文档详情

3.2Functions and graphs A-level考试纯数学P1课件.ppt

发布：2024-02-17约小于1千字共6页下载文档

文本预览下载声明

Chapter3Functionsandgraphs

Graphsofpowersofx(i)Positiveintegerpowersy=xy=x2y=x3y=x4EvenfunctionOddfunctionyxyxyxyx

(ii)Negativeintegerpowersy=x-1y=x-2y=x-3y=x-4yxyxyxyx

(iii)Fractionalpowersy=xy=x1/2y=x1/3y=x1/4(x0)yxyxyxyx

Itistruethatthegraphofy=xncontainsthepoint(1,1)Ifnispositivethegraphalsocontainsthepoint(0,0)Ifn1thex-axisisatangenttothegraph;if0n1theyyyy-axisisatangent.

ThankYou!

显示全部

相似文档

3.1Functions and graphs A-level考试纯数学P1课件.ppt Chapter3Functionsandgraphs ContentsTheideaofafunction1Graphs,domainandrange2Graphsofpowersofx3Themodulusofanumber4Graphsoftheformy=ax2+bx+c5 TheideaoffunctionYouarealreadyfamiliarwithformulaewhichsummarisecalculationsthatneedtobeperformedfrequently,suchas:Theareaofacirclewithradiusxmetresisπx2square
2024-02-18 约1.39千字 9页立即下载
3.3Function and graphs A-level考试纯数学P1课件.ppt FunctionandgraphsChapter3 ContentsThepointofintersectionoftwographsUsingfactorstosketchgraphsPredictingfunctionsfromtheirgraphsThemodulusofanumberTheshapesofgraphsoftheformy=ax2+bx+c Usingfactorstosketchgraphsf(x)=x2–6x+5g(x)=12x–4x2-1y123450321-1x-2 EnhancingVisualEffectsYoucandrawthegraphofanyfunc
2024-02-17 约2.82千字 16页立即下载
11.2Combining and inverting functions A-level考试纯数学P1课件.ppt CombiningandinvertingfunctionChapter11 ReversingfunctionsThefunctions‘add2’and‘subtract2’aresaidtobeinversefunctionsofeachother.Thesefunctionssuchas‘changesign’、‘reciprocal’aresaidtobeself-inverseTheinverseofafunctionfisdenotedbythesymbolf-1 rangeoff-1domainoffxyf-1domainoffrangeoffxyf ExampleFindth
2024-02-17 约1.66千字 12页立即下载
11.1Combining and inverting functions A-level考试纯数学P1课件.ppt CombiningandinvertingfunctionsChapter11 contentsFormingcompositefunctions2Functionnotation31Domainandrange33 FunctionnotationInputoutput ExampleIf,whatisf(3)?yx63inputoutput Formingcompositefunctions ExampleLetand.findgfandgf.Showthatthereisjustonenumberxsuchthatgf(x)=fg(x).Ifand,calculate(a)gf(60),
2024-02-18 约小于1千字 9页立即下载
18Radians A-level考试纯数学P1课件.ppt RadiansChapter18 ContentsRadians01Lengthofandareaofsector02Graphsofthetrigonometricfunctions03Inversetrigonometricfunctions04Solvingtrigonometricequationsusingradians05 RadiansO1rad1unit1unit ExampleConvert40°toradians,leavingyouranswerasamultipleofπ. Lengthofarcandareaofsectororr ExampleFindtheperi
2024-02-14 约小于1千字 12页立即下载
5Inequalities A-level考试纯数学P1课件.ppt InequalitiesChapter5 ContentsNotationforinequalitiesSolvinglinearinequalities Inquadraticinequalities NotationforinequalitesThesefourexpressionsareequivalentabaisgreaterthanbbabislessthanaa≥baisgreaterthanorequaltobb≤abisnotgreaterthana0ab0ab0abThesymbolsandarecalledstrictinequalities,andthesymbols≤
2024-02-14 约2.26千字 12页立即下载
13vectors A-level考试纯数学P1课件.ppt vectors Translationsofaplane+cc0 SuchtranslationiscalledavectorandiswrittenlkHowwouldthetranslationofy=f(x)describedabovebeperformed? +cc0 Vectoralgebraklsksl-k-lAnumbersuchassisoftencalledascalar pqp+qp+qklmnp+q=q+pthisiscalledthecommutativeruleforadditionofvectors ExampleIfandshowthatthereisanumbe
2024-02-18 约3.6千字 23页立即下载
17Volume of revolution A-level考试纯数学P1课件.ppt Chapter17Volumeofrevolution VolumesofrevolutionxyAOxyAO 14 Whentheregionunderthegraphofy=f(x)betweenx=aandx=b(whereab)isrotatedaboutthex-axis,thevolumeofthesolidofrevolutionformedis ExampleFindthevolumegeneratedwhentheregionunderthegraphofy=1+x2betweenx=-1andx=1isrotatedthroughfourrightanglesaboutth
2024-02-16 约小于1千字 8页立即下载
4.1Quadratics A-level考试纯数学P1课件.ppt Chapter4Quadratics QuadraticsexpressionCompletedsquareformCompletingthesquarecontents Quadraticexpressionsyxyxbx+cy=ax2+ Theexpressionax2+bx+c,wherea,bandcareconstants,iscalledaquadraticThenumberbandccanbeanynumbersyouplease,including0,butacannotbe0.Thenumbera,bandcarecalledcoefficients:aisthecoeffi
2024-02-17 约1.22千字 10页立即下载
4.2Quadratics A-level考试纯数学P1课件.ppt Chapter4Quadratics ContentsEquationswhichreducetoquadraticequationsThediscriminantb2–4acSimultaneousequationsSolvingquadraticequations Solvingquadraticequationsx2–6x+8=0→(x–4)(x–2).Getx=4orx=2Ifyoucannotfactoriseaquadraticexpressioneasilytosolveanequation,thenusethequadraticformula:Thesolutionofax2+
2024-02-17 约1.6千字 10页立即下载
6.1Differentiation A-level考试纯数学P1课件.ppt DifferentiationChapter6 Canyoudescribehowthedirectionofthecurvey=x2changes?Think umbrellagrindingwheel 6.1Calculatinggradientsofchordsyxyx yxTherearethreechordswhichgetcloserandclosertothetangentline;itturnsoutthatagoodwaytobeginisbyfindingthegradientofthesechords,becausefortheseyoucanusethetechniqu
2024-02-17 约1.72千字 12页立即下载
6.2Differentiation A-level考试纯数学P1课件.ppt Chapter6Differentiation Thegradientformulaforquadraticgraphsy=x2y=ax2y=bx+cy=ax2+bx+cy=2xy=2axy=by=2ax+b SomenewnotationLettheequationofacurvebey=f(x).Thenthegradientformulaisdenotedbyf’(x).Thisispronounced‘fdashedx’.Theprocessoffindingthegradientofthetangenttoacurveiscalleddifferentiation.Whenyoufi
2024-02-17 约1.43千字 11页立即下载
9The binomial theorem A-level考试纯数学P1课件.ppt ThebinomialtheoremChapter9 x+y(x+y)2(x+y)3(x+y)nThebinomialtheorem Expanding(x+y)nItisusefultostartbylookingat(x+y)nforn=2,3,and4 14641133112111Row1Row2Row3Row4ThecoefficientsformthepatternofPascal’strianglePredictthecoefficientsinthefifthrow15101051Row5 ExampleWritedowntheexpansionof(1+y)6 ExampleM
2024-02-17 约1.4千字 14页立即下载
10.1Trigonometry A-level考试纯数学P1课件.ppt TrigonometryChapter10 contentsTheshapeofcosθ°Theshapeofsinθ°andtanθ°Exactvaluesofsometrigonometricfunctions 0θ°yxP(x,y)NATheshapeofcosθ° ExampleFindthevalueofcosθ°when(a)θ=180,(b)θ=270 f(θ)θ1-1-180-9090180270Thegraphoftheconsinefunctionkeepsrepeatingitself.Functionswiththispropertyarecalledperiodic:
2024-02-19 约小于1千字 14页立即下载
8.1Sequences A-level考试纯数学P1课件.ppt Chapter8Sequences ContentsConstructingsequences1Thetrianglenumbersequences2Thefactorialsequences3Pascalsequences4Arithmeticsequences5 Constructingsequences(a)1491625…(c)9997959391…(e)2481422…(b)…(d)11.11.211.3311.4641…(f)31415…Rowsofthiskindarecalledsequences,andtheseparatenumbersarecalledterms Theu
2024-02-18 约1.89千字 10页立即下载