Skills available for Pennsylvania 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: Pennsylvania Keystone Exams: Algebra I
A1.1 Operations and Linear Equations & Inequalities
A1.1.1 Operations with Real Numbers and Expressions
A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).
A1.1.1.1.1 Compare and/or order any real numbers.
Compare and order rational numbers (A1-A.1)
Compare numbers written in scientific notation (A1-W.2)
A1.1.1.1.2 Simplify square roots (e.g., square root of 24 = 2 square root of 6).
Square roots (A1-A.6)
Simplify radical expressions (A1-EE.1)
A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem-solving settings.
A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
Divide monomials (A1-Y.3)
GCF of monomials (A1-AA.1)
Factor out a monomial (A1-AA.2)
A1.1.1.3 Use exponents, roots, and/or absolute values to solve problems.
A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems.
Square roots (A1-A.6)
Cube roots (A1-A.7)
Graph solutions to absolute value inequalities (A1-L.4)
Exponents with integer bases (A1-V.1)
Exponents with decimal and fractional bases (A1-V.2)
Negative exponents (A1-V.3)
Multiplication with exponents (A1-V.4)
Division with exponents (A1-V.5)
Multiplication and division with exponents (A1-V.6)
Power rule (A1-V.7)
Evaluate expressions using properties of exponents (A1-V.8)
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)
A1.1.1.5.2 Factor algebraic expressions, including difference of squares and trinomials.
Factor out a monomial (A1-AA.2)
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 (A1-BB.7)
A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
Simplify rational expressions (A1-GG.3)
Divide polynomials (A1-GG.5)
A1.1.2 Linear Equations
A1.1.2.1 Write, solve, and/or graph linear equations using various methods.
A1.1.2.1.1 Write, solve, and/or apply a linear equation (including problem situations).
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)
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)
Write variable expressions for arithmetic sequences (A1-P.5)
Write linear, quadratic, and exponential functions (A1-CC.3)
A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation-solving process.
Properties of addition and multiplication (8-V.10)
Properties of equality (8-W.5)
Distributive property (A1-H.2)
Simplify variable expressions using properties (A1-H.3)
Simplify variable expressions involving like terms and the distributive property (A1-I.2)
Solve equations using order of operations (A1-I.7)
Solve a quadratic equation using the zero product property (A1-BB.6)
A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation.
Solve linear equations: word problems (A1-J.9)
A1.1.2.2 Write, solve, and/or graph systems of linear equations using various methods.
A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination.
Is (x, y) a solution to the system of equations? (A1-U.1)
Solve a system of equations by graphing (A1-U.2)
Find the number of solutions to a system of equations by graphing (A1-U.4)
Find the number of solutions to a system of equations (A1-U.5)
Classify a system of equations by graphing (A1-U.6)
Classify a system of equations (A1-U.7)
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)
A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation.
A1.1.3 Linear Inequalities
A1.1.3.1 Write, solve, and/or graph linear inequalities using various methods.
A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).
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)
A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line.
Graph inequalities (A1-K.1)
Graph solutions to one-step linear inequalities (A1-K.7)
Graph solutions to two-step linear inequalities (A1-K.9)
Graph solutions to advanced linear inequalities (A1-K.11)
A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation.
Linear inequalities: word problems (A1-T.4)
A1.1.3.2 Write, solve, and/or graph systems of linear inequalities using various methods.
A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing.
A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation.
A1.2 Linear Functions and Data Organizations
A1.2.1 Functions
A1.2.1.1 Analyze and/or use patterns or relations.
A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
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)
A1.2.1.1.2 Determine whether a relation is a function, given a set of points or a graph.
Identify functions (A1-Q.4)
Identify functions: vertical line test (A1-Q.5)
A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
Domain and range of relations (A1-Q.2)
A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables.
A1.2.1.2.1 Create, interpret, and/or use the equation, graph, or table of a linear function.
Write direct variation equations (A1-R.4)
Write and solve direct variation equations (A1-R.5)
Identify linear functions (A1-S.1)
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)
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: find x- and y-intercepts (A1-S.16)
Standard form: graph an equation (A1-S.17)
Equations of horizontal and vertical lines (A1-S.18)
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)
Slopes of parallel and perpendicular lines (A1-S.23)
Write an equation for a parallel or perpendicular line (A1-S.24)
A1.2.1.2.2 Translate from one representation of a linear function to another (i.e., graph, table, and equation).
Slope-intercept form: graph an equation (A1-S.6)
Slope-intercept form: write an equation from a graph (A1-S.7)
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 from a graph (A1-S.22)
A1.2.2 Coordinate Geometry
A1.2.2.1 Describe, compute, and/or use the rate of change (slope) of a line.
A1.2.2.1.1 Identify, describe, and/or use constant rates of change.
Find the constant of variation (A1-R.2)
Identify linear functions (A1-S.1)
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)
A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.
Find the slope of a graph (A1-S.2)
Find the slope from two points (A1-S.3)
Write linear functions to solve word problems (A1-S.12)
A1.2.2.1.3 Write or identify a linear equation when given
A1.2.2.1.3.a the graph of the line,
Slope-intercept form: write an equation from a graph (A1-S.7)
Point-slope form: write an equation from a graph (A1-S.22)
A1.2.2.1.3.b two points on the line, or
A1.2.2.1.3.c the slope and a point on the line.
Slope-intercept form: write an equation (A1-S.8)
Point-slope form: write an equation (A1-S.21)
A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.
Find the slope of a graph (A1-S.2)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
Standard form: find x- and y-intercepts (A1-S.16)
A1.2.2.2 Analyze and/or interpret data on a scatter plot.
A1.2.2.2.1 Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot.
Scatter plots: line of best fit (A1-KK.12)
A1.2.3 Data Analysis
A1.2.3.1 Use measures of dispersion to describe a set of data.
A1.2.3.1.1 Calculate and/or interpret the range, quartiles, and interquartile range of data.
Mean, median, mode, and range (A1-KK.2)
Quartiles (A1-KK.3)
A1.2.3.2 Use data displays in problem-solving settings and/or to make predictions.
A1.2.3.2.1 Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations.
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)
A1.2.3.2.2 Analyze data, make predictions, and/or answer questions based on displayed data (box-and-whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations).
Interpret stem-and-leaf plots (A1-N.4)
Interpret box-and-whisker plots (A1-N.5)
Mean, median, mode, and range (A1-KK.2)
A1.2.3.2.3 Make predictions using the equations or graphs of best-fit lines of scatter plots.
Interpret a scatter plot (A1-KK.8)
Scatter plots: line of best fit (A1-KK.12)
A1.2.3.3 Apply probability to practical situations.
A1.2.3.3.1 Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent.
Compound events: find the number of outcomes (A1-JJ.3)
Identify independent and dependent events (A1-JJ.4)
Probability of independent and dependent events (A1-JJ.5)