高中数学学考复习知识点

一、集合与函数：B、AB,BA则空集：a,a,,a}2n2n2n12n*NZQRf–x)=–f(x)fx)=f(xyyDf(xx,xx<x1212①f(x)<f(x)f(x)–f(x)<0f(x1212②f(x)>f(x)f(x)–f(x)>0f(x1212y=++（a02b4acb，xb4b24a2,2a4a2af(x)axbxc(a0)f(x)a(xh)k(a0);2;2f(x)a(xx)(xx)(a0).121aaaa•a=a）mn(a)=a()=a•bmnmnm+nmnmnnnnaanbna11naa）ann）a=1(）n）mn0mmbananmy=axa>0且R；(0,）YY11X0X0logNbaN(a0,a1,Nba.a=Nb=1=a=a=aaN=NbbaaaaMN=M+Na()=MNaaaaalogNN=bNN=bbaaalogabnlogblogba0a1,n0m1n1N0(,,,nmmaa1N=N=NA=e=aaeNy=xa>0且a(0,；R）YYXX0110yf(x)yf(xa)bab2N(1p).pyyxxyf(x)f(x)0的X叫yf(x)yf(x)Xyf(x)f(a)fb)0yf(x)f(c)0Ca,ba,b，ca,b二、圆：yyk==α≠xx）21xx1221y=kx+)y–y=k(x–x)00yyxxxy1a0,b0）,（xxyy）（11yyxx21212ab121c0(,）l：y=kx+b11111112222222AC111212AC22AC111212ABC222kk=–1AA+BB=01212122P(x,y)P(x,y|PP|=xxyy2111222121212AxByCP(x,ylAx+By+C=0d0000A2B2x+y=r2）r223–a)+(y–b)=r2）2212DED2E24F2222dr点点PP(x,y)(xa)(yb)r222d(ax)by)220000(xa)(yb)r222dr点Pdr点P(xa)(yb)r2222(xa)(yb)r22C0(xa)(yb)r222①dr0dr0dr0②③.Or，OOd121212drr;12drr;12rrdrr;1212drr;120drr.12三、立体几何：4四、三角函数：sintan=122cos2tansin2=2sincosαcos2=2cos-1=1-2sinα22tan1tan2土干cos(β)=coscosβsinsinβsin(β)=sinβcossinβ1yx)yx)，x∈R(A,ω,Tyx)x,kZ(A,ω,T，.2五、平面向量：aaaa2；||=aax2y2=||=ab=xy=xy11225a∥b（b≠=λb0axxa∥b（b≠xy–xy=00y0y）122122112yy1a=xyb=xy）1122a⊥ba·b=0a⊥bxx+yy=01212xxyy|ABABAB()()(,)xyxy(,)=22dA,B21211122a=xyb=xya+b=x+xy+y）11221212a=xyb=xya-b=x-xy-y）11221212ab|a||b|=xxyya=xyb=xy=12121122x21y2x2y2212a·b=|a||b|a=xyb=xya·b=xx+yy11221212bba与b在a六、解三角形：a,cA+B+C=CB=AC=º(A+B)=,(A+B)=,a+b>c,a–b<6abc2RRa:b:c=::sinAsinBsinCa=,b=,c=,a=b+c–,b=a+c–a,222222c=a+b–2a222bcaacbabc222222222ABC,,221111S=2ah=2b=2=2c八、数列：{an}a=a+(n–1)da=a+(nm)d(m,N)n1nm1n(aa)nS=na+n(n–1)d=1nn122①若m+n=2a+a=2a(m,N)mnp②若m+n=p+a+a=a+a(m,n,p,N)mnpq{aa=aqa=aq(m,N)n–1n–mnn1nmnaq)aaqn当1S==，当q=1S=na1n11nn1q1q①若m+n=2a=a•a(m,N)2pmn②若m+n=p+a•a=a•a(m,n,p,N)mnpqSn1an{aS=a+a+…+a1nn12nSSnnNnn1七、不等式：a,b∈R,a+b≥2ab22ab2a,b∈R,a+b≥2aba,b∈R,ab≤++2a=b=7axbxc0(或0)(a0,b4ac0