Algebra 1 - ALEKS

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Algebra 1This course covers the topics shown below.Students navigate learning paths based on their level of readiness.Inst itut ional users may customize the scope and sequence to meet curricular needs.

Curriculum (494 topics + 673 addit ional topics)

Arithmetic Readiness (65 topics)

Factors, Mult iples, and Equivalent Fract ions (7 topics)FactorsGreatest common factor of 2 numbersLeast common mult iple of 2 numbersLeast common mult iple of 3 numbersEquivalent f ract ionsSimplifying a f ract ionDivision involving zero

Addit ion and Subtract ion with Fract ions (4 topics)Finding the LCD of two f ract ionsAddit ion or subtract ion of f ract ions with the same denominatorIntroduct ion to addit ion or subtract ion of f ract ions with different denominatorsAddit ion or subtract ion of f ract ions with different denominators

Mult iplicat ion and Division with Fract ions (7 topics)Product of a unit f ract ion and a whole numberProduct of a f ract ion and a whole number: Problem type 1Introduct ion to f ract ion mult iplicat ionFract ion mult iplicat ionProduct of a f ract ion and a whole number: Problem type 2The reciprocal of a numberDivision involving a whole number and a f ract ion

Mixed Numbers (2 topics)Writ ing an improper f ract ion as a mixed numberWrit ing a mixed number as an improper f ract ion

Rounding, Ordering, and the Number Line (11 topics)Rounding to tens or hundredsRounding to hundreds or thousandsDecimal place value: Tenths and hundredthsRounding decimalsFract ional posit ion on a number linePlott ing f ract ions on a number lineUsing a common denominator to order f ract ionsIntroduct ion to ordering decimalsOrdering decimalsUsing a calculator to convert a f ract ion to a rounded decimalOrdering f ract ions and decimals

Addit ion and Subtract ion with Decimals (6 topics)Addit ion of aligned decimalsDecimal subtract ion: BasicDecimal subtract ion: AdvancedWord problem with addit ion of 3 or 4 decimals and whole numbersWord problem with addit ion or subtract ion of 2 decimalsWord problem with subtract ion of a whole number and a decimal: Regrouping with zeros

Mult iplicat ion and Division with Decimals (5 topics)Mult iplicat ion of a decimal by a power of tenMult iplying a decimal by a whole numberWord problem with mult iple decimal operat ions: Problem type 1Division of a decimal by a power of tenDivision of a decimal by a whole number

Convert ing Between Fract ions and Decimals (3 topics)Convert ing a f ract ion to a terminat ing decimal: BasicConvert ing a f ract ion to a repeating decimal: BasicConvert ing a decimal to a proper f ract ion in simplest form: Basic


Ratios and Unit Rates (3 topics)Solving a word problem on proport ions using a unit rateFinding missing values in a table of equivalent rat iosUsing a table of equivalent rat ios to find a missing quantity in a rat io

Percents, Decimals, and Fract ions (6 topics)Introduct ion to convert ing a percentage to a decimalIntroduct ion to convert ing a decimal to a percentageConvert ing between percentages and decimalsConvert ing a f ract ion to a percentage: Denominator of 4, 5, or 10Convert ing a f ract ion to a percentage: Denominator of 20, 25, or 50Using a calculator to convert a f ract ion to a rounded percentage

Introduct ion to Percent Applicat ions (5 topics)Finding a percentage of a whole numberFinding a percentage of a whole number without a calculator: BasicFinding a percentage of a total amount: Real-world situat ionsFinding a percentage of a total amount without a calculator: Sales tax, commission, discountWrit ing a rat io as a percentage

Units of Measurement (6 topics)U.S. Customary length conversion with whole number valuesU.S. Customary length conversions involving rounding decimalsU.S. Customary volume conversion with whole number valuesU.S. Customary weight conversions with whole number valuesTime unit conversion with whole number valuesConvert ing between metric and U.S. Customary unit systems

Real Numbers (71 topics)

Plott ing and Ordering (9 topics)Plott ing integers on a number linePlott ing rat ional numbers on a number lineOrdering integersWrit ing a signed number for a real-world situat ionSquare root of a perfect squareUsing a calculator to approximate a square rootOrdering real numbersAbsolute value of a numberFinding all numbers with a given absolute value

Operat ions with Signed Numbers (13 topics)Integer addit ion: Problem type 1Integer addit ion: Problem type 2Integer subtract ion: Problem type 1Integer subtract ion: Problem type 2Integer subtract ion: Problem type 3Addit ion and subtract ion with 3 integersOperat ions with absolute value: Problem type 1Computing the distance between two integers on a number lineInteger mult iplicat ion and divisionMult iplicat ion of 3 or 4 integersSigned f ract ion addit ion or subtract ion: BasicSigned f ract ion mult iplicat ion: BasicSigned decimal addit ion and subtract ion

Exponents and Order of Operat ions (8 topics)Writ ing expressions using exponentsIntroduct ion to exponentsOrder of operat ions with whole numbersOrder of operat ions with whole numbers and exponents: BasicExponents and f ract ionsExponents and integers: Problem type 1Exponents and signed f ract ionsOrder of operat ions with integers

Evaluat ing Expressions (7 topics)Evaluat ing an algebraic expression: Whole number addit ion or subtract ionEvaluat ing an algebraic expression: Whole number mult iplicat ion or divisionEvaluat ing an algebraic expression: Whole numbers with two operat ionsEvaluat ing a formulaEvaluat ing an algebraic expression: Whole numbers with one operat ion and an exponentEvaluat ing a linear expression: Integer mult iplicat ion with addit ion or subtract ionEvaluat ing a quadrat ic expression: Integers


Venn Diagrams and Sets of Real Numbers (7 topics)Identifying numbers as integers or non-integersIdentifying rat ional decimal numbersIdentifying true statements about rat ional and irrat ional numbersIdentifying numbers as rat ional or irrat ionalInterpret ing a Venn diagram of 2 setsConstruct ing a Venn diagram to classify real numbersConstruct ing a Venn diagram to describe relat ionships between sets of real numbers

Propert ies of Operat ions (12 topics)Combining like terms: Whole number coefficientsCombining like terms: Integer coefficientsCombining like terms: Decimal coefficientsMult iplying a constant and a linear monomialDistribut ive property: Whole number coefficientsDistribut ive property: Integer coefficientsDistribut ive property: Fract ional coefficientsFactoring a linear binomialIdentifying parts in an algebraic expressionIdentifying equivalent algebraic expressionsUsing distribut ion and combining like terms to simplify: UnivariateCombining like terms in a quadrat ic expression

One-Step Linear Equations (12 topics)Identifying solut ions to a one-step linear equation: Problem type 1Identifying solut ions to a one-step linear equation: Problem type 2Addit ive property of equality with whole numbersAddit ive property of equality with decimalsAddit ive property of equality with integersAddit ive property of equality with signed f ract ionsMult iplicat ive property of equality with whole numbersMult iplicat ive property of equality with whole numbers: Fract ional answersMult iplicat ive property of equality with f ract ionsMult iplicat ive property of equality with decimalsMult iplicat ive property of equality with integersMult iplicat ive property of equality with signed f ract ions

Geometry (3 topics)Perimeter of a square or a rectangleWrit ing algebraic expressions for the perimeter of a figureArea of a square or a rectangle

Linear Equations (52 topics)

Mult i-Step Linear Equations (18 topics)Identifying solut ions to a linear equation in one variable: Two-step equationsUsing two steps to solve an equation with whole numbersAddit ive property of equality with a negative coefficientSolving a two-step equation with integersIntroduct ion to using subst itut ion to solve a linear equationIntroduct ion to solving an equation with parenthesesSolving a mult i-step equation given in f ract ional formIdentifying propert ies used to solve a linear equationIntroduct ion to solving an equation with variables on the same sideSolving a linear equation with several occurrences of the variable: Variables on the same sideIntroduct ion to solving a linear equation with a variable on each sideSolving a linear equation with several occurrences of the variable: Variables on both sidesSolving a linear equation with several occurrences of the variable: Variables on the same side and distribut ionSolving a linear equation with several occurrences of the variable: Variables on both sides and distribut ionSolving a linear equation with several occurrences of the variable: Variables on both sides and two distribut ionsClearing f ract ions in an equationSolving a two-step equation with signed f ract ionsSolving equations with zero, one, or infinitely many solut ions

Absolute Value Equations (3 topics)Introduct ion to solving an absolute value equationSolving an absolute value equation: Problem type 1Solving an absolute value equation: Problem type 2

Writ ing Expressions and Equations (6 topics)Writ ing a one-step expression for a real-world situat ionTranslat ing a phrase into a one-step expressionTranslat ing a phrase into a two-step expressionTranslat ing a sentence into a one-step equation


Writ ing an equation to represent a proport ional relat ionshipTranslat ing a sentence into a mult i-step equation

Applicat ions of Linear Equations (5 topics)Writ ing an equation of the form Ax + B = C to solve a word problemSolving a decimal word problem using a linear equation of the form Ax + B = CSolving a word problem with two unknowns using a linear equationWrit ing an equation to represent a real-world problem: Variable on both sidesSolving a one-step word problem using the formula d = rt

Applicat ions Involving Geometry (3 topics)Finding side lengths of squares given an area and a perimeterFinding side lengths of rectangles given one dimension and an area or a perimeterFinding the dimensions of a rectangle given its perimeter and a relat ionship between sides

Solving for a Variable and Dimensional Analysis (6 topics)Solving for a variable in terms of other variables using addit ion or subtract ion: BasicSolving for a variable in terms of other variables using mult iplicat ion or division: BasicSolving for a variable in terms of other variables using addit ion or subtract ion with divisionSolving for a variable inside parentheses in terms of other variablesU.S. Customary length conversions involving dimensional analysisConvert ing between compound units: Basic

Proport ions (3 topics)Solving a proport ion of the form x/a=b/c: BasicSolving a proport ion of the form x/a = b/cWord problem on proport ions: Problem type 1

More on Percents (8 topics)Applying the percent equation: Problem type 1Finding the mult iplier to give a final amount af ter a percentage increase or decreaseFinding the final amount given the original amount and a percentage increase or decreaseFinding the sale price given the original price and percent discountFinding the percentage increase or decrease: BasicFinding the percentage increase or decrease: AdvancedFinding the absolute error and percent error of a measurementIntroduct ion to compound interest

Linear Inequalit ies (29 topics)

Writ ing and Graphing Inequalit ies (6 topics)Translat ing a sentence by using an inequality symbolTranslat ing a sentence into a one-step inequalityIntroduct ion to identifying solut ions to an inequalityWrit ing an inequality for a real-world situat ionGraphing a linear inequality on the number lineWrit ing an inequality given a graph on the number line

One-Step Linear Inequalit ies (6 topics)Identifying solut ions to a one-step linear inequalityAddit ive property of inequality with whole numbersAddit ive property of inequality with integersMult iplicat ive property of inequality with whole numbersMult iplicat ive property of inequality with integersMult iplicat ive property of inequality with signed f ract ions

Mult i-Step Linear Inequalit ies (8 topics)Identifying solut ions to a two-step linear inequality in one variableSolving a two-step linear inequality with whole numbersSolving a two-step linear inequality: Problem type 1Solving a two-step linear inequality: Problem type 2Solving a two-step linear inequality with a f ract ional coefficientSolving a linear inequality with mult iple occurrences of the variable: Problem type 1Solving a linear inequality with mult iple occurrences of the variable: Problem type 2Solving inequalit ies with no solut ion or all real numbers as solut ions

Applicat ions (3 topics)Solving a word problem using a one-step linear inequalitySolving a word problem using a two-step linear inequalitySolving a decimal word problem using a two-step linear inequality

Compound Inequalit ies (2 topics)Graphing a compound inequality on the number lineSolving a compound linear inequality: Graph solut ion, basic


Absolute Value Inequalit ies (4 topics)Solving an absolute value inequality: Problem type 1Writ ing an absolute value inequality given a graph on the number lineSolving an absolute value inequality: Problem type 3Solving an absolute value inequality: Problem type 4

Funct ions and Lines (114 topics)

Ordered Pairs (3 topics)Reading a point in the coordinate planePlott ing a point in the coordinate planeFinding distances between points that share a common coordinate given the graph

Tables and Graphs of Lines (14 topics)Funct ion tables with two-step rulesTable for a linear equationWrit ing a funct ion rule given a table of ordered pairs: One-step rulesIdentifying solut ions to a linear equation in two variablesFinding a solut ion to a linear equation in two variablesGraphing a linear equation of the form y = mxGraphing a line given its equation in slope-intercept form: Integer slopeGraphing a line given its equation in slope-intercept form: Fract ional slopeGraphing a line given its equation in standard formGraphing a vert ical or horizontal lineFinding x- and y-intercepts given the graph of a line on a gridFinding x- and y-intercepts of a line given the equation: BasicGraphing a line by first finding its x- and y-interceptsInterpret ing a line graph

Slope (7 topics)Finding slope given the graph of a line in quadrant 1 that models a real-world situat ionClassifying slopes given graphs of linesFinding slope given the graph of a line on a gridFinding slope given two points on the lineFinding the slope of horizontal and vert ical linesGraphing a line given its slope and y-interceptGraphing a line through a given point with a given slope

Direct Variat ion (4 topics)Identifying direct variat ion equationsIdentifying direct variat ion f rom ordered pairs and writ ing equationsWrit ing a direct variat ion equationWord problem on direct variat ion

Equations of Lines (16 topics)Identifying linear funct ions given ordered pairsFinding the slope and y-intercept of a line given its equation in the form y = mx + bFinding the slope and y-intercept of a line given its equation in the form Ax + By = CGraphing a line by first finding its slope and y-interceptWrit ing an equation of a line given its slope and y-interceptFinding the slope, y-intercept, and equation for a linear funct ion given a table of valuesWrit ing an equation in slope-intercept form given the slope and a pointFinding the slope and a point on a line given its equation in point-slope formWrit ing an equation in point-slope form given the slope and a pointWrit ing an equation of a line given the y-intercept and another pointWrit ing the equation of the line through two given pointsComparing linear funct ions to the parent funct ion y=xFinding slopes of lines parallel and perpendicular to a line given in slope-intercept formFinding slopes of lines parallel and perpendicular to a line given in the form Ax + By = CIdentifying parallel and perpendicular lines f rom equationsWrit ing equations of lines parallel and perpendicular to a given line through a point

Applicat ions of Linear Equations with Two Variables (15 topics)Finding outputs of a one-step funct ion that models a real-world situat ion: Two variable equationFinding outputs of a two-step funct ion with decimals that models a real-world situat ion: Two variable equationFinding inputs and outputs of a two-step funct ion that models a real-world situat ion: Two variable equationWrit ing and evaluat ing a funct ion that models a real-world situat ion: BasicWrit ing and evaluat ing a funct ion that models a real-world situat ion: AdvancedWrit ing an equation and drawing its graph to model a real-world situat ion: BasicWrit ing an equation and drawing its graph to model a real-world situat ion: AdvancedFinding the intercepts and rate of change given a graph of a linear funct ionFinding the init ial amount and rate of change given a table for a linear funct ionCombining funct ions to write a new funct ion that models a real-world situat ionComparing propert ies of linear funct ions given in different forms


Interpret ing the parameters of a linear funct ion that models a real-world situat ionApplicat ion problem with a linear funct ion: Finding a coordinate given the slope and a pointApplicat ion problem with a linear funct ion: Finding a coordinate given two pointsSolving a linear equation by graphing

Scatter Plots and Lines of Best Fit (9 topics)Construct ing a scatter plotSketching the line of best fitScatter plots and correlat ionPredict ions f rom the line of best fitApproximating the equation of a line of best fit and making predict ionsComputing residualsInterpret ing residual plotsLinear relat ionship and the correlat ion coefficientIdentifying correlat ion and causat ion

Introduct ion to Funct ions (10 topics)Identifying funct ions f rom relat ionsVert ical line testDomain and range f rom ordered pairsTable for a linear funct ionEvaluat ing funct ions: Linear and quadrat ic or cubicEvaluat ing a piecewise-defined funct ionFinding outputs of a one-step funct ion that models a real-world situat ion: Funct ion notat ionFinding outputs of a two-step funct ion with decimals that models a real-world situat ion: Funct ion notat ionFinding inputs and outputs of a two-step funct ion that models a real-world situat ion: Funct ion notat ionDomain and range of a linear funct ion that models a real-world situat ion

Arithmetic Sequences (9 topics)Finding the first terms of an arithmetic sequence using an explicit ruleFinding the next terms of an arithmetic sequence with whole numbersFinding the next terms of an arithmetic sequence with integersFinding the first terms of a sequence using a recursive ruleIdentifying arithmetic sequences and finding the common differenceFinding a specified term of an arithmetic sequence given the first termsFinding a specified term of an arithmetic sequence given the common difference and first termWrit ing an explicit rule for an arithmetic sequenceWrit ing a recursive rule for an arithmetic sequence

Graphs of Funct ions (19 topics)Finding an output of a funct ion f rom its graphDomain and range f rom the graph of a discrete relat ionFinding domain and range f rom a linear graph in contextFinding where a funct ion is increasing, decreasing, or constant given the graphChoosing a graph to fit a narrat ive: BasicChoosing a graph to fit a narrat ive: AdvancedGraphing an integer funct ion and finding its range for a given domainGraphing a funct ion of the form f (x) = ax + b: Integer slopeGraphing an absolute value equation of the form y = A|x|Graphing an absolute value equation in the plane: BasicGraphing a parabola of the form y = ax2

Graphing a parabola of the form y = ax2 + cGraphing a funct ion of the form f (x) = ax2

Graphing a parabola of the form y = (x-h)2 + kGraphing a piecewise-defined funct ion: Problem type 1Graphing a piecewise-defined funct ion: Problem type 2Finding the average rate of change of a funct ion given its equationFinding the average rate of change of a funct ion given its graphWord problem involving average rate of change

Transformations (8 topics)Translat ing the graph of a parabola: One stepTranslat ing the graph of a parabola: Two stepsHow the leading coefficient affects the shape of a parabolaGraphing quadrat ic funct ions of the form y=ax2 and y=(bx)2 by transforming the parent graph y=x2Translat ing the graph of an absolute value funct ion: One stepTranslat ing the graph of an absolute value funct ion: Two stepsHow the leading coefficient affects the graph of an absolute value funct ionWrit ing an equation for a funct ion af ter a vert ical t ranslat ion

Linear Systems (24 topics)

Systems of Linear Equations (12 topics)


Ident ifying solut ions to a system of linear equationsIdentifying the solut ion of systems of linear equations f rom graphsClassifying systems of linear equations f rom graphsGraphically solving a system of linear equations both of the form y=mx+bGraphically solving a system of linear equationsUsing a graphing calculator to solve a system of linear equations: BasicSolving a system of linear equations of the form y = mx + bSolving a system of linear equations using subst itut ionSolving a system of linear equations using eliminat ion with addit ionSolving a system of linear equations using eliminat ion with mult iplicat ion and addit ionSolving systems of linear equations with 0, 1, or infinitely many solut ionsIdentifying the operat ions used to create equivalent systems of equations

Applicat ions (6 topics)Interpret ing the graphs of two funct ionsSolving a word problem involving a sum and another basic relat ionship using a system of linear equationsWrit ing and solving a system of two linear equations given a table of valuesSolving a word problem using a system of linear equations of the form y = mx + bSolving a value mixture problem using a system of linear equationsSolving a distance, rate, t ime problem using a system of linear equations

Linear Inequalit ies with Two Variables (4 topics)Identifying solut ions to a linear inequality in two variablesGraphing a linear inequality in the plane: Vert ical or horizontal lineGraphing a linear inequality in the plane: Slope-intercept formGraphing a linear inequality in the plane: Standard form

Systems of Linear Inequalit ies (2 topics)Graphing a system of two linear inequalit ies: BasicGraphing a system of two linear inequalit ies: Advanced

Exponents and Exponential Funct ions (60 topics)

Product, Power, and Quotient Rules (13 topics)Introduct ion to the product rule of exponentsProduct rule with posit ive exponents: UnivariateProduct rule with posit ive exponents: Mult ivariateIntroduct ion to the power of a power rule of exponentsIntroduct ion to the power of a product rule of exponentsPower rules with posit ive exponents: Mult ivariate productsPower rules with posit ive exponents: Mult ivariate quotientsSimplifying a rat io of mult ivariate monomials: BasicIntroduct ion to the quotient rule of exponentsSimplifying a rat io of univariate monomialsQuotient of expressions involving exponentsSimplifying a rat io of mult ivariate monomials: AdvancedPower and quotient rules with posit ive exponents

Negative Exponents (11 topics)Evaluat ing expressions with exponents of zeroEvaluat ing an expression with a negative exponent: Whole number baseEvaluat ing an expression with a negative exponent: Posit ive f ract ion baseEvaluat ing an expression with a negative exponent: Negative integer baseRewrit ing an algebraic expression without a negative exponentIntroduct ion to the product rule with negative exponentsQuotient rule with negative exponents: Problem type 1Quotient rule with negative exponents: Problem type 2Power of a power rule with negative exponentsPower rules with negative exponentsPower and quotient rules with negative exponents: Problem type 1

Introduct ion to Radicals (5 topics)Square roots of perfect squares with signsCube root of an integerIntroduct ion to square root addit ion or subtract ionIntroduct ion to square root mult iplicat ionClassifying sums and products as rat ional or irrat ional

Rat ional Exponents (6 topics)Convert ing between radical form and exponent formRational exponents: Unit f ract ion exponents and whole number basesRational exponents: Non-unit f ract ion exponent with a whole number baseRational exponents: Product ruleRational exponents: Quotient rule


Rational exponents: Power of a power rule

Graphs of Exponential Funct ions (6 topics)Table for an exponential funct ionGraphing an exponential funct ion: f (x) = ax

Graphing an exponential funct ion and its asymptote: f (x)=bx

Graphing an exponential funct ion: f (x) = a(b)xTranslat ing the graph of an exponential funct ionFinding domain and range f rom the graph of an exponential funct ion

Applicat ions (9 topics)Using a calculator to evaluate exponential expressionsEvaluat ing an exponential funct ion that models a real-world situat ionFinding a final amount in a word problem on exponential growth or decayFinding the init ial amount and rate of change given an exponential funct ionWrit ing an equation that models exponential growth or decayWrit ing an exponential funct ion rule given a table of ordered pairsFinding the final amount in a word problem on compound interestSolving an exponential equation by finding common bases: Linear exponentsComparing linear, polynomial, and exponential funct ions

Geometric Sequences (10 topics)Finding the first terms of a geometric sequence using an explicit ruleFinding the next terms of a geometric sequence with whole numbersFinding the next terms of a geometric sequence with signed numbersIdentifying arithmetic and geometric sequencesIdentifying geometric sequences and finding the common rat ioFinding a specified term of a geometric sequence given the first termsFinding a specified term of a geometric sequence given the common rat io and first termArithmetic and geometric sequences: Identifying and writ ing an explicit ruleWrit ing recursive rules for arithmetic and geometric sequencesIdentifying linear, quadrat ic, and exponential funct ions given ordered pairs

Polynomials and Factoring (25 topics)

Polynomial Addit ion and Subtract ion (1 topics)Simplifying a sum or difference of two univariate polynomials

Polynomial Mult iplicat ion (8 topics)Mult iplying a univariate polynomial by a monomial with a posit ive coefficientMult iplying binomials with leading coefficients of 1Mult iplying binomials with leading coefficients greater than 1Mult iplying binomials in two variablesMult iplying conjugate binomials: UnivariateSquaring a binomial: UnivariateMult iplying binomials with negative coefficientsMult iplicat ion involving binomials and trinomials in one variable

Factoring Using the GCF (2 topics)Introduct ion to the GCF of two monomialsFactoring out a monomial f rom a polynomial: Univariate

Factoring by Grouping (2 topics)Factoring a univariate polynomial by grouping: Problem type 1Factoring a univariate polynomial by grouping: Problem type 2

Factoring Quadrat ic Trinomials (5 topics)Factoring a quadrat ic with leading coefficient 1Factoring out a constant before factoring a quadrat icFactoring a quadrat ic with leading coefficient greater than 1: Problem type 1Factoring a quadrat ic with leading coefficient greater than 1: Problem type 2Factoring a quadrat ic with a negative leading coefficient

Factoring Special Products (5 topics)Factoring a perfect square trinomial with leading coefficient 1Factoring a perfect square trinomial with leading coefficient greater than 1Factoring a difference of squares in one variable: BasicFactoring a difference of squares in one variable: AdvancedFactoring a polynomial involving a GCF and a difference of squares: Univariate

Polynomial Division (2 topics)Polynomial long division: Problem type 1Closure propert ies of integers and polynomials


Quadrat ic Funct ions and Equations (32 topics)

Solving Quadrat ic Equations by Factoring (5 topics)Solving an equation writ ten in factored formFinding the roots of a quadrat ic equation of the form ax2 + bx = 0Finding the roots of a quadrat ic equation with leading coefficient 1Finding the roots of a quadrat ic equation with leading coefficient greater than 1Solving a word problem using a quadrat ic equation with rat ional roots

Quadrat ic Funct ions (15 topics)Finding the vertex, intercepts, and axis of symmetry f rom the graph of a parabolaGraphing a parabola of the form y = a(x-h)2 + kComplet ing the squareGraphing a parabola of the form y = x2 + bx + cGraphing a parabola of the form y = ax2 + bx + c: Integer coefficientsFinding the zeros of a quadrat ic funct ion given its equationWrit ing a quadrat ic funct ion given its zerosFinding the x-intercept(s) and the vertex of a parabolaUsing a graphing calculator to find the x-intercept(s) and vertex of a quadrat ic funct ionRewrit ing a quadrat ic funct ion to find its vertex and sketch its graphFinding the maximum or minimum of a quadrat ic funct ionWord problem involving the maximum or minimum of a quadrat ic funct ionDomain and range f rom the graph of a parabolaSolving a quadrat ic equation by graphingComparing propert ies of quadrat ic funct ions given in different forms

Square Root Property (3 topics)Solving an equation of the form x2 = a using the square root propertySolving a quadrat ic equation using the square root property: Decimal answers, basicSolving a quadrat ic equation using the square root property: Decimal answers, advanced

Complet ing the Square and the Quadrat ic Formula (3 topics)Solving a quadrat ic equation by complet ing the square: Decimal answersApplying the quadrat ic formula: Decimal answersSolving a word problem using a quadrat ic equation with irrat ional roots

Nonlinear Systems (2 topics)Graphically solving a system of linear and quadrat ic equationsSolving a system of linear and quadrat ic equations

Composit ion and Inverse Funct ions (4 topics)Introduct ion to the composit ion of two funct ionsComposit ion of two funct ions: BasicInverse funct ions: Linear, discreteFinding, evaluat ing, and interpret ing an inverse funct ion for a given linear relat ionship

Data Analysis and Probability (22 topics)

Frequency Tables (6 topics)Construct ing a f requency distribut ion for grouped dataConstruct ing a two-way f requency table: BasicConstruct ing a two-way f requency table: AdvancedComputing a percentage f rom a table of valuesMaking an inference using a two-way f requency tableCalculat ing relat ive f requencies in a contingency table

Graphs of Data (6 topics)Construct ing a line plotConstruct ing a bar graph for non-numerical dataInterpret ing a bar graphInterpret ing a double bar graphConstruct ing a f requency distribut ion and a histogramInterpret ing a stem-and-leaf plot

Measures of Center and Spread (6 topics)Mode of a data setRange of a data setMean of a data setMean and median of a data setHow changing a value affects the mean and medianChoosing the best measure to describe data

Comparing Data (4 topics)


Using back-to-back stem-and-leaf plots to compare data setsFive-number summary and interquart ile rangeConstruct ing a box-and-whisker plotUsing box-and-whisker plots to compare data sets

Other Topics Available(*) (673 addit ional topics)

Arithmetic Readiness (64 topics)Prime numbersPrime factorizat ionGreatest common factor of 3 numbersWord problem involving the least common mult iple of 2 numbersWord problem with common mult iplesAddit ion and subtract ion of 3 f ract ions with different denominatorsWord problem involving addit ion or subtract ion of f ract ions with different denominatorsFract ional part of a circleMult iplicat ion of 3 f ract ionsWord problem involving f ract ions and mult iplicat ionMult i-step word problem involving f ract ions and mult iplicat ionFract ion divisionComplex f ract ion without variables: Problem type 1Word problem involving f ract ions and divisionMixed number addit ion with the same denominator and renamingMixed number subtract ion with the same denominator and renamingAddit ion or subtract ion of mixed numbers with different denominators without renamingAddit ion of mixed numbers with different denominators and renamingSubtract ion of mixed numbers with different denominators and renamingWord problem involving addit ion or subtract ion of mixed numbers with different denominatorsMixed number mult iplicat ionMult iplicat ion of a mixed number and a whole numberDivision with a mixed number and a whole numberMixed number divisionWord problem involving mult iplicat ion or division with mixed numbersReading decimal posit ion on a number line: TenthsReading decimal posit ion on a number line: HundredthsDecimal addit ion with 3 numbersSubtract ion of aligned decimalsDecimal addit ion and subtract ion with 3 or more numbersEst imating a sum of whole numbers: Problem type 1Est imating a sum of whole numbers: Problem type 2Est imating a decimal sum or differenceDecimal mult iplicat ion: Problem type 1Mult iplicat ion of a decimal by a power of 0.1Est imating a product of decimalsWord problem with mult iplicat ion of two decimalsDivision of a decimal by a 1-digit decimalDivision of a decimal by a 2-digit decimalWord problem with mult iple decimal operat ions: Problem type 2Word problem with division of two decimalsConvert ing a f ract ion to a terminat ing decimal: AdvancedConvert ing a f ract ion to a repeating decimal: AdvancedConvert ing a decimal to a proper f ract ion in simplest form: AdvancedConvert ing a decimal to a mixed number and an improper f ract ion in simplest form: AdvancedWrit ing rat ios using different notat ionsWrit ing rat ios for real-world situat ionsIdentifying statements that describe a rat ioSimplifying a rat io of whole numbers: Problem type 1Simplifying a rat io of decimalsFinding a unit priceUsing tables to compare rat iosComputing unit prices to find the better buyWord problem on unit rates associated with rat ios of whole numbers: Decimal answersFinding a rate given a pictorial representat ion of a real-world situat ionConvert ing a percentage to a f ract ion in simplest formEstimating a t ip without a calculatorWrit ing a rat io as a percentage without a calculatorFinding the rate of a tax or commissionWord problem involving a U.S. Customary length conversionMetric distance conversion with whole number valuesMetric distance conversion with decimal valuesSimplifying a rat io of whole numbers: Problem type 2Conversions with currency


Real Numbers (83 topics)Plott ing opposite integers on a number lineReading the temperature f rom a thermometerUsing a number line to compare integersFinding opposites of integersApproximating the locat ion of irrat ional numbers on a number lineAddit ion and subtract ion with 4 or 5 integersWord problem with addit ion or subtract ion of integersOperat ions with absolute value: Problem type 2Word problem with mult iplicat ion or division of integersIdentifying equivalent signed f ract ionsSigned f ract ion subtract ion involving double negationSigned f ract ion addit ion or subtract ion: AdvancedAddit ion and subtract ion of 3 f ract ions involving signsSigned f ract ion mult iplicat ion: AdvancedSigned f ract ion divisionSigned decimal addit ion and subtract ion with 3 numbersSigned decimal mult iplicat ionSigned decimal divisionPower of 10: Posit ive exponentOrder of operat ions with whole numbers and grouping symbolsOrder of operat ions with whole numbers and exponents: AdvancedOrder of operat ions with f ract ions: Problem type 1Order of operat ions with f ract ions: Problem type 2Order of operat ions with f ract ions: Problem type 3Squaring decimal bases: Products greater than 0.1Exponents and decimals: Products less than 0.1Order of operat ions with decimals: Problem type 1Order of operat ions with decimals: Problem type 2Order of operat ions with decimals: Problem type 3Exponents and integers: Problem type 2Order of operat ions with integers and exponentsEvaluat ing an algebraic expression: Whole number operat ions and exponentsConvert ing between temperatures in Fahrenheit and CelsiusEvaluat ing a linear expression: Signed f ract ion mult iplicat ion with addit ion or subtract ionEvaluat ing a linear expression: Signed decimal addit ion and subtract ionEvaluat ing a linear expression: Signed decimal mult iplicat ion with addit ion or subtract ionInterpret ing a Venn diagram of 3 setsConstruct ing a Venn diagram to classify rat ional numbersConstruct ing a Venn diagram to describe relat ionships between sets of rat ional numbersPropert ies of addit ionIntroduct ion to adding f ract ions with variables and common denominatorsCombining like terms: Fract ional coefficientsUnderstanding the distribut ive propertyPropert ies of real numbersIdentifying propert ies used to simplify an algebraic expressionUsing distribut ion with double negation and combining like terms to simplify: Mult ivariateAddit ive property of equality with f ract ions and mixed numbersPerimeter of a polygonFinding the missing length in a figureIntroduct ion to area of a piecewise rectangular figureArea of a piecewise rectangular figureArea between two rectanglesWrit ing algebraic expressions for the area of a figureWord problem involving the area of a rectangle: Problem type 2Word problem involving the area between two rectanglesArea of a parallelogramArea of a triangleArea of a trapezoidCircumference of a circlePerimeter involving rectangles and circlesArea of a circleCircumference and area of a circleCircumference and area of a circle: Exact answers in terms of piArea involving rectangles and circlesArea between two concentric circlesWord problem involving the area between two concentric circlesArea involving inscribed figuresVolume of a rectangular prismWord problem involving the volume of a rectangular prismWord problem involving the rate of filling or emptying a rectangular prismVolume of a triangular prismVolume of a pyramidVolume of a cylinder


Word problem involving the volume of a cylinderWord problem involving the rate of filling or emptying a cylinderVolume of a coneVolume of a cone: Exact answers in terms of piVolume of a sphereSurface area of a cube or a rectangular prismSurface area of a triangular prismSurface area of a cylinderSurface area of a cylinder: Exact answers in terms of piSurface area of a sphere

Linear Equations (80 topics)Solving an equation to find the value of an expressionSolving a two-step equation with signed decimalsSolving a linear equation with several occurrences of the variable: Fract ional forms with monomial numeratorsSolving a linear equation with several occurrences of the variable: Variables on both sides and f ract ional coefficientsSolving a linear equation with several occurrences of the variable: Fract ional forms with binomial numeratorsSolving an absolute value equation: Problem type 3Solving an absolute value equation: Problem type 4Solving a f ract ion word problem using a linear equation of the form Ax = BChoosing stories that can be represented by given one-step equationsComparing arithmetic and algebraic solut ions to a word problemChoosing stories that can be represented by given two-step equationsWrit ing an equation of the form A(x + B) = C to solve a word problemWrit ing and solving a real-world problem given an equation with the variable on both sidesWrit ing a mult i-step equation for a real-world situat ionSolving a decimal word problem using a linear equation with the variable on both sidesSolving a f ract ion word problem using a linear equation with the variable on both sidesSolving a word problem with three unknowns using a linear equationSolving a word problem involving consecutive integersSolving a value mixture problem using a linear equationSolving a word problem involving rates and t ime conversionSolving a distance, rate, t ime problem using a linear equationConvert ing a repeating decimal to a f ract ionFinding the perimeter or area of a rectangle given one of these valuesFinding a side length given the perimeter and side lengths with variablesFinding supplementary and complementary anglesSolving equations involving vert ical anglesFinding an angle measure of a triangle given two anglesFinding angle measures of a triangle given angles with variablesWrit ing an equation to find angle measures of a triangle given angles with variablesFinding angle measures of an isosceles triangle given angles with variablesSolving for a variable in terms of other variables using addit ion or subtract ion: AdvancedSolving for a variable in terms of other variables using mult iplicat ion or division: AdvancedSolving for a variable in terms of other variables in a linear equation with f ract ionsWord problem involving U.S. Customary length conversions using dimensional analysisWord problem involving a conversion between U.S. Customary units of weight and metric units of massConvert ing between compound units: AdvancedWord problem involving conversion between compound units using dimensional analysisSolving a proport ion of the form (x+a)/b = c/dSolving a proport ion of the form a/(x+b) = c/xIntroduct ion to solving a rat ional equationSolving a rat ional equation that simplifies to linear: Denominator xWord problem on proport ions: Problem type 2Finding a missing side length given two similar trianglesRelat ionships about rat ios within and between similar trianglesSimilar polygonsSimilar right trianglesIndirect measurementFinding lengths using scale modelsUsing a scale drawing to find actual areaCircumference rat iosApplying the percent equation: Problem type 2Finding the total amount given the percentage of a part ial amountFinding the sale price without a calculator given the original price and percent discountFinding the total cost including tax or markupCombined effect of more than one markup or discountFinding the original amount given the result of a percentage increase or decreaseFinding the original price given the sale price and percent discountComputing a percent mixtureSolving a percent mixture problem using a linear equationFinding simple interest without a calculatorFinding the interest and future value of a simple interest loan or investmentFinding the principal, rate, or t ime of a simple interest loan or investment


Computing the interest and repayment amount for a simple interest loan whose term is given in months or daysFinding the principal, rate, or t ime for a simple interest loan whose term is given in months or daysCalculat ing income taxComparing discountsComputat ions involving cost of living and hourly wageUsing a family budget est imator to determine the minimum monthly budget and average hourly wage needed for afamilyHourly gross pay with overt imeGross pay with commission and salaryGross pay with variable commission scaleCalculat ions involving purchases with debit and credit cardsComparing costs of checking accountsReading a credit reportUnderstanding the impact of a credit scoreCalculat ing and comparing monthly payments using the ALEKS loan calculatorCalculat ing monthly payment, total payment, and interest using the ALEKS loan calculatorCalculat ing and comparing total loan payments using the ALEKS loan calculatorCalculat ing and comparing simple interest and compound interestUsing the ALEKS periodic deposit calculator to compute savings which include periodic deposits

Linear Inequalit ies (36 topics)Addit ive property of inequality with signed f ract ionsAddit ive property of inequality with signed decimalsSolving a linear inequality with mult iple occurrences of the variable: Problem type 3Solving a word problem involving area using a one-step linear inequality: Area and lengthsTranslat ing a sentence into a mult i-step inequalitySolving a word problem using a two-step linear inequality and describing the solut ionSolving a decimal word problem using a linear inequality with the variable on both sidesWrit ing sets of numbers using descript ive and roster formsIdentifying elements of sets for a real world situat ionWrit ing sets for a real-world situat ion using descript ive and roster formsIdentifying infinite sets and determining cardinalit ies of finite setsIdentifying equivalent and equal setsIdentifying equivalent and equal sets for a real-world situat ionWrit ing sets of numbers using set-builder and roster formsSet-builder notat ionMembership and cardinality of setsIdentifying true statements involving subsets and proper subsetsIdentifying true statements about set membership and subsetsWrit ing subsetsDetermining the total number of subsets of a setWrit ing subsets for a real-world situat ionDetermining the number of subsets for a real-world situat ionFinding sets and complements of setsFinding sets and complements of sets for a real-world situat ionUnion and intersect ion of finite setsConstruct ing a Venn diagram with 2 setsInterpret ing Venn diagram cardinalit ies with 2 sets for a real-world situat ionConstruct ing a Venn diagram with 2 sets to solve a word problemConstruct ing a Venn diagram with 3 setsInterpret ing Venn diagram cardinalit ies with 3 sets for a real-world situat ionConstruct ing a Venn diagram with 3 sets to solve a word problemTranslat ing a sentence into a compound inequalityWrit ing a compound inequality given a graph on the number lineSolving a compound linear inequality: Graph solut ion, advancedSolving an absolute value inequality: Problem type 2Solving an absolute value inequality: Problem type 5

Funct ions and Lines (40 topics)Plott ing a point in the coordinate plane: Mixed number coordinatesNaming the quadrant or axis of a point given its graphNaming the quadrant or axis of a point given its coordinatesNaming the quadrant or axis of a point given the signs of its coordinatesFinding distances between points that share a common coordinate given their coordinatesIdentifying proport ional relat ionships in equationsIdentifying proport ional relat ionships in tables by calculat ing unit rates: Whole numbersIdentifying proport ional relat ionships in tables by calculat ing unit rates: Fract ionsIdentifying proport ional relat ionships in graphs: BasicIdentifying proport ional relat ionships in graphs: AdvancedWrit ing a funct ion rule given a table of ordered pairs: Two-step rulesFinding x- and y-intercepts of a line given the equation: AdvancedGraphing a line given its x- and y-interceptsFinding the coordinate that yields a given slopeInterpret ing direct variat ion f rom a graph


Ident ifying linear equations: BasicIdentifying linear equations: AdvancedRewrit ing a linear equation in the form Ax + By = CWrit ing an equation and graphing a line given its slope and y-interceptGraphing a line given its equation in point-slope formWrit ing an equation in standard form given the slope and a pointWrit ing the equations of vert ical and horizontal lines through a given pointIdentifying parallel and perpendicular lines f rom coordinatesIdentifying independent and dependent quantit ies f rom tables and graphsIdentifying independent and dependent variables f rom equations or real-world situat ionsClassifying linear and nonlinear relat ionships f rom scatter plotsIdentifying out liers and clustering in scatter plotsVariable expressions as inputs of funct ions: Problem type 1Finding inputs and outputs of a funct ion f rom its graphFinding intercepts of a nonlinear funct ion given its graphFinding local maxima and minima of a funct ion given the graphGraphing a funct ion of the form f (x) = ax + b: Fract ional slopeGraphing an absolute value equation in the plane: AdvancedGraphing a funct ion of the form f (x) = ax2 + cGraphing a cubic funct ion of the form y = ax3Introduct ion to graphing a piecewise-defined funct ion involving lines with non-zero slopeTranslat ing the graph of a funct ion: One stepTranslat ing the graph of a funct ion: Two stepsTransforming the graph of a funct ion by reflect ing over an axisWrit ing an equation for a funct ion af ter a vert ical and horizontal t ranslat ion

Linear Systems (22 topics)Using a graphing calculator to solve a system of linear equations: AdvancedWrit ing a system of linear equations given its graphSolving a system of linear equations with f ract ional coefficientsSolving a system of linear equations with decimal coefficientsIntroduct ion to solving a 3x3 system of linear equationsSolving a 3x3 system of linear equations: Problem type 1Solving a 3x3 system of linear equations: Problem type 2Scalar mult iplicat ion of a matrixAddit ion or subtract ion of matricesLinear combinat ion of matricesComplet ing Gauss-Jordan eliminat ion with a 2x2 matrixGauss-Jordan eliminat ion with a 2x2 matrixSolving a word problem using a system of linear equations of the form Ax + By = CSolving a percent mixture problem using a system of linear equationsSolving a tax rate or interest rate problem using a system of linear equationsSolving a word problem using a 3x3 system of linear equations: Problem type 1Writ ing an inequality given its graph in the plane: Horizontal or vert ical boundary lineWrit ing an inequality given its graph in the plane: Slanted boundary lineGraphing a system of three linear inequalit iesWrit ing a linear inequality in two variables given a table of valuesWrit ing a mult i-step inequality for a real-world situat ionSolving a word problem using a system of linear inequalit ies: Problem type 1

Exponents and Exponential Funct ions (38 topics)Understanding the product rule of exponentsOrdering numbers with posit ive exponentsUnderstanding the power rules of exponentsPower and product rules with posit ive exponentsPower of 10: Negative exponentOrdering numbers with negative exponentsProduct rule with negative exponentsPower and quotient rules with negative exponents: Problem type 2Power, product, and quotient rules with negative exponentsFinding all square roots of a numberEst imating a square rootSquare root of a rat ional perfect squareFinding nth roots of perfect nth powers with signsSimplifying the square root of a whole number less than 100Simplifying the square root of a whole number greater than 100Rational exponents: Unit f ract ion exponents and bases involving signsRational exponents: Negative exponents and f ract ional basesRational exponents: Products and quotients with negative exponentsRational exponents: Powers of powers with negative exponentsIntroduct ion to scient ific notat ion with posit ive exponentsScient ific notat ion with posit ive exponentIntroduct ion to scient ific notat ion with negative exponentsScient ific notat ion with negative exponent


Convert ing between scient ific notat ion and standard form in a real-world situat ionExpressing calculator notat ion as scient ific notat ionMult iplying numbers writ ten in scient ific notat ion: BasicMult iplying numbers writ ten in scient ific notat ion: AdvancedMult iplying numbers writ ten in decimal form or scient ific notat ion in a real-world situat ionDividing numbers writ ten in scient ific notat ion: BasicDividing numbers writ ten in scient ific notat ion: AdvancedFinding powers of numbers writ ten in scient ific notat ionFinding the scale factor between numbers given in scient ific notat ion in a real-world situat ionGraphing an exponential funct ion and its asymptote: f (x) = a(b)xGraphing an exponential funct ion and its asymptote: f (x)=b-x or f (x)=-baxFinding the init ial amount and asymptote given a graph of an exponential funct ionChoosing an exponential model and using it to make a predict ionFinding the future value and interest for an investment earning compound interestFinding the present value of an investment earning compound interest

Polynomials and Factoring (31 topics)Degree and leading coefficient of a univariate polynomialDegree of a mult ivariate polynomialSimplifying a sum or difference of three univariate polynomialsSimplifying a sum or difference of mult ivariate polynomialsMult iplying a univariate polynomial by a monomial with a negative coefficientMult iplying a mult ivariate polynomial by a monomialMult iplying conjugate binomials: Mult ivariateSquaring a binomial: Mult ivariateMult iplicat ion involving binomials and trinomials in two variablesGreatest common factor of three univariate monomialsGreatest common factor of two mult ivariate monomialsFactoring out a monomial f rom a polynomial: Mult ivariateFactoring out a binomial f rom a polynomial: GCF factoring, basicFactoring a mult ivariate polynomial by grouping: Problem type 1Factoring a mult ivariate polynomial by grouping: Problem type 2Factoring a quadrat ic in two variables with leading coefficient 1Factoring a quadrat ic with leading coefficient greater than 1: Problem type 3Factoring a quadrat ic by the ac-methodFactoring a quadrat ic in two variables with leading coefficient greater than 1Factoring a perfect square trinomial in two variablesFactoring a difference of squares in two variablesFactoring a polynomial involving a GCF and a difference of squares: Mult ivariateFactoring a product of a quadrat ic trinomial and a monomialFactoring with repeated use of the difference of squares formulaFactoring a sum or difference of two cubesDividing a polynomial by a monomial: UnivariateDividing a polynomial by a monomial: Mult ivariateSimplifying a rat io of factored polynomials: Linear factorsSimplifying a rat io of polynomials using GCF factoringPolynomial long division: Problem type 2Polynomial long division: Problem type 3

Quadrat ic Funct ions and Equations (15 topics)Solving a quadrat ic equation needing simplificat ionWrit ing a quadrat ic equation given the roots and the leading coefficientGraphing a parabola of the form y = ax2 + bx + c: Rat ional coefficientsUsing a graphing calculator to find the zeros of a quadrat ic funct ionRewrit ing a quadrat ic funct ion in standard formRange of a quadrat ic funct ionWrit ing the equation of a quadrat ic funct ion given its graphClassifying the graph of a funct ionChoosing a quadrat ic model and using it to make a predict ionSolving a quadrat ic equation by complet ing the square: Exact answersApplying the quadrat ic formula: Exact answersDiscriminant of a quadrat ic equationGraphing a quadrat ic inequality: Problem type 1Graphing a quadrat ic inequality: Problem type 2Using a graphing calculator to solve a system of linear and quadrat ic equations: Basic

Radicals (80 topics)Square roots of integers raised to even exponentsIntroduct ion to simplifying a radical expression with an even exponentSquare root of a perfect square monomialUsing absolute value to simplify square roots of perfect square monomialsFinding the nth root of a perfect nth power f ract ionFinding the nth root of a perfect nth power monomial


Table for a square root funct ionDomain of a square root funct ion: BasicDomain of a square root funct ion: AdvancedGraphing a square root funct ion: Problem type 1Graphing a square root funct ion: Problem type 2Graphing a square root funct ion: Problem type 3Simplifying a radical expression with an even exponentIntroduct ion to simplifying a radical expression with an odd exponentSimplifying a radical expression with an odd exponentSimplifying a radical expression with two variablesSimplifying a higher root of a whole numberIntroduct ion to simplifying a higher radical expressionSimplifying a higher radical expression: UnivariateSimplifying a higher radical expression: Mult ivariateSquare root addit ion or subtract ionSquare root addit ion or subtract ion with three termsIntroduct ion to simplifying a sum or difference of radical expressions: UnivariateSimplifying a sum or difference of radical expressions: UnivariateSimplifying a sum or difference of radical expressions: Mult ivariateSquare root mult iplicat ion: BasicSquare root mult iplicat ion: AdvancedIntroduct ion to simplifying a product of radical expressions: UnivariateSimplifying a product of radical expressions: UnivariateSimplifying a product of radical expressions: Mult ivariateIntroduct ion to simplifying a product of higher rootsSimplifying a product of higher radical expressionsIntroduct ion to simplifying a product involving square roots using the distribut ive propertySimplifying a product involving square roots using the distribut ive property: BasicSimplifying a product involving square roots using the distribut ive property: AdvancedSpecial products of radical expressions: Conjugates and squaringSimplifying a quotient of square rootsSimplifying a quotient involving a sum or difference with a square rootRat ionalizing a denominator: Quotient involving square rootsRationalizing a denominator: Square root of a f ract ionRationalizing a denominator: Quotient involving a monomialRat ionalizing a denominator using conjugates: Integer numeratorRat ionalizing a denominator using conjugates: Square root in numeratorIntroduct ion to solving a radical equationSolving a radical equation that simplifies to a linear equation: One radical, basicSolving a radical equation that simplifies to a linear equation: One radical, advancedSolving a radical equation that simplifies to a linear equation: Two radicalsSolving a radical equation that simplifies to a quadrat ic equation: One radical, basicSolving a radical equation that simplifies to a quadrat ic equation: One radical, advancedSolving a radical equation with a quadrat ic expression under the radicalSolving a radical equation with two radicals that simplifies to sqrt (x) = aSolving a radical equation that simplifies to a quadrat ic equation: Two radicalsAlgebraic symbol manipulat ion with radicalsWord problem involving radical equations: BasicWord problem involving radical equations: AdvancedSolving an equation of the form x3 = a using integersFinding the side length of a cube given its volumeIntroduct ion to the Pythagorean TheoremPythagorean TheoremWord problem involving the Pythagorean TheoremIdentifying side lengths that give right trianglesInformal proof of the Pythagorean TheoremUsing the Pythagorean Theorem and a quadrat ic equation to find side lengths of a right triangleDistance between two points in the plane: Exact answersDistance between two points in the plane: Decimal answersMidpoint of a line segment in the planeFinding an endpoint of a line segment given the other endpoint and the midpointSine, cosine, and tangent rat ios: Numbers for side lengthsSine, cosine, and tangent rat ios: Variables for side lengthsUsing a calculator to approximate sine, cosine, and tangent valuesUsing the Pythagorean Theorem to find a trigonometric rat ioFinding trigonometric rat ios given a right triangleUnderstanding trigonometric rat ios through similar right trianglesRelat ionship between the sines and cosines of complementary anglesUsing a trigonometric rat io to find a side length in a right triangleSolving a right triangleUsing trigonometry to find a length in a word problem with one right triangleUsing trigonometry to find a length in a word problem with two right trianglesUsing a trigonometric rat io to find an angle measure in a right triangleUsing trigonometry to find angles of elevat ion or depression in a word problem


Data Analysis and Probability (96 topics)Identifying stat ist ical quest ionsClassifying samplesChoosing an appropriate method for gathering data: Problem type 1Choosing an appropriate method for gathering data: Problem type 2Introduct ion to expectat ionMaking predict ions using experimental data for compound eventsConstruct ing a f requency distribut ion for non-grouped dataConstruct ing a relat ive f requency distribut ion for grouped dataFinding if a quest ion can be answered by the dataMaking a reasonable inference based on proport ion stat ist icsConstruct ing a line plot with f ract ional values: FourthsMaking part-to-whole, part-to-part , and equivalence comparisons given a line plotMaking part-to-whole, part-to-part , and equivalence comparisons given a bar graphInterpret ing a histogramInterpret ing a circle graph or pie chartFinding a percentage of a total amount in a circle graphMaking part-to-part and equivalence comparisons given a circle graphComputat ions f rom a circle graphAngle measure in a circle graphConstruct ing a percent bar graphFinding the mode and range f rom a line plotFinding the mean of a symmetric distribut ionComputat ions involving the mean, sample size, and sum of a data setFinding the value for a new score that will yield a given meanReject ing unreasonable claims based on average stat ist icsWeighted meanFinding out liers in a data setIdentifying peaks, symmetry, gaps, and clusters in a line plotIdentifying the center, spread, and shape of a data setComputing mean absolute deviat ion f rom a list of numerical valuesPercentage of data below a specified valueInterpret ing percentile ranksPercentilesComparing measures of center and variat ionFinding sample size and comparing samples for est imating the meanInterpret ing a tree diagramIntroduct ion to the counting principleCounting principleCounting principle with repetit ion allowedFactorial expressionsCounting arrangements of objects that are not all dist inctComputing permutat ions and combinat ionsWord problem involving permutat ionsWord problem involving combinat ionsIntroduct ion to permutat ions and combinat ionsPermutat ions, combinat ions, and the mult iplicat ion principle for countingDetermining a sample space and outcomes for a simple eventIntroduct ion to the probability of an eventProbability involving one die or choosing f rom n dist inct objectsProbability involving choosing f rom objects that are not dist inctProbability of select ing one card f rom a standard deckProbabilit ies of an event and its complementExperimental and theoret ical probabilityFinding the odds in favor and againstConvert ing between probability and oddsFinding odds in favor and against drawing a card f rom a standard deckArea as probabilityComputing expected value in a game of chanceComputing expected value in a business applicat ionDetermining a sample space and outcomes for a compound eventOutcomes and event probabilityExperimental and theoret ical probability for compound eventsProbabilit ies involving two rolls of a dieProbabilit ies of a permutat ion and a combinat ionIdentifying independent events given descript ions of experimentsProbability of independent eventsProbability of independent events involving a standard deck of cardsProbability of dependent eventsProbability of dependent events involving a surveyProbability of dependent events involving a standard deck of cardsDetermining outcomes for compound events and complements of eventsUsing a Venn diagram to understand the addit ion rule for probabilityOutcomes and event probability: Addit ion rule


Probability of the union of two eventsWord problem involving the probability of a unionComputing probability involving the addit ion rule using a two-way f requency tableProbability of intersect ion or union: Word problemsComputing condit ional probability using a sample spaceUsing a Venn diagram to understand the mult iplicat ion rule for probabilityOutcomes and event probability: Condit ional probabilityIdentifying independent events given values of probabilit iesComputing condit ional probability using a two-way f requency tableComputing condit ional probability to make an inference using a two-way f requency tableComputing condit ional probability using a large two-way f requency tableCondit ional probability: BasicIdentifying outcomes in a random number table used to simulate a simple eventUsing a random number table to simulate a simple eventGenerat ing a random number table with technology to simulate a simple eventIdentifying outcomes in a random number table used to simulate a compound eventUsing a random number table to simulate a compound eventGenerat ing a random number table with technology to simulate a compound eventGenerat ing random samples f rom a populat ion with known characterist icsUsing a random number table to make a fair decisionPopulat ion standard deviat ionUsing the empirical rule to identify values and percentages of a normal distribut ionWord problem involving calculat ions f rom a normal distribut ion

Rational Expressions (88 topics)Restrict ion on a variable in a denominator: LinearRestrict ion on a variable in a denominator: Quadrat icEvaluat ing a rat ional funct ion: Problem type 1Evaluat ing a rat ional funct ion: Problem type 2Domain of a rat ional funct ion: Excluded valuesSimplifying a rat io of factored polynomials: Factors with exponentsSimplifying a rat io of linear polynomials: 1, -1, and no simplificat ionSimplifying a rat io of polynomials by factoring a quadrat ic with leading coefficient 1Simplifying a rat io of polynomials: Problem type 1Simplifying a rat io of polynomials: Problem type 2Simplifying a rat io of polynomials: Problem type 3Simplifying a rat io of mult ivariate polynomialsMult iplying rat ional expressions involving mult ivariate monomialsMult iplying rat ional expressions made up of linear expressionsMult iplying rat ional expressions involving quadrat ics with leading coefficients of 1Mult iplying rat ional expressions involving quadrat ics with leading coefficients greater than 1Mult iplying rat ional expressions involving mult ivariate quadrat icsDividing rat ional expressions involving mult ivariate monomialsDividing rat ional expressions involving linear expressionsDividing rat ional expressions involving quadrat ics with leading coefficients of 1Dividing rat ional expressions involving quadrat ics with leading coefficients greater than 1Dividing rat ional expressions involving mult ivariate quadrat icsMult iplicat ion and division of 3 rat ional expressionsIntroduct ion to the LCM of two monomialsLeast common mult iple of two monomialsFinding the LCD of rat ional expressions with linear denominators: Relat ively primeFinding the LCD of rat ional expressions with linear denominators: Common factorsFinding the LCD of rat ional expressions with quadrat ic denominatorsWrit ing equivalent rat ional expressions with monomial denominatorsWrit ing equivalent rat ional expressions with polynomial denominatorsWrit ing equivalent rat ional expressions involving opposite factorsAdding rat ional expressions with common denominators and monomial numeratorsAdding rat ional expressions with common denominators and binomial numeratorsAdding rat ional expressions with common denominators and GCF factoringAdding rat ional expressions with common denominators and quadrat ic factoringAdding rat ional expressions with different denominators and a single occurrence of a variableAdding rat ional expressions with denominators ax and bx: BasicAdding rat ional expressions with denominators ax and bx: AdvancedAdding rat ional expressions with denominators axn and bxmAdding rat ional expressions with mult ivariate monomial denominators: BasicAdding rat ional expressions with mult ivariate monomial denominators: AdvancedAdding rat ional expressions with linear denominators without common factors: BasicAdding rat ional expressions with linear denominators without common factors: AdvancedAdding rat ional expressions with linear denominators with common factors: BasicAdding rat ional expressions with linear denominators with common factors: AdvancedAdding rat ional expressions with denominators ax-b and b-axAdding rat ional expressions involving different quadrat ic denominatorsAdding 3 rat ional expressions with different quadrat ic denominatorsComplex f ract ion without variables: Problem type 2


Complex f ract ion involving univariate monomialsComplex f ract ion involving mult ivariate monomialsComplex f ract ion: GCF factoringComplex f ract ion: Quadrat ic factoringComplex f ract ion made of sums involving rat ional expressions: Problem type 1Complex f ract ion made of sums involving rat ional expressions: Problem type 2Complex f ract ion made of sums involving rat ional expressions: Problem type 3Complex f ract ion made of sums involving rat ional expressions: Problem type 4Complex f ract ion made of sums involving rat ional expressions: Problem type 5Complex f ract ion made of sums involving rat ional expressions: Problem type 6Complex f ract ion made of sums involving rat ional expressions: Mult ivariateSolving a rat ional equation that simplifies to linear: Denominator x+aSolving a rat ional equation that simplifies to linear: Denominators a, x, or axSolving a rat ional equation that simplifies to linear: Denominators ax and bxSolving a rat ional equation that simplifies to linear: Like binomial denominatorsSolving a rat ional equation that simplifies to linear: Unlike binomial denominatorsSolving a rat ional equation that simplifies to linear: Factorable quadrat ic denominatorSolving a rat ional equation that simplifies to quadrat ic: Proport ional form, basicSolving a rat ional equation that simplifies to quadrat ic: Denominator xSolving a rat ional equation that simplifies to quadrat ic: Binomial denominators, constant numeratorsSolving a rat ional equation that simplifies to quadrat ic: Binomial denominators and numeratorsSolving a rat ional equation that simplifies to quadrat ic: Factorable quadrat ic denominatorSolving a rat ional equation that simplifies to quadrat ic: Proport ional form, advancedSolving for a variable in terms of other variables in a rat ional equation: Problem type 1Solving for a variable in terms of other variables in a rat ional equation: Problem type 2Solving for a variable in terms of other variables in a rat ional equation: Problem type 3Word problem involving mult iple ratesSolving a work problem using a rat ional equationSolving a distance, rate, t ime problem using a rat ional equationOrdering f ract ions with variablesWrit ing an inverse variat ion equationIdentifying direct and inverse variat ion equationsIdentifying direct and inverse variat ion f rom ordered pairs and writ ing equationsWord problem on inverse variat ionWord problem on inverse proport ionsFinding the asymptotes of a rat ional funct ion: Constant over linearFinding the asymptotes of a rat ional funct ion: Linear over linearGraphing a rat ional funct ion: Constant over linearGraphing a rat ional funct ion: Linear over linear

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Algebra 1 - ALEKS

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