sat2數(shù)學精講精練電子講義

π、3（1）（2）22B4、時間：60題型：選擇題，5011/40分。4個以內(nèi)（level2)。5、悲劇原因三種不做一定練習題，不能提前出題方式Fourcategories（分類）NumbersandOperations（12%）AlgebraandFunctions（50%）GeometryandMeasurement（30%）StatisticsandProbability（8%）ⅠNumbersand基本計算(basic+-×square,squareroot,exponential,logarithmratioandproportionInventedExample2)TwopositiveintegersjandksatisfytherelationjRkifandonlyifj=k2+1.Ifm,andpsatisfytherelationsmRnandnRp,whatisthevalueofmintermsof基本數(shù)論(basicnumbertheory)positiveintegersconsecutiveintegers,fractions,reciprocals,absolutevalue,rational(irrational)numbers,even,odd,factors,multiples, mbers,primefactors,primefactorizationsExample2Theonlyprimefactorsofanumbernare2,5,7,and17.WhichofthefollowingcouldNOTbeafactorofn?(A) (B) (C) (D) (E)ComplexNumbers復數(shù)）a+bi(a,b∈R)形式的a叫作實部（realpart),b（imaginarypart) —conjugatecomplexExamplei3=?i4+(-i)4=?P307T25，T36,T40計數(shù)原理（Counting加法原理：完成一件事情，一共有n類不同的方法，其中第一類有 種不K1+K2++Kn種不同的方法.nK1種K1×K2××Kn種不同的方法.排列(permutation)：n個不同的對象中，選出r（r≤n)個對象，并對這r個對象進行排序，nr個對象的一個排列。組合(combination)nr（r≤n)r個對象nr個對象的一個組合。組合(combination)nr（r≤n)r個對象nr個對象的一個組合。ExampleHowmanydifferentseatingarrangementscanbemadefor5studentsinarowof10seats?Howmany committeescanbeformedfromagroupof93）Acommitteeof3juniorsand3seniorsistobeselectedfromagroupof15and28seniors.HowmanydifferentcommitteesareLogical如果命題“Ifp,thenq”pq的充分（sufficientcondition)條件，q叫p的必要(necessarycondition)條件。 Matrices矩陣Amatrixisarectangulararrayofnumberswrittenin題目告訴AmatrixMhasdimensionsm×n，即M矩陣有m行，n列（scalarproductofarealnumberandamatrix)矩陣相乘（productsofjij千萬注意AB行列式計算時，不不同列的數(shù)字相乘，再相加減。Example,matirxX=2) 數(shù)列級數(shù) Example 既有方向又有大小的量叫向量(Avectorisavisualrepresentationofsomethingthathasbothdirectionandmagnitude).零向量（zero單位向量（units共線（平行）向量（collinear/parallel相等向量（equivalent幾何表示的加減法—向量的模（norm/magnitude/absoluteExample整式的計算(operationsonalgebraicⅡAlgebraandExample9x3+2x2-x-kisdividedbyx-2,theremainderis4,Whatistheremainderwhenthepolynomialx4-5x2-10x-12isdividedbyx+22f(x)6x3-11x2-3x+2的一個零點（zeropoint)方程一次方程(linear二次方程(quadratic復合函數(shù)(compositefunctions)奇偶性(evenorodd)周期性Afunctionf(x)isperiodic,ifsuchnon-zeronumberTexiststhatforanyxfromafunction:f(x+T)=f(xAlltrigonometricfunctionsareperiodicAfunctionisbounded,ifsuchpositivenumberMexists,that|f(x)|≤Mforvaluesofx.Ifsuchpositivenumberdoesnotexist,thenthisfunctionisunbounded.Example11f(x)=3lnx-1,g(x)=ex,thenf[g(5)f(a)<f(b),abf(-x)=f(x),x∈R,(3,8),f(x)的圖像上,f(x)P134線性函數(shù)(linearfunctions)：y=kx+b二次函數(shù)(quadraticfunctions)：y=ax2+bx+c(a多項式函數(shù)(polynomial f(x)=a0xn+a1xn-1+a2xn-2+…+an-有理函數(shù)（rational取整函數(shù):x的最大整數(shù)(thegreatestintegerthatisnotgreaterthanx.）1-2[x]=-3,x∈?指數(shù)函數(shù)（exponential對數(shù)函數(shù)（exponential指數(shù)函數(shù)（exponentialExampleloga3=x,loga5=y,thenlogalog2(x-16)=log4(x-4),thenIf5x=2700,the分段函數(shù)(piecewiseApiecewisefunctionisdefinedbydifferentformulasindifferentintervalsofits參數(shù)函數(shù)(parametricExample反函數(shù)(inverseLety=f(x)“one-to-one“function. Weusuallyshowtheinversefunctionofy=f(x)asy=f-Theoff(x)isequaltotherangeoff-1(x).Therangeoff(x)isequaltotheoff-1(x).Thegraphoff-1(x)isthereflectionabouttheliney=xofthegraphoff(x).If(a,b)isonthegraphoff(x),then(b,a)isonthegraphoff-1(x).Examplef(x)+c、f(x)-f(-x)- 三角函數(shù)（trigonometric定義sin2α+cos2α=1 1+tan2α=sec2α1+cot2α=csc2α tanα=sinα/cosα α=cosα/sinα sinα.cscα=1cosα.secαy=sinR [-1,Evenoroddsinx=-sin(-increasinginterval(2kπ-π/2,2kπ+π/2)(k∈z)Decreasinginterval(2kπ+π/2,2kπ+3π/2)(k∈z) y=cosR [-Evenorevencosx=cos(-increasinginterval(2kπ-π,2kπ)(k∈z)Decreasinginterval(2kπ,2kπ+π)(k∈z) y=tan{x∈Rlx≠kπ+π/2}(k∈z)RangeEvenoroddoddincreasinginterval(kπ-π/2,kπ+π/2)(kPeriodicityy=cot{x∈Rlx≠kπ}(k∈z) Evenorodd decreasinginterval(kπ,kπ+ (k 誘導公式—sin(kπ/2+ cos(kπ/2+ π/2+sin(α+β)=sinα.cosβ+cosα.sinsin(α-β)=sinα.cosβ–cosα.sinβcos(α+β)=cosα.cosβ–sinα.sinβcos(α-β)=cosα.cosβ+sinα.sintan(α+β)=(tanα+tanβ)/(1-tanα.tanβ)tan(α-β)=(tanα-tanβ)/(1+tanα.tanβ)sin2α=2sinα.coscos2α=cos2α-sin2α=2cos2α–1=1-2sin2α1+cos2α=2cos2α1-cos2α=2sin2A:振幅變 B:上下平移w:周期變化φ:左右平Example反三角函數(shù)(inversetrigonometricExample函數(shù)的極限(thelimitofaWhatisthedefinitionofalimitinmathematics?Let’sseeanexample!Asx esextremelylarge,thevalueoff(x)approaches2,thevalueoff(x)canbemadeascloseto2asonecouldwishjustbypickingxsufficientlylarge.ConsidertheWhatishappeningtof(x)asxapproachesSupposethevalueofthefunctionf(x)cangetarbitrarilyclosetoso mberAasxgetsclosetox0(orapproachesinfinity),thenwesaythatthelimitoff(x)isAasapproachesx0(orapproachesThelimitoff(x)asxapproachesx0(orinfinity)iswrittenas f(x)→ x→ f(x)→A x→∞(A) (B) (C) (D) (E)ItdoesnotapproachauniqueAnasymptoteofacurveisalinesuchthatthedistancebetweenthecurveandthelineapproacheszeroastheytendtoinfinity.Anasymptoteisalinethatthecurveapproaches,butdoesnotAliney=cisahorizontalasymptoteofthecurvey=f(x),ifAlinex=kisaverticalasymptoteofthecurvey=f(x),ifExampleFindtheasymptotesoftheflowingⅢGeometryand該該部分內(nèi)容將于20153月中下旬完成更請密切關注哦1、直角三角形（righttriangles)特殊三角形三邊的關系(30-60-90,45-45-等腰三角形（isoscelestriangles)等邊三角形（equilateraltriangles)相似三角形（similar正弦定理(Sinerule)、余弦定理（cosine解析幾何(coordinategeometry) point-lope y-y0=k(x-x)斜率(slope（兩點的坐標確定斜率平行(parallel)圓圓心(center)在（a,b)，半徑(radius)r的圓,