Beginning Algebra - ALEKS

Copyright © 2022 McGraw Hill - ALEKS® is a registered trademark of ALEKS CorporationPage 1 / 13

Beginning AlgebraThis 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 (375 topics + 443 addit ional topics)

Arithmetic Readiness (89 topics)

Whole Numbers (15 topics)Writ ing expressions using exponentsIntroduct ion to exponentsPower of 10: Posit ive exponentOrder of operat ions with whole numbersOrder of operat ions with whole numbers and grouping symbolsOrder of operat ions with whole numbers and exponents: BasicOrder of operat ions with whole numbers and exponents: AdvancedEvaluat ing an algebraic expression: Whole numbers with two operat ionsEvaluat ing an algebraic expression: Whole number operat ions and exponentsPrime numbersPrime factorizat ionGreatest common factor of 2 numbersLeast common mult iple of 2 numbersLeast common mult iple of 3 numbersSolving a word problem on proport ions using a unit rate

Fract ions (21 topics)Equivalent f ract ionsSimplifying a f ract ionAddit ion or subtract ion of f ract ions with the same denominatorAddit ion or subtract ion of f ract ions with the same denominator and simplificat ionFinding the LCD of two f ract ionsIntroduct ion to addit ion or subtract ion of f ract ions with different denominatorsAddit ion or subtract ion of f ract ions with different denominatorsWord problem involving addit ion or subtract ion of f ract ions with different denominatorsProduct 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 2Mult iplicat ion of 3 f ract ionsExponents and f ract ionsWord problem involving f ract ions and mult iplicat ionThe reciprocal of a numberDivision involving a whole number and a f ract ionFract ion divisionWord problem involving f ract ions and divisionOrder of operat ions with f ract ions: Problem type 1

Mixed Numbers (13 topics)Writ ing an improper f ract ion as a mixed numberWrit ing a mixed number as an improper f ract ionMixed 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 numbers

Decimals (24 topics)Decimal place value: Tenths and hundredthsRounding decimalsConvert ing a decimal to a proper f ract ion in simplest form: BasicConvert ing a decimal to a proper f ract ion in simplest form: AdvancedDecimal addit ion with 3 numbers


Decimal subtract ion: BasicDecimal subtract ion: AdvancedDecimal addit ion and subtract ion with 3 or more numbersWord problem with addit ion of 3 or 4 decimals and whole numbersWord problem with subtract ion of a whole number and a decimal: Regrouping with zerosMult iplying a decimal by a whole numberDecimal mult iplicat ion: Problem type 1Mult iplicat ion of a decimal by a power of tenWord problem with mult iplicat ion of two decimalsWord problem with decimal addit ion and mult iplicat ionDivision of a decimal by a whole numberDivision of a decimal by a 1-digit decimalDivision of a decimal by a 2-digit decimalDivision of a decimal by a power of tenWord problem with division of two decimalsWord problem with decimal subtract ion and divisionConvert ing a f ract ion to a terminat ing decimal: BasicConvert ing a f ract ion to a terminat ing decimal: AdvancedConvert ing a f ract ion to a repeating decimal: Basic

Convert ing Between Fract ions, Decimals, and Percentages (9 topics)Convert ing a f ract ion with a denominator of 100 to a percentageConvert ing a percentage to a f ract ion with a denominator of 100Introduct 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 percentage to a f ract ion in simplest formConvert 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

Geometry (7 topics)Perimeter of a polygonPerimeter of a square or a rectangleArea of a square or a rectangleArea of a triangleCircumference of a circleCircumference and area of a circleVolume of a rectangular prism

Real Numbers and Algebraic Expressions (48 topics)

Plott ing and Ordering (7 topics)Plott ing integers on a number lineWrit ing a signed number for a real-world situat ionIntroduct ion to ordering decimalsOrdering integersSquare root of a perfect squareUsing a calculator to approximate a square rootAbsolute value of a number

Operat ions with Rat ional Numbers (22 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 integersAddit ion and subtract ion with 4 or 5 integersWord problem with addit ion or subtract ion of integersInteger mult iplicat ion and divisionMult iplicat ion of 3 or 4 integersDivision involving zeroIdentifying numbers as integers or non-integersIdentifying numbers as rat ional or irrat ionalSigned f ract ion addit ion or subtract ion: BasicSigned f ract ion subtract ion involving double negationSigned f ract ion mult iplicat ion: BasicSigned f ract ion mult iplicat ion: AdvancedSigned f ract ion divisionSigned decimal addit ion and subtract ionSigned decimal addit ion and subtract ion with 3 numbersSigned decimal mult iplicat ionSigned decimal division


Exponents and Order of Operat ions (5 topics)Exponents and integers: Problem type 1Exponents and integers: Problem type 2Exponents and signed f ract ionsOrder of operat ions with integersOrder of operat ions with integers and exponents

Evaluat ing Expressions (2 topics)Evaluat ing a linear expression: Integer mult iplicat ion with addit ion or subtract ionEvaluat ing a quadrat ic expression: Integers

Propert ies of Real Numbers (12 topics)Combining like terms: Whole number coefficientsCombining like terms: Integer coefficientsIntroduct ion to propert ies of addit ionPropert ies of addit ionMult iplying a constant and a linear monomialDistribut ive property: Whole number coefficientsDistribut ive property: Integer coefficientsIntroduct ion to propert ies of mult iplicat ionPropert ies of real numbersUsing distribut ion and combining like terms to simplify: UnivariateUsing distribut ion with double negation and combining like terms to simplify: Mult ivariateCombining like terms in a quadrat ic expression

Linear Equations (73 topics)

One-Step Linear Equations (9 topics)Addit 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 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

Mult i-Step Linear Equations (19 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 solving an equation with parenthesesSolving a mult i-step equation given in f ract ional formSolving a two-step equation with signed decimalsIntroduct ion to solving an equation with variables on the same sideSolving a linear equation with several occurrences of the variable: Variables on the same 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 ionsSolving a linear equation with several occurrences of the variable: Fract ional forms with monomial numeratorsSolving a two-step equation with signed f ract ionsSolving a linear equation with several occurrences of the variable: Variables on both sides and f ract ional coefficientsSolving equations with zero, one, or infinitely many solut ionsSolving a proport ion of the form x/a = b/cSolving a proport ion of the form (x+a)/b = c/d

Solving Formulas for a Variable (7 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 addit ion or subtract ion: AdvancedSolving for a variable in terms of other variables using mult iplicat ion or division: BasicSolving for a variable in terms of other variables using mult iplicat ion or division: AdvancedSolving 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 variablesSolving for a variable in terms of other variables in a linear equation with f ract ions

Writ ing Expressions and Equations (5 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 equationTranslat ing a sentence into a mult i-step equation


Applicat ions (14 topics)Solving a f ract ion word problem using a linear equation of the form Ax = BSolving a word problem with two unknowns using a linear equationSolving a decimal word problem using a linear equation of the form Ax + B = CSolving a decimal word problem using a linear equation with the variable on both sidesSolving a word problem involving consecutive integersSolving a value mixture problem using a linear equationSolving a one-step word problem using the formula d = rtSolving a distance, rate, t ime problem using a linear equationConvert ing between temperatures in Fahrenheit and CelsiusFinding the side length of a rectangle given its perimeter or areaFinding a side length given the perimeter and side lengths with variablesFinding the perimeter or area of a rectangle given one of these valuesFinding an angle measure of a triangle given two anglesFinding angle measures of a triangle given angles with variables

Applicat ions Involving Percentages (19 topics)Finding a percentage of a whole numberFinding a percentage of a whole number without a calculator: BasicFinding a percentage of a whole number without a calculator: AdvancedApplying the percent equation: Problem type 1Applying the percent equation: Problem type 2Finding 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 without a calculatorFinding the rate of a tax or commissionFinding the total amount given the percentage of a part ial amountFinding the final amount given the original amount and a percentage increase or decreaseFinding the sale price given the original price and percent discountFinding the sale price without a calculator given the original price and percent discountFinding the total cost including tax or markupFinding the original price given the sale price and percent discountFinding the percentage increase or decrease: BasicFinding the percentage increase or decrease: AdvancedFinding a percentage of a total amount in a circle graphFinding simple interest without a calculator

Linear Inequalit ies (18 topics)

Writ ing and Graphing Inequalit ies (5 topics)Translat ing a sentence by using an inequality symbolTranslat ing a sentence into a one-step 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

Linear Inequalit ies and Applicat ions (13 topics)Addit ive property of inequality with whole numbersAddit ive property of inequality with integersAddit ive property of inequality with signed f ract ionsAddit ive property of inequality with signed decimalsMult iplicat ive property of inequality with integersMult iplicat ive property of inequality with signed f ract ionsSolving 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 a linear inequality with mult iple occurrences of the variable: Problem type 3Solving a decimal word problem using a two-step linear inequality

Lines and Funct ions (46 topics)

Ordered Pairs (5 topics)Reading a point in the coordinate planePlott ing a point in the coordinate planeTable for a linear equationIdentifying solut ions to a linear equation in two variablesFinding a solut ion to a linear equation in two variables

Graphing and Intercepts (9 topics)Graphing 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 slope


Graphing 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 given its x- and y-interceptsGraphing a line by first finding its x- and y-intercepts

Slope (6 topics)Classifying 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

Equations of Lines (14 topics)Rewrit ing a linear equation in the form Ax + By = CFinding 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-interceptWrit ing an equation in slope-intercept form given the slope and a pointWrit 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 pointsWrit ing the equations of vert ical and horizontal lines through a given pointFinding 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 (5 topics)Writ 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: AdvancedInterpret 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 points

Identifying Funct ions, Domain, and Range (3 topics)Identifying funct ions f rom relat ionsVert ical line testDomain and range f rom ordered pairs

Funct ion Evaluat ion and Applicat ions (4 topics)Table for a linear funct ionEvaluat ing funct ions: Linear and quadrat ic or cubicFinding 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 ion

Systems (12 topics)

Systems of Linear Equations (7 topics)Identifying solut ions to a system of linear equationsClassifying systems of linear equations f rom graphsGraphically solving a system of linear equationsSolving 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 a 2x2 system of linear equations that is inconsistent or consistent dependent

Applicat ions (5 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 equationsSolving a word problem using a system of linear equations of the form Ax + By = CSolving a value mixture problem using a system of linear equationsSolving a distance, rate, t ime problem using a system of linear equations

Exponents (53 topics)

Product, Power, and Quotient Rules (53 topics)Understanding the product rule of exponentsIntroduct ion to the product rule of exponentsProduct rule with posit ive exponents: UnivariateProduct rule with posit ive exponents: Mult ivariate


Understanding the power rules of exponentsIntroduct 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 quotientsPower and product rules with posit ive exponentsSimplifying 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 (14 topics)Evaluat ing expressions with exponents of zeroPower of 10: Negative exponentEvaluat 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 exponentsProduct 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 1Power and quotient rules with negative exponents: Problem type 2

Scient ific Notat ion (7 topics)Scient ific notat ion with posit ive exponentScient ific notat ion with negative exponentConvert ing between scient ific notat ion and standard form in a real-world situat ionMult iplying numbers writ ten in scient ific notat ion: BasicMult iplying numbers writ ten in scient ific notat ion: AdvancedDividing numbers writ ten in scient ific notat ion: BasicDividing numbers writ ten in scient ific notat ion: Advanced

Polynomials and Factoring (52 topics)

Polynomial Addit ion, Subtract ion, and Mult iplicat ion (15 topics)Degree and leading coefficient of a univariate polynomialSimplifying a sum or difference of two univariate polynomialsSimplifying 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 posit ive coefficientMult iplying a univariate polynomial by a monomial with a negative coefficientMult iplying a mult ivariate polynomial by a monomialMult iplying binomials with leading coefficients of 1Mult iplying binomials with leading coefficients greater than 1Mult iplying binomials in two variablesMult iplying conjugate binomials: UnivariateMult iplying conjugate binomials: Mult ivariateSquaring a binomial: UnivariateSquaring a binomial: Mult ivariateMult iplicat ion involving binomials and trinomials in one variable

Polynomial Division (3 topics)Dividing a polynomial by a monomial: UnivariateDividing a polynomial by a monomial: Mult ivariatePolynomial long division: Problem type 1

Factoring Using the GCF (6 topics)Factoring a linear binomialIntroduct ion to the GCF of two monomialsGreatest common factor of three univariate monomialsGreatest common factor of two mult ivariate monomialsFactoring out a monomial f rom a polynomial: UnivariateFactoring out a monomial f rom a polynomial: Mult ivariate

Factoring by Grouping (4 topics)Factoring out a binomial f rom a polynomial: GCF factoring, basicFactoring a univariate polynomial by grouping: Problem type 1Factoring a univariate polynomial by grouping: Problem type 2


Factoring a mult ivariate polynomial by grouping: Problem type 1

Factoring Quadrat ic Trinomials (6 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 leading coefficient greater than 1: Problem type 3Factoring a quadrat ic by the ac-method

Factoring Special Products (8 topics)Factoring a perfect square trinomial with leading coefficient 1Factoring a perfect square trinomial with leading coefficient greater than 1Factoring a perfect square trinomial in two variablesFactoring a difference of squares in one variable: BasicFactoring a difference of squares in one variable: AdvancedFactoring a difference of squares in two variablesFactoring a polynomial involving a GCF and a difference of squares: UnivariateFactoring a product of a quadrat ic trinomial and a monomial

Solving Quadrat ic Equations by Factoring (6 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 quadrat ic equation needing simplificat ionSolving a word problem using a quadrat ic equation with rat ional roots

Pythagorean Theorem (4 topics)Introduct ion to the Pythagorean TheoremPythagorean TheoremWord problem involving the Pythagorean TheoremUsing the Pythagorean Theorem and a quadrat ic equation to find side lengths of a right triangle

Other Topics Available(*) (443 addit ional topics)

Arithmetic Readiness (59 topics)FactorsWord problem with common mult iplesAddit ion and subtract ion of 3 f ract ions with different denominatorsFract ional part of a circleMult i-step word problem involving f ract ions and mult iplicat ionOrder of operat ions with f ract ions: Problem type 2Order of operat ions with f ract ions: Problem type 3Addit ion and subtract ion of 3 mixed numbers with different denominatorsConvert ing a decimal to a mixed number and an improper f ract ion in simplest form: BasicConvert ing a decimal to a mixed number and an improper f ract ion in simplest form: AdvancedEst imating a decimal sum or differenceEst imating a product of decimalsSquaring decimal bases: Products greater than 0.1Exponents and decimals: Products less than 0.1Convert ing a f ract ion to a repeating decimal: AdvancedConvert ing a mixed number to a terminat ing decimal: BasicConvert ing a mixed number to a terminat ing decimal: AdvancedOrder of operat ions with decimals: Problem type 1Order of operat ions with decimals: Problem type 2Order of operat ions with decimals: Problem type 3Convert ing a mixed number percentage to a decimalConvert ing between percentages and decimals in a real-world situat ionConvert ing a decimal percentage to a f ract ionConvert ing a f ract ion to a percentage in a real-world situat ionMode of a data setAverage of two numbersMean of a data setMean and median of a data setWeighted meanInterpret ing a bar graphInterpret ing a line graphPerimeter of a polygon involving mixed numbers and f ract ionsSides of polygons having the same perimeterDist inguishing between the area and perimeter of a rectangleArea of a rectangle involving f ract ions


Area of a rectangle involving mixed numbers and f ract ionsFinding the missing length in a figureArea of a piecewise rectangular figureWord problem involving the area between two rectanglesArea of a parallelogramArea of a trapezoidPerimeter involving rectangles and circlesArea involving rectangles and circlesWord problem involving the area between two concentric circlesArea involving inscribed figuresVolume of a triangular prismVolume of a pyramidVolume of a cylinderWord problem involving the rate of filling or emptying a cylinderVolume of a coneVolume of a sphereSurface area of a cube or a rectangular prismSurface area of a triangular prismSurface area of a cylinderSurface area of a sphereAcute, obtuse, and right anglesFinding supplementary and complementary anglesAcute, obtuse, and right trianglesClassifying scalene, isosceles, and equilateral t riangles by side lengths or angles

Real Numbers and Algebraic Expressions (17 topics)Fract ional posit ion on a number lineReading decimal posit ion on a number line: TenthsReading decimal posit ion on a number line: HundredthsPlott ing rat ional numbers on a number lineUsing a common denominator to order f ract ionsOrdering decimalsOrdering f ract ions and decimalsEst imating a square rootOrdering real numbersSigned f ract ion addit ion or subtract ion: AdvancedAddit ion and subtract ion of 3 f ract ions involving signsOperat ions with absolute value: Problem type 2Computing distances between decimals on the number lineEvaluat 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 ionUnderstanding the distribut ive property

Linear Equations (25 topics)Addit ive property of equality with f ract ions and mixed numbersSolving an equation to find the value of an expressionIdentifying propert ies used to solve a linear equationSolving a linear equation with several occurrences of the variable: Fract ional forms with binomial numeratorsIntroduct ion to solving an absolute value equationSolving an absolute value equation: Problem type 1Solving 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 equationWrit ing a mult i-step equation for a real-world situat ionSolving a word problem involving rates and t ime conversionFinding the radius or the diameter of a circle given its circumferenceSolving equations involving vert ical anglesFinding angle measures of a right or isosceles triangle given angles with variablesFinding an angle measure given extended trianglesFinding an angle measure given a triangle and parallel linesFinding the value for a new score that will yield a given meanEst imating a t ip without a calculatorComputing a percentage f rom a table of valuesFinding the mult iplier to give a final amount af ter a percentage increase or decreaseFinding the original amount given the result of a percentage increase or decreaseFinding the absolute error and percent error of a measurementComputing a percent mixtureSolving a percent mixture problem using a linear equationInterpret ing a circle graph or pie chartComputat ions f rom a circle graph

Linear Inequalit ies (13 topics)Translat ing a sentence into a mult i-step inequalityTranslat ing a sentence into a compound inequality


Graphing a compound inequality on the number lineWrit ing a compound inequality given a graph on the number lineSet-builder notat ionSet-builder and interval notat ionUnion and intersect ion of finite setsIdentifying solut ions to a two-step linear inequality in one variableSolving inequalit ies with no solut ion or all real numbers as solut ionsSolving a compound linear inequality: Graph solut ion, basicSolving a compound linear inequality: Interval notat ionSolving an absolute value inequality: Problem type 1Solving a decimal word problem using a linear inequality with the variable on both sides

Lines and Funct ions (46 topics)Midpoint of a line segment in the planeFinding x- and y-intercepts of a line given the equation: AdvancedFinding the coordinate that yields a given slopeIdentifying linear equations: AdvancedIdentifying linear funct ions given ordered pairsWrit ing an equation and graphing a line given its slope and y-interceptGraphing a line given its equation in point-slope formWrit ing a funct ion rule given a table of ordered pairs: One-step rulesWrit ing a funct ion rule given a table of ordered pairs: Two-step rulesCombining funct ions to write a new funct ion that models a real-world situat ionComparing propert ies of linear funct ions given in different formsIdentifying independent and dependent variables f rom equations or real-world situat ionsSolving a linear equation by graphingSketching 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 ionTranslat ing the graph of an absolute value funct ion: One stepTranslat ing the graph of an absolute value funct ion: Two stepsGraphing an absolute value equation of the form y = A|x|Graphing an absolute value equation in the plane: BasicGraphing an absolute value equation in the plane: AdvancedHow the leading coefficient affects the graph of an absolute value funct ionVariable expressions as inputs of funct ions: Problem type 1Finding 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 ionFinding an output of a funct ion f rom its graphFinding inputs and outputs of a funct ion f rom its graphDomain and range f rom the graph of a discrete relat ionDomain and range f rom the graph of a continuous funct ionGraphing an integer funct ion and finding its range for a given domainGraphing a funct ion of the form f (x) = ax + b: Integer slopeGraphing a funct ion of the form f (x) = ax + b: Fract ional slopeGraphing 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 funct ion of the form f (x) = ax2 + cFinding intercepts of a nonlinear funct ion given its graphFinding where a funct ion is increasing, decreasing, or constant given the graph: Interval notat ionFinding local maxima and minima of a funct ion given the graphChoosing a graph to fit a narrat ive: BasicChoosing a graph to fit a narrat ive: Advanced

Systems (17 topics)Solving a system of linear equations with f ract ional coefficientsSolving a system of linear equations with decimal coefficientsIdentifying the operat ions used to create equivalent systems of equationsSolving a 3x3 system of linear equations: Problem type 1Solving a word problem using a system of linear equations of the form y = mx + bSolving 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 1Identifying 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


Graphing a system of two linear inequalit ies: BasicGraphing a system of two linear inequalit ies: AdvancedGraphing a system of three linear inequalit iesWrit 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 (15 topics)Ordering numbers with posit ive exponentsOrdering numbers with negative exponentsPower, product, and quotient rules with negative exponentsTable for an exponential funct ionEvaluat ing an exponential funct ion that models a real-world situat ionIntroduct ion to compound interestFinding a final amount in a word problem on exponential growth or decayFinding the final amount in a word problem on compound interestFinding the init ial amount and rate of change given an exponential funct ionWrit ing an equation that models exponential growth or decaySolving an exponential equation by finding common bases: Linear exponentsGraphing an exponential funct ion: f (x) = ax

Graphing an exponential funct ion: f (x) = a(b)xWrit ing an exponential funct ion rule given a table of ordered pairsComparing linear, polynomial, and exponential funct ions

Polynomials and Factoring (13 topics)Degree of a mult ivariate polynomialMult iplying binomials with negative coefficientsMult iplicat ion involving binomials and trinomials in two variablesPolynomial long division: Problem type 2Polynomial long division: Problem type 3Closure propert ies of integers and polynomialsFactoring a mult ivariate polynomial by grouping: Problem type 2Factoring a quadrat ic in two variables with leading coefficient 1Factoring a quadrat ic in two variables with leading coefficient greater than 1Factoring a quadrat ic with a negative leading coefficientFactoring a polynomial involving a GCF and a difference of squares: Mult ivariateFactoring with repeated use of the difference of squares formulaFactoring a sum or difference of two cubes

Rational Expressions (119 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: Linear factorsSimplifying a rat io of factored polynomials: Factors with exponentsSimplifying a rat io of polynomials using GCF factoringSimplifying 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 factorsIntroduct ion to adding f ract ions with variables and common denominatorsAdding rat ional expressions with common denominators and monomial numerators


Adding 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 1Complex f ract ion without variables: Problem type 2Complex 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 ivariateComplex f ract ion with negative exponents: Problem type 1Complex f ract ion with negative exponents: Problem type 2Complex f ract ion that contains a complex f ract ionSolving a proport ion of the form a/(x+b) = c/xSolving a rat ional equation that simplifies to linear: Denominator xSolving 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, advancedWrit ing rat ios using different notat ionsWrit ing rat ios for real-world situat ionsSimplifying a rat io of whole numbers: Problem type 1Simplifying a rat io of whole numbers: Problem type 2Simplifying a rat io of decimalsFinding a unit priceComputing unit prices to find the better buyWord problem on unit rates associated with rat ios of whole numbers: Decimal answersU.S. Customary unit conversion with whole number valuesMetric distance conversion with whole number valuesConvert ing between metric and U.S. Customary unit systemsConvert ing between compound units: BasicConvert ing between compound units: 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 on proport ions: Problem type 1Word problem on proport ions: Problem type 2Similar polygonsSimilar right trianglesIndirect measurementCircumference rat iosWord 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 variablesIdentifying direct variat ion equationsIdentifying direct variat ion f rom ordered pairs and writ ing equations


Writ ing a direct variat ion equationWord problem on direct variat ionInterpret ing direct variat ion f rom a graphWrit 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 ionsWrit ing an equation that models variat ionWord problem on combined variat ion

Radicals (80 topics)Finding all square roots of a numberSquare root of a rat ional perfect squareSquare roots of perfect squares with signsIntroduct ion to simplifying a radical expression with an even exponentSquare root of a perfect square monomialCube root of an integerFinding nth roots of perfect nth powers with signsFinding the nth root of a perfect nth power f ract ionFinding the nth root of a perfect nth power monomialSimplifying the square root of a whole number less than 100Simplifying the square root of a whole number greater than 100Simplifying 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 ivariateIntroduct ion to square root addit ion or subtract ionSquare 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 ivariateSimplifying a sum or difference of higher rootsSimplifying a sum or difference of higher radical expressionsIntroduct ion to square root mult iplicat ionSquare 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 squaringClassifying sums and products as rat ional or irrat ionalSimplifying 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 numeratorRat ionalizing a denominator using conjugates: Variable in denominatorRat ionalizing a denominator: Quotient involving a higher radicalIntroduct 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 with two radicals that simplifies to sqrt (x) = aSolving 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 that simplifies to a quadrat ic equation: Two radicalsSolving an equation with a root index greater than 2: Problem type 1Solving an equation with a root index greater than 2: Problem type 2Algebraic symbol manipulat ion with radicalsWord problem involving radical equations: Basic


Word problem involving radical equations: AdvancedDistance between two points in the plane: Exact answersTable 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 2Convert ing between radical form and exponent formRational exponents: Unit f ract ion exponents and whole number basesRational exponents: Unit f ract ion exponents and bases involving signsRational exponents: Non-unit f ract ion exponent with a whole number baseRational exponents: Negative exponents and f ract ional basesRational exponents: Product ruleRational exponents: Quotient ruleRational exponents: Products and quotients with negative exponentsRational exponents: Power of a power ruleRational exponents: Powers of powers with negative exponentsSimplifying products or quotients of higher radicals with different indices: Univariate

Complex Numbers and Quadrat ic Equations (39 topics)Using i to rewrite square roots of negative numbersSimplifying a product and quotient involving square roots of negative numbersAdding or subtract ing complex numbersMult iplying complex numbersDividing complex numbersSimplifying a power of iSolving an equation of the form x2 = a using the square root propertySolving a quadrat ic equation using the square root property: Exact answers, basicSolving a quadrat ic equation using the square root property: Exact answers, advancedComplet ing the squareSolving a quadrat ic equation by complet ing the square: Exact answersApplying the quadrat ic formula: Exact answersApplying the quadrat ic formula: Decimal answersSolving a quadrat ic equation with complex rootsDiscriminant of a quadrat ic equationSolving a word problem using a quadrat ic equation with irrat ional rootsFinding the vertex, intercepts, and axis of symmetry f rom the graph of a parabolaTranslat ing the graph of a parabola: One stepGraphing a parabola of the form y = (x-h)2 + kGraphing a parabola of the form y = x2 + bx + cGraphing a parabola of the form y = ax2 + bx + c: Integer coefficientsGraphing a parabola of the form y = ax2 + bx + c: Rat ional coefficientsFinding the x-intercept(s) and the vertex of a parabolaRewrit ing a quadrat ic funct ion to find the vertex of 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 parabolaRange of a quadrat ic funct ionSolving a quadrat ic equation by graphingComparing propert ies of quadrat ic funct ions given in different formsClassifying the graph of a funct ionHow the leading coefficient affects the shape of a parabolaIdentifying linear, quadrat ic, and exponential funct ions given ordered pairsGraphing a cubic funct ion of the form y = ax3Sum, difference, and product of two funct ionsComposit ion of two funct ions: BasicExpressing a funct ion as a composit ion of two funct ionsDetermining whether an equation defines a funct ion: BasicDetermining whether an equation defines a funct ion: Advanced

*Other Topics Available By default , these topics are NOT included in the course, but can be added using the content editor inthe Teacher Module.

Documents

Beginning Algebra - ALEKS