河北省衡水市部分重点高中2023届高三二模数学试题（含答案）

2023

W;M:

->

1.B^fl^'â’A=|xj2x2-x-3<O|,B=|y|y=2-3x+x2},WJAB=()

fi•31f,,11

A.Jxl—-<x<->B.lx|-l<x<—

(42J[4J

C.{x|-l<x<3}D.Jx|—3<x<——[

l4J

I3

2.iSM^z,=l+ai(üeR),Z2=2~2i’^-lZ|l“N’WJ«()

A.1B.2C.2^3D.3^2

3.Bÿllw'^/’:3xeR,taiu-<Ku£e>+2>7t,ÜMBP()

A.3xsR,tarir>7tuJie"2<Æ

x+2

B.VxGR,tanx<nHe>n

C.3xGR,tanx<7tKex+2>K

D.VxeR.tanr>7tJ|ex+2<7t

4.a^tWij{a„}KMHW^39,676-6a5+9«4=O,JJJU=()

A.81B.243C.27D.729

5.

R.J\RJWWJAK5w-W,id>#ARJWrM§%

TtëRJ”,W^c^'RWEPRJWW”,WJ/’(A|B)=()

32

A.

3245

6.B^fl—^l!ÛÔܱ.TJ£ffiîîSïfH±l±7'Jl:4,M^WïWiW'J9,-fi^-OjiJîsrfiïU

ftWm>/îÔfê,WJSMUÛW1*F^()

A.3ÆB.5JTC.litD.97T

7.B^a^/(x)=sin(20237t+x)-sin2j+cos2|,()

A./(x)lft«^[->/2,^]

7T3JT

B./(X)IM^OMIXI'B]^--+2km—+2kn(keZ)

(5TÏ

C.>’=/X+1-

l4)

D.IWWA»--^+kn^kit(teZ)

8.BfcUeR,®|V(x)=^4“-V2.£#ÆreR,tt^|/'(r+2)-/'(/)|<l,WJâ«

9^2^4

A.0B.----C.—D.-

1699

9.16ÙJE^^ABCD-ABICIDI-f,ÆP«W4('â-HWM)

îs^j,()

A.BB,ACC.A

B.S^AP^CDJTr^ÆtKJjE^WMMffl^fO,!]

C.%4AP=ACl,^CP^^OCC^^s&^sEM^^ÏÎ

10

D.H«B-ADP^»âÜW»±<^TiEMABCD-ABlClDl

ÏR

io.a^®^/(x)=ev-^x2,Tjij&'ÆimM()

A./(%)ax=o%-?+1=o

3

B--</(ln2)<2

C.Mg(x)=-e"-^

D./(x)W^-^^

/IA3(।y

11.«,-.£(%)=-,-«U=-ar,MTÿüœiEliWê

\4)2^A-J

()

A.a=l

(iY

B.Z2»-k-ar2iWffJWW^IWSW?9256

(1V

C.“I^ï^-7=-ux2fttl^n-ï':41'â’A^W^^^j252

«M25Ï,«451

\8

-ax-ÛWJMI'A/’5418

12.iâP^EIC:4+4=l(«>*>0)±^^,V^MlICfôÈ,

a'b'

m^)2c,^IF2HÜâÜ£Ë^ffl^,.M()

A.âP5lJ#ÊB|CW^M®AIÊ^^4

Q

B.PF-F.F^O,JIIJ|PF2|=-

c./\PFXF_ÉKl®^Û<jfiA(ÉLA8

13.«1,2,a,6fiWW^3,2023,fOJ

14.“¥®rt

âA,BA(A^i)wmorjB&

A(-3,l),B(-3,6),

^p^ïRÆA=^-WWK®l±Û<jffi-A,=

36

W«Mfôtœft®5W*J.

15.e^ia^/(x)â«j^a^r(x),K^Æ^M^/W=3x2-#'(1)+21n^.ra/(^)

ii/o

16.Ü^n-5]21®|n]>a,b,cïffiÆ.a|=V2Ib\=•J2,cos(a,b\=-cos(c-a,c-b\=-----,W1]W

mfiWJIfôSA<A.

ra.

17.B^IIABCtKjF'gÆA.B.C^X^ià^JA"^-.K2csin2f^--|j+ôcos-|=c.

(D^^CWAd';

(2)>RsinAsinBÉK]fiAfit

18.ïw'Æa,=1,S„=14+/]«•

/1\fln+)

19.M/bâa^lOA.

»JA3,3,4.W&10Aimo2AftWIWWfêê.

(i)i£AAW“fèttiâû2A#JJIIAXfësMtefnA4”,WftASÆâùW;

(2)fêxA&Ü1W2A#MIii^œi»fi,

20.iinS,lEÀfêttABCDEF-A,BlC,D,E>F,(flJWfêiéA2,M,NACC,,FF,(fl

(l)<RiiT.:S^BElS^ÂC,;

(2)^¥®BME'N^fàBEF,

21.EL&l@<i^/(x)=ln(x+l)-2x+x2.

(im(x)lft^Wl'B];

(2)^/(x)+2<x2+(tz+l)x4-/?iÉExe(-l,+2o)A'I'B.hJcÏL,ARÜE:b>a+4-\n(a+3).

fo/yA

22.1(0>O.h>0)(flÆ',A,M«A3,*^,ir±

a~b~4

(DsRXXifl^WWA®;

(2)AB^IJA^®^WÆ,^*PAMX=|±-^,

»M45Ï,«4^

1.A

[WlB,Mi+W^BPoT.

fo

[W]={xl2x2-x-3<O}=xl-1<x<-

B={y|y=2-3x+x2}=bly>~

fjffAnB=|x|-<x<|

l&jÆ:A.

2.C

BRnT.

1313(3+2i)....,.

Z==3+211R

[1¥M1@>3M^2=3Z2Î(3?2Î)(3+2i)’Xz,=+ai(ae),J=L|z||<|z2|,

JWa2+l<32+22,Wfê-2x/3<a<2^3,.

C.

3.D

[W1«ïfôm,BPïïj^M-

w2

[IW1@^®p:3xeR,tanx<7r^e>ît»Æ

JtiPJliîïjEÜbPJrBJ.w^/,â<JlÜÆ>jVxeR,laar>7tKe'+2<n.

D.

4.B

[1Ètt®i+WBPnf.

2

[1WJÉ^s-6«5+9a4=0=>tf4-(6/-64+9)=0.ffi]tf„*0,.‘.q=3,

Xa,+a,+a3-üy+3A,+9at-13a,=39=>a}=3,

5

.•.tzn=3",a5=3=243.

i&i&:B.

5.A

P(ÂB)

(W1KÀ^#<$^P(A|B)=

P(B)

BTÂRM.

(WJWMfi:

mWMltil4£RW-ÿÜÆMfe4«g,Wffl1'09Ai,

WB:4£4B,W^Æffl|B]^0w,

P(Ag)

&P(A|fl)===3

P(iï)4432

ïftfê:A.

6.C

[^tJTlB&~^0ÛÛܱ.TM®F'Ztt^l:4,t#CD:AB=l:2,Sft®ÛÈWl«ffi

0099,MUAC-CO=3,Ü^D^DEJ.AB,VfBD=jAC2+CD2>

\OCD2=AC2+CD2>WAC=3CD,^AC=3,CD=\,Æ=2,

(WJM,i$Elû±'TJOEl^W9CA,

^^mcD,AB,

É1ÜBWCD:AB=1:2,®)AB=2CD,

HnÉlWfcffiOn^9.

^^^(2AB+2CD)AC=9,^ff^AC-CD=3,

Ü*DDE±AB-f-*E,

^fWBD=^AC2+{AB-CD)2=XJAC2+CD2,

s?g±)®s@Ô<JwwVÎÔFÊ,

#fW10CD2=AC2+CD2,BPAC=3CD.

^\^AC=3,CD=\,^^AB=2,

0TPU0ÛWv-1(S!.+SK+7$±ST)A=|(7r+4K+VîtX4K)X3=77T.

^12^,£18Jï

C

7.D

BPWWfM.

[HA/(x)=sin(2023ît+x)-sin2—+cos2—=-sinr+cosx=->/2sinlx-—

Ffr(Uf(x)=-V2sinIx-rrW/(^)e[-V2,V2],«AM

|||-^+2kn<x-^<^+2kn(keZ)W~^+2kn<x<^-+2kn(keZ),

W(x)m««ft~+2kTt,^-+2kn(keZ),œiBiEtô;

5n

4

I5TUi

ffiBb=/x+-«CE»;

\4)

g[J-—+2kn<x--<--+2kn(keZ)

646V’

——+2fet<x<-^+2kn(keZ),

/(x)>^--—+2kTt,—+2kn(^eZ),

1212

fôiâ:D.

8.C

[^-tfr]«*f'(t+2)-f'(r)=2a(3r+6t+4)-2,

79

a2

«mffc8(3,2+6r+4)--8(3/+6r+4)’ÉÊf(x)

ÈâÔW«mf(x)wg/b<

HA/(x)=|ar4-|x2,#fLU/'(*)=^3-*’

£18m

fôMr(r+2)-/'{ï)=[«^+2)3-(/+2)]-(a?-r)=2a(3z2+6z+4)-2,

B^W./GR,®t#|/'(r+2)-/'(/)|<l,

^W|2«(3/2+6Z+4)-2|<^,BP-^<2a(3r2+6/+4)-2<^<^,

B^/eR,Rij3r+6r+4=3(r+l)2+l>l,

79,F9

^^8(3f2+6/+4)8(3r2+6z+4)W’8(3r2+6/+4)’

99

o<£

mao<5r-ï-ïSi,0TH8(3,.+6,+4)J.

9

O

itm/(A-)=—%4--x2=—fx2--ï-->--,

v'3223219J993

C.

9.AC

[^]A®,WTWtë;BS,Æ^ZPABHP^^,SW

MMBPnj;cS,ftPô±ffi£>Cz,W^mnL^Mi+MBPnT;DS,MW^M

ÆBPWfé.

[WJWA,ÈIE##»»,i¥ffiÂCC,A,

W±fWl-ÆJij™ACC,A,&&SAiEfà;

SHFB,ABCD,

JWlujâ^AP.*5CDJWJOHPAPABJWJJSÆ,

rt(-â-KWM)ÿnTSJW^,apfrPG1AC-T-G,

nTT71

aGHVABTH,^.^PHLAB,Z.GAH=-,Z.PAG&0,-,

42

AHAGAH

ÈH^^/ÊS^D:COSAPAB==cosAPAG■cosAGAH=-----------,

APAPAG

BPcosAPABG=>sinAPABG

^M4l,£18M

ffiLUAPtgCDffîOlÔÜlE-JMtÉJjiâïÆBÎHIS;

ütfc,I*I^4/\P-AC1,OÆp&AC,±Si5A

WWW^MSÆ^je,ÜQ^QKZCC/^K,&&PK,

JQUZPCQCP^¥ffiCDDtC,,

Ȍ^IftWifcb&&CQ,

ÆRtAPCÔ^1,^'^PQ=-,CQ=12+—I-2xlx—x—=—,

4t4J424

JW^tan^PCQ=^=^,iftMCini;

CQ10

4TD,HMPÆH»ACCIA1*1(â-rawwa)ÎS^J,

ÈâPÆÆA^c,ÆM,

2

PABCDÛ<JMA^±^M^^7B},SB-ADPR,

4

=R2,m#/?=->—,

82

M:AC.

10.ABD

[^Jrlrlf/(In2)B|JP]WTB;

C;D

[iWlMTA,Mf(x)=e-^x2,^^f(x)=ex-x,W/(0)=l,/'(°)=1’

W(x)iÙ=0OMW-l=*-0,BPx-.y+l=0,AOi;

MTB,®ü[/(x)=eA-|x2,W/(ln2)=e"’2-|(ln2)2=2-|(ln2)2,

M0<ln2<l,jw|</(ln2)<2,BŒ5Ê;

MTC,ffiüc/(x)=et-|x2,®^g(x)â9m^/(x)fi<jffi^T^«âM^,

g(x)=-f(-x)=-[e-r-|(-x)2]=-e-'+|x2,C

MTD,®t/(x)=e'-^x2®È>(S^R.^c#W/'(x)=ev-x,g(x)=/'(x)=eA-x,

g'(x)=ex-l,Sx>0M#'(x)>0,gjxOH’f,g'(x)<0,JÜ!ia^/'(x)iï(0,+oo)±j&tg,

S(-~,O)±&M,

M/'(x)=/'(O)=1>0,M/(x)r±R.tWM.ffif(0)=1>0,f(-1)=--<0,

mine2

É^^M'r±ÆS.^/(x)Æ(-l0)W/(x)W-^Æ,DOt

ABD

11.BCD

zI

[Ttff]È£(X)=«xl=|,WJÆa^.^x=1>^#j3rr-<û<]û<]MOi,WJÆB1E

ÏÆ;r-4-4+|r=l,RAM,BJ^JÆCIECÆ:

5(1Y

^-4+|r=,RAM-7=-ax2lWffR^x6MM^,SM^lJÆDlE^.

26LVx)

1

[M1MTA4,H£(X)=6ZX1=|,fjlf^a=3,WA^

i-X;

(1Y

MTB4>,i£-^-3x2T,^x=l,MWTRTJWlft^MA(l-3)8=256,JW

tÂBŒfift:

(1V’r-45

xïTC4>,-/=-(-3x2)'=(-3)r-q-x^-r,

\\jx)

4‘“4+-r=l,fflfêr=2,

(i2Y22

W-O-±=-ax0<J^^^+-â-x^â<j^^j(-3)-C8=252,JWCiEifô;

Vyjx)

22

ÏÏW,ÈW*rW-!=-«r|WMW^WO-3)-Cg=252,

)

W4’-4+|r=6,Jjj?ffr=4,

2

nT#—WÆWWSWK=5670,

p/f(1-x5)|-j=-ax11âW^ïÇ4*-ax6ÏJ0W5670-252=5418,JWDJEïÆ.iftiâ;

BCD.

12.ABD

iftfé^WÆSi+IÏHPnJ;OTC,tIOfiRWnTJÉLfê^lJ^ffi^M^ntP^.1(T)®

G/C

)frf-TD,3£K/7$X$ÙT~G,=

|/P|a

IF2«W.

c_1

a3b=2y[2

22

2b=4>/2c=l^+^=1.

98

a2=b2+c2a=3

SfTA,®^PW^(x0,y0),

x0e[-a,a]=>de[a-c,a+c],

B|JPÿiJffiHCW<$fiW^Æi®^+c=4,AlEîfô;

#TB,^PF2-F}F2=O,^PF2A.FtF2,

^^M7M,£18m

22

i£|PF2|=m=>|T’Æ,|=2a-m=6-/n,|F,F,|=2c=^FFj-|FF,|,1WW:|PF,|=|,B

JEïîft;

ra®AF/‘F2â<J®^ô{j<^fi^l|f;F2|-è=ZJc)&=2>/2,c=l)ÏÏi&bc=2j2,

X'J-fD.iîfêPIG.0^Igj△P/',F,

|FG|\GI\|F,G|\GI\

2222

gP(^,y0),/(%„>;),G(xc,O),^4+^-=!.,=

ClUClA.»

c-x_ci-ex

G{,51ljx=c\.

a+ex.c

=—,^x,=ex0,JW*.

xn-x,.a+c

b21

1gy0

(a+c)2Xg-a2(a+c)22

/F,/F2Dm

ABD.

+■

x

IG/|C

D&Æ

[Æsti1*1wa^awaU|/P|=-a,AMMa

P(xg,y0),I,yr),G(xc,0)Zfa]Û<J^M>ÈiktW

81,£18M

[WJJW3=1+2+"+6,WW«=3,

4

2023,MlJff^ÉI<j¥W^x=2026,

s2=x[(2024-2026)2+(2025-2026)2+(2026-2026)2+(2029-2026)2]=.

2

14.10^+7123

WKilfiWS,MÉIlflWmWW-.

X+

BP=I’«x2+j2+6x+l8y-60=0.

;(x+3f)P2+?(y-6B)23

W(x+3)2+(.y+9)2=150,flrlMâP«4>^(-3-9),^IS^JSTÔIttlaU,

I<3A

HC:y=±x2fiF.PJr0,-,

6\)

(3

S^(0+3)2+-+9=—<150.PJTWfiFÆ®(x+3)2+(.V+9)2=150|Aj,

®fiF$IJil‘ùFKJii'l'

JWÈt£F=VÎ23,ftjfiF27150=1oVô,

WiO,FÛÜftiéfë1076+7Î23•

1076+7123

15.[473-4,+flo)

[^Jr]MJs4x=l,ÀRIV'(I),AM^giJ/'(x),^mjg/'(x)

(W)H^/(x)=3x2-#'(l)+21nx,W/'(x)=6x-/'(l)+p

^TlA/'(l)=6-/'(l)+2,^TIA/'(1)=4’

)VrLJ./(x)=3x2—4x+21nx(x>0),

JW/'(x)=6x-4+->2.6x---4=4>/3-4,^Kfô^6x=-,Bpx=—Fr

xVxx3

lU/'(x)^J^/J'>tt?94^-4,

[473-4,+^).

16.—7t

2

[Wrl

(WlS^|«I=72|6|=V2,^rl^|a|=>/2,|è|=l,

^/2

XS^Jcos^n,/?^=-cos^c-a,c-b^=——,(a,b^G[0,?r],^c—a,c-b^G[0,TT],

fiTrWa5b^-,(a-c,b-c}=-,

ÿUlU,\^OA=a.OB=b,OC=c,

'j&feAC,BC,ty&a-c=CA,b-c=CB,&TMZACB=-,

4

XZAOB=^,ffiMO,A,C,BŒtâ#Œ,

4

A=B=-,OA=y[2,OB=\,ZBOC=—-ZAOC,

14

OA

-fc.RtAOC^,

cos^AOC

oc.-™,

&RtBOC^,

cosz^BOC

rr»i0A0Ben------------------

------777^=----7777’BPcosZ'ÂOC

cosZAOCcosZBOCcosZAOC

l4

rV2V2

JÿîL7cosZ'4OC=V2——cos^ZAOC+—sin^AOC

2cos^CAOC=sin^AOC,

J5jmtanzfAOC=2,cosZ"AOC=-j=.

Jïr—

^rP^C’C=X=V10’

ioJï,&18M

5

flrWWâü®MÀfOjnx=—71.

2

[^JTKDW;»W^cos|=cos(|-flj-c,ÈjE&£mm?OJcos|=sinC,

Wsinf=iWW;

22

(2)ÈîEKÆiWSiJsiny4=^,sinfi=^,WJWSIJC2>ab,%

2c2c

^•sinAsinB=^<|^,BRW».

4c4ab

[WJ(DM:@^2csin2f^—|J+ècosy=cTïZD

ÇJ,beos—=c1—2sin2

4ïïj

g|Jbeos—=cosI—-B•c,

2UJ

ÉÏF'J^ZE®>nJ^sinBeos—=sinCsinB,

2

H^fl.Ce(0.7t),nH#0<-<-fisinfi>0,cos->0,

222

FJfycos—=sinC,®)cos—=2sin—cos—,FJfFAsin—=—,

222222

S^yefoÆ=WIJC=^.

Z\Z)Zo3

(2)M:É(DnTWsinC=—,

2

J

ÉŒ^/Ea-4=^-=-^-)nTWsiivl=—,sinB=—,

sinAsinBsinC2c2c

)!)ry.sinAsinÆ=—-.

4c

11M,18m

=a2+b2-2aZ>cos—=a2+b2-ab,

3

2

XlÈgW^ïtfl+/r>2fl/>.=

nTWc2-a2+b2-ab>2ab-ab-ab>

0fWsinAsinB=jsinAsinfîlW.

4c4ab44

18.(l)a„=n(neN*)

Sn-S„_vn>2,n&^

(1)fflSBfcOa,=1,

S„n=\

ÆBPPJ;

(2)M(1)

[W1(1)4«=i,sl=«,=(j+n,W/=p

W\=[j«+£)»,

ân>2Ht,

PTWa„=S„-S„,=1[n2-(H-1)2]+1=n,

Ær=n(n>2,neN'),

XS^«I=1'^Ʊ^,

JW7>lx+nx

—W:

4

^1851

4

»,=-

"9

19.(1)|

Q

rwi(Dwoæmm.

(2)Mâo+MxawwwmTJ^.

[MJ(1)^B^P(A)=C'C^C;=1.

C!0J

(2)Xft5Wfi^0,l,2,

c'c14

p(X=2)=-4_±

^IO15’

ffiWBSWfiXlW^!l?9

X012

474

P

151515

474

E(X)=0x—+lx—+2x—=1.

v’151515

z^xHo-i)2_8_

15

20.(DÜE0ÆMW

13M,£18M

[frtJÎ1(1)«AC,W-Ï'jAF/IBE,BE1C,CMAF=2,AC=2VIFC=2AF=4,

BEIAC.MiiEW-BElYïEÎAC,C,B|1nWJBE1AC,;

(2)^JWW^FîOMEi/v^YÏBÎ^n<j—

fà*,BIJnJW.

[WKDim&fflF^,«AC,^ABCDEF-AiB,C,D,E,FlM

i£^2,

BH#AF//BE,BE±C,C.§.AF=2,AC=2VlFC=2AF=4,

XH^AF2+AC2=FC2,FT^AFIAC,FHUBE1AC,

ÈCC,IAC=C,KCC.MCc^SAC.C,FWBE±¥®AC,C,

XÈAC,c-Y-ffiAC,C,FyBE1AC,.

(2)M:OJW«CBF,BB,FrF-Û<]Ma>9A-$È.y$ùffiz$È,a±èl'B]

ÿnSF/5,

S^ŒÀWABCDEF-A,B,C,D1E,f;ÔÙFW^V'J2KÀ/,/V^IJ^CC„FE;nJW

B(0,0,0),M(2,0,1),A/(O,2>/3,1),E(2,2VI0),Ft(0,2>/3,2),

FrWBM-(2,0,1),BN=(0,2V3,1),BE=(2,2Ao),BF}=(0,2^3,2),

m■BN=2\/3y+z=0

i5¥®BME}NÉfà~'bfëIRJm=(x,y,z),WJ

m■BM=2x+z=0

^z=2V3,nH#x=-V3,y=-l>pJrl^/n=(-V3,-l,2V3),

n■BE=2x,+2A/3)’,=0

&YSBEF,W-^£rè]*^n=(x1

n-BF}=2y/3yt+2zt=0’

^z,=V3,BTWx,=V3,y,=-l,FrWH=(>/3,-l,>/3).

/\m-n(-V3,-1,2V3)-(V3,-I,V3)

FWcos(m,«)=AA=X----------------A--------------,

''|m||/i|4xV77

WifllBME,/VWffiBEF,0,WJ|cosB|=|cos(/n,n)|=,

JWLUsin#=\/l-cos2#=J1-—=——•

N77

JWBMENYJ-WIIBEFrrrôÆfôŒœ.

}}7

(2)iiEiÿJJJlfhW

[frm(1)

(2))|$|n]®^-{£^è>g(x)=ln(x+l)-(a+3)x+2î£XG(-1,4<»)±fmfâ,<?(*)

f#a+3>OHj-,g(x)Wft>UÈ^—^|^=a+4-ln(<7+3)g|JijEHJi.

[WJ(DS^/(x)=ln(x+l)-2x+x2ÈÛ^5!.^(-l,4<»),

JW[Uf'(x)=—î-j--2+2x=2X2-1

x+1

2

(2)S^/(x)=ln(x+l)-2x+x:

/(x)+2<x2+(«+l)x+bÆxG(—l,+oo).h-ÏH,

gpè>ln(x+l)-(a+3)x+2^xG(-l,-H»)±tHj^ïE,

'litg(x)=ln(x+l)-(«+3)x+2(x>-l).

15M,18M

MSI‘&91

nv

?

V8=c<7[fâ‘£

.q,/79l-c!-Difrl

‘l=V~TTÏ^I‘^TWEl(I)[O1

loiZZlCyc।

(oï)

i?WOWm‘(o‘E)’ÿ^o=<¥S^^®IW='£s£=*i^

•o-^-wo.,g■(_j(?6-8n)(^I>6)4?6-^£)(8n^»6)=Æ^_x

|j£-V6-J(_/6+t79)/96_/96

^smywwMWw

'96utyy^COIoCI•z'^/

¥‘(i+*);|=‘<^mywwrowr‘(oi^GrHvmiWEp

znhnn~q-z79i

‘kdaM^<£=^+ll=~^i^=ô=^‘1=^-^-#^^U)[>&]

(oï)^'BRgWOT(z)

8

l=—-£*■(!)’2Z

•(£+»)q-V+»<^YÏi^

(£+»)ui--|7+n

(£+t}

‘0>(^)/î‘-ffl|û9+‘—-sr^

:o<(-^)^‘-^lY+V~X~‘0<£+c,W

■^W‘WM^^3+-^(£