Math conceptsFind a conceptNumbers and operations18 topicsNumber senseNatural numbers and place valueAdditionSubtractionMultiplicationDivisionMixed operations and operation lawsFactors and multiplesPrime numbers and prime factorizationThe meaning of fractionsTypes and forms of fractionsFraction size and equivalenceThe four operations with fractionsDecimal meaning and notationThe four operations with decimalsEstimation and approximationsIntegers and rational numbersSquare roots and real numbersRatios, rates, and proportionality9 topicsRatiosRelative quantitiesPercentagesConverting representationsProportionsProportional divisionDirect and inverse proportionUnit ratesReal-world applicationsVariables and expressions10 topicsUsing lettersParts of an expressionSubstitution and expression valuesLike terms and simplifying expressionsLaws of exponentsPolynomial operationsSpecial productsFactorizationIdentities, the remainder theorem, and the factor theoremRational and radical expressionsEquations and inequalities12 topicsEquality and equation basicsLinear equationsApplications of linear equationsSimultaneous linear equationsQuadratic equationsProperties of quadratic equationsComplex numbers and equationsOther equationsInequality basicsLinear and simultaneous inequalitiesQuadratic inequalitiesOther inequalitiesRelationships, coordinates, and functions13 topicsCorrespondence and relationsThe coordinate planeReading graphsFunction basicsDirect- and inverse-proportion functionsLinear functionsQuadratic functionsPolynomial functionsRational and radical functionsFunction transformationsComposite and inverse functionsExponents and logarithmsExponential and logarithmic functionsGeometry and measurement18 topicsBasic geometric objectsAnglesPerpendicular and parallel linesTrianglesQuadrilateralsPolygonsCirclesCircle propertiesTransformations and symmetryConstructions and congruenceSimilarityKey triangle propertiesThe Pythagorean theoremSolid shapesSpatial reasoningMeasurement and unitsPerimeter and areaSurface area and volumeTrigonometric ratios, trigonometric functions, and coordinate geometry11 topicsTrigonometric ratiosApplications of trigonometric ratiosExtending anglesTrigonometric functionsTrigonometric identities and formulasGeneral triangle relationshipsPlane coordinates and distanceEquations of linesEquations of circlesConic sectionsSpace coordinatesVectors and matrices8 topicsThe meaning of vectorsVector operationsVector componentsThe dot productVector applicationsThe meaning of matricesMatrix operationsFurther matrix ideasSets, statements, logic, and proof9 topicsBasics of setsSet operationsRelationships between setsStatements and conditionsConnecting conditionsNecessary and sufficient conditionsMethods of proofCounterexamples and generalizationMathematical inductionPatterns and sequences8 topicsBasic patternsBasics of sequencesArithmetic sequencesGeometric sequencesSums of sequencesOther sequencesRecurrence relationsApplications of sequencesLimits, differentiation, and integration12 topicsLimits of sequencesInfinite seriesLimits of functionsContinuity of functionsMeaning of differentiationDerivative functionsDifferentiation rulesApplications of differentiationIndefinite integralsDefinite integralsIntegration methodsApplications of integrationCounting, probability, and statistics19 topicsBasic countingPermutationsCombinationsThe binomial theoremBasics of probabilityRelationships between eventsCalculating probabilitiesConditional probability and independenceRepeated trials and random variablesCollecting and classifying dataTables and basic graphsData distributionsMeasures of central tendencyMeasures of spreadPosition and shape of distributionsRelationships between two variablesCommon probability distributionsSamples and estimationFurther statistical reasoningFurther university-level fields14 topicsLinear algebraMultivariable calculusAnalysisComplex analysisDifferential equationsAbstract algebraNumber theoryGeometryTopologyDiscrete mathematics and combinatoricsProbability theory and mathematical statisticsNumerical analysis and optimizationMathematical logic and foundationsApplied mathematics
