Skills available for South Carolina high school math standards
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: South Carolina College- and Career-Ready Standards: Algebra 1
A1.AAPR Arithmetic with Polynomials and Rational Expressions
A1.AAPR.1 Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations. (Limit to linear; quadratic.)
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)
A1.ACE Creating Equations
A1.ACE.1 Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable. (Limit to linear; quadratic; exponential with integer exponents.)
Write variable equations (A1-I.4)
Does x satisfy the equation? (A1-I.5)
Which x satisfies an equation? (A1-I.6)
Solve equations using order of operations (A1-I.7)
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)
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 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)
A1.ACE.2 Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.)
Graph a proportional relationship (A1-R.3)
Write direct variation equations (A1-R.4)
Write inverse variation equations (A1-R.7)
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)
Write linear functions to solve word problems (A1-S.12)
Write equations in standard form (A1-S.15)
Standard form: graph an equation (A1-S.17)
Graph a horizontal or vertical line (A1-S.19)
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)
Write linear, quadratic, and exponential functions (A1-CC.3)
A1.ACE.4 Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.
Rearrange multi-variable equations (A1-I.8)
Linear equations: solve for y (A1-S.11)
Write linear functions to solve word problems (A1-S.12)
A1.AREI Reasoning with Equations and Inequalities
A1.AREI.1 Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.
Properties of equality (A1-H.4)
A1.AREI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Solve equations using order of operations (A1-I.7)
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)
Solve linear equations: mixed review (A1-J.10)
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)
Solve two-step linear inequalities (A1-K.8)
Solve advanced linear inequalities (A1-K.10)
Solve compound inequalities (A1-K.14)
A1.AREI.4 Solve mathematical and real-world problems involving quadratic equations in one variable.
A1.AREI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x -h)² = k that has the same solutions. Derive the quadratic formula from this form.
Complete the square (A1-BB.8)
Solve a quadratic equation by completing the square (A1-BB.9)
A1.AREI.4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b. (Limit to non-complex roots.)
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)
A1.AREI.5 Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation.
Solve a system of equations using elimination (A1-U.10)
Solve a system of equations using elimination: word problems (A1-U.11)
Solve a system of equations using augmented matrices (A1-U.12)
Solve a system of equations using augmented matrices: word problems (A1-U.13)
A1.AREI.6 Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in two variables.
A1.AREI.6.a Solve systems of linear equations using the substitution method.
Solve a system of equations using substitution (A1-U.8)
Solve a system of equations using substitution: word problems (A1-U.9)
A1.AREI.6.b Solve systems of linear equations using linear combination.
Solve a system of equations using elimination (A1-U.10)
Solve a system of equations using elimination: word problems (A1-U.11)
A1.AREI.10 Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
Relations: convert between tables, graphs, mappings, and lists of points (A1-Q.1)
Complete a function table from an equation (A1-Q.10)
Interpret the graph of a function: word problems (A1-Q.11)
Complete a table and graph a linear function (A1-S.13)
A1.AREI.11 Solve an equation of the form f(x) = g(x) graphically by identifying the x - coordinate(s) of the point(s) of intersection of the graphs of y = f (x) and y = g(x). (Limit to linear; quadratic; exponential.)
Is (x, y) a solution to the system of equations? (A1-U.1)
Solve a system of equations by graphing (A1-U.2)
Solve a system of equations by graphing: word problems (A1-U.3)
Systems of linear and quadratic equations (A1-BB.13)
A1.AREI.12 Graph the solutions to a linear inequality in two variables.
Is (x, y) a solution to the system of inequalities? (A1-T.5)
Solve systems of linear inequalities by graphing (A1-T.6)
Solve systems of linear inequalities by graphing (A2-F.2)
A1.ASE Structure and Expressions
A1.ASE.1 Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear; quadratic; exponential.)
Polynomial vocabulary (A1-Z.1)
A1.ASE.2 Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.
Identify equivalent linear expressions (A1-I.3)
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)
A1.ASE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A1.ASE.3.a Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation.
Solve a quadratic equation using the zero product property (A1-BB.6)
A1.FBF Building Functions
A1.FBF.3 Describe the effect of the transformations kf (x), f(x) + k, f(x + k), and combinations of such transformations on the graph of y = f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph. (Limit to linear; quadratic; exponential with integer exponents; vertical shift and vertical stretch.)
Transformations of linear functions (A1-S.25)
Transformations of quadratic functions (A1-BB.3)
Transformations of absolute value functions (A1-DD.5)
A1.FIF Interpreting Functions
A1.FIF.1 Extend previous knowledge of a function to apply to general behavior and features of a function.
A1.FIF.1.a Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.
Identify functions (A1-Q.4)
Identify functions: vertical line test (A1-Q.5)
A1.FIF.1.b Represent a function using function notation and explain that f(x) denotes the output of function f that corresponds to the input x.
Slope-intercept form: write an equation from a table (A1-S.9)
A1.FIF.1.c Understand that the graph of a function labeled as f is the set of all ordered pairs (x,y) that satisfy the equation y =f(x).
Find values using function graphs (A1-Q.6)
Complete a function table from a graph (A1-Q.9)
Interpret the graph of a function: word problems (A1-Q.11)
Complete a table and graph a linear function (A1-S.13)
A1.FIF.2 Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation.
Evaluate a function (A1-Q.7)
Evaluate a function: plug in an expression (A1-Q.8)
Complete a function table from an equation (A1-Q.10)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Complete a function table: quadratic functions (A1-BB.2)
A1.FIF.4 Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. (Limit to linear; quadratic; exponential.)
Find the slope of a graph (A1-S.2)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
Compare linear functions: graphs, tables, and equations (A1-S.14)
Characteristics of quadratic functions (A1-BB.1)
Match quadratic functions and graphs (A1-BB.12)
A1.FIF.5 Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (Limit to linear; quadratic; exponential.)
Interpret the graph of a function: word problems (A1-Q.11)
Slope-intercept form: write an equation from a table (A1-S.9)
Complete a table and graph a linear function (A1-S.13)
Domain and range of exponential functions: equations (A1-X.4)
A1.FIF.6 Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context. (Limit to linear; quadratic; exponential.)
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)
A1.FIF.7 Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. (Limit to linear; quadratic; exponential only in the form y = a^{x} + k.)
Graph a proportional relationship (A1-R.3)
Slope-intercept form: graph an equation (A1-S.6)
Standard form: graph an equation (A1-S.17)
Graph a horizontal or vertical line (A1-S.19)
Point-slope form: graph an equation (A1-S.20)
Match exponential functions and graphs (A1-X.2)
Graph quadratic functions in vertex form (A1-BB.4)
Match quadratic functions and graphs (A1-BB.12)
Identify linear, quadratic, and exponential functions from graphs (A1-CC.1)
Graph a quadratic function (A2-J.3)
Match quadratic functions and graphs (A2-J.11)
A1.FIF.8 Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. (Limit to linear; quadratic; exponential.)
A1.FIF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
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)
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 by completing the square (A2-J.8)
A1.FIF.9 Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal. (Limit to linear; quadratic; exponential.)
A1.FLQE Linear, Quadratic, and Exponential
A1.FLQE.1 Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval.
A1.FLQE.1.a Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
Linear functions over unit intervals (A1-CC.4)
Exponential functions over unit intervals (A1-CC.5)
Describe linear and exponential growth and decay (A1-CC.6)
A1.FLQE.2 Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables. (Limit to linear; exponential.)
Write variable expressions for arithmetic sequences (A1-P.5)
Write variable expressions for geometric sequences (A1-P.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)
Compare linear functions: graphs, tables, and equations (A1-S.14)
Point-slope form: write an equation (A1-S.21)
Point-slope form: write an equation from a graph (A1-S.22)
Match exponential functions and graphs (A1-X.2)
Write linear, quadratic, and exponential functions (A1-CC.3)
A1.FLQE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function.
A1.FLQE.5 Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.)
Write linear functions to solve word problems (A1-S.12)
A1.NQ Quantities
A1.NQ.1 Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales when constructing graphs and other data displays.
Scale drawings: word problems (A1-C.7)
Convert rates and measurements: customary units (A1-E.1)
Convert rates and measurements: metric units (A1-E.2)
Unit prices with unit conversions (A1-E.3)
A1.NQ.2 Label and define appropriate quantities in descriptive modeling contexts.
Interpret bar graphs, line graphs, and histograms (A1-N.1)
Create bar graphs, line graphs, and histograms (A1-N.2)
Circle graphs (A1-N.3)
Interpret stem-and-leaf plots (A1-N.4)
Interpret box-and-whisker plots (A1-N.5)
Interpret a scatter plot (A1-KK.8)
Scatter plots: line of best fit (A1-KK.12)
A1.NQ.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities in context.
Precision (A1-E.4)
Greatest possible error (A1-E.5)
A1.NRNS Real Number System
A1.NRNS.1 Rewrite expressions involving simple radicals and rational exponents in different forms.
Evaluate expressions using properties of exponents (A1-V.8)
Evaluate integers raised to rational exponents (A1-V.10)
A1.NRNS.2 Use the definition of the meaning of rational exponents to translate between rational exponent and radical forms.
Evaluate integers raised to rational exponents (A1-V.10)
A1.NRNS.3 Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
A1.SPID Interpreting Data
A1.SPID.6 Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data.
Interpret a scatter plot (A1-KK.8)
Scatter plots: line of best fit (A1-KK.12)
Interpret regression lines (A1-KK.14)
Analyze a regression line of a data set (A1-KK.15)
A1.SPID.7 Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem.
Find the equation of a regression line (A1-KK.13)
A1.SPID.8 Using technology, compute and interpret the correlation coefficient of a linear fit.
Match correlation coefficients to scatter plots (A1-KK.10)