1Elementaryalgebra
Introduction
l.1Algebraicexpressionsandequations
l.2Theadditionandsubtractionofalgebraicforms
1.3Productsofpositiveandnegativerealnumbers
l.4Expansionofbracketedterms
l.5Fractions
l.6Exponents
l.7Negativeexponents
1.8Cancellingoutterms
l.9Theorderandhierarchyofoperations
1.10Factorization
1.l1Degreeofanexpression
l.12Perfectsquares
l.l3Applications
Additionalexamples
2Solvingequations
Introduction
2.1Drawinggraphs
2.2Straight-lineorlinearfunctions
2.3Quadraticfunctions
2.4Cubicfunctions
2.5Algebraicsolutionofequations
2.6Equationsinvolvingfractions
2.7Quadraticequations
2.8Formulaforsolvingquadraticequations
2.9Solutionofcubicequahons
2.l0Applications
Additionalexamples
3Simultaneousequationsandinequalities
Introduction
3.lSimpleequationswithonevariable
3.2Pairsofequations
3.3Usingasetofequationsasamodel
3.4Setsofthreeormoreequations
3.5Independentanddependentequations
3.6Linearandnon-linearequations
3.7Inequalities
3.8Simultaneousinequalities
3.9Applicationsofinequalities
Additionalexamples
4Series
Introduction
4.lArithmeticprogression(AP)
4.2Thesigmanotationforsummation
4.3SumoftermsofanAP
4.4Geometricprogression(GP)
4.5SumoftermsofaGP
4.6NotahonfOrintErestcalculations
4.7Compoundinterest
Additionalexamples
5Logarithmsandexponentials
Inttoduction
5.lLogarithmsandexponents
5.2Howlogarithmswork
5.3Rulesforcombininglogarithms
5.4Theexponentialfunctionandcontinuous
compounding
5.5Nominalinterestratesandeffectiveinterestrates
5.6Negativegrowth
5.7Application
Additionalexamples
6Matrices
Introduction
6.1Matrixnotation
6.2Equality,additionandsubtractionofmatrices
6.3Multiplicationofmatrices
6.4Transposingmatrices
6.5Matrixformulationofsimultaneousequations
6.6Theidentitymatrixandtheinverse
6.7Determinants
6.8Theinverseofa2x2matrix
6.9Summary
Additionalexamples
7Differentiation
Introduchon
7.lTheslopeofastraightline
7.2Findingtheequationofastraightline
7.3Anumericalmethodforfindingtheslopeofacurve
7.4Thegeneralmethodofdifferentiation
7.5Rulesforderivatives
7.6Thederivativeoftheredprocalofafunction
Additionalexamples
8Moreaboutdifferentiation
Introduction
8.1Thesecondandhigherderivatives
8.2Alternativenotationforthederivative
8.3Makimaandminima
8.4Pointsofinflexion
8.5Thefunctionofafunctionrule
8.6Theproductrule
8.7Mixingthefunctionofafunctionandproductrules
8.8Differentiatingexpressionscontainingfractions
8.9Continuousfunctions
8.l0Partialderivatives
Additionalexamples
9Integration
Introduction
9.lIntegrationasthereverseofdifferentiation
9.2Rulesforintegration
9.3Thedefiniteintegral
9.4Theintegralastheareabetweenthecurve
andthex-axis
9.5Ageneralremarkonintegrationanddifferentiation
Additionalexamples
10Theapplicationofmathematics
l0.lMathematicalstyle
l0i2Tacklingmathematicalexaminationquestions
10.3Formulatingreal-lifeproblems
10.4Sovingreal-lifeproblems
AppendixTheGreekalphabet
Solutionstoadditionalexamples
Index
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