高三数学基础知识复习提纲

2010届高三数学基础知识复习提纲、，，CARU、ABAUABA；；CAUBUU；CABU；CACBC(AB)U；；UU用，A是BAA是BA。AA；ABAA=AABAC.，BCBn2n21n22nnn.p或p且q；逆命题qp为若则互否互为否否命题若则逆否命题pqqp互逆若则pp是q的qp是q的pqpp是q的）”）；“）。1是n个ab若a,b0abab2abb；()2；a2a2b2aba,bRab2ab()222，22当abp；当abS；a,bRa0,()0ab22）|aa|aa；1111b,ab0abab）a；11abb(a0)a0b(a0)a0a0a0；；2a0|xa；|xa；判别式二次函数方程不等式不等式axbxc0axbxc0axbxc022222C0Cx,yAxByC0000C0C0C0）））BAB中BA到3B合AxB中A到B；；。；；。y=fII内xx，12当xxy=f)II12当xxy=f)II12y=f有x为y=f0有y=f))y=ff(x)g(x)f(x)g(x)f(x)g(x)f(x)g(x)fg(x)y若f与gfg(x)若f(x)与g(x)fg(x)4Tf(xT)f(x)则T；；；.kx2ax）4b4b22当a0,a0,；4a4akxy,kx0yy0；ya且ax；xRylogx且a；a；kx2；yf(xa(a0)(的图象沿轴yfxx个单位得到的；yf(xa(a0)yfx(轴x移a；yf(x)a,(a0)(的图象沿轴yfxy；yf(x)a,(a0)yf(x的图象沿轴移a。5yf(x)yf(x)yyf(x)yf(x)xyf(x)yf(x)yf(x)xR,f(xa)f(xa)yf(x)yf(ax)yf(ax)xaf(x)yf(x)④yf(x)yf(x)⑤y⑥yf(x)yf(x)yx1与①y(x(a0)yf(x)(a(0aa②yf(ax(a的图象，可将yf(x)的图象上的每一点的横坐标伸长1(0a(aa6x)=0x)x）个c)))))；x；1x：1xx11)x)=xxx）1101)x)a=xxx）1101aba或）)导数yx()()()到xxfxxfx00yfx0x0xlimylimxf(xx)f(x)yf(x)=，00x0xx0x0()yfx()在()或yfxxfx'x000limylimxf(xx)f(x)y'|()=f'x0.0xx00xx0x0'f(x)g(x)f'(x)g'(x)'f(x)g(x)f'(x)g(x)f(x)g'(x)()fx''()()()'()fxgxfxgx(x)g2g(x)C'0（Cx)'x(x)'1（）nnx)'xnR111(lnx)'(logx)loge'xxlnaxaa(e)'exx(a)'aaxx7f/0s00//()0①fx与fx()()0fx()(x)x(,)3fxf在()0fx()0fx()是fx()0②fx()0fx与fx()()0f(x)0fxfx为()()0fx()0fx()0fx()是fx()0③fx与fx()f(x)f(x)0f(x)0()0fx()0f(x)0或fxfx()()0fx是f(x)yf(x)yf(x);()yfx()0fx()0fxyf(x):()0fx()0fx08()0()0fxxfxx00()0()0fxxfxx00yf(x)a[:yf(x)yf(x)、”f(x)0时，函数有极值/0f(x)000/0则则.aa=a)=ab=mnmnmna=a=Na>0,且x对x以aN。以e；loga1a1log10aa>0,且NaaaMN(aMNaaMM∈naalogblogb④a>0,且>0,且clogaac；9axb(a0)a0函数；当a0yyyyaxbxc(a0)2；a(xx)(xx)x；12a(xk)h2；当a0当a0ya(xk)h2a0a0a0a0yxxx[2yxxx[a,a2f(x)axbxc02为x,x1212122或10[m,n]f(x)0(m,n)xnxm和=xαx1α，12xxya(aaxaa分和ylogx(aaaaa分和a）yaylogxx与a1011αα{|α．x.xy＝）π°l||r.ya的终边11lr||rs222（扇形roxxy；y；cos；tanrxryTPOMAxα°°°°°°°°°°°ααα12sincossincos1，.22=n(1)sin,n2nsin()2n1(1)cos,2n(1)cos,2cos()2n1(1)sin,n2););tantan.)1tantanbasinbcos=ab)tansin(((,)辅助角ab)22a；2tantan1tan2coscossin2cos112sin。2222sin(x))xyRyω,ω)xkkZ,Tyx，ω,，2ωT.abc2R.sinAsinBsinCa2bcbccosAbca2cacosBcab2abcosC；；.22222222Ab2c2a2Ba2c2b2cosCa；2b2c2；2213111）Sahbhchh、h、h（c.222abcabc121212）sinbcAsincasinB.SabCA(x,y)B(x,y)C(x,y),、、112233xxxyyy的重心的坐标是G(1).3,231233记OAxyOBxy)1112则OA+,+)OBxxyy1212OBxxyy）2121ABλaλRλaλλ)两个向量的数(,),(,)abab,b记1122则²=abxxyy1212abba②(ab)cabc)))(a)()()babaaaaa;②③:①a²b=b²a;②(λa)²b=a²(λbλ(a²b③(a+b²c=a²c+b²c222abb(a±b)=a2OAxyxyxxyy)1122212114abab(b0)坐标语言为：设非零向量ax,y,bx,y,则∥bxyλxy)，即a11221122xyxy1221abab0ax,y,bx,yabxxyy01122121222|a|2|①a即aa②abab0abcos③④。abcos在a.bba1n2；nnan，a，aaaa。123nnnna}n①aana=fnnnnnk1(kZ)；②a=1)=③nnknS1(n1)a）{aSS(n≥2)nSannnnnn12d表aad(n2)aad(n1)或。nn1n1n．等差数列的通项公式：aa(n1)d；n115d0d0d0a3，A，A与babababAa。，A，bAn(aa)。22n(n1)Snand。1n22n1a2nana，a，a，aa，a，a，a1357381318aamn；()a，mnN，()aannmnmddnmnmqNmnpqaaaa；mna，，p，且nmnpq）a0d0，Sa0d0，S11nn）SnSnNna0a0nnNaSn或。n0a0an1nnn1q(q0)a：aqq(0)n1qn．等比数列通项公式为：aaq(aq0)。1nn1q1aa}q。mnmanna与b,,a与b中间插入一个数GaGbGGGG2na,a,a,,a,nSaaaa，123nn123naq)aq或Sa1n当q1S1；n1q1qnn当Sna。n1a,q,n,Sa,a,q,S和q，n1n1nnqn1q1q116；aqnmanmanmuvaaaannmu，van，S成nnkS2kk3kS2kSkN*SS3kaaaaaaaa123kk2k23kSSSSSk2kk3k2k八、算法、概率统计与复数）YXy。mnBB+BBB+A1711n(xxxx)xxn123nnii11S=－x)－x)+－x)+－x)]22222n123nS2i=12abicdiac,bd（a,b,c,dR）zazaab。22(abi)(cdi)(ac)(bd)i;(abi)(cdi)(ac)(bdi;(abi)(cdi)(acbd)(bcad)i;acbdbcad(abi)(cdi)i(cdi0).c2d2c2d25dzxyi.|zz(xx)(yy)（zxyi，22122121111222πrππ；2πr+ππ2圆π′+r+22π2VSh1V=Sh31V=+sshSh'34R3V=318}00(3)19ααAAxByC0B－Bααyyx,yx,y则121x122x21yk(xx)ylP(x,y)k．11111ykxbl在yyyxxxy、Pxy(xxyP(,)(,)1(y1yyxx21211122212121xy1abAxByC0Bl:ykxbl:ykxb，111222llkk且bb121212②llkk1.1