph a resultant vector using the triangle method (PC-U.5)
Graph a resultant vector using the parallelogram method (PC-U.6)
Add and subtract vectors (PC-U.7)
Find the magnitude and direction of a vector sum (PC-U.8)
Multiply a vector by a scalar (PC-U.9)
Find the magnitude of a vector scalar multiple (PC-U.10)
Find a unit vector (PC-U.12)
Linear combinations of vectors (PC-U.13)
Find the magnitude of a three-dimensional vector (PC-V.1)
Find the component form of a three-dimensional vector (PC-V.2)
Add and subtract three-dimensional vectors (PC-V.3)
Scalar multiples of three-dimensional vectors (PC-V.4)
Find a three-dimensional unit vector (PC-V.5)
Linear combinations of three-dimensional vectors (PC-V.6)
9-12.MA.12 The student will use parametric equations to model and solve application problems.
9-12.MA.13 The student will identify, create, and solve real-world problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines.
Pythagorean Theorem (G-Q.1)
Law of Sines (PC-M.13)
Law of Cosines (PC-M.14)
9-12.MA.14 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.
Solve a system of equations using augmented matrices (A2-G.18)
Solve a system of equations using augmented matrices: word problems (A2-G.19)
Matrix vocabulary (PC-L.1)
Matrix operation rules (PC-L.2)
Add and subtract matrices (PC-L.3)
Multiply a matrix by a scalar (PC-L.4)
Add and subtract scalar multiples of matrices (PC-L.5)