2023-2024學年北京市海淀區(qū)錦秋學校八年級（上）開學數(shù)學試卷（含解析）

2023-2024(±)JFWiS

-v*24.0M/h^iJtilaW^,

i.)

2.)

A.HiiMY5W<J$?B.xMM

C.H>WW3￡*D.

3.#n?,^h/?/??AAF?MWM

4.T?üisMO^^()

A.4a—a=3aB.a45?a2=a8C.a6+a3=a2D.(-2a2)3=8a6

5.BSOJESiO?,a,8,fioMS-)

A.24B.34C.44D.54

6.M,&AABC^,AB=AC,ZA=36°,BDY^zABC^ACY^,D,ED/

/BC^AB^^E,T?iJPW￡5i-ê:

?Z.BDE=36°;

(3)S^^W54"WH?^;

(?)AAED=ABCD;

A.44

B.34

C.24

D.14

7.2.3),'hW

^3^/ti^?.frumm?a?^j

A.SASB.ASAC.AASD.SAS

8.tin?,?éEA/4SC41,féiéCAS?F,f?fêAF=CA,t?fcAB^tiD,f?faBD=2AB,Si

iéBCS?E,&fêCE=3CB,MEF,FD.DE,%S^DEF=36,WJSA4BC^()

A.2B.3C.4D.5

8/J'gg,it36.054)

9.M,B&OE=OC,￡W“SAS”^MMAAOB=ADOC,

fcSWimft?____

10.a^lzAOE=30°,tiP&Z-AOBù<J|*|$P,OP=4,OA±W^AM,OB±f?—&N,'^iAMNP

AMNPlftW^

H.#nS,&RtAABCKAB=90°,E^JBCüL-^,EDIAC^-D,j&gAE,AD=CD,

^ABAE=20°,üIiJzC='

12.KJW-Km^?1986<m<2022,AüJ?éféWH?ft

W?'b.

13.BtolOa=2,10b=3,WJ102a+3b=..

14.AnS,-WjItt?H?fé't',z/l=60°,Z.D=30°,zE=Z.B=45°,

WMAMCféJfêAuS^?^Sta.Bü^AC^,±L0°<

/-ACE<180°,n^üi=?JfMDCW-^ià-WWWW^?CEWJW

15.Ans,△4EC4>,zE=90°,AB=12,BC=5,1ABp

TA?,￡E,D^^^AB^mAP±.&^],Xti&W&DE=AC,D

'^^ABC^hDAE^,WMEW-lé^.

AEB

16.AnS,?AK^OAbH1,^,M5XJ0lW^i5°,Ma5XJsXlW^i5°,

?fêA?0atBSAoAb,

Hx*58.0#o

17.(*/J^16.0^-)

i+g:

232425

(l)(a)-(a)4-(-a);

(2)(2x+5y)(3x—2y)—2x(x—3y).

18.(*/b^6.0:fr)

AUS,?U4>B.C,DlE—M^±,EA//BF,EC//FD,AB=CD.$<.&?.EC=FD.

EF

ABCD

19.O'bJ^?.o#)

Dffi?,&?F±&-?P,D.

?,?tBjJt?#MSè.

(2)$n?2,?zylOf?rtafWra^M,N,fè&fcOA,OB±Mfa&tiE>F,f?f?JE,F,M,

N,HaMwraimw^ié?,&tBE.FM,wm

20.($/h^6.0$-)

jfeffl,BfrlA??C^iiH?JI^,DE1ABT&E,DF1ACT^F,BE=CF,^iiE:

(1)ABDE=^CDF-,

^AD^BC^JM^^.

21.G￡/h^6.05>)

^W+?x+sMiMM?,

+X2+6X+9-1;

PjSJsto^JH>t^￥^^?^W?lJ:(X+3)2-1;

fik￡MiWSW^i2,ilbnWé￥^^?t(x+

3-l)(x+3+1)=(x4-2)(x+4).

(l)05Wi?:X2+Sx+6;

(2)0^^-^:x2+(m+ri)x+mn.

22.(WS8M)

(?)I'?IOTM:frlffl?,B&AABC+,/-BAC=90°,AB=AC,OW?fctaA,BDIjg^

m,CElOm,E,>ffi:=+;(fflBD,CE,DEtfi

?)

(2)ffi^M:&J?@,^(1)4>èü^#^3:?AABC4>,AB=AC,D,A,

i&mk,#E/ft/.BDA=^AEC=^BAC,i^sRMWF,BD,CE^.^^]M^,

(3)^&ffl:?AXC541,z>4CB=90°,AC=BC,^Caù^S^J(-2,0),

23.(*/bIE10.0#)

SnBfl,?ABC^iil^fiii?km<zAC^^,D,^^D^k&BC^^^i^E,

^,F^CF=CD,&&CE,EF,BE,AF,ü^AF^^CET&P,^BE^^ACk

tiQ,i?fêPQ.iWW^SJf^^IJWTACPQ^W,

A

A

BC

1.[?]D

(W)A,B,M

iW^TO?fflM?,fi?-,

DW?WOWK-mWMMt,IMW#trai￡.

M:D.

I?mO5ffllt￡(ià^TOnqm^?^

ia&?êfenqw^mWlf?BP?i?.

twwraowmii,mraw?ri?nTS-ê-.

2.[^]D

[Wffil??:?i§?￥WI4^W:

D.

??T^WtWlI?,??A￥^W^iJ??Sè<)rtMI￥Mèù^,&jS:

3.i^aiD

(mrl[^IJi]

OM±jg

?^lHJa^^a.WWWaj'/?^n,i?*B^cüi±?ùi^.??M,MI'^^BEMAXSCWIW.

[W^l

W:??fflnTW?MBF>A?1BCéI<J?WK^DM.

M:D.

4.[^^1A

[WtJr]W:A.■■■4a-a=3a,c^?J;

B.-.-a4■a2=a6,

C"a64-a3=a6’3=a3,

D.-.-(-2a2)3=(—2)3?(a2)3=-8a6,

iftjf?:A.

A.W^R^WKIJ:iaw^;

WèO;

C-MTO??OM,

D.^WW^On+l?,TO!^W?#OJi+MBPnJ.

*^±g?T^5W^i??,^ùW

^W'éKJ<￡FOJ.

5.[^fé]A

imir)?:=^=iiK^W'j3,a,8,

??■8—3<a<8+3,H|J5<a<11,Ha^Wi?,

???9,

??■H?^Siàié^-?J^3,7,8A￡3,9,8,

A.

t?igH?MB[JnTsRW?

6.[^]A

[WJ?:"AB=AC,

■■■/.ABC=^c=-AX(180°-zA)=|x(180°-36°)=72°,

??■BD^ft^ABC,

??■￡ABD=/.CBD=36°,

vDE//BC,

;.tBDE=JLCBD=36°,W(?)lEfà;

7/.A=^ABD=36°,

??■DA=DB,

■.^D/EAB^:^^±.,W@jEta;

7^BDC=ZA+^ABD=36°+36°=72°,

.-.zf?DC=ZC,

???BD=BC,

VDE//BC,

/.AED=/ABC=72°,/ADE=/ACB=72°,

/AED=/ADE,

AE=AD,

■■■/.ADE,/ABC,/BDE,/ADB,△BCDM^^fijf?,0flU(3)jEfà;

￡A?ED#ABCD^,

/A=/CBD

AD=BD,

./ADE=ZC

■■■/AED=/BCD?ASA'),JW(?)1E^.

A.

pBtWtlU/lBC=zC=72°,

WftJ^Z/IflD=/CBD=/BDE=/.CBD=36°,/AffijW?@iaOlJ?T;

7.B

[Wtlf]W:1>

i,

ft^ASA,

ifeia:B.

,eià3±A^^4>W4^1$^|J??^|J

S5S,SAS,ASA,AAS,HL.

8.[gmA

LWtfrlW:inS,&&AE,CD,SA

VBD=2AB,

■??AFCDf?W?Wm,A?CD?'J?WJj3m,

???AC=AF,

.-.A4DFf?W'=A4CDèW*R=3m,

vEC=3BC,

???AEC?a-J?W,=3m,AFDCf?E&=6m,

"AC=AF,

.-.A?EFéWH=A3m,

??■AZ)EFéKjjE?W=m+2m+6m+3m+3m+3m=18m=36,

???m—2,

.??A?BClWlWv2,

A.

M,i?fê/lF,CD,

nJWA0EFOlWjl8m,nJW-

?SfêO

9.[^1OA=OD

(WtJflW:?>ft-O/l=OD.

Sè:?A/WB=ADOC^I,

OA=OD

tAOB=Z.COD,

OB=OC

.-?AAOB=ADOC(SAS).

OA=OD.

M^/.AOB=/.COD,%V),“SAS”MWàAOB^DOC,

10.4

[WW)JS:^P^n^OA^M^.C,frPXT&&OBfàXtfa￡D,&&CD,^AB^M,^tOB

T/V,K01ttl^APMWé<jMIK?/J>,iêfêoc,OD,

;.CM=PM,PN=ND,/.COE=/.POE,/.POF=/.DOF,OC—OP-OD-4,

?:/.POM+Z.PON=/.AOB=30°,

/.COD=/.COE+/.POE+/.DOF+/.POF=30°+30°=60°,

???△COD&giàE.ftf?,

CD-OC-OD-4,

BPAPMVf?^4￡a<jft<hO:PM+MN+PN=CM4-MN+DN=CD=4,

4.

'&&CD,3EABTM,?EOB^N,?ijllt

0\|'A/’M/VaùJWiéft'h.i?fêOC,OD,TOW'Mf?tBCAf=PM,PN=ND,/.COE^POE,

/.POF=/.DOF,OC=OP=OD=4,^HUCOD=60°,MLHACOD^&^fiiM,ffi.T.CD=

OC=OD=4,PMN^^i^^^PM+MN+PN=CD,RàHPnJWtEl^.

/V?WM,Bsttm?,

11.[^135

t?^&MW^IéM?ljEA=EC,m^EAC=^ECA,

?BT.

[?]

W:???DEA.AC,AD=CD,

??■EA=EC,

Z.EAC=/.EGA,

/.EAC+Z.ECA+/.BAE=90°,

m,zC=35°.

35

12.11

[ftWl1W:^4’1’aJati^^jx,-1,Mffi—4^x+1,

1986<x—l+x+x+l<2022,

W-W;662<x<674,

x^663,664,665,666,667,668,669,670,671,672,673,

il.

?ijM-^x-i,JH?I-^^JX+I,

W1986<x-l+x+x+l<2022,RT.

ü,

13.[^1108

IWrl[##T1

R|?￥SW&WaW;mfifWBPnj.

[W^l

W:???10“=2,10b=3,

.-.io2a+3fc=102“x103fc

=(10“)2x(lO*)3

=4x27

=108.

14.45°,135°,165

[|?Fr]IS:%^-ACE-ZE-45°B'?,AC//BE,3è$UT>MJ3^:

???Z?CE=Z.DCB=45°,ZE=45°,

???BE1CD,

XvAC1CD,

??AC//BE-,

^ACE=135°nt,BE//CD,SèfrlT,

???ADCE=135°-90°=45°,

???ZE=45°,

ZECE=zE,

???BE//CD-.

az/ICE=165°0^,BE//AD&èifeT:

5?OCXEE?E,

V/.ACE=165°,

/.ECF=15°,

vZE=45°,

zCEE=/.ECF+/.E=60°,

???/.A=60°,

■■■AA=/.CFB,

BEUAB,

=^^ADC^—^^EB^T^^/yiCE^J&^:45°,135°,165°.

45°,135°,165°.

?f?TOaùHRT.

MWTTO*￡?^iJ?,￡MdTO^?^iJ?W.

15.r^'^15^12

[Wffilfr?:?■?DE=AC,

.-.g{éA?BCWADAE±^,H

.-.AE=AB^AE=BC,

.-.AE=5alU2.

5^12.

16.[^]120

[WW)W:zkn^?'f?l/jV.-

■■^?im^^U360°,

15n=360,

mn=24,

x24=120(^),

120.

W?à-fe.

17.W:(l)(a2)3?(a2)4-e-(—a2)5

=a6?a8+(-a10)

=a14-r-(-a10)

=—a4;

(2)(2x+5y)(3x-2y)—2x(x—3y)

=6x2—4xy+15xy-10y2-2x2+6xy

=4x2+17xy-10y2.

[wwi

(2)?i+M^S;?W'/i,

W^^?<]jgW'/￡wyêW^?<]?.

18.iiEHJj:-:EA//BF,EC//FD,

:.Z4=Z.FBD,/.ACE=/.D,

??■AB=CD,

.-.AB+BC=CD+BC,

H[UC=BD,

&&AEC??1ABFDfy,

/.A=/.FBD

AC—BD,

tACE=tD

■■■^AEC^ABFD?ASA),

???EC=FD.

[WWlè￥?T^aü14^f#z?=±FBD,^ACE=/.D,^.AC=BD.^^üEAAEC^a,BFD(ASA'),

WWHiéètè.

19.[^^1M:(l)?Ulil^,?J’HP^J^;

(2)^?24’,&E,F?M.

[MFr](l)?AC^Sa&4Bf?#W^O^C'&4B^?P,?êfêPC,CD,^PBP^J^;

(2)ft^f04f?OaM'-AN^OBlW^AAr,&f?M'N'$.0A5tiE,^OB^^F,i￡

f?EM,FN,MN,&E,FBP^J^.

20.[^]iiEBJJ:(1)V/IDMA/IBCW?T^,

.-./.EAD=^FAD.

??■DE1ABT-&E,DF1/ICT^F,

A<LAED=Z.AFD=90°.

&A?E￡>^A?FD4’>

￡EAD=tFAD

/.AED=/AFD,

AD=AD

.■■&AED^AAFD(AAS').

ADE=DF.

■■DE1ABT&E,DF1ACT&F,

■■■tBED=/.CFD=90°.

?EABDE^WLCDF^,

BE=CF

tBED=/.CFD=90°,

DE=DF

■■.&BDE=&CDF?SAS).

(2)■;^AED=AAFD,

:.AE-AF.

XvBE=FC,

:.AB=AC.

fè.AABD#\AACD^,

AB=AC

/.BAD=S.CAD,

AD=AD

■■AABD=AACD(SAS).

AzJBDA=ACDA=90°,BD=DC.

■■■AD%BCtfj*&&.

[Wtlrl(l)f?^lAS?iE0JjA4EDsA4FD,=DF,faJsWfèSAS

ijE^ABDE=ACDF^nf;

(2)&ijEHW=AC,??fsWt?SASilWUABD^ACD,=

zCZM=90°,BD=DC,

21.[?^]JW:(l)x2+5x+6

2,r.2525,,

—x+Sx+-------r+6

44

=(x+l)2-?

_rJSJIW_L5

(X+2+2^X+22^

=(X+2)(x+3);

(2)x2+(m+n)x+mn

22

,z,x.(m+n)(m+n)

=x2+(m+n)x+ù—---------^-L-+mn

2

.,m+m-,(m+n).

=(x+-y)--~4+mn

2

,,m+m(m—n)

=(x+—)72-----—

=(x+^y+!y)(x+^y-^y)

=(x+m)(x+n).

[OrJ(l)?,

22.[^M]ft￥:(1)DE,BD,CE-,

(2~)DE=BD+CE,

üEHJ1:&A?BD+1,/ABD=180°—/ADB-/BAD,

v/CAE=180°-/BAC-/BAD,/BDA=/BAC,

:./ABD=/CAE.

f?./ABDft\ZC?E1^,

/ABD=/CAE,

/BDA=/AEC,

AB=CA,

:./ABD=/CAE?AAS),

:.AE=BD,AD=CE,

.-.DE=AE+AD=BD+CE-,

(3)?S?Wfà>'J(l,4).

?-WJ

(l)ilF.I!JjA/16￡)SAC^E,