2019年新课标人教A版高一数学必修1知识点总结.doc

112123(1)(2)(3)(4)3{}{}{,,,}1A={},B={1,2,3,4,5}2{}x-32{xR|x-32}{x|x-32}34NN*N+ZQR5aAaAaAaAaA61231.ABABABAB1AB2AB:AB,BA,ABBAAn,A2n.2(55555=5)A={x|x2-1=0}B={-1,1}ABAB,BAABA=BABBAAA:AB,ABABAB(BA)AB,BC,ACABBAA=B3.:1AB,A,BAB(AB)AB={x|xAxB}2ABA,BAB(AB)AB={x|xAxB}3AA=AA=,AB=BAAA=AA=A,AB=BA.41SU2SASASSASACSACSA={x|xSxA}3CU(CUA)=A(CUA)A=(CUA)A=U(4)(CUA)(CUB)=CU(AB)(5)(CUA)(CUB)=CU(AB)1ABfAxBf(x)fABABy=f(x)xAxxAxy{f(x)|xA}1y=f(x)2x(1)(2)(3)(4)1.(5).x.6(7).()212()(1).(2)3.(1)y=f(x),(xA)xyP(xy)Cy=f(x),(xA)C(xy)y=f(x)y=f(x)xy(xy)C.C={P(x,y)|y=f(x),xA}C(),YSCsAA(2)Ax,y(x,y)P(x,y).B:1y=f(x)xy=f(x)P2152y=f(x)y=f(-x)y1xxxyayaa3y=f(x)y=-f(x)x1logloglogaaayxyxx:f(x)f(xa)f(x)f(x)a(3)ABC41235ABfAxByfABABfABABaA,bB.abbaab:ABfABBAfABABABBA61x23412y=f(u),(uM),u=g(x),(xA),y=f[g(x)]=F(x)(xA)fg71y=f(x)IIDx1x2x1x2f(x1)f(x2)f(x)DDy=f(x)Dx1x2x1x2f(x1)f(x2)f(x).Dy=f(x).12Dx1x2x1x2f(x1)f(x2)f(x1)f(x2)2y=f(x)y=f(x)().(3).(A)1x1x2Dx1x22f(x1)f(x2)34f(x1)f(x2)5f(x)D(B)()(C)f[g(x)]u=g(x)y=f(u)1,.4()yfx()yfx()yfx1()yfx()yfx()yfx()yfxCCC0C()yfx()yCfxC0C()yfx()yCfx()fx()gx()()fxgx()0,()0fxgx()fx()gx()()fxgx()0,()0fxgx()fx()gx()()fxgx()0fx()fx()nfx()(0)kfxk()(1)nfxn1()fx.81f(x)xf(x)=f(x)f(x)2f(x)xf(x)=f(x)f(x)1,2xx3yu=g(x)y=f(u)y=f[g(x)]12f(x)f(x)3f(x)=f(x)f(x)f(x)=0f(x)f(x)=f(x)f(x)f(x)=0f(x).(1);(2)f(-x)=f(x)f(-x)f(x)=0f(x)/f(-x)=1;(3)..,y.()fx()()(||)fxfxfx.()fx0(0)0f.()Fx()Gx.)(xfR()()()2fxfxFx()()()2fxfxGx..()0fx.91.2ABf[g(x)]Cf(x)10p30123y=f(x)[ab][bc]y=f(x)x=bf(b)y=f(x)[ab][bc]y=f(x)x=bf(b)1000n=0(1)()nnaa(2)nnnaan,0||,0nnaaaaaa2(0,,,1)mnmnaaamnNn_1(0,,,1)mnmnaamnNna00031(0,,)rsrsaaaarsR2()(0,,)rsrsaaarsR3(b)(0,0,)rrraababrR122[(12)]1221=1xyaxR1a0a120a1a1R,0+101,x=0y=1(2)R(2)R3x0,0y1;x0,y13x0,y1;x0,0y1xRxR+y01010a11x0,0y1;1x0,y1a11x0,y1;1x0,0y1y=N(1+p)xy=kax31ab=N,b0a,N1b0a,N121(=a0)134a1=ax=1(5)y=N(1+p)xy=kax1xaNxaNlogaxNaNlogaN1.a0a12.N03.2110,10loglgNN2e,loglneNN3logxaxNaNaxN12logaa=1,loga1=0lg10=1,lg1=0,lne=1,ln1=0(3)logNaaNa0a1M0N01logMNloglogaaaMN2NMNMaaalogloglog3loglognnaaMnMRnn:1):=2)3)(0,)4)NMMNaaalogloglogNMNMaaalogloglogloglglog0,1,0,1,0loglgcacbbbaaccbaaabbalog1logloglogloglogabcabcddloglogmnaanbbm1logayx(a0a1)x0+1log1ayxlog2ayx2a0a12logayx(a0a1)0a1a10R(1,0),x1,y0(0,+)(0,+)x1y0x=1y=00x1y0x1y0x=1y=00x1y0logaba,b(0,1)(1,+)logab0;a,b(0,1)(1,+),logab0.00.0logab3axyalog:,4logab,a,b1,logab0a,b1,logab011(=logaa)01=logaay=1y=ax(a0a1)y=logax(a0a1)y=xyx0(1,0)yx0(1,0)5:(1),.(2),.(3),.10.6(1)()(2):0,1.(3)(4)1yxx210+1120[0,+101300+xyyx+xx1y=f(x),f(x)=0xy=f(x)x2f(x)=0?y=f(x)x?y=f(x)3y=f(x)[a,b]f(a)f(b)0,y=f(x)a,bcf(c)=0,cf(x)=04y=f(x)1f(x)=02y=f(x)5f(x)=ax2+bx+c(a0)10f(x)=0x20f(x)=0x30f(x)=0x1[a,b]f(a)f(b)0y=f(x),f(x),,2:[a,b],f(a)f(b)0(a,b)c;f(c),f(c)=0,cf(a)f(c)0,b=cx0(a,c)f(c)f(b)0,a=cx0(c,b)(4)|a-b|,a(b);~12y=ax+b(a0)y=ax(a1)y=kax(k0,a1)y=xnn?N*)y=logax(a1)y=ax2+bx+c(a0)V(ax)V(xn)V(logax)(1)log2x2xx2(2)log2xx22x34y=ax2+bx+c(a0)5(6)ax2+bx+c=0a0m,n)m,n)x1(m,n)x2(p,q)f(m)f(n)0KKKKf(k)0yxnmmnmnpqyxkkk02()0()0bmnafmfn()0()0()0()0fmfnfpfq02()0bkafk02()0bkafk