2021-2022学年河北省唐山市某中学高二（上）月考数学试卷（10月份）（附答案详解）

《2021-2022学年河北省唐山市某中学高二（上）月考数学试卷（10月份）（附答案详解）》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2021-2022
ᓅḕᖆᓭᨴὃᦪᔁ10ᨴI.ᑡḄ!A.ᓫ$ᔣ&'()B.+ᔣ&,-Ḅ(.ᔣ&/()C.1|3=|5|,78,9Ḅ:;()<9ᔣ(=ᡈ(.D.1.,5!(.ᔣ&<ᑣA=|1|2.ᑡᩩE/3=0B.x-w-2-473=0C.V3x+y+4-2V3=0D.x+V3y-2-4V3=05.z{ST/NHO42,3,1,_ᐗ=0,1,1eᐸ~9ᔣᔣ&<ᑣOP4,3,2ᑮST/ḄeA.—B.-C.—D.V22226.z{ᩩSTkax-by+4=0,la-lx+y+b=0,lbx+2y+a=0,231%<_<2஻b<ᑣa+b=A.2B.4C.2ᡈ1D.4ᡈ17.ᙠABCD-<4A1☢ABC£>,AA=3,☢!:e4Ḅr<_NZMB=60°,ACQBD=0,E!஺⍗ḄO<ᑣOEᑮ☢OiBCḄeA.2B.1C.-D.328.1ST<+<=1NOMcosa,sina,ᑣA.a24-h2<1B.a2+h2>1C.+1D.+1a2b2a2b29.¢kᑡ£⚪<ᐸ!¥£⚪Ḅ!A.1ST/Ḅ9ᔣᔣ&¦=1,1,2,ST§Ḅ9ᔣᔣ&5=2,1,-¨<ᑣ/,ᚖSB.1ST/Ḅ9ᔣᔣ&Z=0,1,—1,☢aḄᔣ&ᐗ=1,1,-1,7

1C.1☢a,ªḄᔣ&ᑖZe«=(0,1,3),C=(1,0,2),ᑣa"D.1☢a¬NO4(1,0,-1),B(0,l,0),C(-1,2,0),ᔣ&ᐗ=(1,%t)!☢aḄᔣ&<ᑣu+t=110.ST/N®O<ᐸlcmea,¯ST/°ᙶ᪗®O³⌮µ┐9ᔣ·¸45஺<¹ᑮSTkᑣST஺Ḅlcme()A.a+45°B.45°-aC.a-135°11.ST¼<%Ḅ9rᑖZek½x+ay+b=0,lx+cy+2d=0,-¾ᙠᙶ᪗¿Ḅ$À᝞ÂᡠÄ<ᑣᑡÅÆḄ!()A.b>0,d<0B.b<0,d>0C.a>cD.a

2D19.çNO4(1,4),_ñò×Ḅóèä()ḄST9r(ᨬqÅõ'ᑏᡂ÷ø)20.᝞Â<ᙠ┵P-4BCD

3ᫀ᪆1.ூᫀ௃Dூ᪆௃4᪷ᓫᔣḄ!"#ᔣ$%ᦑA┯(B-.)ᔣḄ*ᔣ+")ᔣᡠ-"ᔣᦑB┯(CḄᔣ#ᔣ$%᝞ᙠᙊ123ᡠᙠḄᔣ!"#ᔣ$%ᦑC┯(D-.᪷*ᔣḄ4*ᔣḄᦑ஺6%ᦑ⌱D.᪷ᓫᔣ)ᔣḄ-8*ᔣḄ9ᔜ;⌱⚗⌲;ᑨ?ᓽ
.A⚪ὃDE)ᔣ*ᔣḄὃDEFGḄᳮIJKLMẠ⚪.2.ூᫀ௃Cூ᪆௃᪷ᔣᐳ☢ᳮ0M=xOA+yOB+zOC,PA,B,C$ᐳQRA,B,C,Mᐳ☢ᑣᐸᐙ⌕ᩩX"x+y+z=1.ᵫZ4A,B,஺$6%.⌱⚗C[\]^_ABCḄ`aᡠ-ᐳ☢.ᦑ⌱C.᪷ᔣᐳ☢ᳮ0M=xOA+yOB+zOC,PA,B,C$ᐳQRA,B,C,Mᐳ☢ᑣᐸᐙ⌕ᩩX"x+y+z=1.A⚪ὃDbᐳ☢ᑨᩩX-c]ᐳQᳮᑨ9deᔠghij.3.ூᫀ௃Dூ᪆௃:᪷⚪l,nA(a,O),B(O,b),oᵫP(-l,2)\A8Ḅ1ᑣᨵg1=2=rᑣa=—2,b=4ᦑ4(-2,0),8(0,4),ᑣABḄs᳛k=u=2,ᦑ⌱:D.᪷⚪lᵫ1ᙶ᪗xy
zA,8Ḅᙶ᪗{|ᵫ}QḄs᳛xy~4ᫀ.A⚪ὃD}QḄs᳛~81ᙶ᪗xyKLMẠ⚪.4.ூᫀ௃Cூ᪆௃tan60°=V^,:.k=tan(180°—60°)——y/3,.4(2,4)ᐵLxḄ94(2,-4)ᙠ*ᐝQn*ᐝQᡠᙠḄ}Q#y=-V3x+b,'■—4=-V3x2+b,4⚓ᐳ14⚓

44b=273-4,ᦑ*ᐝQᡠᙠḄ}Q#y=-V3x+2V3-4,ᓽ+y+4-2=0,ᦑ⌱C.ᑭᵨ4(2,4)ᐵLxḄ94(2,-4)ᙠ*ᐝQ᪷ᐭᐝQx6#ᔣᡂ60஺^tanl200=-V3,4ᑮ*ᐝQᡠᙠḄ}Q#Ḅs᳛=tanl20஺ᵫsyᑏz*ᐝQᡠᙠḄ}Q#.A⚪ὃD
g;ᐵL}QḄ9ᙶ᪗Ḅ#ᵨy
}QḄ#*Ḅᵨ.ὃD~IJ.5.ூᫀ௃Aூ᪆௃ூᑖ᪆௃A⚪ὃDEᑭᵨᔣ
QKL1᫏⚪.ᐜ~9iḄᜳ^4z}QPA}Q/Ḅᜳ^~Pᑮ}Q/Ḅ.ூ௃PA=(-2,0,-1),ᦑ¡|=£,oᐗ=(0,1,1),ccooss<>-=§ߟ¨g=%T&-=gᒹ'10n}QPA}Q/ᡠᡂḄ^\0,ᑣcos஺=|cos\=ªᦑsin஺=10Pᑮ}Q/Ḅ\|P4|sin஺=x«=¬.ᦑ⌱A.6.ூᫀ௃Dூ᪆௃:]ᩩ}Qax-by+4=0,%#-1)%+y+b=0஻3#bx+2y+Q=0,P஺,஺ᑣ-஺-1)gJ=0,জR//᝞ᑣ2(a—l)—b=0,ঝᵫজঝ4Q=1,b=0,ᡈa=2,b=2,)•)a+b=1ᡈQ+b=4,ᦑ⌱D.᪷}QḄᚖ}±Ḅᐵ²4a(Q-1)-b=0,জᑣ2(@-1)-b=0,ঝ#
z஺஻Ḅ´ᓽ
za+b

5A⚪ὃDE}Qᚖ}±ḄᩩXὃDEµIJKLMẠ⚪.7.ூᫀ௃Cூ᪆௃:nAC,BD-ஹ/0,¶·0஺¸ᑣ஺011☢ABCD,0஺1==3,b¹_A8CD"¹º\4Ḅ»_/.DAB=60°,OB=2,0C=2V3,AC=20c=4¨OB1AC,.OB=V13,01c=¼oBC=4,rc13+21-169,*♦COS/LB01-iC-2V13XVHV13xVnsinSC=^|^'•••^=1x713x721x^=4732nAᑮ☢01BCḄ\h,ᑣ-_80⍝=x4V3xh=,o%L4BC=-0(?!=|xjx4V3x2x3=4A/3,=4V3,ᦑh=3.•♦•E"0:Ḅ1,•••EÀlj☢OiBCḄÁÂ\2=j.ᦑ⌱C.ᐜᑭᵨÃÄ
zAᑮ☢RBCḄ4zEᑮ☢0/CḄ.A⚪ὃDEÅ┵ḄÃÄḄ~KL1᫏⚪.8.ூᫀ௃Dூ᪆௃P}Q+Ç1ÈÉM(cosa,sina),ᑣ+•bcosa+asina=ab,•(bcosa+asina)2=a2b2.v(bcosa+asina)2<(a2+b2)•(cos2a+sin2a)=(a2+h2),2222Aa&<(a4-b),+ᦑ⌱D.ᵫ⚪l4(bcosa+asina)2=a2b2,ᑭᵨ(bcosa+asina)2<(a2+b2)•(cos2a+siMa),ᓄË4ᫀ.A⚪ὃDឤÉḄ}Q$yឋÎḄᵨᑭᵨ(bcosa+asina)2<(a2+b2)-(cos2a4-sin2a),"⚪ḄÏ.9.ூᫀ௃ADூ᪆௃9LA,a-b=lx2-lxl+2x(-|)=0,ᑣÐ,Ñ./Òᚖ}ᦑA"ÓÔ⚪;6⚓ᐳ14⚓

69LB,a-n=0x1+1x(-1)+(-1)x(-1)=0,ᑣW_Là:"//aᡈua,ᦑ8"ᎷÔ⚪9LC,|ᡃ=6஺0,..0_!.£$ᡂêᦑC"ᎷÔ⚪ë9L஺=(-1,1,1),‒=(g1,1,0),♦ᐗ="☢aḄᔣ).?î=T+"+t=°,4a+t=l,ᦑ஺"ÓÔ⚪.m-BC=-1+u=0ᦑ⌱:AD.ᵫ}QḄ#ᔣᔣᦪÄ\04}Qᚖ}ᑨ?4ᵫᦪÄ\04஻/aᡈIuaᑨ?Bëᵫ☢ᔣḄᦪÄ$\0ᑨ?Cë
zö÷Ḅᙶ᪗ᵫᦪÄ\0ᑡᐵL“Ḅ#ú
4a+tᑨ?D.A⚪ὃDÔ⚪ḄÓᎷᑨ?ᵨὃD}QḄ#ᔣᔣ8☢ᔣḄᵨὃD~IJ"MẠ⚪.10.ூᫀ௃ACூ᪆௃᪷⚪lᵫLüs^Ḅþ"ÿ0°,180஺)(TWa<135°kḄa+45஺135°0,--<0,aaᦑa<0,h<0Lx+cy+d=0,ᡠDy=——g᪷"ᙠᙶ᪗IJḄKLᡠD—N>0,——>0,ccᡠDcvo,d>0.ᵫ9M[>MNacᡠDc>a.ᦑ⌱BD.✌ᐜ^ḄM_`aᣚc`dMeᑭᵨḄ᳛&ḄciḄᜧkᐵIm6no.

72⚪ὃ4Ḅpq⌕sḄABḄM_`AB&c`ABḄaᣚt⌕ὃ4uvḄwxyz&ᦪu|}yz89J᫏⚪.12.ூ=ᫀ௃BDூ0᪆௃0AABCD-aB1C1D1JAB=1,sᙠ☢BCGB1ᐸwᢝ4P1BD1,9A,•••sPᙠ☢BCGB1☢BCC1&஻☢44•••sPᑮ☢ḄiᓽsCᑮᑮ☢24DḄiᓽAḄ•••zT4M=9sA4AM-CD=ixixlxlXl=|,ᦑA┯©98,Ds஺ᙶ᪗ªs«¬®ᙶ᪗I᝞°ᑣ4(1,0,0),P(x,l,z),8(1,1,0),(0,0,1),ᓰ(1,1,1),C(O.l,O),.-.AP=(x-l,l,z),µ¶·=(-1,0,-1),■•APLBD^--AP-BD[=1—X—1+Z=0,-.X=Z,AP(X,1,X),ACP=(%,0,x),CP=-xB^C,ᓽ&,C,P¹sᐳ•••s»ᙠ¼஺ᦑBm9C,•••½=(x-l,l,x),¾=(-1,0,1),•••AP-BC[=1—x+x=l,•••4P_LBCiÀᡂ¬ᦑC┯©9஺•••Ai(l,0,l),(0,1,1),£)(0,0,0),µ=(1,0,1),µ=(0,1,1),Ã☢4G஺ḄÄᔣÆÇ=(%y,z),ᑣÈÉ5=*+z=°,Ë”=1,/ᐗ1),(n-DC1=y+z=0AP-n=x-l+l-x=0,AP1n,•.•zpa☢4G஺•AP஻☢41ci஺ᦑ஺m.ᦑ⌱BD.ÐÑ/.4A£)ᑨÔA;D஺ᙶ᪗ªs«¬®ᙶ᪗IᑭᵨᔣÆÄᑨÔBCD.2⚪ὃ4®ᚖḄᑨ6ஹ☢ÈḄᑨ6ஹ¹┵ḄÙÚ:Ạpqὃ4wxÛ8⚓ᐳ14⚓

8Ð0yzJ᫏⚪.13.ூ=ᫀ௃Iூ0᪆௃ூᑖ᪆௃2⚪ὃ4ÝᦪÞḄÐÄὃ4®ᔣÆᙶ᪗wxÄᑣஹᔣÆᚖḄឋàÚ:Ạpq:Ạ⚪.ᑭᵨ®ᔣÆᙶ᪗wxÄᑣÐÑká+â2a-b,ãᵫkk+3ä2áMAåæᚖyÐÑk.ூ0=௃0•.•ᔣÆá=(1,L1),b=(-1,0,2),ka+b=(k-l,k,k+2),2a-b=(3,2,0),vk+Aä2a—3åæᚖ•••(ka+K)-(2a—b)=3(k-1)+2k=0,0/k=|.ᦑ=ᫀ|.14.ூ=ᫀ௃Iூ0᪆௃0ê/ḄAB2x+(k—3)y—2k+6=0,ᓽব-2)k+2x-3y+6=0,í8-3y6=(r0/x=஺y=2,ᡠD/ï6s(0,2),íy=0,ðk=k—3,ê/ᙠxñஹyñḄciò&Ú90,ᡠDkߟ3+2=0,:;k=1,ᦑ=ᫀ(0,2)1.^AB᦮ᳮ(y—2)k+2x—3y+6=0,ᯠ÷í=ÐÑ^ḄÞᓽ.ÐÑïḄ6sãᑖùíx=0,y=0,ᵫú᪷"ciḄ67Dûpᩩý«¬ABᓽ.Ð0.2⚪ὃ4þï6sÿ⚪
ḄḄᵨὃḄẠ⚪.15.ூᫀ௃1

9ூ᪆௃":$☢&048cḄᡠᨵ-./0VL.•.$☢&஺43c67$☢&Ὂ9:;ᐳ☢᝞>,OA-OB=0C-OB=>/2x>/2xcos600=1,•••E,F,GᑖGH஺4,OC,BCKL•GE=GC+C0^0E=-BC-OC-^-OA=-0A--0BMNOC,22222GF=--0B,21121.■■GEGF=-(-OA+OB+OCyOB=-^-OA-OB+'OB+0C-OS)=-.ᦑᫀH"UVWḄMXYᵨY⊤[ᔣ]^_ᑭᵨᔣ]ᦪ]bcdeᓽg.h⚪ὃᔣ]ᦪ]bcdஹᔣ]jឋlᑣ0Ạnoὃe6K᫏⚪.16.ூᫀ௃(M8,M|]ᕖ,+8)ூ᪆௃"•.)uᦪx,yxyz{x+2y=6,}1WXW3~⊤[jx+2y=6ḄLM(%y)LN(2,l)jḄ᳛Aஹ3Hjx+2y=6ḄXL4(1,|)ஹB(3,|),24Ḅ᳛H=M;2—12NBḄ᳛H=2—32ᦑN|ḄH(ߟ8,—|]UE+8),ᦑᫀH"(-00,-1]U[i,+<»)..ᵫ⚪ᑭᵨjḄ᳛cde.h⚪⌕ὃjḄ᳛cdḄᵨẠ⚪.17.ூᫀ௃"(1)/CBC='U=2,•••4V/BC,%D=2)•)jADz{Hy—7=2(%+4),ᓽ2%—y+15=0-3-75ফ…¦=M§,:¨©ª«j¬ᚖ8஺14஺.•)¯஺=°±10⚓ᐳ14⚓

109ACKL(M1,2),³68஺ḄKLjBDḄz{Hy—2=|(x+1),ᓽ3%—5y+13=0.ூ᪆௃(1)ᑭᵨ¬´µḄj᳛0ஹLdᓽg¶.(2)ᑭᵨ¬ᚖḄj᳛·WḄᐵ¹ஹKLᙶ᪗cdᓽg¶h⚪ὃ¬´µḄj᳛0ஹLdஹ¬ᚖḄj᳛·WḄᐵ¹ஹKLᙶ᪗cdஹ¨©Ḅឋ¼ὃ½ᳮ¿Ạ⚪18.ூᫀ௃"•••ᙠ´µ$Á©ABC஺KAB=AC=1,AACD=90",ÄÅADCǪ«jACᢚÉÊAB8ᡂ60஺•••=60஺ᡈ=120°,Ε••AB=AC=CD=1,AC1CD,ACLAB,•••|Ï|==J(BA+AC+CD)2=JBA2+AC2+CD2+2BA-AC+2AC-CD+2BA-CD=Jl+l+l+0+0+2xlxlxcos—J3+2cos<,CD>,}ீÓ9>=60஺~M|=V3+2cos6(r=2,}ீÕz>=120°~|Ö|=,3+2cosl20஺=×.•••8஺Ḅ.H2ᡈVIூ᪆௃ᵫ>©ᢚÙḄᐵnoᑮᢚÙÛ>©KjÜḄÝÞᐵ¹ßᦪ]ᐵ¹ᯠÛᵨAB,AC,᩵⊤[Ö᪷ã|Ö|=J^e.h⚪ὃjÜ.ḄelὃVWKjjஹj☢ஹ☢☢WḄÝÞᐵ¹0ẠnoὃeஹVWåæᦪ©ᔠèå6K᫏⚪.19.ூᫀ௃"}éêH0~jz{Hy=kx,ᑣ4=Axl,ᓽk=4,ᡠ
jz{H"4%—y=0,}éê;H0~jz{H"ì+*=l(a40),ïᐭL(L4),ᑣᔁ+Ü=1,ᓽ|a|=5,ᡠ
a=±5,ᑣjz{H"x+y-5=0ᡈx+y+5=0.ூ᪆௃ᑖéêH0;H0óôõö÷ø¶jz{ïᐭùnLᓄûᓽge.h⚪ὃejz{Ḅü⚪ýᑮḄὃḄẠ⚪.

1120.ூᫀ௃"(1)þÿv^BAP=CDP=90஺PA1AB,PD1CD,■■AB//CD,.ABLPD,•••PAflPD=P,PAu☢PAD,PDu☢PAD,■.ABJL☢PAD,u☢PAB,☢PABJ_☢PAD,(2)vAB11CD,AB=CD,.•.48C£>ᵫ(1)AB_L☢PAD,4B14஺ᑣABCDᙠCAPCᵫPA=PD,^APD=90°,PADῪPA=AB=2a,ᑣ4஺=2g.!O,BC!E,"#POஹOE,%஺ᙶ᪗(!ᑖ*%OAஹOEஹOPᡠᙠ,xஹyஹz-./01ᙶ᪗2,ᑣ0(45a,0,0),F(V2a,2a,0),P(0,0,V2a),C(-V2a,2a,0).PD=(-V2a,0,-V2a),PB=(V2a,2a,-V2a),BC=(-2V2a,0,0).☢PBCḄ478ᔣ:ᐗ=(x,y,z),ᵫ<==஺,+2@-&az=0,ᐗ=ᵯ1,?=i=-=i=^==-.Tᵫ@A☢4-PB-CBA☢APBC☢P3CᜳḄEFGூI᪆௃(1)ᵫLPA_L4B2PD1CD,Mᵫ4B஻CD,N81PO,ᑭᵨ,☢ᚖḄᑨSZBJ■☢PAD,U4Vᑮ☢H4B1☢PADফᵫLABC஺ᵫপ4B1☢PAD,ᑮ4BJ.AO,ᑣA8COP2=AB=2a,ᑣAD=2&a.A஺!O,8c!E,"#P஺ஹOE,%஺ᙶ᪗(!ᑖ*%OAஹOEஹOZᡠᙠ,xஹyஹz-./01ᙶ᪗2[\☢PBCḄ478ᔣ:M]^PD1☢PAB,_☢PA8`12⚓ᐳ14⚓

12Ḅ478ᔣ:ᵫc8ᔣ:ᡠᡂḄEFG☢AP2C☢PBCᜳḄEFG.e⚪ὃh☢i☢ᚖḄᑨSjklᑭᵨ01ᔣ:[A☢Ḅ☢ὃh01mnoNCpqoNr᫏⚪.21.ூtᫀ௃v1]^᝞@PB!G,"#AG,NG,•••NPCḄ!•••NG//BC,NG=^BC,4M="0=2,BC=4,4D஻BC,AM//BC,4M=[BC,ᑣNG஻AM,NG=AM,•••4MNGᑣNM஻4G,•••AGu☢PAB,NMy☢PAB,MN஻☢PAB(2)I:BC!Q,"#AQ,LAB=AC,ᑣᨵ4Q18C,QC=AM=2,QC//AM,ᑣAQCMᓽ4M1MC,•••PA}☢ABCD,PAu☢PAD,••)☢ABCD1•☢PAD,•••☢4BC£)n☢P4஺=AD,CMu☢ABC஺CM1☢PAD,CMu☢PNM,ᑣ☢PNMJL☢PAD,ᙠ☢PA஺ᑁAAFIPM,PMF,"#NF,ᑣN4NF,ANi☢PMNᡠᡂᙠᵫNPCḄ!;AN=ipC=^y/PA2+PC2=|,ᙠRtAPAMᵫP4TM=PMMF,NZ-FT-ᜓ-T'

13..AF-T~8V5•sinANF=—=-4-=——AN2252A,ANi☢PMNᡠᡂḄFG.ூI᪆௃e⚪ὃh,i☢ḄᑨSὃh,i☢ᡠᡂḄ[8ὃhᦪᓄpm8ὃhl01mnoNCoNr᫏⚪.(1)PB!G,"#AG,NG,ᵫḄ,SᳮNG஻BC,NG=#BC,MᵫLAM஻BC,=ᑮNG஻2M,DNG=AM,^AMNGNM஻4G,ᵫ,☢ḄᑨSᑮMN஻☢PABD(2)ᵫSᳮCM12D,U4Vᑮ☢PNM_L☢PA஺ᙠ☢PAOᑁA4F1PM,-.PMEF,"#NR4NF,ANi☢PMNᡠᡂ.ᯠ[I,ANi☢PMNᡠᡂḄFG.22.ூtᫀ௃I(1)PA}☢ABCD,BCu☢ABCD,.PA1BC,•4ACB=90°,+••BC1AC.^PAf]AC=A,ABCl¥ffiPACD(2)vAB//CD,AD=CD=1,/.BAD=120",)•.CZCDAC=1,P4=x2ᑣSN4c=]S=|X1Xlx2+1-hPCD•••A☢஺-PC-4ḄEFGg,4஺1PC,ᑣAO1☢PBC,CPACᵫ☢AO===ᩩA!Aᑮ☢PBCḄூI᪆௃(1)⌕]BC_L☢PAC,◤]^P4_LBC,BC14Cᓽ¢(2)4஺1PC,ᑣ40_L☢P8C,ᑭᵨ☢[Iᓽ.e⚪ὃh,i☢ᚖA☢!ᑮ☢Ḅὃh01mnoN£¤pqoN᫏⚪.`14⚓ᐳ14⚓