S1 Math Notes

CHSY1NotesArrangedaccordingtoCHSOrder of Learning1.Primes,HCF,LCM(TBChapter 1)2.Integers,Rational NumbersandReal Numbers(TBChapter 2)3.ApproximationandEstimation(TBChapter 3)4.Percentage(TBChapter 8)5.RatioandRate(TBChapter 9)6.BasicAlgebraandManipulation(TBChapter 4)7.Linear Equations(TBChapter 5),SimpleInequalities(Sec2TBChapter 2)8.Linear FunctionsandGraphs(TBChapter 6)9.Number Patterns(TBChapter 7)10.BasicGeometry(TBChapter 10)11.PolygonsandGeometrical Constructions(TBChapter 11)12.PythagorasTheorem(Sec2TBChapter 9)13.Perimeter andAreaof PlaneFigures(TBChapter 12)14.VolumeandSurfaceAreaof PrismsandCylinders(TBChapter 13)15.VolumeandSurfaceAreaof Pyramids,conesandSphere(Sec2TBChapter11)16.Statistical DataHandling(TBChapter 14)17.Statistical Diagrams(Sec2TBChapter 13)18.Averagesof Statistical Data(Sec2TBChapter 14) Primes. HCF, LCMPrimeNumber● Number that onlyhas2factorsandisawholenumber greater than1,suchas2, 3, 7, 13UnderstandingPrimeFactorisation● Usedtoexpressacompositenumber asaproduct of itsprimefactors,usingafactor treeor longdivision● WhenPrimeFactorisationisperformedsomefactorsarerepeated,eg8=2x2x2, with thefactor 2appearing3times● Useconcisenotationtorepresent theproduct● Notationwithnumber abovethebelownumber iscalledindexnotation,readas8tothepower of 3● Number locatedat thetopright handcorner calledtheindex,number atthelevel iscalledbase● Indexshowsthenumber of timesthebaseismultipliedbyitself● UseLadder Methodtofindprimefactorizationof anumber,start withsmallest primefactor of thenumber anddivide,keepdividingtill youget 1thentimesall thenumbersSquareroots andCuberoots 1

● 9canbeexpressedasproduct of 2identical numbers, 9=3x3=3 2 ● Since3 2 =9,9isthesquareof 3,wecanalsosay3isthepositivesquarerootof 9andit isdenoted9squareroot=3● 8canbeexpressedasaproduct of 3identical numbersas8=2x2x2=2 3 ,since2 3 =8,8iscalledcubeof 2● Wecanalsosay2isthepositivecuberoot of 8anddenotedcuberoot 8=2● For squarenumbers,power of primefactorsmust bedivisibleby2● For cubenumbers,power of primefactorsmust bedivisibleby3Highest commonfactor andLowest commonmultipleHighest commonfactor● Largest commonfactor of agroupiscalledHCF756expressedasaproduct of itsprimefactorsis2 2 x3 3 x7,360expressedasaproduct of itsprimefactorsis2 3 x3 2 x5,findhcf of 360and756Method1360=2 3 x3 2 x5756=2 2 x3 3 x7HCF=2 2 x3 2 ● Comparebothnumberswhenexpressedasaproduct of itsprimefactorsthenlookfor commonfactors(best squared/cubed)LCM● Findusingprimefactorisation756expressedasaproduct of itsprimefactorsis2 2 x3 3 x7,360expressedasaproduct of itsprimefactorsis2 3 x3 2 x5,findLCMof 360and756360=2 3 x3 2 x5756=2 2 x3³x7LCM=2 2 x3 3 x5x7● Between2 3 and2 2 bringdownbigger number, thenbringdowneverythingelse 2. Integers, Rational NumbersandReal NumbersNegativeNumbersNegativeIntegers● Wholenumbersare1,2,3,4,knownaspositiveintegers● Negativeintegersare-5,-4,-3● Zeroisneither positivenor negativeintegerNumber line● All negativenumberstotheleft of zero,whileAll positivenumberstotheright of