sat2数学精讲精练电子讲义

π、3（1）（2）22B4、时间：60题型：选择题，5011/40分。4个以内（level2)。5、悲剧原因三种不做一定练习题，不能提前出题方式Fourcategories（分类）NumbersandOperations（12%）AlgebraandFunctions（50%）GeometryandMeasurement（30%）StatisticsandProbability（8%）ⅠNumbersand基本计算(basic+-×square,squareroot,exponential,logarithmratioandproportionInventedExample2)TwopositiveintegersjandksatisfytherelationjRkifandonlyifj=k2+1.Ifm,andpsatisfytherelationsmRnandnRp,whatisthevalueofmintermsof基本数论(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复数）a+bi(a,b∈R)形式的a叫作实部（realpart),b（imaginarypart) —conjugatecomplexExamplei3=?i4+(-i)4=?P307T25，T36,T40计数原理（Counting加法原理：完成一件事情，一共有n类不同的方法，其中第一类有 种不K1+K2++Kn种不同的方法.nK1种K1×K2××Kn种不同的方法.排列(permutation)：n个不同的对象中，选出r（r≤n)个对象，并对这r个对象进行排序，nr个对象的一个排列。组合(combination)nr（r≤n)r个对象nr个对象的一个组合。组合(combination)nr（r≤n)r个对象nr个对象的一个组合。ExampleHowmanydifferentseatingarrangementscanbemadefor5studentsinarowof10seats?Howmany committeescanbeformedfromagroupof93）Acommitteeof3juniorsand3seniorsistobeselectedfromagroupof15and28seniors.HowmanydifferentcommitteesareLogical如果命题“Ifp,thenq”pq的充分（sufficientcondition)条件，q叫p的必要(necessarycondition)条件。 Matrices矩阵Amatrixisarectangulararrayofnumberswrittenin题目告诉AmatrixMhasdimensionsm×n，即M矩阵有m行，n列（scalarproductofarealnumberandamatrix)矩阵相乘（productsofjij千万注意AB行列式计算时，不不同列的数字相乘，再相加减。Example,matirxX=2) 数列级数 Example 既有方向又有大小的量叫向量(Avectorisavisualrepresentationofsomethingthathasbothdirectionandmagnitude).零向量（zero单位向量（units共线（平行）向量（collinear/parallel相等向量（equivalent几何表示的加减法—向量的模（norm/magnitude/absoluteExample整式的计算(operationsonalgebraicⅡAlgebraandExample9x3+2x2-x-kisdividedbyx-2,theremainderis4,Whatistheremainderwhenthepolynomialx4-5x2-10x-12isdividedbyx+22f(x)6x3-11x2-3x+2的一个零点（zeropoint)方程一次方程(linear二次方程(quadratic复合函数(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)的图像上,f(x)P134线性函数(linearfunctions)：y=kx+b二次函数(quadraticfunctions)：y=ax2+bx+c(a多项式函数(polynomial f(x)=a0xn+a1xn-1+a2xn-2+…+an-有理函数（rational取整函数:x的最大整数(thegreatestintegerthatisnotgreaterthanx.）1-2[x]=-3,x∈?指数函数（exponential对数函数（exponential指数函数（exponentialExampleloga3=x,loga5=y,thenlogalog2(x-16)=log4(x-4),thenIf5x=2700,the分段函数(piecewiseApiecewisefunctionisdefinedbydifferentformulasindifferentintervalsofits参数函数(parametricExample反函数(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)- 三角函数（trigonometric定义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 诱导公式—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:振幅变 B:上下平移w:周期变化φ:左右平Example反三角函数(inversetrigonometricExample函数的极限(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该该部分内容将于20153月中下旬完成更请密切关注哦1、直角三角形（righttriangles)特殊三角形三边的关系(30-60-90,45-45-等腰三角形（isoscelestriangles)等边三角形（equilateraltriangles)相似三角形（similar正弦定理(Sinerule)、余弦定理（cosine解析几何(coordinategeometry) point-lope y-y0=k(x-x)斜率(slope（两点的坐标确定斜率平行(parallel)圆圆心(center)在（a,b)，半径(radius)r的圆,