2023-2024学年重庆市南岸区文德中学八年级（上）入学数学试卷（含解析）

2023-2024(±)

-x(^±is#io/hgg,*40.0^0Æ<<hl^mW3i+,IÆ)

i.«/bM»()

A.-<7B.1C.-3D.n

2.T?iJîê^lE^W<()

A.(ah3)2=d2bbB.(a2)3=a5C.a2•a3=a6D.a3+a4=a7

3.A

«Æ'bElMM-/\

KiJÆEfetÈ^ÆAÂBCC)/____________AC

B"

A.

B.

C.

D.

4.^ÆTJÜ^IW,UBC^mHWX)

A.Z./1:ZB:ZC=3:4:5B.AB:BC:AC=3:4:5

C.AB=\PÏÎ’BC=4,AC=5D.z4=40°,zB=50°

5.ABUCD,FELDB,SÆ>jB,Z1=50°,51iJz2Û<BgM()

A.60°B.50°C.40°D.30°

6.m-^ÆB

Ki<âW^^/A

|C150>-190°

()

120

B

7.

fflTi4»fê,^@4-®MfflTi9tg^,....m»OJT

-i,)

A.39B.44C.49D.54

8.ftü-<7«8+<ÏÔ)WffiÊÆ()

A.7W8±|H]B.8fn9±|H]C.9moZ|0]D.lOmiZl'â]

9.ftlffl,faEfifîtABCD^,,ftE,Fft%të.BC,CD±.,'&&AE,AF,A

EF,Z.EAF=45°.^Z.BAE=a,KU-FEC—fë^f-()\\

\/F

A.2a\

B.90°-2aC

C.45°—a

D.90°-a

10.-y-z-m-n^'t'x>y>z>m>nyV,

^/siafî-é^^aiëW-,“*Ê>O-

.#!]£[]:x—y—\z—m\—n=x—y—z+m—n,\x—y\—z—\m—n\=x—y—z—

m+n,....

M+Oôô<Jt^()

A.0B.1C.2D.3

($±^*8/]^,*32.05»

II.WêÈOHÈyjWÆ.-----

^Æ2023^FWfêlO-£0.000000028m(28nm)I^H!feW^7tOL,M

+M0.000000028fflWiB1&fëW^

12.ifM:V~32+V8-|TT°-<1|-(i)-1=.

13.ÜIiJxâÜM^S^,___________________________________________.

14.foWMMtMio,

5050,WfôWfc,$£'h&ÜWilW’

15.ÎÉËÆt△ABCb,zACB=90°,BC=4cm,CD1AB,&AC

±^~,&F,fëEC=4cm,ftAFftEF1AC^CD^J^^

^F.fëAE=1cm,piijEF=cm.

16.

cm.

17.ftlin,ÆùÂfiCtb,AC1BC,D&AB1.—&,S.CD=AD,F&

BC'fëfc&ê.l.—ti,CF=^DC,Z.DCF=120°,^^DF^ACTE,

AE=24,PliJ^aCFW.

18.fâ£âb-bc=cd’

“iMMÜf"-Wn:0fôi(4129,•••41-12=29,.-.4129^“^^”;

X$D:Hfëi[5324,•••53-32=2124,•••53244^“iMMSk”^Ja312-

H.ft?g®8/Jxgg,*78.05\

19.(*/b®8.0^)

JWTWStâ:

p(y-2x)+4y=2x-1

1J(2x+5y=7;

p+1_2y—2

(2)|2~3

(2(x—1)+3(y+2)=5

20.(MlO-Oft)

7t+h|H],[(x+2y)2-(x+y)(3x-y)-5y2]4-(-jx),M:i+'x=-2,y=|.

21.(*<hmo.o#)

MIMWW“W”lOmomTOlOm.gtif

■iw»;13«+»M,TÏBÏ0<J:

(i)Æ^«§b4,(«^“M”sg);

(2)^W^^JKÔÙI;J4'^WÀ.wmi-s4'7nmm____;

“100<x<110”+

A^lOig^ÊÈ4IWIOMXl£jâfj-W'&,M—JIÈMXiWIfêtt+11|sj,üJiJfè^îÈïiJ

_____;

(^M^W^J^^IOOOO^,RiJTO<^7U^Wi£i£“70<x<80”

_____X.

7^TiWX£iWll'.n-f-£

owm

A:60«t<70

B:70SK80

C:80s=t<90

D:90«t<100

Esl00s=t<110

#11®,WJfW=AD=26m,BC=16m,CD=12m,B.BD=20m.

(l)îiWJ3:£BCD=90°

(2)^Kià^E(|SJ1W)|'|<J[MH-

23.($/b®10.05>)

ÏËMy(fcm)tpWWJH'tl'B]t(h)Z1'0]Ô<Ja#11®P/f.

(l)/k-T-^,ZÆttqa^SiJ.___________'W;

^R3,jRtÛW.

24.O<h®10.0#)

3+2/1=(1+/I)2,#T®^WY«JJjSfïT^T^:^i&a+/>/"2=(m+n/3)2=

m2+2n2+b.m.WJWa=m2+2n2,b=2mn.&W/hBJI«ft

iOOT-M«a+bj2iHTOfl^bBJl

inlM:

(l)3aa+b^TÏ=(m+n/3)2.Sa>b.m,n.Bj/^^lll',ffl'ê'm,b,

fà:a=,b=;

(2)^^T?Üfê^:

®74+2/3;

@V7-2/3Ü;

(3)J4->T10+2/3+J4+V10+2/3-

25.G£/hmo.o#)

ftRt^ABC^,z4C£=90o,Z.4=30°,BD&A.ABCtt]ÆYM»DELABRE.

(1)M1,'&&CE,

(2)$nS2,àMÏjCEt—^BM,^HlùBMN,&fëEN,jRŒ;EN//BC-,

(3)^n®3,àPïtëZ&ADt-£,ï&%BP,frz.BPQ=60°,PQ^DE^^Q,^K^PD,

DQ^ADZ^^I.^^,/HJEHJJ.

26.($/h^lO.O#)

£nS,M^ABCD#,AC=AD=AB,^BAC=90°.

(l)jEAfîCDiWIWfOJABCE,ü^A^AFEBE,£8JsF,^ijE:BE=2AF-,

(2)i£(2)fô&ftT,&&DE,WMABCD^jm^45,AD=5<7,BC=10,

1.r^]c

[JOf]ft?:'.•<^<3,

-3<—/~2<1<TT-

ï&jît:C.

W»MXItSWi-B|J«T.

JE«TO,

ÉKjOvh.

2.[gmiA

UWlW-:ÂM:(ab3')2=a2b6,

(a2)3=a6,i^i&IJÜ'FJ'ï'â’ISB;

Ci&B/î:a2-a3=a5,

a3+a4a7,

ÜJâ:A.

»J®igWHé^risWJèWJ»WâtJ^TTisM^WJ,|H]WWJlUZt-â-(s)WJil—

^IJWTBPPT.^ÛWW>MJïïrrWW

JWfflJJn.

M«T|ËJ«ff6<]^i4,Witë^isg&WJWg

3.[^]D

[w^]W:

D.

w^MMWâwtÉ^imPRr.

4.[^1A

[OÎJM:A,vX.A-./-B:Z.C=3:4:5,Z4+ZF+ZC=180°,

•••z4=45°,ZF=60°,ZC=75°,HPAABC^&ME-fiiM,

B,'&AB=3x,KljBC=4x,AC=5x,

•■•(3x)2+(4x)2=(5x)2,

.■■ùABC^MEfiW,

C>42+52=(VU)2,

D,•••z4=40°,zF=50°,ZÂ+zF+zC=180°,

.-.zC=90°,BPA4FCMÆHÆ^.

A.

5.C

[W4Jf]W:^SJ9r^,

VFE1BD,

:./.FED=90°,

•••Z1+ZD=90°,

vZ1=50°,

•••zü=40°,

vAB//CD,

:./.2=/_D=40°.

C.

^tHzD=40°,MOTOMiPOg.

(»]W:=i

ÛOUû

C.

BÊWWttW)

%L.

7.[^£]B

[OrlW:ÈfflnJW,S^©W:4+5=9mzb^#>

SM@W:4+5x2=14</h*W,

®^(3)W:4+5x3=19|R/b*#,

(4+5n)^/b7K#,

•••M®M^W:4+5x8=44114

SJdâ:B.

8.[^]B

[WIJT]W:^^=4+2^.

v2.52=6.25,

.-.2<\T5<2.5,

••■4<2yT5<5,

.-.8<4+2V~5<9.

«:B.

+2<5,i+Wttj2<v~5<2.5.>FiJffl^W^WWbWWÆtK]

fê®.

*^Wi+W«tW79W>«TM^MfôW,

'h:£»im®ffWWÈ<J^.

9.A

[Or]IW:&JE7ÏÏÏÏABCD^,AD=AB,/.BAD=^ABC=AADC=90°,

^•A4DF^ÆÆll!W't#fô^90o,'fâ&ABG,

JU0/1F=AG,ADAF=^BAG,

/.EAF=45°,

•••/.BAE+Z.DAF=45°,

.-.Z.GAE=Z.FAE=45°,

ÏAŒfilAFAE'P,

AF=AG

Z.FAE=Z.GAE,

AE=AE

•••AGAE=AFAE(SAS),

AZ.AEF=/.AEG,

/.BAE=a,

•■/.AEB=90°—a,

Z.AEF=/.AEB=90°-a,

ZLFEC=180°-zAEF-/_AEB=180°-2x(90°-a)=2a,

:A.

=AB,/LBAD=tABC=^ADC=90°,^A^90°,

^■ùABG,^iiEAGAE^AFAE(SAS),WnTWz/lEF=/.AEG,

AFEC=180°-£AEF-£AEB;W$ÿ]lnf.

10.(^1c

[fô?#rlft?:\x—y\-z—m—n=x-y—z-m-n,féifeü(î)IE^.

^W4^1#i5ïl,^SÜZEIX-y|—z-m-n=x—y-z-m-n-,x—|y—

z\—m—n=x—y+z—m—n-,x—y—\z—m\—n=x—y—z+m—n-,x—y—z—\m—n\=

x-y-z-m+W,^W3^1#Î5£,^®J^|x-y\-\z-m\-n=x-y-z+

m—n-,\x—y\—z—\m—n\=x—y—z—m+n-,x—\y—z\—\m—n\—x—y+z—m+n.^

W7^'|'tW?5t;

7

7

‘o<i+%z:W[-IO1

1~<XTl

•®:1WlMWOWTO'SWè'Mî'HWO»

‘ZJ'-Z=

£—I+Z_/-—Z+Z_/fr=

£-(l-ZjO-Z+ZJM^=

£-|Z_^-l|-Z+Z_/^=

i-(|)-lz_/-o“l-8A+Z£_A:iW[J-^W]

U"£(M&JTI

^-®W^W^EP^U‘OT>l»l>Trf.M‘u-0lXü^x»_

■g-0lX8'Z:¥W^V

!

•8_0lX8Z=8Z00000000Mt-*/+iW]

g—01x8'Z[W^j‘H

w

•w^wri*‘WM®

•J:W

•^^^±©w-w

OrœWMWmW^tBxâWWffil.

14[y~>'1\x~y~10

11J*J((lOOx+y)+(lOOy+x)=5050

(WWJW;fô'blftffi'fW^y,

WSB,^{(100x+y)+(100y+x)=5050'

~y=10

XÿR/J((100x+y)+(lOOy+x)=5050’

MffitëW©îW'bWWlttMlo,

@100x+y-^îlOOy+XÛ^WTB5050,W.

»tti“fô/b6Wà

WïiJ-'bHfW^iooy+x”,

t&Æii,'bElfëS^lOOx+y.

15.[#£]5

(WWJW:"CD1AB,EFLAC,

••■AFEC=<LADC=AACB=90°,

•••Z.ACD+Z4=^ACD+LF=90°,

•■•z4=zF,

vBC=EC=4cm,

ÆAÂBC^AFCE^,

Z.ACB=/.FEC

LA=LF

BC=EC

:.^ABC^txFCEÇAAS),

■■AC=FE,

■:AC=AE+EC,

:■FE=AE+EC,

•■•EC=4cm,AE=1cm,

■■FE=4+1=5cm.

5.

ÉCD1AB,EF14C,tftWlUMf£UFEC=^ADC=90°,,?JCWA4=ZF,A4EC=AFCE,

iïtëîEF=4CMfWi£.

WiOH:O£^:m

16.<89

ræw]w-.

vlé^^J^WÜbc^cni,~^^j5cm.

■■AC=2x4=8(cm),BC—5cm,

•^»JlWÉfiWÆ?^4S=VBC2+AC2=V52+82=<89(cm);

•••i£;6W&ÏÏÏIîà4x;Mcm,W^j5cm.

■■AD=4cm,BD=5+4=9(cm),

.•Mtëfï=VAD2+BD2=V42+9=<97(cm),

.-.<97><89,

•••fflîM^TÛÜtW%h/~89cm■

<89-

fë.

17.8

[WtJrlW:xt&DftDHEAC^fcH,

"AC1BC,AE=24,

•••ZECF=90°,

vZ.DCF=120°,

Z.ACD=30°,

DH=^DC,

•••CF=±DC,

•••DH=CF,

ÆADHF^AFCE<^,

Z.DEH=<cFEC

Z.DHE=Z.FCE,

.DH=CF

■■àDHE=àFCE(AAS),

•••EH=EC,

"AD=CD,

■■AH=CH,

■■AE=3CE=24,

CE=8.

8.

iAC^&H,1BC,/.DCF=120°HJ’WÜZ.4CD=30°,=|DC,

$iJJTlÆ4S)ÈïlnrWtHADHE=AFCE,^_EH=EC,=CDnT^fWW=CH,fenJWHd/lF=3CE,

,

aïïnWH1Éëv&.

18.43128165

IWtlrlW:È^^nTWlOa+3-31=12,

=4,

.••^^4312,

10a+b—(106+c)=10c+d,

ôJWlOa—9b—11c=d,

100a+10b+c+100b+10c+d

=100a+10b+c+100b+10c+10a—9b—11c

=110a+101b

—99(a+b)—lia+2b,

l&,

•••lla+2^^lk,Ka*b*c*d,1<a<9,1<b<9,1<c<9,0<d<9,

9n

a=9Ht,iftntbR^Mxo,

^a=8Ht,b=l,JW71-llc=d,

cJft9Bg8B't,

^cJÏX7EI't,d=5,

.^Æ>ftiWlftft;MtM8i65,

4312;8165.

ftiMîM^ÛW^^10a-9b-llc=d,

Éê^n^9g|^ÉI<J^âWîÆ^^Æ^^â<J>>c{S.

19.[»]W:(l^^^gaft^lSW:

(Sx—7y=1(T)

[2x+5y=7(2)’

@x4^;8%+20y=28®,

(3)-©^:27y=27,

WW:y=1,

ÎEy=lKÀ@+W:2x+5=7,

WW:X=1,

{*ZJ:

(3x—4y=—7©

(2x+3y=1(2)

©X3W:9x—12y=-21(3),

(2)x4W:8x+12y=4@,

@+@W:17X=-17,

WW:X=-1,

$Ex=-lftAf^+W:-2+3y=l,

WW;y=1,

mœœmœW:[?*"?'=J?,Mi+W«î

(2x+5y=7(2)

(2)W.WmWSW:=afri+WW^

(2x+3y=1(2)

20.W:[(x+2y)2-(x+y)(3x-y)-5y2]4-(-|x)

1

=[x2+4xy+4y2—(3x2—xy+3xy—y2)—5y2]4-(——x)

1

=(x2+4xy+4y2—3x2+xy—3xy+y2—5y2)-?(——x)

1

=(-2x2+2xy)4-(-—x)

—4x-4y

^x=-2,y=|nt,

1

]^=4x(-2)-4xi=-8-2=-10.

W^x,yâ<JMKÀifMnJW.

21.2002512500

[wtfriW:

g,

ÏÈW«;

(2)^:804-40%=200(A),

Pify1-10%-5%-20%-40%=m%,

77

‘(z^)96=Zlx91x-=Qj•jg-=OJffVÇ

7aav

‘(Z“)otz=vz*oz=3v-oa-=*s■■

*OHz=gOi-z9ZA=zaa-zavA=av■■

*^9Z=av‘^sawitr#

•7

‘(w)oi=oa-=ao=sa•••

‘ov=av■■

‘□06=d3V7■■

n3

‘aïs-ïoaT

:o06=aja?‘^=n^oja?•■•

‘zoa=z03+zja■■

‘00t=z0Z=zGff‘OOfr=zZl+z9T=ZO3+z3d

v‘iuoz=oa‘UIZÏ=O3‘Ui9ï=3a‘4JGJSV5E(I)7Z

•MrlaWYxU^-H¥}%sz^WY^W^WY^os>?>ozrhYM»W

‘^Y£j0«^WfH^Ià[lS‘%0W$^WWW08W^06>?>osâfâtfz)

!^WtlXÉdOOO®^>W#W:ÉWWW^MWMT)

•oosz

‘(Y)oosz=%szxOOOOT

«08>x>oz„WWW¥¥mfvt®‘^oooor^WW^Gû

g

!|

<s_oi_.

z~V-d■•'

:sz‘ooz

‘SZ=WoSZ=%^FILÏ

~S^ABD$&BCD—24096—144(m2).

HÜ/WK(PBfO^)Iftffl^^l44m2.

[OîlÈ^JSÆSWîÉÆSilE#AFCD^<AHÆ^,W^W-zBCO=90°;

(2)hM^/lE1BDTE,MW3XfâAE,ÉHMWÆ

J-'^91^1^^480^^ùBCD’WIJJ•

M±^«TWjëawÆaifttëîffl,Æ^m$fSmiOA

ÉPl^l.

23.3001

[WJW-:(i)È@Mfê.A,BïWWR£Ë300^?K,ZÆtkW^-ïiJ5-4=1(/W)>

300,1;

(2)iSi$M?fÂ^â<]£ËMy(fc7n)^^$e^KBtl'0]t(h)±l'B]WaMtfr^y=kt+b,

W(l,0),(4,300)RAW:

(k+b=0

Ufc+b=300’

Ci

=100t-100;

(3)lllSfUOl,?fîtM1300+•5-ÔOC^X/'JO,

3EPïÉEzL^f-?K4O-T-^0't,60t-(100t-100)=40,

mt=|,

âZÜÉE^HlT40TXBt,(lOOt-100)-60t=40,

mt=-7,

^iw^fflSE4or->r<R'j-,

(l)ÉSWW,/LB^WBÏfl300^-X,^^Lt^WïlJVbnt:

(2)iâZÆ&MMytbn)!?EP^fî’5^ÛWrB|t(/i)^|'H](Kj®WtJrMy=kt+b,W(l,0),

(4,300)RÀ^#®Mt)Tj£?9y=lOOt-ioo;

(3)ÉSIO,¥WMM300+5=60(^HQW).^tpÆ2L^40r-W,60t-

(lOOt-100)=40,âZdÉEEPlIUO^XBt,(lOOt-100)-60t=40,BPWWtâW>vf^.

fféîEmm

24.m24-7n22mn-\T7

[iWlJr]W;(1)•••(m+n-/~7)2=m2+2mn\/~7+7n2=a+byj~7,

a=m2+7n2,h-2mny/~7,

m2+7n2,2mny/~7;

(2)®1MÏU(<3)2+2xT^x1+l2=(<3+l)2=+1:

J(>f5)2-2XV~5XAT2+(V~2)2=J(y/~5-JT)2=y/~5-yT2i

=4-110+2V~5+210+2^~5x4+110+2V~5+4+J10+2\T5

NA

=8+2

=8+2

=8+2(V~5-l)2

=6+2V~5

=(<5+l)2,

(V^+1)2=<5+1-

(l))W(ni+nxr~7)2'lt^Jm2+2mny/~7+7n2SP«J:

J(<3+l)2>

J(Vs-7-2)2,IWÆW»BPoj;

T-MBPÔT.

25.(l)iO:•••^ACB=90°,z4=30°,

.-.tABC=60°,

vBD^ùABCffj^^^,

•••ADBA=^AABC=30°,

AA=ADBA,

•••AD=BD,

■:DE1AB,

AE=BE,

CE=^AB=BE,

.■.ABCE&&ÜL=fijJ&;

(2)ÜEHJ1:"ABCE-^A

•••BC=BE,BM=BN,AEBC=AMBN=60°,

•••ACBM=AEBN,

#ACBMfflAEBN^,

BC=BE

ACBM=AEBN,

BM=BN

.■■ACBM=AEBN(SAS),

ABEN=ABCM=60°,

ABEN=AEBC,

:■EN//BC-,

(3)W:DQ=AD+DP-,

ÜEHJJ:M-fefiDSF,^DF=PD,tëtëPF,

VAPDF=ABDC=AA+ADBA=30°+30°=60°,

■■APDF^Ül^^,

•••PF=PD=DF,AF=60°,

•••APDQ=90°-AA=60°,

•••AF=APDQ=60°,

ABDQ=180°-ABDC-APDQ=60°,

•••ABPQ=ABDQ=60°,

AQ=APBF,

^EAPDQ^ÏiAPFB^,

(APQD=/.PBF

Ï/.PDQ=/.PFB,

\PD=PF

•••△PDQ=&PFBÇAAS'),

DQ=BF=BD+DF=BD+DP,

AA-/.ABD,

AD=BD,

.-.DQ=AD+DP.

[MtJf=60°,=/-DBA,ijEtH/lD=

BD,=BE,=

BE,

(2)