Introduction to Statistics with Corequisite Support - ALEKS

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Introduction to Statistics with Corequisite SupportThis 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 (409 topics + 321 addit ional topics)

Arithmetic Readiness (68 topics)

Integers (14 topics)Plott ing integers on a number lineOrdering integersWord problem on unit rates associated with rat ios of whole numbers: Whole number answersDescribing an increasing or decreasing pattern f rom a table of valuesWrit ing a signed number for a real-world situat ionAbsolute value of a numberInteger addit ion: Problem type 1Integer addit ion: Problem type 2Integer subtract ion: Problem type 1Integer subtract ion: Problem type 3Addit ion and subtract ion with 3 integersComputing the distance between two integers on a number lineInteger mult iplicat ion and divisionMult iplicat ion of 3 or 4 integers

Fract ions and Decimals (31 topics)Introduct ion to non-unit f ract ionsSimplifying a f ract ionProduct 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 2Signed f ract ion mult iplicat ion: BasicThe reciprocal of a numberDivision involving a whole number and a f ract ionFract ion divisionComplex f ract ion without variables: Problem type 1Addit ion or subtract ion of f ract ions with the same denominator and simplificat ionAddit ion or subtract ion of f ract ions with different denominatorsSigned f ract ion addit ion or subtract ion: BasicDecimal place value: Tenths and hundredthsOrdering decimalsRounding decimalsDecimal addit ion with 3 numbersDecimal subtract ion: BasicAverage of two numbersSigned decimal addit ion and subtract ionMult iplying a decimal by a whole numberMult iplicat ion of a decimal by a power of tenWord problem with decimal addit ion and mult iplicat ionDivision of a decimal by a whole numberDivision of a decimal by a power of tenWord problem with decimal subtract ion and divisionConvert ing a f ract ion with a denominator of 10 or 100 to a decimalConvert ing a proper f ract ion with a denominator of 2, 4, or 5 to a decimalConvert ing a f ract ion to a terminat ing decimal: BasicUsing a calculator to convert a f ract ion to a rounded decimal

Exponents and Order of Operat ions (8 topics)Writ ing expressions using exponentsIntroduct ion to exponentsOrder of operat ions with whole numbersOrder of operat ions with whole numbers and grouping symbolsOrder of operat ions with whole numbers and exponents: BasicExponents and integers: Problem type 1Order of operat ions with integers and exponentsExponents and integers: Problem type 2

Introduct ion to Expressions (6 topics)Evaluat ing an algebraic expression: Whole number addit ion or subtract ion


Evaluat ing an algebraic expression: Whole number mult iplicat ion or divisionEvaluat ing an algebraic expression: Whole numbers with two operat ionsEvaluat ing a formulaEvaluat ing an algebraic expression: Whole numbers with one operat ion and an exponentEvaluat ing a linear expression: Integer mult iplicat ion with addit ion or subtract ion

Plott ing, Ordering, and Classifying Real numbers (3 topics)Square root of a perfect squareUsing a calculator to approximate a square rootInterpret ing a Venn diagram with 2 sets for a real-world situat ion

Propert ies of Real Numbers (6 topics)Mult iplying a constant and a linear monomialDistribut ive property: Whole number coefficientsCombining like terms: Whole number coefficientsCombining like terms: Integer coefficientsDistribut ive property: Integer coefficientsUsing distribut ion and combining like terms to simplify: Univariate

Ratios and Percentages (20 topics)

Rat ios and Unit Rates (1 topics)Solving a word problem on proport ions using a unit rate

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

Convert ing Between Fract ions, Decimals, and Percentages (10 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 between percentages and decimals in a real-world situat ionConvert 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 percentageConvert ing a f ract ion to a percentage in a real-world situat ion

Applicat ions Involving Percentages (6 topics)Finding a percentage of a whole numberApplying the percent equation: Problem type 1Finding a percentage of a total amount: Real-world situat ionsWrit ing a rat io as a percentageComputing a percentage f rom a table of valuesFinding the sale price given the original price and percent discount

Linear Equations and Inequalit ies (32 topics)

One-Step Linear Equations (7 topics)Addit ive property of equality with decimalsAddit ive property of equality with integersMult iplicat ive property of equality with whole numbers: Fract ional answersMult iplicat ive property of equality with f ract ionsMult iplicat ive property of equality with decimalsMult iplicat ive property of equality with integersMult iplicat ive property of equality with signed f ract ions

Mult i-Step Linear Equations (7 topics)Solving 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 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 ion

Solving Formulas for a Variable (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 mult iplicat ion or division: AdvancedSolving for a variable in terms of other variables using addit ion or subtract ion with division


Applicat ions (5 topics)Writ ing a one-step expression for a real-world situat ionTranslat ing a phrase into a one-step expressionTranslat ing a sentence into a one-step equationSolving a decimal word problem using a linear equation of the form Ax + B = CSolving a word problem with two unknowns using a linear equation

Writ ing and Graphing Inequalit ies (5 topics)Translat ing a sentence by using an inequality symbolWrit ing an inequality for a real-world situat ionGraphing a linear inequality on the number lineGraphing a compound inequality on the number lineWrit ing and graphing inequalit ies given in context

Linear Inequalit ies and Applicat ions (2 topics)Addit ive property of inequality with integersMult iplicat ive property of inequality with integers

Set Notat ion and Operat ions (2 topics)Finding sets and complements of setsUnion and intersect ion of finite sets

Lines (33 topics)

Graphing and Intercepts (17 topics)Reading a point in the coordinate planePlott ing a point in the coordinate planeFinding distances between points that share a common coordinate given the graphTable for a linear equationFinding a solut ion to a linear equation in two variablesGraphing a line given two of its pointsGraphing 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 formFinding x- and y-intercepts given the graph of a line on a gridY-intercept of a lineFinding x- and y-intercepts of a line given the equation: BasicX- and y-intercepts of a line given the equation in standard formGraphing a line given its x- and y-interceptsWrit ing an equation to represent a proport ional relat ionshipInterpret ing a line graph

Slope (7 topics)Finding slope given the graph of a line in quadrant 1 that models a real-world situat ionClassifying slopes given graphs of linesFinding slope given the graph of a line on a gridFinding slope given two points on a lineGraphing a line given its slope and y-interceptFinding a coordinate pair given the slope and a point on a lineGraphing a line through a given point with a given slope

Equations of Lines (6 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 = CWrit 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 the equation of a line given the y-intercept and another pointWrit ing the equation of a line through two given points

Applicat ions (3 topics)Finding outputs of a two-step funct ion with decimals that models a real-world situat ion: Two variable equationFinding the intercepts and rate of change given a graph of a linear funct ionInterpret ing the parameters of a linear funct ion that models a real-world situat ion

Exponents and Funct ions (11 topics)

Product, Power, and Quotient Rules (5 topics)Introduct ion to the product rule of exponentsProduct rule with posit ive exponents: UnivariateIntroduct 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 products


Negative Exponents (1 topics)Power of 10: Negative exponent

Scient ific Notat ion (4 topics)Scient ific notat ion with a posit ive exponentScient ific notat ion with a 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

Exponential Funct ions (1 topics)Using a calculator to evaluate exponential expressions involving base e

Descript ive Stat ist ics (74 topics)

Collect ing Data (10 topics)Differentiat ing between parameters and stat ist icsClassificat ion of variablesClassificat ion of variables and levels of measurementDiscrete versus continuous variablesChoosing units of measurement and an appropriate method to gather dataChoosing an appropriate method to conduct a survey and making an est imationClassifying samplesUnderstanding the differences between designed experiments and observat ional studiesIdentifying confounders and ways to eliminate them in an observat ional studyIdentifying and reducing stat ist ical bias

Displaying Data (19 topics)Interpret ing a tally tableConstruct ing a f requency distribut ion for non-grouped dataConstruct ing a line plotConstruct ing a bar graph for non-numerical dataInterpret ing a bar graphInterpret ing a double bar graphUnderstanding how adjust ing the vert ical scale can make a graph misleadingUnderstanding how two dimensional graphs can be misleadingConstruct ing a f requency distribut ion for grouped dataConstruct ing a f requency distribut ion and a histogramHistograms for grouped dataConstruct ing a relat ive f requency distribut ion for grouped dataInterpret ing relat ive f requency histogramsShapes of discrete distribut ionsConstruct ing a f requency distribut ion and a f requency polygonCumulat ive distribut ions and ogivesInterpret ing a stem-and-leaf displayInterpret ing a pie chartFinding a percentage of a total amount in a circle graph

Venn Diagrams (3 topics)Interpret ing Venn diagram cardinalit ies with 2 sets for a real-world situat ionIntroduct ion to shading a Venn diagram with 2 eventsShading a Venn diagram with 2 events: Unions, intersect ions, and complements

Measures of Center (18 topics)Introduct ion to summation notat ionSummation of indexed dataMean 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 meanReject ing unreasonable claims based on average stat ist icsWeighted mean: Tabular dataApproximating the mean of a data set given a f requency distribut ionComparing means without calculat ionApproximating the mean of a data set given a histogramMedian of a data setMode of a data setMean, median, and mode: Computat ionsHow changing a value affects the mean and medianChoosing the best measure to describe dataComparing the mean, median, and mode of a data setMaking reasonable inferences based on proport ion stat ist ics

Measures of Variat ion (10 topics)Range of a data set


Comparing measures of center and variat ionIdentifying the center, spread, and shape of a data setUsing back-to-back stem-and-leaf displays to compare data setsPopulat ion standard deviat ionSample standard deviat ionNotat ion for the populat ion mean, sample mean, populat ion standard deviat ion, and sample standard deviat ionComparing standard deviat ions without calculat ionApproximating the standard deviat ion of a data set given a histogramThe Empirical Rule for discrete distribut ions

Measures of Posit ion (14 topics)Finding a z-score for a given data valueFinding a z-score and interpret ing it in terms of the populat ion mean and standard deviat ionComparing the relat ive sizes of data values based on their z-scoresPercentage of data below a specified valuePercentilesInterpret ing percentile ranksFinding quart ilesFive-number summary and interquart ile rangeIntroduct ion to finding out liers in a data setUsing the IQR to find out liers in a data setInterpret ing a box-and-whisker plotBox-and-whisker plotsConstruct ing a box-and-whisker plot involving out liersUsing box-and-whisker plots to compare data sets

Correlat ion and Simple Linear Regression (15 topics)

Scatterplots and Correlat ion (6 topics)Construct ing a scatter plotSketching the least-squares regression lineScatter plots and correlat ionLinear relat ionship and the sample correlat ion coefficientClassifying linear and nonlinear relat ionships f rom scatter plotsIdentifying correlat ion and causat ion

Simple Linear Regression (9 topics)Interpret ing the slope of the least-squares regression lineInterpret ing the equation of the least-squares regression line to make predict ionsApproximating the equation of a line of best fit and making predict ionsPerforming a simple linear regressionRelat ing the sample correlat ion coefficient and the parameters of the least-squares regression lineUsing summations to compute the sample correlat ion coefficient and the slope of the least-squares regression lineComputing residualsInterpret ing residual plotsSimple linear regression: Explained and unexplained variat ion

Probability (44 topics)

Fundamental Counting Principle (4 topics)Interpret ing a tree diagramIntroduct ion to the counting principleCounting principleCounting principle with repetit ion allowed

Permutat ions and Combinat ions (5 topics)Factorial expressionsComputing permutat ions and combinat ionsIntroduct ion to permutat ions and combinat ionsPermutat ions and combinat ions: Problem type 1Permutat ions and combinat ions: Problem type 2

Probability and Odds of an Event (10 topics)Determining a sample space and outcomes for an event: Experiment involving a single select ionDetermining a sample space and outcomes for an event: Experiment involving mult iple select ionsIntroduct ion to the probability of an eventProbability involving one die or choosing f rom n dist inct objectsProbability involving choosing f rom objects that are not dist inctProbability of select ing one card f rom a standard deckProbabilit ies of an event and its complementFinding probabilit ies of events and complementsExperimental and theoret ical probabilityOutcomes and event probability


Addit ion and Mult iplicat ion Rules for Probability (15 topics)Determining outcomes for unions, intersect ions, and complements of eventsCalculat ing relat ive f requencies in a contingency tableCalculat ing relat ive f requencies in a contingency table: AdvancedProbability of independent events: Decimal answersProbability of dependent events: Decimal answersProbabilit ies involving two rolls of a die: Decimal answersProbabilit ies of draws with replacementUsing a Venn diagram to understand the addit ion rule for probabilityWord problem involving the probability of a unionWord problem involving the probability of a union or an intersect ionComputing probability involving the addit ion rule using a two-way f requency tableProbability of the union and intersect ion of independent eventsProbability of the union of mutually exclusive events and independent eventsProbabilit ies involving two mutually exclusive eventsProbabilit ies involving two independent events

Condit ional Probability (10 topics)Computing condit ional probability using a sample spaceUsing a Venn diagram to understand the mult iplicat ion rule for probabilityIdentifying independent events given values of probabilit iesComputing condit ional probability using a two-way f requency tableComputing condit ional probability using a large two-way f requency tableCondit ional probability: BasicIntersect ion and condit ional probabilityTree diagrams for condit ional probabilit iesLaw of total probabilit iesBayes' theorem

Random Variables and Distribut ions (35 topics)

One Random Variable (7 topics)Discrete probability distribut ion: BasicDiscrete probability distribut ion: Word problemsDiscrete probability distribut ion: Word problem involving cumulat ive probabilit iesExpectat ion and variance of a random variableIntroduct ion to expectat ionComputing expected value in a game of chanceComputing expected value in a business applicat ion

The Binomial Distribut ion (7 topics)Histograms of binomial distribut ions well approximated by the normal distribut ionGraphs of binomial distribut ions with less than 20 trialsBinomial problems: Mean and standard deviat ionUsing the binomial formula to find the probability of exact ly m successesUsing the binomial formula to find the probability of more or less than m successesBinomial problems: BasicBinomial problems: Advanced

The Normal Distribut ion (13 topics)Using the graph of a distribut ion to find probabilit ies: BasicUsing the graph of a distribut ion to find probabilit ies: AdvancedUsing 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 probabilityStandard normal probabilit iesStandard normal values: BasicStandard normal values: AdvancedNormal versus standard normal curvesNormal distribut ion: Finding a probability, basicNormal distribut ion: Finding a probability, advancedNormal distribut ion: Finding a raw scoreDrawing a normal quantile plot and using it to assess normality

Central Limit Theorem (8 topics)The sampling distribut ion of the sample meanUnderstanding the histogram of the sampling distribut ion of the sample meanSampling distribut ion of the sample mean: Mean and standard deviat ionCentral limit theorem: Sample meanNotat ion for the populat ion proport ion and sample proport ionSampling distribut ion of a sample proport ion: Mean and standard deviat ionCentral limit theorem: Sample proport ionNormal approximation to binomial


Confidence Intervals and Hypothesis Test ing (65 topics)

Confidence Intervals for the Populat ion Mean (12 topics)Select ing appropriate distribut ions for construct ing confidence intervals for the populat ion meanComparing confidence intervals for the populat ion mean when the populat ion standard deviat ion is knownComputing and comparing confidence intervals for the populat ion mean when the populat ion standard deviat ion isknownIntroduct ion to construct ing a confidence interval for a populat ion mean using the standard normal distribut ionConstruct ing a confidence interval to test a claim about the populat ion mean: Standard normalConfidence interval for the populat ion mean: Use of the standard normalIntroduct ion to the t distribut ionIntroduct ion to finding the value that cuts off a given area under the curve: t distribut iont distribut ionIntroduct ion to construct ing a confidence interval for a populat ion mean using the t distribut ionConstruct ing a confidence interval to test a claim about the populat ion mean: t distribut ionConfidence interval for the populat ion mean: Use of the t distribut ion

Confidence Intervals for a Populat ion Proport ion (4 topics)Computing and comparing confidence intervals for a populat ion proport ionIntroduct ion to construct ing a confidence interval for a populat ion proport ionConstruct ing a confidence interval to test a claim about a populat ion proport ionConfidence interval for a populat ion proport ion

Confidence Intervals for the Populat ion Standard Deviat ion (6 topics)Introduct ion to the chi-square distribut ionIntroduct ion to finding the value that cuts off a given area under the curve: chi-square distribut ionChi-square distribut ionIntroduct ion to construct ing a confidence interval for a populat ion standard deviat ionConstruct ing a confidence interval to test a claim about the populat ion standard deviat ionConfidence interval for the populat ion standard deviat ion

Hypothesis Tests for the Populat ion Mean (13 topics)Choosing and calculat ing test stat ist ics for hypothesis tests on the populat ion meanDetermining null and alternat ive hypotheses for a test of a populat ion meanIntroduct ion to performing a hypothesis test : Crit ical value methodIntroduct ion to performing a hypothesis test : p value methodIntroduct ion to hypothesis tests for the populat ion mean using the crit ical value method: Z testIntroduct ion to hypothesis tests for the populat ion mean using the p value method: Z testHypothesis test for the populat ion mean: Z test using the crit ical value methodHypothesis test for the populat ion mean: Z test using p valuesUnderstanding how the choice of a level of significance affects the results of a hypothesis test using the crit ical valuemethodIntroduct ion to hypothesis tests for the populat ion mean using the crit ical value method: t testIntroduct ion to hypothesis tests for the populat ion mean using the p value method: t testHypothesis test for the populat ion mean: t test using the crit ical value methodHypothesis test for the populat ion mean: t test using the p value method

Hypothesis Tests for a Populat ion Proport ion (7 topics)Finding the value of the test stat ist ic for a hypothesis test for a populat ion proport ionDetermining null and alternat ive hypotheses for a test of a populat ion proport ionIntroduct ion to hypothesis tests for a populat ion proport ion using the crit ical value methodExamining Type I and Type II errors for a hypothesis test for a populat ion proport ion using the p value methodIntroduct ion to hypothesis tests for a populat ion proport ion using the p value methodHypothesis test for a populat ion proport ion using the crit ical value methodHypothesis test for a populat ion proport ion using the p value method

Hypothesis Tests for the Populat ion Variance or Standard Deviat ion (6 topics)Finding the value of the test stat ist ic for a hypothesis test for a populat ion variance or standard deviat ionDetermining null and alternat ive hypotheses for a test of a populat ion variance or standard deviat ionIntroduct ion to hypothesis tests for the populat ion variance or standard deviat ion using the crit ical value methodIntroduct ion to hypothesis tests for the populat ion variance or standard deviat ion using the p value methodHypothesis test for the populat ion variance or standard deviat ion using the crit ical value methodHypothesis test for the populat ion variance or standard deviat ion using the p value method

Sample Size, Effect Size, and Power (3 topics)Choosing an appropriate sample sizeType I and Type II errorsType Ⅰ and Type Ⅱ errors and power

Confidence Intervals for Two Populat ions (7 topics)Confidence interval for the difference of populat ion means: Use of the standard normalConfidence interval for the difference in populat ion means: Paired comparisonsConfidence interval for the difference of populat ion means: Use of the t distribut ion for populat ions with equalvariances


Confidence interval for the difference of populat ion means: Use of the t distribut ion for populat ions with unequalvariancesConfidence interval for the difference of populat ion proport ionsF distribut ionConfidence interval for the rat io of populat ion variances

Hypothesis Tests for Two Populat ions (7 topics)Determining whether two samples are independent or paired and the test stat ist ic for a hypothesis test for thedifference of two populat ion meansHypothesis test for the difference of populat ion means: Z testHypothesis test for the difference of populat ion means: Paired comparisonsHypothesis test for the difference of populat ion means: t test for populat ions with equal variancesHypothesis test for the difference of populat ion means: t test for populat ions with unequal variancesHypothesis test for the difference of populat ion proport ionsHypothesis test for the rat io of populat ion variances

Chi-square Tests, Inferences for Regression, and ANOVA (12 topics)

Chi-square Tests (3 topics)Contingency tables: Expected f requenciesChi-square goodness-of -fit testChi-square test of independence

Inferences for Regression (2 topics)Confidence intervals and predict ion intervals f rom simple linear regressionHypothesis tests for the correlat ion coefficient and the slope of the least-squares regression line

One-way, Independent-samples ANOVA (3 topics)ANOVA: Mean squares and the common populat ion varianceANOVA: Degrees of f reedom and the F stat ist icANOVA: Hypothesis tests and the ANOVA table

Advanced ANOVA (2 topics)Interpret ing group means f rom a factorial designTwo-way, independent-samples ANOVA

Non-parametric Tests (2 topics)Sign testWilcoxon signed-ranks test

Other Topics Available(*) (321 addit ional topics)

Arithmetic Readiness (51 topics)Prime numbersPrime factorizat ionInterpret ing a table of signed numbers that relate to a real-world situat ion: Problem type 1Interpret ing a table of signed numbers that relate to a real-world situat ion: Problem type 2Identifying relat ive change when combining two quantit iesWord problem with addit ion or subtract ion of integersOperat ions with absolute value: Problem type 1Word problem with mult iplicat ion or division of integersDivision involving zeroIdentifying equivalent signed f ract ionsWrit ing an improper f ract ion as a mixed numberFract ional posit ion on a number linePlott ing f ract ions on a number lineWord problem involving f ract ions and mult iplicat ionSigned f ract ion divisionWord problem involving f ract ions and divisionWrit ing f ract ions with a common denominator to add or subtractSigned f ract ion subtract ion involving double negationWord problem involving addit ion or subtract ion of f ract ions with different denominatorsFract ional part of a circleReading decimal posit ion on a number line: TenthsReading decimal posit ion on a number line: HundredthsSigned decimal addit ion and subtract ion with 3 numbersSigned decimal mult iplicat ionSigned decimal divisionPower of 10: Posit ive exponentOrder of operat ions with integersOrder of operat ions with whole numbers and exponents: AdvancedExponents and f ract ionsExponents and signed f ract ions


Evaluat ing expressions with exponents of zeroEvaluat ing a quadrat ic expression: IntegersArea of a circlePlott ing rat ional numbers on a number lineCube root of an integerOrdering real numbersIdentifying numbers as integers or non-integersIdentifying numbers as rat ional or irrat ionalConstruct 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 numbersIntroduct ion to propert ies of addit ionDistribut ive property: Fract ional coefficientsPropert ies of addit ionIntroduct ion to propert ies of mult iplicat ionPropert ies of real numbersCombining like terms: Fract ional coefficientsIdentifying propert ies used to simplify an algebraic expressionUsing distribut ion with double negation and combining like terms to simplify: Mult ivariateCombining like terms in a quadrat ic expression

Ratios and Percentages (33 topics)Writ ing rat ios for real-world situat ionsIdentifying statements that describe a rat ioFinding a unit priceUsing tables to compare rat iosComputing unit prices to find the better buyWord problem on unit rates associated with rat ios of whole numbers: Decimal answersSolving a one-step word problem using the formula d = rtFinding missing values in a table of equivalent rat iosUsing a table of equivalent rat ios to find a missing quantity in a rat ioWord problem on proport ions: Problem type 2Finding the percentage of a grid that is shadedConvert ing a percentage to a f ract ion in simplest formComputing percentages for categories of a budgetMaking an inference using a two-way f requency tableFinding the rate of a tax or commissionFinding the total amount given the percentage of a part ial amountFinding 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 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 percentage increase or decrease: BasicFinding the percentage increase or decrease: AdvancedU.S. Customary length conversions involving rounding decimalsU.S. Customary length conversions involving dimensional analysisWord problem involving U.S. Customary length conversions using dimensional analysisFinding the absolute error and percent error of a measurementMetric distance conversion with whole number valuesConvert ing between metric and U.S. Customary unit systemsConvert ing between compound units: BasicConvert ing between compound units: AdvancedConversions with currencyWord problem involving conversion between compound units using dimensional analysis

Linear Equations and Inequalit ies (43 topics)Addit 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 coefficientIdentifying propert ies used to solve a linear equationSolving a two-step equation with signed decimalsIntroduct ion to solving an equation with variables on the same sideIntroduct ion to solving a linear equation with a variable on each sideSolving a linear equation with several occurrences of the variable: Variables on both 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: Fract ional forms with binomial numeratorsSolving a proport ion of the form (x+a)/b = c/dSolving for a variable in terms of other variables using addit ion or subtract ion: AdvancedSolving 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


Translat ing a phrase into a two-step expressionTranslat ing a sentence into a mult i-step equationSolving a f ract ion word problem using a linear equation of the form Ax = BWrit ing an equation of the form Ax + B = C to solve a word problemWrit ing a mult i-step equation for a real-world situat ionTranslat ing a sentence into a one-step inequalityWrit ing an inequality given a graph on the number lineTranslat ing a sentence into a compound inequalityWrit ing a compound 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 ionsIdentifying solut ions to a two-step linear inequality in one variableSolving 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 compound linear inequality: Graph solut ion, basicSolving a word problem using a one-step linear inequalitySolving a word problem using a two-step linear inequalitySolving a decimal word problem using a two-step linear inequalityIdentifying elements of sets for a real world situat ionFinding sets and complements of sets for a real-world situat ionUnions, intersect ions, and complements involving 2 setsUnions and intersect ions involving the empty set or universal set

Lines (20 topics)Identifying solut ions to a linear equation in two variablesGraphing a vert ical or horizontal lineGraphing a line by first finding its x- and y-interceptsMaking a table and plott ing points given a unit rateFinding the slopes of horizontal and vert ical linesWrit ing a funct ion rule given a table of ordered pairs: One-step rulesGraphing a line by first finding its slope and y-interceptWrit 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 valuesWrit ing the equation of a line in point-slope form given the slope and a pointWrit ing the equations of vert ical and horizontal lines through a given pointFinding outputs of a one-step funct ion that models a real-world situat ion: Two variable equationFinding inputs and outputs of a two-step funct ion that models a real-world situat ion: Two variable equationWrit ing and evaluat ing a funct ion that models a real-world situat ion: AdvancedGraphing ordered pairs and writ ing an equation f rom a table of values in contextWrit ing an equation and drawing its graph to model a real-world situat ion: AdvancedFinding the init ial amount and rate of change given a table for a linear funct 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 pointsIdentifying independent and dependent variables f rom equations or real-world situat ions

Exponents and Funct ions (86 topics)Understanding the product rule of exponentsProduct rule with posit ive exponents: Mult ivariateUnderstanding the power rules of exponentsPower 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 exponentsEvaluat 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


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 basesSimplifying a sum or difference of two univariate polynomialsMult iplying binomials with leading coefficients of 1Squaring a binomial: UnivariateFactoring a quadrat ic with leading coefficient 1Factoring a perfect square trinomial with leading coefficient 1Identifying 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 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 ionFinding inputs and outputs of a two-step funct ion that models a real-world situat ion: Funct ion notat ionFinding an output of a funct ion f rom its graphFinding inputs and outputs of a funct ion f rom its graphFinding domain and range f rom a linear graph in contextGraphing 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 funct ion of the form f (x) = ax2

Graphing a funct ion of the form f (x) = ax2 + cFinding where a funct ion is increasing, decreasing, or constant given the graphChoosing a graph to fit a narrat ive: BasicSolving an equation writ ten in factored formFinding the roots of a quadrat ic equation with leading coefficient 1Solving an equation of the form x2 = a using the square root propertyFinding the vertex, intercepts, and axis of symmetry f rom the graph of a parabolaGraphing a parabola of the form y = ax2

Graphing a parabola of the form y = ax2 + cGraphing a parabola of the form y = (x-h)2 + kFinding the x-intercept(s) and the vertex of a parabolaDomain and range f rom the graph of a parabolaTable for an exponential funct ionUsing a calculator to evaluate exponential expressionsEvaluat ing an exponential funct ion that models a real-world situat ionFinding a final amount in a word problem on exponential growth or decayFinding the t ime to reach a limit in a word problem on exponential growth or decayFinding the init ial amount and rate of change given an exponential funct ionWrit ing an equation that models exponential growth or decayGraphing 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) = -bx or f (x) = -b-xWrit ing an exponential funct ion rule given a table of ordered pairsFinding domain and range f rom the graph of an exponential funct ionComparing linear, polynomial, and exponential funct ionsIdentifying linear, quadrat ic, and exponential funct ions given ordered pairsUsing a calculator to evaluate natural and common logarithmic expressionsConvert ing between logarithmic and exponential equationsEvaluat ing logarithmic expressionsSolving an equation of the form logba = cGraphing a logarithmic funct ion: BasicBasic propert ies of logarithmsUsing propert ies of logarithms to evaluate expressionsExpanding a logarithmic expression: Problem type 1Writ ing an expression as a single logarithmChange of base for logarithms: Problem type 1Solving 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 exponential equation by using logarithms: Decimal answers, basic

Descript ive Stat ist ics (21 topics)Construct ing a two-way f requency table: AdvancedInterpret ing a pictograph tableConstruct ing a percent bar graphComputat ions f rom pie chartsAngle measure in a circle graphConstruct ing a Venn diagram with 2 setsConstruct ing a Venn diagram with 2 sets to solve a word problem


Interpret ing a Venn diagram with 3 sets for a real-world situat ionInterpret ing Venn diagram cardinalit ies with 3 sets for a real-world situat ionIntroduct ion to shading a Venn diagram with 3 eventsShading a Venn diagram with 3 events: Unions, intersect ions, and complementsShading a Venn diagram with 3 sets to represent a groupUsing a model to find the meanUnderstanding the mean graphically: Two barsUnderstanding the mean graphically: Four or more barsFinding the value for a new score to yield a mean that sat isfies a given criterionFinding the mode and range f rom a line plotComparing sample meansChebyshev's theoremTransforming the mean and standard deviat ion of a data setComputing mean absolute deviat ion f rom a list of numerical values

Correlat ion and Simple Linear Regression (2 topics)Choosing a quadrat ic model and using it to make a predict ionChoosing an exponential model and using it to make a predict ion

Probability (35 topics)Counting principle involving a specified arrangementCounting arrangements of objects that are not all dist inctPermutat ions and combinat ions: Problem type 3Counting using combinat ions and addit ionCounting using combinat ions and a complementCounting five-card hands f rom a standard deckUnderstanding likelihoodProbabilit ies of a permutat ion and a combinat ionArea as probabilityFinding the odds in favor and againstConvert ing between probability and oddsFinding odds in favor and against drawing a card f rom a standard deckIdentifying independent events given descript ions of experimentsExperimental and theoret ical probability for compound eventsProbability of independent events involving a standard deck of cardsProbability of dependent events involving a standard deck of cardsProbability of dependent events involving a surveyProbabilit ies of draws without replacementProbability of five-card handsOutcomes and event probability: Addit ion ruleProbabilit ies involving three mutually exclusive eventsProbabilit ies involving three independent eventsThe curious dieOutcomes and event probability: Condit ional probabilityComputing condit ional probability to make an inference using a two-way f requency tableCondit ional probability: Mutually exclusive eventsCondit ional probability: Independent eventsIdentifying outcomes in a random number table used to simulate a simple eventUsing a random number table to simulate a simple eventGenerat ing a random number table with technology to simulate a simple eventIdentifying outcomes in a random number table used to simulate a compound eventUsing a random number table to simulate a compound eventGenerat ing a random number table with technology to simulate a compound eventGenerat ing random samples f rom a populat ion with known characterist icsUsing a random number table to make a fair decision

Random Variables and Distribut ions (16 topics)Cumulat ive distribut ion funct ionMaking predict ions using experimental data for compound eventsRules for expectat ion and variance of random variablesMarginal distribut ions of two discrete random variablesJoint distribut ions of dependent or independent random variablesProbabilit ies of two random variables given their joint distribut ionCondit ional probabilit ies of two random variables given their joint distribut ionChoosing histograms to match Poisson distribut ionsFinding the mean and standard deviat ion of a Poisson random variableComputing the probability that a Poisson random variable takes a single value: Time intervalComputing the probability that a Poisson random variable takes a single value involving distance, area, or volumeComputing the probability that a Poisson random variable takes a value in a range: Time intervalComputing the probability that a Poisson random variable takes mult iple values involving distance, area, or volumeCalculat ing a probability using the binomial distribut ion and using the Poisson distribut ion as an approximationNormal distribut ion: Finding a mean or standard deviat ionCentral limit theorem: Sample sum


Confidence Intervals and Hypothesis Test ing (2 topics)Effect size, sample size, and powerTest ing the plausibility of the results of mult iple hypothesis tests

Chi-square Tests, Inferences for Regression, and ANOVA (8 topics)Interpret ing the regression coefficientsIdentifying degrees of f reedomANOVA table: Problem type 1ANOVA table: Problem type 2F test of a mult iple regression modelt test of a mult iple regression modelOne-way, repeated-measures ANOVASelect ing among t tests and ANOVA tests

Quality Control (4 topics)Interpret ing a control chartR chartsx-bar chartsp charts

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

Introduction to Statistics with Corequisite Support - ALEKS

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