Edexcel IAL
P3 - Pure Mathematics 3
Algebraic MethodsThe Modulus FunctionFunctionsTrigonometric Functions & IdentitiesTrigonometric Addition FormulaeDouble Angle & SimplifyingNatural Exponentials & LogarithmsDifferentiationIntegrationNumerical MethodsAlgebraic FractionsDividing PolynomialsPartial FractionsPartial Fractions (Repeated & Quadratic)The Modulus FunctionSolving Modulus EquationsModulus InequalitiesGraphs of Modulus FunctionsCombined Modulus ProblemsFunctions: Domain & RangeComposite FunctionsInverse FunctionsTransformations of FunctionsCombining TransformationsHarder Function ProblemsReciprocal Trig Functions (sec, cosec, cot)Pythagorean Identities (sec², cosec², cot²)Solving Equations with sec, cosec, cotProving Trig IdentitiesHarder Trig ProblemsInverse Trig Functions (arcsin, arccos, arctan)Addition FormulaeUsing Addition Formulae (Exact Values)Proving & Applying Addition FormulaeDouble Angle FormulaeSolving Double Angle EquationsHalf Angle FormulaeR·cos(x+α) and R·sin(x+α) FormApplications of R FormThe Natural Exponential e^xThe Natural Logarithm ln(x)Solving Equations with e and lnExponential ModelsLogarithmic Graphs (log-linear data)Harder Exponential & Log ProblemsDifferentiating sin(x) and cos(x)Chain RuleProduct RuleQuotient RuleDifferentiating Exponentials & LogarithmsCombined Differentiation RulesImplicit DifferentiationConnected Rates of ChangeTangents & NormalsSecond Derivatives & ConcavityOptimisation ProblemsStandard Integrals (trig, eˣ, 1/x)Reverse Chain RuleIntegration by SubstitutionIntegrating with Partial FractionsIntegrating Trig FunctionsAreas & VolumesChange of Sign (Locating Roots)Fixed Point IterationStaircase & Cobweb DiagramsConvergence of Iterative SequencesNewton-Raphson MethodMixed Numerical Methods Problems