Algebra 2 - ALEKS

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Algebra 2This 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 (528 topics + 766 addit ional topics)

Real Numbers (37 topics)

Plott ing and Ordering (3 topics)Using a calculator to approximate a square rootAbsolute value of a numberFinding all numbers with a given absolute value

Operat ions with Signed Numbers (17 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 3Operat 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 integersLeast common mult iple of 2 numbersSigned f ract ion addit ion or subtract ion: BasicSigned f ract ion subtract ion involving double negationLeast common mult iple of 3 numbersSigned f ract ion mult iplicat ion: BasicSigned f ract ion divisionComplex f ract ion without variables: Problem type 1Signed decimal addit ion and subtract ion

Exponents and Order of Operat ions (3 topics)Exponents and integers: Problem type 1Exponents and signed f ract ionsOrder of operat ions with integers

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

Venn Diagrams and Sets of Real Numbers (1 topics)Interpret ing a Venn diagram of 2 sets

Propert ies of Operat ions (9 topics)Introduct ion to adding f ract ions with variables and common denominatorsCombining like terms: Integer coefficientsCombining like terms: Fract ional coefficientsDistribut ive property: Whole number coefficientsDistribut ive property: Integer coefficientsDistribut ive property: Fract ional coefficientsUsing 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

Review of Geometry (2 topics)Writ ing algebraic expressions for the perimeter of a figureCircumference of a circle

Linear Equations and Inequalit ies (64 topics)

Linear Equations (18 topics)Mult iplicat ive property of equality with whole numbersAddit ive property of equality with signed f ract ionsMult iplicat ive property of equality with signed f ract ionsIdentifying solut ions to a linear equation in one variable: Two-step equationsAddit ive property of equality with a negative coefficient


Solving a two-step equation with integersSolving a mult i-step equation given in f ract ional formSolving 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 ionsClearing f ract ions in an equationSolving 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 a linear equation with several occurrences of the variable: Fract ional forms with binomial numeratorsSolving equations with zero, one, or infinitely many solut ions

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

Applicat ions of Linear Equations (8 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 = rtSolving a distance, rate, t ime problem using a linear equationFinding 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 (4 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 variables

Applicat ions with Proport ions and Percents (7 topics)Solving a proport ion of the form x/a = b/cSolving a proport ion of the form (x+a)/b = c/dSolving a proport ion of the form a/(x+b) = c/xWord problem on proport ions: 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 discount

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 and Graphing Inequalit ies (4 topics)Translat ing a sentence into a one-step inequalityWrit ing an inequality for a real-world situat ionGraphing a linear inequality on the number lineGraphing a compound inequality on the number line

Linear Inequalit ies (9 topics)Addit ive property of inequality with integersMult iplicat ive property of inequality with integersIdentifying 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 linear inequality with mult iple occurrences of the variable: Problem type 1Solving a word problem using a two-step linear inequalitySolving a decimal word problem using a two-step linear inequality

Sets (1 topics)Set-builder and interval notat ion

Compound Inequalit ies (1 topics)Solving a compound linear inequality: Graph solut ion, basic


Absolute Value Inequalit ies (3 topics)Solving an absolute value inequality: Problem type 1Solving an absolute value inequality: Problem type 3Solving an absolute value inequality: Problem type 4

Graphs and Funct ions (78 topics)

Ordered Pairs (2 topics)Naming the quadrant or axis of a point given its coordinatesNaming the quadrant or axis of a point given the signs of its coordinates

Graphs of Lines (11 topics)Table for a linear equationIdentifying 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-intercepts

Slope (3 topics)Finding slope given the graph of a line on a gridFinding slope given two points on the lineFinding the slope of horizontal and vert ical lines

Equations of Lines (8 topics)Finding 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 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 point

Applicat ions of Linear Equations with Two Variables (7 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: 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 formsInterpret ing the parameters of a linear funct ion that models a real-world situat 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 cubicVariable expressions as inputs of funct ions: Problem type 1Evaluat ing a piecewise-defined funct 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

Graphs of Funct ions (25 topics)Finding 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 ionFinding domain and range f rom a linear graph in contextDomain and range f rom the graph of a continuous funct ionFinding where a funct ion is increasing, decreasing, or constant given the graphFinding where a funct ion is increasing, decreasing, or constant given the graph: Interval notat ionFinding intercepts of a nonlinear funct ion given its graphFinding local maxima and minima of a funct ion given the graphFinding values and intervals where the graph of a funct ion is zero, posit ive, or negativeChoosing a graph to fit a narrat ive: BasicChoosing a graph to fit a narrat ive: AdvancedGraphing a funct ion of the form f (x) = ax + b: Integer slope


Graphing 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 cubic funct ion of the form y = ax3Graphing 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 (12 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 ionTranslat ing the graph of a funct ion: One stepTranslat ing the graph of a funct ion: Two stepsTransforming the graph of a quadrat ic, cubic, square root, or absolute value funct ionWrit ing an equation for a funct ion af ter a vert ical and horizontal t ranslat ion

Linear Systems (21 topics)

Systems of Linear Equations in Two Variables (9 topics)Identifying solut ions to a system of linear equationsGraphically solving a system of linear equationsUsing a graphing calculator to solve a system of linear equations: BasicUsing a graphing calculator to solve a system of linear equations: AdvancedSolving 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 ions

Applicat ions (4 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 value mixture 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 Inequalit ies and Linear Programming (4 topics)Graphing a system of two linear inequalit ies: BasicGraphing 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 and Polynomials (56 topics)

Product, Power, and Quotient Rules (12 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: Advanced


Negative Exponents (9 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 1Power of a power rule with negative exponentsPower rules with negative exponents

Polynomial Addit ion and Subtract ion (3 topics)Degree and leading coefficient of a univariate polynomialSimplifying a sum or difference of two univariate polynomialsSimplifying a sum or difference of mult ivariate polynomials

Polynomial Mult iplicat ion (12 topics)Mult iplying a univariate polynomial by a monomial with a posit ive coefficientMult iplying a univariate polynomial by a monomial with a negative coefficientMult 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 iplying binomials with negative coefficientsMult iplicat ion involving binomials and trinomials in one variableMult iplicat ion involving binomials and trinomials in two variables

Polynomial Division (6 topics)Dividing a polynomial by a monomial: UnivariatePolynomial long division: Problem type 1Polynomial long division: Problem type 2Polynomial long division: Problem type 3Synthetic divisionClosure propert ies of integers and polynomials

Factoring Using the GCF (4 topics)Greatest common factor of 2 numbersFactoring a linear binomialIntroduct ion to the GCF of two monomialsFactoring out a monomial f rom a polynomial: Univariate

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

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 (4 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: Advanced

Quadrat ic and Polynomial Funct ions (69 topics)

Solving Quadrat ic Equations by Factoring (8 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 ionRoots of a product of polynomialsWrit ing a quadrat ic equation given the roots and the leading coefficientSolving 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 parabola


Graphing 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 parabolaRewrit 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 parabolaRange of a quadrat ic funct ionWrit ing the equation of a quadrat ic funct ion given its graphComparing propert ies of quadrat ic funct ions given in different forms

Introduct ion to Radicals (11 topics)Square root of a rat ional perfect squareSquare roots of perfect squares with signsCube root of an integerSimplifying the square root of a whole number less than 100Introduct ion to square root addit ion or subtract ionIntroduct ion to square root mult iplicat ionSquare root mult iplicat ion: BasicSquare root mult iplicat ion: AdvancedIntroduct ion to simplifying a product involving square roots using the distribut ive propertySimplifying a quotient of square rootsSimplifying a quotient involving a sum or difference with a square root

Complex Numbers (6 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 i

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: Exact answers, basicSolving a quadrat ic equation using the square root property: Exact answers, advanced

Complet ing the Square and the Quadrat ic Formula (5 topics)Solving a quadrat ic equation by complet ing the square: Exact answersApplying the quadrat ic formula: Exact answersSolving a quadrat ic equation with complex rootsDiscriminant of a quadrat ic equationSolving a word problem using a quadrat ic equation with irrat ional roots

Quadrat ic Inequalit ies (4 topics)Solving a quadrat ic inequality writ ten in factored formSolving a quadrat ic inequalityGraphing a quadrat ic inequality: Problem type 1Graphing a quadrat ic inequality: Problem type 2

Polynomial Funct ions (8 topics)Finding zeros of a polynomial funct ion writ ten in factored formFinding zeros and their mult iplicit ies given a polynomial funct ion writ ten in factored formFinding a polynomial of a given degree with given zeros: Real zerosFinding x- and y-intercepts given a polynomial funct ionDetermining the end behavior of the graph of a polynomial funct ionDetermining end behavior and intercepts to graph a polynomial funct ionMatching graphs with polynomial funct ionsUsing a graphing calculator to find local extrema of a polynomial funct ion

Remainder and Factor Theorems (2 topics)Using the remainder theorem to evaluate a polynomialThe Factor Theorem

Real Zeros of Polynomial Funct ions (5 topics)Finding all possible rat ional zeros using the rat ional zeros theorem: Problem type 1Finding all possible rat ional zeros using the rat ional zeros theorem: Problem type 2Using the rat ional zeros theorem to find all zeros of a polynomial: Rat ional zerosUsing the rat ional zeros theorem to find all zeros of a polynomial: Irrat ional zeros


Using a graphing calculator to find zeros of a polynomial funct ion

Complex Zeros of Polynomial Funct ions (2 topics)Mult iplying expressions involving complex conjugatesUsing the rat ional zeros theorem to find all zeros of a polynomial: Complex zeros

Rational Expressions (54 topics)

Simplifying Rat ional Expressions (9 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 polynomials using GCF factoringSimplifying a rat io of polynomials by factoring a quadrat ic with leading coefficient 1Simplifying a rat io of polynomials: Problem type 1

Mult iplicat ion and Division (6 topics)Mult 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 1Dividing rat ional expressions involving mult ivariate monomialsDividing rat ional expressions involving linear expressionsDividing rat ional expressions involving quadrat ics with leading coefficients of 1

Addit ion and Subtract ion (14 topics)Introduct ion to the LCM 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 polynomial denominatorsAdding 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 linear denominators without common factors: BasicAdding rat ional expressions with linear denominators with common factors: BasicAdding rat ional expressions involving different quadrat ic denominators

Complex Fract ions (4 topics)Complex f ract ion without variables: Problem type 2Complex f ract ion involving univariate monomialsComplex f ract ion: GCF factoringComplex f ract ion: Quadrat ic factoring

Rational Equations and Applicat ions (15 topics)Solving 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: 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 for a variable in terms of other variables in a rat ional equation: Problem type 1Word problem involving mult iple ratesSolving a work problem using a rat ional equationSolving a distance, rate, t ime problem using a rat ional equation

Graphs of Rat ional Funct ions (6 topics)Finding the intercepts, asymptotes, domain, and range f rom the graph of a rat ional funct ionFinding 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 linearTransforming the graph of a rat ional funct ion


Radicals (46 topics)

Roots of Perfect Powers (2 topics)Introduct ion to simplifying a radical expression with an even exponentSquare root of a perfect square monomial

Radical Funct ions (7 topics)Table for a square root funct ionEvaluat ing a cube 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 cube root funct ion

Rational Exponents (7 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: Negative exponents and f ract ional basesRational exponents: Product ruleRational exponents: Quotient ruleRational exponents: Power of a power rule

Simplifying Expressions (3 topics)Simplifying a radical expression with an even exponentIntroduct ion to simplifying a radical expression with an odd exponentSimplifying a radical expression with an odd exponent

Addit ion and Subtract ion (1 topics)Square root addit ion or subtract ion

Mult iplicat ion (4 topics)Introduct ion to simplifying a product of radical expressions: UnivariateSimplifying a product of radical expressions: UnivariateSimplifying a product involving square roots using the distribut ive property: BasicSimplifying a product involving square roots using the distribut ive property: Advanced

Division and Rat ionalizat ion (3 topics)Rat ionalizing a denominator: Quotient involving square rootsRationalizing a denominator: Square root of a f ract ionRationalizing a denominator using conjugates: Integer numerator

Radical Equations and Applicat ions (10 topics)Introduct 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, advancedAlgebraic symbol manipulat ion with radicalsWord problem involving radical equations: BasicWord problem involving radical equations: AdvancedSolving an equation with a root index greater than 2: Problem type 1

The Pythagorean Theorem (1 topics)Pythagorean Theorem

Function Operat ions (4 topics)Sum, difference, and product of two funct ionsQuotient of two funct ions: BasicIntroduct ion to the composit ion of two funct ionsComposit ion of two funct ions: Basic

Inverse Funct ions (4 topics)Determining whether two funct ions are inverses of each otherInverse funct ions: Linear, discreteFinding, evaluat ing, and interpret ing an inverse funct ion for a given linear relat ionshipEven and odd funct ions: Problem type 1

Exponential and Logarithmic Funct ions (39 topics)

Graphs of Exponential Funct ions (5 topics)Table for an exponential funct ion


Graphing an exponential funct ion: f (x) = ax

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 of Exponential Funct ions (10 topics)Using a calculator to evaluate exponential expressionsEvaluat ing an exponential funct ion that models a real-world situat ionUsing a calculator to evaluate exponential expressions involving base eEvaluat ing an exponential funct ion with base e 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 decayFinding the init ial amount and asymptote given a graph of an exponential funct ion

Logarithmic Funct ions (6 topics)Using a calculator to evaluate natural and common logarithmic expressionsConvert ing between logarithmic and exponential equationsConvert ing between natural logarithmic and exponential equationsEvaluat ing logarithmic expressionsSolving an equation of the form logba = cGraphing a logarithmic funct ion: Basic

Propert ies of Logarithms (4 topics)Basic propert ies of logarithmsExpanding a logarithmic expression: Problem type 1Expanding a logarithmic expression: Problem type 2Change of base for logarithms: Problem type 1

Logarithmic and Exponential Equations (10 topics)Solving a mult i-step equation involving a single logarithm: Problem type 1Solving a mult i-step equation involving a single logarithm: Problem type 2Solving an equation involving logarithms on both sides: Problem type 1Solving an equation involving logarithms on both sides: Problem type 2Solving an exponential equation by finding common bases: Linear exponentsSolving an exponential equation by using logarithms: Decimal answers, basicSolving an exponential equation by using natural logarithms: Decimal answersSolving an exponential equation by using logarithms: Decimal answers, advancedSolving an exponential equation by using logarithms: Exact answers in logarithmic formUsing a graphing calculator to solve an exponential or logarithmic equation

Applicat ions Involving Exponential Funct ions and Logarithms (4 topics)Finding the t ime to reach a limit in a word problem on exponential growth or decayFinding the t ime given an exponential funct ion with base e that models a real-world situat ionFinding the final amount in a word problem on continuous compound interestFinding half -life or doubling t ime

Stat ist ics and Probability (64 topics)

Collect ing Data (2 topics)Choosing an appropriate method for gathering data: Problem type 2Introduct ion to expectat ion

Frequency Tables (1 topics)Construct ing a f requency distribut ion for grouped data

Graphs of Data (2 topics)Construct ing a f requency distribut ion and a histogramConstruct ing a percent bar graph

Measures of Center and Spread (12 topics)Mode of a data setRange of a data setReject ing unreasonable claims based on average stat ist icsMean and median of a data setMean, median, and mode: ComparisonsApproximating the mean of a data set given a f requency distribut ionApproximating the mean of a data set given a histogramFive-number summary and interquart ile rangeConstruct ing a box-and-whisker plotPercentage of data below a specified valueInterpret ing percentile ranks


Percentiles

Comparing Data (1 topics)Using box-and-whisker plots to compare data sets

Permutat ions and Combinat ions (10 topics)Introduct ion to the counting principleCounting principleCounting principle with repetit ion allowedFactorial expressionsComputing permutat ions and combinat ionsWord problem involving permutat ionsIntroduct ion to permutat ions and combinat ionsPermutat ions and combinat ions: Problem type 1Permutat ions and combinat ions: Problem type 2Binomial formula

Probability of Simple Events (8 topics)Determining a sample space and outcomes for a simple 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 deckExperimental and theoret ical probabilityUsing the graph of a distribut ion to find probabilit ies: BasicComputing expected value in a game of chanceComputing expected value in a business applicat ion

Probability of Compound Events (16 topics)Determining a sample space and outcomes for a compound eventOutcomes and event probabilityIdentifying independent events given descript ions of experimentsProbability of independent eventsProbability of dependent eventsProbabilit ies of draws with replacementDetermining outcomes for compound events and complements of eventsUsing a Venn diagram to understand the addit ion rule for probabilityWord problem involving the probability of a unionProbability of intersect ion or union: Word problemsComputing condit ional probability using a sample spaceOutcomes and event probability: Condit ional probabilityComputing 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: Basic

Simulat ions (3 topics)Identifying outcomes in a random number table used to simulate a simple eventGenerat ing random samples f rom a populat ion with known characterist icsUsing a random number table to make a fair decision

The Binomial Distribut ion (2 topics)Using the binomial formula to solve a word problem: Problem type 1Using the binomial formula to solve a word problem: Problem type 2

Standard Deviat ion and the Normal Distribut ion (7 topics)Populat 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 ionShading a region and finding its standard normal probabilityComputing standard normal probabilit iesFinding a probability given a normal distribut ion: BasicFinding a probability given a normal distribut ion: Advanced

Other Topics Available(*) (766 addit ional topics)

Real Numbers (80 topics)Fract ional posit ion on a number linePlott ing integers on a number linePlott ing rat ional numbers on a number lineOrdering integersSquare root of a perfect squareOrdering real numbersAddit ion and subtract ion with 3 integers


Operat ions with absolute value: Problem type 2Signed 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 decimal addit ion and subtract ion with 3 numbersSigned decimal mult iplicat ionSigned decimal divisionExponents and integers: Problem type 2Order of operat ions with integers 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 ionIdentifying 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 3 setsConstruct ing a Venn diagram to classify rat ional numbersConstruct ing a Venn diagram to describe relat ionships between sets of rat ional numbersConstruct ing a Venn diagram to classify real numbersConstruct ing a Venn diagram to describe relat ionships between sets of real numbersPropert ies of addit ionPropert ies of real numbersIdentifying parts in an algebraic expressionIdentifying equivalent algebraic expressionsIdentifying propert ies used to simplify an algebraic expressionU.S. Customary length conversion with whole number valuesU.S. Customary length conversions involving rounding decimalsWord problem involving a U.S. Customary length conversionU.S. Customary volume conversion with whole number valuesU.S. Customary weight conversions with whole number valuesMetric distance conversion with whole number valuesMetric distance conversion with decimal valuesTime unit conversion with whole number valuesConvert ing between metric and U.S. Customary unit systemsConversions with currencyPerimeter of a square or a rectangleSides of polygons having the same perimeterArea of a square or a rectangleIntroduct 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 trapezoidPerimeter 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 cylinderWord 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 and Inequalit ies (102 topics)Addit ive property of equality with integersMult iplicat ive property of equality with integersSolving an equation to find the value of an expressionSolving a two-step equation with signed decimalsIdentifying propert ies used to solve a linear equationSolving a f ract ion word problem using a linear equation of the form Ax = BWrit ing an equation of the form A(x + B) = C to solve a word problemWrit 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 equationWord problem on unit rates associated with rat ios of whole numbers: Decimal answersSolving a word problem involving rates and t ime conversionConvert 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 variablesSolving equations involving vert ical 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 ionsU.S. Customary length conversions involving dimensional analysisConvert ing between compound units: BasicWord 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 analysisWord 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 measurementCircumference rat iosFinding 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 discountFinding the percentage increase or decrease: BasicFinding the percentage increase or decrease: AdvancedFinding the absolute error and percent error of a measurementComputing 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 investmentComputing 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 daysGross pay with commission and salaryGross pay with variable commission scaleSolving an absolute value equation: Problem type 3Solving an absolute value equation: Problem type 4Solving an absolute value equation of the form |ax+b| = |cx+d|Translat ing a sentence by using an inequality symbolWrit ing an inequality given a graph on the number lineAddit ive property of inequality with signed f ract ionsAddit ive property of inequality with signed decimalsMult iplicat ive property of inequality with signed f ract ionsSolving a two-step linear inequality with a f ract ional coefficientSolving 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 inequalit ies with no solut ion or all real numbers as solut ionsTranslat ing a sentence into a mult i-step inequalitySolving 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 forms


Ident ifying 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 setsUnion and intersect ion of intervalsConstruct 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 a compound linear inequality: Interval notat ionWrit ing an absolute value inequality given a graph on the number lineSolving an absolute value inequality: Problem type 2Solving an absolute value inequality: Problem type 5

Graphs and Funct ions (53 topics)Reading a point in the coordinate planePlott ing a point in the coordinate planeNaming the quadrant or axis of a point given its graphFinding distances between points that share a common coordinate given their coordinatesFinding x- and y-intercepts of a line given the equation: AdvancedGraphing a line given its x- and y-interceptsClassifying slopes given graphs of linesFinding the coordinate that yields a given slopeGraphing a line given its slope and y-interceptGraphing a line through a given point with a given slopeIdentifying linear equations: BasicIdentifying linear equations: AdvancedIdentifying linear funct ions given ordered pairsRewrit ing a linear equation in the form Ax + By = CWrit ing an equation and graphing a line given its slope and y-interceptFinding the slope, y-intercept, and equation for a linear funct ion given a table of valuesFinding the slope and a point on a line given its equation in point-slope formGraphing 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 in standard form given the slope and a pointComparing 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 pointIdentifying parallel and perpendicular lines f rom coordinatesIdentifying coordinates that give right trianglesApplicat 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 pointsIdentifying independent and dependent quantit ies f rom tables and graphsIdentifying independent and dependent variables f rom equations or real-world situat ionsSolving a linear equation by graphingConstruct 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 plotsClassifying linear and nonlinear relat ionships f rom scatter plotsLinear relat ionship and the correlat ion coefficientIdentifying out liers and clustering in scatter plotsIdentifying correlat ion and causat ion


Finding outputs of a one-step funct ion that models a real-world situat ion: Funct ion notat ionDomain and range f rom the graph of a piecewise funct ionGraphing an integer funct ion and finding its range for a given domainGraphing 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 piecewise-defined funct ion: Problem type 3Transforming the graph of a funct ion by reflect ing over an axisTransforming the graph of a funct ion by shrinking or stretchingTransforming the graph of a funct ion using more than one transformation

Linear Systems (45 topics)Classifying systems of linear equations f rom graphsWrit 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 coefficientsSolving a 2x2 system of linear equations that is inconsistent or consistent dependentCreat ing an inconsistent system of linear equationsIdentifying the operat ions used to create equivalent systems of equationsSolving a word problem using a system of linear equations of the form Ax + By = CSolving 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 distance, rate, t ime problem using a system of linear equationsSolving a tax rate or interest rate problem using a system of linear equationsWrit 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 two linear inequalit ies: AdvancedWrit ing a linear inequality in two variables given a table of valuesSolving a word problem using a system of linear inequalit ies: Problem type 2Linear programmingSolving a word problem using linear programmingIntroduct 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 2Solving a 3x3 system of linear equations that is inconsistent or consistent dependentSolving a word problem using a 3x3 system of linear equations: Problem type 1Solving a word problem using a 3x3 system of linear equations: Problem type 2Scalar mult iplicat ion of a matrixAddit ion or subtract ion of matricesLinear combinat ion of matricesSquaring and mult iplying 2x2 matricesMult iplicat ion of matrices: BasicMult iplicat ion of matrices: AdvancedWord problem involving mult iplicat ion of matricesComplet ing Gauss-Jordan eliminat ion with a 2x2 matrixGauss-Jordan eliminat ion with a 2x2 matrixComplet ing Gauss-Jordan eliminat ion with a 3x3 matrixWrit ing solut ions to 3x3 systems of linear equations f rom augmented matricesSolving a system of linear equations given its augmented matrixFinding the inverse of a 2x2 matrixFinding the inverse of a 3x3 matrixFinding the inverse of a matrix to solve a 2x2 system of linear equationsUsing the inverse of a matrix to solve a 3x3 system of linear equationsFinding the determinant of a 2x2 matrixFinding the determinant of a 3x3 matrixUsing Cramer's rule to solve a 2x2 system of linear equationsUsing Cramer's rule to solve a 3x3 system of linear equations

Exponents and Polynomials (47 topics)Understanding the product rule of exponentsOrdering numbers with posit ive exponentsUnderstanding the power rules of exponentsPower and product rules with posit ive exponentsPower and quotient rules with posit ive exponentsOrdering numbers with negative exponentsProduct rule with negative exponentsQuotient rule with negative exponents: Problem type 2Power and quotient rules with negative exponents: Problem type 1Power and quotient rules with negative exponents: Problem type 2Power, product, and quotient rules with negative exponentsScient 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 ionExpressing calculator notat ion as scient ific notat ion


Mult 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 ionDegree of a mult ivariate polynomialSimplifying a sum or difference of three univariate polynomialsMult iplying a mult ivariate polynomial by a monomialDividing a polynomial by a monomial: Mult ivariatePrime numbersPrime factorizat ionGreatest common factor of 3 numbersGreatest 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 univariate polynomial by grouping: Problem type 2Factoring 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: UnivariateFactoring 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 cubes

Quadrat ic and Polynomial Funct ions (29 topics)Graphing a parabola of the form y = ax2 + bx + c: Rat ional coefficientsUsing a graphing calculator to find the zeros of a quadrat ic funct ionUsing a graphing calculator to find the x-intercept(s) and vertex of a quadrat ic funct ionRewrit ing a quadrat ic funct ion in standard formWord problem involving optimizing area by using a quadrat ic funct ionSolving a quadrat ic equation by graphingClassifying the graph of a funct ionChoosing a quadrat ic model and using it to make a predict ionFinding all square roots of a numberEst imating a square rootSimplifying the square root of a whole number greater than 100Plott ing complex numbersSolving a quadrat ic equation using the square root property: Decimal answers, basicSolving a quadrat ic equation using the square root property: Decimal answers, advancedSolving an equation of the form x3 = a using integersSolving a quadrat ic equation by complet ing the square: Decimal answersApplying the quadrat ic formula: Decimal answersDiscriminant of a quadrat ic equation with parameterIdentifying polynomial funct ionsInferring propert ies of a polynomial funct ion f rom its graphUsing a graphing calculator to solve a word problem involving a local extremum of a polynomial funct ionRemainder theorem: AdvancedUsing a given zero to write a polynomial as a product of linear factors: Real zerosDescartes' Rule of SignsUsing a graphing calculator to solve a word problem involving a polynomial of degree 3Finding a polynomial of a given degree with given zeros: Complex zerosUsing a given zero to write a polynomial as a product of linear factors: Complex zerosUsing the conjugate zeros theorem to find all zeros of a polynomialLinear factors theorem and conjugate zeros theorem

Rational Expressions (62 topics)Variable expressions as inputs of funct ions: Problem type 2Simplifying a rat io of factored polynomials: Factors with exponentsFinding a difference quotient for a linear or quadrat ic funct ionSimplifying a rat io of linear polynomials: 1, -1, and no simplificat ionSimplifying 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 quadrat ics with leading coefficients greater than 1Mult iplying rat ional expressions involving mult ivariate quadrat ics


Dividing 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 expressionsLeast common mult iple of two monomialsWrit ing equivalent rat ional expressions with monomial denominatorsWrit ing equivalent rat ional expressions involving opposite factorsAdding 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: AdvancedAdding rat ional expressions with linear denominators with common factors: AdvancedAdding rat ional expressions with denominators ax-b and b-axAdding 3 rat ional expressions with different quadrat ic denominatorsComplex f ract ion involving mult ivariate monomialsComplex 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 rat ional equation that simplifies to quadrat ic: Proport ional form, basicSolving 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 2Solving for a variable in terms of other variables in a rat ional equation: Problem type 3Ratio of volumesOrdering f ract ions with variablesIdentifying 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 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 ionFinding horizontal and vert ical asymptotes of a rat ional funct ion: Quadrat ic numerator or denominatorFinding the asymptotes of a rat ional funct ion: Quadrat ic over linearGraphing a rat ional funct ion: Quadrat ic over linearGraphing rat ional funct ions with holesMatching graphs with rat ional funct ions: Two vert ical asymptotesFinding x- and y-intercepts of the graph of a nonlinear equationGraphing a rat ional funct ion with more than one vert ical asymptoteSolving a rat ional inequality: Problem type 1Solving a polynomial inequality: Problem type 1Solving a rat ional inequality: Problem type 2

Radicals (67 topics)Square roots of integers raised to even exponentsUsing absolute value to simplify square roots of perfect square monomialsFinding 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 monomialUsing absolute value to simplify higher radical expressionsEvaluat ing funct ions: Absolute value, rat ional, radicalVariable expressions as inputs of funct ions: Problem type 3Graphing a square root funct ion: Problem type 3Rational exponents: Unit f ract ion exponents and bases involving signsRational exponents: Products and quotients with negative exponentsRational exponents: Powers of powers with negative exponentsSimplifying 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 ion with three terms


Introduct 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 expressionsSimplifying a product of radical expressions: Mult ivariateSimplifying a product of radical expressions: Mult ivariate, f ract ional expressionsIntroduct ion to simplifying a product of higher rootsSimplifying a product of higher radical expressionsSpecial products of radical expressions: Conjugates and squaringClassifying sums and products as rat ional or irrat ionalRat ionalizing a denominator: Quotient involving a monomialRat ionalizing a denominator using conjugates: Square root in numeratorRat ionalizing a denominator using conjugates: Variable in denominatorRat ionalizing a denominator: Quotient involving a higher radicalRat ionalizing a denominator: Quotient involving higher radicals and monomialsSimplifying products or quotients of higher radicals with different indices: UnivariateSimplifying products or quotients of higher radicals with different indices: Mult ivariateSolving 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 radicalsSolving an equation with a root index greater than 2: Problem type 2Solving an equation using the odd-root property: Problem type 1Solving an equation using the odd-root property: Problem type 2Solving an equation with exponent 1/a: Problem type 1Solving an equation with exponent 1/a: Problem type 2Solving an equation with posit ive rat ional exponentSolving an equation with negative rat ional exponentSolving an equation that can be writ ten in quadrat ic form: Problem type 1Solving an equation that can be writ ten in quadrat ic form: Problem type 2Introduct ion to the Pythagorean TheoremWord problem involving the Pythagorean TheoremIdentifying side lengths that give right trianglesUsing the Pythagorean Theorem and a quadrat ic equation to find side lengths of a right triangleComposit ion of a funct ion with itselfExpressing a funct ion as a composit ion of two funct ionsComposit ion of two funct ions: Domain and rangeComposit ion of two funct ions: AdvancedWord problem involving composit ion of two funct ionsRewrit ing a mult ivariate funct ion as a univariate funct ion given a relat ionship between its variablesDetermining whether an equation defines a funct ion: BasicDetermining whether an equation defines a funct ion: AdvancedHorizontal line testInverse funct ions: Quadrat ic, square rootInverse funct ions: Cubic, cube rootInverse funct ions: Rat ionalGraphing the inverse of a funct ion given its graphDetermining if graphs have symmetry with respect to the x-axis, y-axis, or originEven and odd funct ions: Problem type 2

Exponential and Logarithmic Funct ions (27 topics)Graphing an exponential funct ion and its asymptote: f (x)=bx

Graphing 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)=-baxThe graph, domain, and range of an exponential funct ionTransforming the graph of a natural exponential funct ionGraphing an exponential funct ion and its asymptote: f (x) = a(e)x-b + cCalculat ing and comparing simple interest and compound interestFinding the future value and interest for an investment earning compound interestFinding the present value of an investment earning compound interestWrit ing an exponential funct ion rule given a table of ordered pairsChoosing an exponential model and using it to make a predict ionComparing linear, polynomial, and exponential funct ionsTranslat ing the graph of a logarithmic funct ionThe graph, domain, and range of a logarithmic funct ionGraphing a logarithmic funct ion: AdvancedUsing propert ies of logarithms to evaluate expressionsExpanding a logarithmic expression: Problem type 3Writ ing an expression as a single logarithmChange of base for logarithms: Problem type 2Solving a mult i-step equation involving natural logarithmsSolving an exponential equation by finding common bases: Linear and quadrat ic exponentsFinding the t ime in a word problem on compound interest


Finding the init ial amount in a word problem on continuous compound interestFinding the final amount in a word problem on continuous exponential growth or decayFinding the rate or t ime in a word problem on continuous exponential growth or decayWrit ing and evaluat ing a funct ion modeling continuous exponential growth or decay given doubling t ime or half -lifeWrit ing and evaluat ing a funct ion modeling continuous exponential growth or decay given two outputs

Stat ist ics and Probability (57 topics)Classifying samplesMaking 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 dataComputing 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 tableMaking a reasonable inference based on proport ion stat ist icsConstruct ing a line plotConstruct ing a bar graph for non-numerical dataInterpret ing a bar graphInterpret ing a double bar graphInterpret ing a histogramInterpret ing a stem-and-leaf displayFinding a percentage of a total amount in a circle graphComputat ions f rom a circle graphAngle measure in a circle graphFinding the mode and range f rom a line plotMean of a data setFinding 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 meanWeighted meanFinding out liers in a data setChoosing the best measure to describe dataIdentifying the center, spread, and shape of a data setComparing measures of center and variat ionFinding sample size and comparing samples for est imating the meanUsing back-to-back stem-and-leaf displays to compare data setsInterpret ing a tree diagramCounting arrangements of objects that are not all dist inctPermutat ions and combinat ions: Problem type 3Probabilit ies of an event and its complementFinding 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 probabilityExperimental and theoret ical probability for compound eventsProbabilit ies involving two rolls of a dieProbabilit ies of a permutat ion and a combinat ionProbability of independent events: Decimal answersProbability of independent events involving a standard deck of cardsProbability of dependent events: Decimal answersProbability of dependent events involving a surveyProbability of dependent events involving a standard deck of cardsProbabilit ies of draws without replacementOutcomes and event probability: Addit ion ruleProbability of the union of two eventsComputing probability involving the addit ion rule using a two-way f requency tableProbability of the union and intersect ion of independent eventsUsing a Venn diagram to understand the mult iplicat ion rule for probabilityIdentifying independent events given values of probabilit iesUsing 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 event

Sequences and Conics (77 topics)Finding the first terms of an arithmetic sequence using an explicit ruleFinding the first terms of a geometric sequence using an explicit ruleFinding the first terms of a sequence using an explicit rule with mult iple occurrences of nFinding 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 terms


Finding a specified term of an arithmetic sequence given the common difference and first termFinding a specified term of an arithmetic sequence given two terms of the sequenceWrit ing an explicit rule for an arithmetic sequenceWrit ing a recursive rule for an arithmetic sequenceSum of the first n terms of an arithmetic sequenceFinding 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 termFinding a specified term of a geometric sequence given two terms of the sequenceArithmetic and geometric sequences: Identifying and writ ing an explicit ruleWrit ing recursive rules for arithmetic and geometric sequencesSum of the first n terms of a geometric sequenceSum of an infinite geometric seriesIdentifying linear, quadrat ic, and exponential funct ions given ordered pairsDistance between two points in the plane: Exact answersDistance between two points in the plane: Decimal answersIdentifying scalene, isosceles, and equilateral t riangles given coordinates of their vert icesMidpoint of a line segment in the planeFinding an endpoint of a line segment given the other endpoint and the midpointGraphing a parabola of the form y2 = ax or x2 = ayGraphing a parabola of the form x=a(y-k)2+h or y=a(x-h)2+kGraphing a parabola of the form ay2 + by + cx + d = 0 or ax2 + bx + cy + d = 0Writ ing an equation of a parabola given the vertex and the focusWrit ing an equation of a parabola given the focus and the directrixDeriving the equation of a parabola given its focus and directrixFinding the vertex, focus, directrix, and axis of symmetry of a parabolaFinding the focus of a parabola of the form ay2 + by + cx + d = 0 or ax2 + bx + cy + d = 0Writ ing an equation of a parabola given its graphWord problem involving a parabolaIdentifying the center and radius to graph a circle given its equation in standard formIdentifying the center and radius to graph a circle given its equation in general form: BasicIdentifying the center and radius to graph a circle given its equation in general form: AdvancedWrit ing the equation of a circle centered at the origin given its radius or a point on the circleWrit ing an equation of a circle and identifying points that lie on the circleWrit ing an equation of a circle given its center and radius or diameterDeriving the equation of a circle using the Pythagorean TheoremWrit ing an equation of a circle given its center and a point on the circleWrit ing an equation of a circle given the endpoints of a diameterGraphing an ellipse given its equation in standard formGraphing an ellipse centered at the origin: Ax2 + By2 = CGraphing an ellipse given its equation in general formFinding the center, vert ices, and foci of an ellipseFinding the foci of an ellipse given its equation in general formWrit ing an equation of an ellipse given the center, an endpoint of an axis, and the length of the other axisWord problem involving an ellipseGraphing a hyperbola given its equation in standard formGraphing a hyperbola centered at the origin: Ax2 + By2 = CGraphing a hyperbola given its equation in general formFinding the center, vert ices, foci, and asymptotes of a hyperbolaFinding the foci of a hyperbola given its equation in general formWrit ing an equation of a hyperbola given the foci and the vert icesWrit ing an equation of a hyperbola given the foci and the asymptotes: BasicClassifying conics given their equationsGraphically solving a system of linear and quadrat ic equationsUsing a graphing calculator to solve a system of linear and quadrat ic equations: BasicUsing a graphing calculator to solve a system of equationsSolving a system of linear and quadrat ic equationsSolving a system of nonlinear equations: Problem type 1Solving a system of nonlinear equations: Problem type 2Solving a word problem involving geometry using a system of nonlinear equationsGraphing an inequality involving a circleGraphing a system of nonlinear inequalit ies: Problem type 1Graphing a system of nonlinear inequalit ies: Problem type 2Complet ing a table and choosing a graph given a pair of parametric equationsWrit ing the equation of a line and sketching its graph given its parametric equationsWrit ing the equation of a parabola and sketching its graph given its parametric equations

Trigonometry (120 topics)Sine, cosine, and tangent rat ios: Numbers for side lengthsSine, cosine, and tangent rat ios: Variables for side lengths


Using the Pythagorean Theorem to find a trigonometric rat ioFinding trigonometric rat ios given a right triangleUsing a calculator to approximate sine, cosine, and tangent valuesUnderstanding trigonometric rat ios through similar right trianglesRelat ionship between the sines and cosines of complementary anglesUsing similar right triangles to find trigonometric rat iosUsing a trigonometric rat io to find a side length in a right triangleUsing trigonometry to find a length in a word problem with one right triangleUsing 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 problemSolving a right triangleUsing trigonometry to find a length in a word problem with two right trianglesSpecial right triangles: Decimal answersSpecial right triangles: Exact answersConvert ing degrees-minutes-seconds to decimal degreesConvert ing a decimal degree to degrees-minutes-secondsConvert ing between degree and radian measure: Problem type 1Convert ing between degree and radian measure: Problem type 2Sketching an angle in standard posit ionCoterminal anglesArc length and central angle measureArea of a sector of a circleFinding coordinates on the unit circle for special anglesTrigonometric funct ions and special angles: Problem type 1Finding trigonometric rat ios f rom a point on the unit circleTrigonometric funct ions and special angles: Problem type 2Trigonometric funct ions and special angles: Problem type 3Evaluat ing expressions involving sine and cosineEven and odd propert ies of trigonometric funct ionsUsing a calculator to approximate cosecant, secant, and cotangent valuesEvaluat ing a sinusoidal funct ion that models a real-world situat ionReference angles: Problem type 1Reference angles: Problem type 2Determining the locat ion of a terminal point given the signs of trigonometric valuesFinding values of trigonometric funct ions given information about an angle: Problem type 1Finding values of trigonometric funct ions given information about an angle: Problem type 2Finding values of trigonometric funct ions given information about an angle: Problem type 3Finding values of trigonometric funct ions given information about an angle: Problem type 4Values of inverse trigonometric funct ionsSolving a triangle with the law of sines: Problem type 1Solving a triangle with the law of sines: Problem type 2Solving a word problem using the law of sinesProving the law of sinesSolving a triangle with the law of cosinesProving the law of cosinesSolving a word problem using the law of cosinesUsing trigonometry to find the area of a right triangleFinding the area of a triangle using trigonometryExpressing the area of a triangle in terms of the sine of one of its anglesHeron's formulaSketching the graph of y= a sin(x) or y= a cos(x)Sketching the graph of y= sin(bx) or y= cos(bx)Sketching the graph of y= sin(x)+ d or y= cos(x)+ dSketching the graph of y= sin(x+c) or y= cos(x+c)Sketching the graph of y= a sin(x+c) or y= a cos(x+c)Sketching the graph of y= a sin(bx) or y= a cos(bx)Sketching the graph of y= a sin(bx+c) or y= a cos(bx+c)Sketching the graph of y= a sin(bx)+ d or y= a cos(bx)+ dAmplitude and period of sine and cosine funct ionsAmplitude, period, and phase shif t of sine and cosine funct ionsWrit ing the equation of a sine or cosine funct ion given its graph: Problem type 1Writ ing the equation of a sine or cosine funct ion given its graph: Problem type 2Word problem involving a sine or cosine funct ion: Problem type 1Word problem involving a sine or cosine funct ion: Problem type 2Domains and ranges of trigonometric funct ionsMatching graphs and equations for secant, cosecant, tangent, and cotangent funct ionsSketching the graph of a secant or cosecant funct ion: Problem type 1Sketching the graph of a secant or cosecant funct ion: Problem type 2Sketching the graph of a tangent or cotangent funct ion: Problem type 1Sketching the graph of a tangent or cotangent funct ion: Problem type 2Simplifying trigonometric expressionsUsing cofunct ion identit iesVerifying a trigonometric identityProving trigonometric identit ies: Problem type 1


Proving trigonometric identit ies: Problem type 2Proving trigonometric identit ies: Problem type 3Proving trigonometric identit ies: Problem type 4Proving trigonometric identit ies using odd and even propert iesSum and difference identit ies: Problem type 1Sum and difference identit ies: Problem type 2Sum and difference identit ies: Problem type 3Proving trigonometric identit ies using sum and difference propert ies: Problem type 1Proving trigonometric identit ies using sum and difference propert ies: Problem type 2Double-angle identit ies: Problem type 1Double-angle identit ies: Problem type 2Half -angle identit ies: Problem type 1Half -angle identit ies: Problem type 2Proving trigonometric identit ies using double-angle propert iesFinding solut ions in an interval for a basic equation involving sine or cosineFinding solut ions in an interval for a basic tangent, cotangent, secant, or cosecant equationUsing a calculator to approximate inverse trigonometric valuesSolving a basic trigonometric equation using a calculatorSolving a basic trigonometric equation involving sine or cosineSolving a basic trigonometric equation involving tangent, cotangent, secant, or cosecantFinding solut ions in an interval for a trigonometric equation in factored formFinding solut ions in an interval for a trigonometric equation with a squared funct ion: Problem type 1Finding solut ions in an interval for a trigonometric equation with a squared funct ion: Problem type 2Finding solut ions in an interval for a trigonometric equation using Pythagorean identit ies: Problem type 1Finding solut ions in an interval for a trigonometric equation using Pythagorean identit ies: Problem type 2Finding solut ions in an interval for an equation with sine and cosine using double-angle identit iesSolving a trigonometric equation modeling a real-world situat ionUsing a graphing calculator to solve a trigonometric equationSolving a trigonometric equation involving a squared funct ion: Problem type 1Solving a trigonometric equation involving a squared funct ion: Problem type 2Solving a trigonometric equation involving more than one funct ionSolving a trigonometric equation using double-angle identit iesWrit ing a vector in component form given its init ial and terminal pointsMagnitude of a vector given in component formVector addit ion and scalar mult iplicat ion: Component formLinear combinat ion of vectors: Component formMult iplicat ion of a vector by a scalar: Geometric approachVector addit ion: Geometric approachVector subtract ion: Geometric approachFinding the magnitude and direct ion of a vector given its graphFinding the components of a vector given its graphDot product of vectors given in component formFinding the angle between two vectors given in component formUsing the dot product to find perpendicular vectors

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

Algebra 2 - ALEKS

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