Free Mathematics LessonsTake care of yourself! New lessons are being added every week. Give it a go!Methods of IntegrationIntegration by Substitution ❯ Indefinite IntegrationEasy Method of Integration by SubstitutionMathematical InductionInequality Proofs ❯ Using AssumptionsInequality Proof using AssumptionsInequality Proofs ❯ Finding Initial Values for Proving InequalityFinding Initial Values for Proving InequalityInequality Proofs ❯ Using DifferencesInequality Proof using Differences by Mathematical InductionInequality Proofs ❯ Basic ComparisonInequality Proof by Basic ComparisonDivisibility Proofs ❯ Finding Initial ValuesDivisibility Proof by Mathematical Induction by Finding Initial ValuesDivisibility Proofs ❯ Using SubstitutionsDivisibility Proof by Mathematical Induction using SubstitutionsDivisibility Proofs ❯ Addition of Consecutive nth PowersDivisibility Proof of Two Indices (Divisible by 15)Divisibility Proof of Sum of Three Consecutive Cubes (divisible by 9)Divisibility Proofs ❯ Two IndicesDivisibility Proof of Two Indices (Divisible by 3)Divisibility Proof of Two Indices (Divisible by 10)Divisibility Proofs ❯ Even Numbers (Divisible by 4)Divisibility Proof of Non-Linear Indices (Divisible by 4)Divisibility Proofs ❯ Non-Linear Indices (Divisible by 5)Divisibility Proof of Non-Linear Indices (Divisible by 5)Divisibility Proofs ❯ Linear Indices (Divisible by 5)Linear Indices (Divisible by 5)Proof by Mathematical Induction ❯ Production FormulaProduction Formula by Mathematical InductionProduction of Fractions Proof by Mathematical InductionProof by Mathematical Induction ❯ Summation ProofSummation Proof by Mathematical InductionSum of Fractions by Mathematical InductionSum of Geometric Series by Mathematical InductionProof by Mathematical Induction ❯ Two Initial ValuesTwo Initial Values in Mathematical InductionProof by Mathematical Induction ❯ Using Recurring FormulaeUsing Recurring Formulae in Mathematical InductionProof by Mathematical Induction ❯ Sum of FactorialsSum of Factorials by Mathematical InductionProof by Mathematical Induction ❯ Sum of Terms with IndicesSum of Terms with Indices by Mathematical InductionProof by Mathematical Induction ❯ Sum of Odd NumbersSum of Odd Numbers: AssumptionSum of Odd Numbers: ProofProof by Mathematical Induction ❯ Sum of Even NumbersFundamental Process of Mathematical InductionSum of Even Numbers: AssumptionSum of Even Numbers: ProofProbabilityProbability ❯ Probability of Complement EventsProbability with At LeastProbability with RatiosProbability without ReplacementProbability ❯ Probability without ReplacementProbability Complement EventsProbability without Replacement with AND ORProbability without Replacement with Order of EventsProbability ❯ Product Rule of ProbabilityProbability Regarding ANDProduct Rule and Independent EventsProbability ❯ Addition Rule of ProbabilityProbability Regarding ORAddition Rule and Mutually Exclusive EventsProbability ❯ Probability with DiceTwo-Digit Numbers by DiceSum of Two DiceProbability ❯ Regular Pack of 52 CardsCounting Number of CardsProbability using Regular Pack of 52 CardsMeasurementGeometry ❯ CircumferenceCircumference and ArcRadius and ArcGeometry ❯ PerimetersFinding PerimetersFinding Perimeters using Pythagoras' TheoremFinding Sides using Pythagoras' Theorem and PerimetersGeometry ❯ Pythagoras' TheoremPythagorean TriadsFinding Hypotenuse Sides using Pythagoras' TheoremFinding Other Sides using Pythagoras' TheoremTwo Triangles using Pythagoras' TheoremGeometrical FiguresAccuracy ❯ Approximation, Estimation and Percentage ErrorTheoryPractical QuestionsAccuracy ❯ Accuracy and PrecisionAccuracy of MeasurementLower Bounds and Upper Bounds of MeasurementTime ❯ Time ConversionConverting Seconds, Minutes, Hours and DaysTime Duration using a CalculatorTime Duration in Multiple Days using a CalculatorTimes Before and AfterCapacity ❯ Simplifying Different Capacity UnitsSimplifying Different Capacity Units in LSimplifying Different Capacity Units in mL and cLSimplifying Different Capacity Units in kL and MLCapacity ❯ Capacity ConversionRules of Capacity ConversionConvert to mLConvert to cLConvert to LConvert to kLConvert to MLMass ❯ Simplifying Different Mass UnitsSimplifying Different Mass Units in gramsSimplifying Different Mass Units in kilogramsSimplifying Different Mass Units in milligramsSimplifying Different Mass Units in tonnesMass ❯ Mass ConversionMass Conversion: Convert to milligramsMass Conversion: Convert to gramsMass Conversion: Convert to kilogramsMass Conversion: Convert to tonnesLength ❯ Simplifying Different Length UnitsSimplifying Different Length Units in mSimplifying Different Length Units in kmSimplifying Different Length Units in cmSimplifying Different Length UnitsLength ❯ Length ConversionUnit Converter LengthLength Conversion between km and mLength Conversion between m and cmLength Conversion between m and mmLength Conversion between km and mmLength Conversion between cm and mmLength Conversion between km and cmIndicesBasic Laws of Indices ❯ Negative BasesOdd Power and Even Power of Negative BasesNegative Bases in BracketsBasic Laws of Indices ❯ Negative IndicesRational Fractions and Negative IndicesHandling Negative IndicesExpressing with Negative IndicesZero IndicesBasic Laws of Indices ❯ Power of PowerEquations involving Power of PowerSimplifying by Power of PowerEvaluation by Power of PowerBasic Laws of Indices ❯ Index Law of SubtractionSimplifying by Subtracting IndicesSimplifying by Adding and Subtracting IndicesEvaluation by Subtracting IndicesBasic Laws of Indices ❯ Index Law of AdditionEquations by Adding IndicesSimplifying by Adding IndicesEvaluation by Adding IndicesBasic Laws of Indices ❯ Index NotationExpanded Form to Index FormIndex Form to Expanded FormBasic Laws of Indices ❯ Prime FactorisationFactor Tree of Bases 2 and 3Factor Tree of Bases 5 and 7Indicial Equations in Single BasesIndicial Equations in Multiple BasesArithmetic and AlgebraQuadratic Fractions ❯ Addition of Algebraic FractionsMonic DenominatorsDifference of SqauresQuadratic Fractions ❯ Simplifying Algebraic FractionsMonic ExpressionsDifference of SqauresCommon FactorsNon-Monic ExpressionsQuadratic Fractions ❯ Fractions involving Quadratic TermsMonic ExpressionsDifference of SqauresCommon FactorsNon-Monic ExpressionsQuadratic Fractions ❯ Fractions involving Quadratic and Linear TermsMonic ExpressionsCommon FactorsDifference of SquaresNon-Monic ExpressionsQuadratic Factorise ❯ Factorising Difference of SquaresIntroductionNon-Monic CoefficientsPolynomial Terms and Common FactorsHigher Order FactoriseQuadratic Factorise ❯ Factorising Non-Monic Quadratic TrinomialsIntroductionMixed SignsPerfect SquaresCommon FactorsQuadratic Factorise ❯ Factorising Quadratic Trinomials using Common FactorsIntroductionPositive Common FactorsNegative Common FactorsPerfect SquaresRational CoeffieicntsQuadratic Factorise ❯ Perfect Square of Quadratic TrinomialsIntroductionPositive Linear TermNegative Linear TermRational CoeffieicntsQuadratic Factorise ❯ Factorising Monic Quadratic TrinomialsIntroductionPlus Plus FormMinus Plus FormMinus Minus formPlus Minus FormLinear Algebra ❯ Algebraic FractionsAddition and SubtractionMultiplicationDivisionMultiplication and DivisionSimplify by FactoriseSimplify by DenominatorsSimplify by Multiple DenominatorsLinear Algebra ❯ FactoriseUsing Common FactorsUsing Common Factors and IndicesCommon Factors in BracketsCommon Factors in Brackets and IndicesDouble Common FactorsLinear Algebra ❯ Expand and SimplifyLinear ExpansionsBinomial ExpansionsDifference of SquaresCubic ExpressionsTrinomial ExpressionsLinear Algebra ❯ Like TermsDefinition of Like TermsSimplifying Single Like TermsSimplifying Multiple Like Terms
