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广东省2020届高三年级第一次教学质量检测 文科数学(PDF版)PDF版)
书书书 【!"#($ 1%)】 【!"#($ 2%)】 ! " # $ % & ' ( ) * ( + * , - * . / 0 1 2 3 4 5 2020&'()*$+,-"./01 ! " (#)$ %&'(: 1.2345$Ⅰ4(678)9$Ⅱ4(:678);<5,=4>5 1505.?3@A 1205B.C 8D,?EFGHIJKLM、N?OPQRSTUVC8WX. 2.YC$Ⅰ4@,6Z[8C]^,_`abC8WXcd8eKC]fPgh.ijkl,_m nopq^,r6gstC]fP.UV234Xuv. 3.YC$Ⅱ4@,HC]UVC8WX.UV234Xuv. 4.?3wx^,H2349C8W+yzY. )Ⅰ$(*+, - 60.) /、*+,(01,- 122,,32, 5.,- 60..432,56789*(:,;(=>?,@ AB7) 1.{|}~ M= x∈N|-5<x{ }<4,N= -2,0,2,4,{ }6, M∩N= A.0,{ }2 B. -2,0,{ }2 { }C.2 D.0,2,{ }4 2.sin300°cos600°= A.1 4 B.槡3 4 C.-1 4 D.-槡3 4 3.6K A.4.71.5>4.72 B. 1 3x槡 +4 < 1 3x槡 +2 C.lg13>lg2+1 D.5 1 4 <2 1 4 4.! a{ }n KD n9 Sn, a1a2…an=3n2-2n, a5= A.34 B.35 C.36 D.37 5.{| f(x)=(x-n)2,x∈[2n-1,2n+1)(n∈Z), f(2019)= A.10082 B.10092 C.10102 D.10112 6.{|! f(x)= 6-2槡 x+ 2槡 x,K A.! f(x)Kc x=3 2,V[0,3 2]X B.! f(x)Kc x=3 2,V[3 2,3]X C.! f(x)Kc(3 2,0),V[0,3 2]X D.! f(x)Kc(3 2,槡23),V[3 2,3]X 7.{|! a{ }n ,a2=5a1=10,cK n∈N ,an+2+an=an+1, a2019= A.12 B.16 C.8 D.10 8.! f(x)=x·e sinxK !!!! "# $ %$ %"# %!%!! " # A. !!!"!"!! #$ #% $ ! "$ "&% '&$ " B. !!!"!"!! !!!"!"!! ! " #$ #% $ "$ # C. !!!"!"!! ! " ##$ #% $ "$ "&% '&$ D. 9. 2K ABCD,→DE=1 2 →EC,→AF=3 5 →AD, →AE· →BF= A.13 15 B.6 5 C.16 15 D.14 15 10.H!f(x)=sinωx 槡+ 3cosωx(ω>0)K ¡¢ π 3£¤,¥¦K§¨ yc,f(x) ©ªK«¬ A.4π 5 B.6π 5 C.5π 4 D.5π 6 11.{|Q! a{ }n KD n9 Sn, S10<0,S11>0, Tn=a1 2+a2 22 +… +an 2n«@ nK¬ A.10 B.11 C.5 D.6 12.{|! f(x)= x3-ax2+a,x≤0, (1 2)(a-2)x+1 4,x>0{ , ! f(x)V RX,®! aK¯¬°± A.[0,3 4] B.[0,1 4] C.[0,2) D.[0,5 4] )Ⅱ$(C*+, - 90.) 24²³G?896?8;<5,$ 138 ~$ 218G?8,[£38?E´Gµ¶C.$ 228 ~$ 2386?8,?E·¸¹º¶C. D、EF,(01,- 42,,32, 5.,- 20..GHIEJ4,:7KLM) 13.{|¡»/ m=(2,-3),n=(6,λ). m⊥n, n = . 14.¼½ y=(lnx+1 x)·exV¾(1,e)¿KÀ½Á . 15.! f(x)=cos2x+ sinxK¬Â . 16.{| an=2n+1,! 1 anan{ }+1 KD n9 Tn,c¨K n∈N ,Tn <an+11 t ,®! tK¯ ¬°± . 【!"#($ 3%)】 【!"#($ 4%)】 ! " # $ % & ' ( N、OH,:- 70..OHPJ6#QRS、TSUVWXYZ[.) 17~21,]^,,39_,^` a]bcH.) 22、23,*^,,^`deABcH. (/)]^,:- 60.. 17.(28>5 125) {|△ABC,à A,B,CÄcK5Å a,b,c, cosA=3 4,4(a2+c2)=4b2+ac. (1)ºO:B=2A; (2) ab=12,º cK¬. 18.(28>5 125) {|Æ 3K! a{ }n KD n9 Sn,log2 an+1-an 3n =1. (1)º! a{ }n KÇÈÉ; (2)ºO:-3,Sn,Sn+1-SnÊQ!. 19.(28>5 125) Ë SnQ! a{ }n KD n9,{| a3=S2+2,S3=a4+2. (1)º an; (2) a1,a2,ak1,ak2,…,akn,…ÊQÌ!,º k{ }n KD n9 Tn. 20.(28>5 125) {|! f(x)=(x-1)ex. (1)§¨ xKÁ f(x)=λxÍÎ 1£®!·,º®! λK¯¬°±; (2) x=0 ! g(x)=2f(x)-ax2KϬ¾,º®! aK¯¬°±. 21.(28>5 125) {|! f(x)=ex-lnx-(a-1)x.(s eIÐc!KÑ!) (1) a=e,º f(x)KÒA; (2) a=1,ºO:f(x)>3 2+ln3 2. (D)*^,:- 10..f^`4) 22、23,:g*/,cH.hijk,lmnk7)/,o.. 22.(28>5 105)【6Ó 4-4:ÔfÕÖ×!Á】 ÏÔfÕ,¼½ CKÏÔfÁ ρ=2.ØϾپ,Ï xÚÛ¡»ÜÃÔfÕ xOy,ܽ lK×!Á x=a+槡3 2t, y=1 2t{ , (t×!). (1)º¼½ CKÜÃÔfÁØÝܽ lKÞÇÁ; (2)¼½ CXßÎà£áâK¾¦Ü½ lKãäQ¨ 1,º®! aK¯¬°±. 23.(28>5 105)【6Ó 4-5:áQÉ6å】 {|!f(x)= x-1 + 2x+4. (1)ºáQÉf(x)≥5Kæ}; (2) m>1,n>1,ºO:f(mn)- 2mn+4 > n-m . 书书书 !"#$[% 1 &] 2020'()*+%,-."/012 !"#$%&'( 1.【34】A 【56】789,M= x∈N -5<x{ }<4 = 0,1,2,{ }3,: M∩N= 0,{ }2,:; A. 2.【34】B 【56】sin300°cos600°=sin(360°-60°)cos(720°-120°)=sin(-60°)cos(-120°)= (-槡3 2)(-1 2)=槡3 4,:; B. 3.【34】B 【56】789,4.71.5<4.72, 1 3x槡 +4 < 1 3x槡 +2 ,lg13<lg2+1=lg20,5 1 4 >2 1 4,:; B. 4.【34】D 【56】< n=5=,a1a2a3a4a5=315,< n=4=,a1a2a3a4=38,>? a5=37,:; D. 5.【34】B 【56】@ 2019=2×1010-1,AB f(2019)=(2019-1010)2=10092,:; B. 6.【34】A 【56】789,6-2x≥0, x≥0{ , 5B 0≤x≤3,CD f(3 2-x)=f(3 2+x),:E! f(x)FGHID x =3 2,JK C、D;CD f(3 2) 槡=23,f(3) 槡= 6,: f(3 2)>f(3),JK B,:; A. 7.【34】C 【56】789,an+2=an+1-an,an+3 =an+2 -an+1,LMNOAB an+3 =-an,P an+6 =an,:Q RD 6,: a2019=a3=8. 8.【34】A 【56】789,x∈R,f(-x)=-x·e sin(-x) =-x·e sinx =-f(x),:E! f(x)DSE!,T UVWXYGH,JK C;Zf(π)=π·e sinπ =π<5,JK B;Z f(3π 2)=3π 2·e sin3π 2 =3π 2·e, f(2π)=2π·e sinπ =2π,:f(3π 2)>f(2π),JK D,:; A. 9.【34】C 【56】? ADXY,[]T>^F_`abcde,P A(0,0),E(2 3,2),B(2,0),F(0,6 5), : →AE=(2 3,2),→BF=(-2,6 5),P →AE· →BF=-4 3+12 5=16 15,:; C. !" # $ % &' ( 10.【34】A 【56】789,f(x)=2sin(ωx+π 3),P f(x-π 3)=2sin(ωx+π 3-ωπ 3),P π 3-ωπ 3 =π 2+kπ(k∈ Z),: ω=-1 2-3k(k∈Z),: ωFfghD 5 2,Pf(x)QRFfihD T=2π ω=4π 5,:; A. !"#$[% 2 &] 11.【34】C 【56】@ S11=11(a1+a11) 2 =11a6>0,B a6>0,@ S10 =10(a1+a10) 2 =5(a5 +a6)<0,B a5 < 0,>? n≤5= an<0,an 2n <0,n≥6= an>0,an 2n >0,>? Tnfg= n=5,:; C. 12.【34】D 【56】CDE! f(x)j Rklmno,pq y=(1 2)(a-2)x+1 4j(0,+∞)klmno,: a- 2<0,P a<2①;r- y=x3-ax2+aj(-∞,0]klmno,Z y′=3x2-2ax=x(3x-2a),s y′=0,: x=0t x=2a 3,:2a 3≥0,u a≥0②;fv,< x=0=,a≤ 5 4③;wx①②③,y! aF zh{|D[0,5 4],:; D. 13.【34】 槡2 13 【56】789,m·n=0,P 12-3λ=0,5B λ=4,P n=(6,4),: n 槡 槡= 36+16=2 13. 14.【34】y=ex 【56】789,y′=(1 x-1 x2)·ex+(lnx+1 x)·ex,: k=y′x=1 =e,:>}~D y =ex. 15.【34】[0,9 8] 【56】f(x)=cos2x+ sinx =1-2 sinx2 + sinx =-2( sinx -1 4)2 +9 8,>?< sinx =1 4=,f(x)zfih 9 8,< sinx =1=,f(x)zfgh 0,>? f(x)Fh D[0,9 8]. 16.【34】(0,162) 【56】789, 1 anan+1 = 1 (2n+1)(2n+3)=1 2( 1 2n+1- 1 2n+3),∴Tn=1 2[(1 3-1 5)+(1 5- 1 7)+… +( 1 2n+1- 1 2n+3)]=1 2(1 3 - 1 2n+3)= n 3(2n+3).∵Tn <an+11 t ,u n 3(2n+3)< 2n+12 t , t>0,∴ t<3(2n+12)(2n+3) n =3(4n2+30n+36) n =12(n+9 n)+90, n+9 n≥ 6,<< n=3=,,∴12(n+9 n)+90≥162,∴t<162,u 0<t<162. 17.5:(1)789,a2+c2-b2=ac 4,Pa2+c2-b2 2ac =1 8=cosB, cos2A=2cos2A-1=2×(3 4)2-1=1 8=cosB, CD B,2A∈(0,π),: B=2A.(5) (2)789,sinA= 1-cos2槡 A=槡7 4,sinB= 1-cos2槡 B= 槡37 8 , sinC=sin(A+B)=sinAcosB+cosAsinB= 槡57 16,(8) CD a sinA= b sinB,u a 槡7 4 = b 槡37 8 ,AB 3a=2b, !"#$[% 3 &] ab=12,>? a 槡=22,b 槡=32;(10) @ a sinA= c sinC,B c=asinC sinA= 槡22× 槡57 16 槡7 4 = 槡52 2 .(12) 18.5:(1)CDlog2 an+1-an 3n =1,: an+1-an=2·3n, an-an-1=2·3n-1(n≥2),an-1-an-2=2·3n-2, an-2-an-3=2·3n-3,…,a3-a2=2·32,a2-a1=2·31, k` n-1MO,B an-a1=2·(3+32+… +3n-1)=3n-3,: an=3n(n≥2),(5) Z a1=3,: an=3n(n∈N ).(6) (2)@(1)AB Sn+1-Sn=an+1=3n+1,Sn=3(1-3n) 1-3 =3n+1-3 2 , : Sn-(-3)=3n+1-3 2 +3=3n+1+3 2 , (Sn+1-Sn)-Sn=an+1-Sn=3n+1-3n+1-3 2 =3n+1+3 2 , >? Sn-(-3)=(Sn+1-Sn)-Sn, : -3,Sn,Sn+1-Sn!.(12) 19.5:(1)! a{ }n FD d,@ a3=S2+2,S3=a4+2B a1+2d=2a1+d+2 3a1+3d=a1+3d{ +2,5B a1=1,d=3, >? an=a1+(n-1)d=3n-2.(6) (2)@(1),a1=1,a2=4, >?! a1,a2,ak1,ak2,…,akn,…FpD 1,D 4, akn!F% n+2,>? akn =4n+1, akn =3kn-2,>? 3kn-2=4n+1,kn=4n+1+2 3 , >? Tn=1 3(42+43+… +4n+1)+2 3n =42(1-4n) 3(1-4) +2 3n=4n+2+6n-16 9 .(12) 20.5:(1)789,(x-1)ex=λx, x=0F, :(x-1)ex x =λ,s m(x)=(x-1)ex x ,P m′(x)=(x2-x+1)ex x2 , :E! m(x)j(-!,0)(0,+!)klmno,< x→ -!=,m(x)→0,< xW 0=? x→ +!=,m(x)→ +!,< x¡W 0=,m(x)→ -!, ¢£E! m(x)FTU]T>^, ¤¥A,λ≤0,uy! λFzh{|D(-!,0].(6) ! " #$" $! # " % ! & $& $! ! " (2)g(x)=2f(x)-ax2=2(x-1)ex-ax2,P g′(x)=2xex-2ax=2x(ex-a). !"#$[% 4 &] ①¦ a>1,P< x∈(-!,0)=,x<0,ex<1,ex-a<0,>? g′(x)>0; < x∈(0,lna)=,x>0,ex-a<elna-a=0,>? g′(x)<0. >? g(x)j x=0§zB¨ih. ②¦ a≤1,P< x∈(0,1)=,x>0,ex-a≥ex-1>0,>? g′(x)>0. >? x=0 g(x)F¨ihY. wk>©,y! aFzh{|(1,+∞).(12) 21.5:(1)¦ a=e,P f(x)=ex-lnx-(e-1)x, >? f′(x)=ex-1 x-e+1(x>0), f′(x)j(0,+!)koE!, f′(1)=0, >? x∈(0,1)=,f′(x)<0,f(x)ªE!;x∈(1,+!)=,f′(x)>0,f(x)oE!, >? f(x)Fnª«¬D(0,1),no«¬D(1,+!).(5) (2)¦ a=1,P f(x)=ex-lnx,f′(x)=ex-1 x, f′(x)j(0,+!)koE!, f′(1 2) 槡= e-2<0, f′(2 3)=e 2 3 -3 2=(e2) 1 3 -(27 8) 1 3,@ e2>4>27 8,AB f′(2 3)>0, >?j x0∈(1 2,2 3),®B f′(x0)=0,u ex0 =1 x0 , x∈(0,x0)=,f′(x)<0,f(x)ªE!;x∈(x0,+!)=,f′(x)>0,f(x)oE!, >? f(x)≥f(x0)=ex0 -lnx0=1 x0 -lnx0, g(x)=1 x-lnx(1 2<x<2 3),P g(x)j(1 2,2 3)kªE!, >? g(x)>g(2 3)=3 2+ln3 2, >? f(x)≥f(x0)>3 2+ln3 2.(12) 22.5:(1)789,ρ2=4, ¯°M ρ2=x2+y2,B± CFabcdD x2+y2=4, @aF²!³´²! t,Ba lFµ¶D x 槡- 3y-a=0;(5) (2)789AB,·¸ Oa l:x 槡- 3y-a=0F¹º d<1, ∴ a 槡1+3 <1, 5B -2<a<2.(10) 23.5:(1) x-1 + 2x+4≥5»W x<-2 1-x-2x-4≥{ 5t -2≤x≤1 1-x+2x+4≥{ 5t x>1 x-1+2x+4≥{ 5, 5B x≤ -8 3t 0≤x≤1t x>1, >?XMF5¼D(-!,-8 3]∪[0,+!).(5) (2)½¾:f(mn)- 2mn+4 > n-m , ¿½¾|mn-1|>|n-m|, ¿À¾(mn-1)2>(n-m)2, Z(mn-1)2-(n-m)2=m2n2-m2-n2+1=(m2-1)(n2-1)>0, ZXM.(10)查看更多