2022年浙江省宁波市鄞州强基招生数学模拟试卷（附答案详解）

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2022
ḕᦪᔁ1.a+=?+3b"0,ᑣ&Ḅ()____.ba3a+b2.ᐵ-xḄ/0/+2bx+3c=0Ḅ34᪷ᑖ78X]=T<%2=>?@AA8CDEᦪy=/+2bx-3cḄGH>yIḄJAx2IḄ34JA

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2*'•ᙠpᦪöᑁ<÷øᙠR4ᦪ8ᐵ-XḄ/0ù=3x+kḄú”ûᦪ”Ḅü(ö.12.┦XYXZABCḄ᜜þ)஺<᜜ãᙊ
d,A஺BO,CO,ᑖBC,CA,AB஺E,F.প+ᘤ+;(2):♦+,+,=*

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9b+b5ᦑᫀ$ᐜ+ᩩ-./0Q=3ᓃ12ᐭ.4⚪ὃ78ᑖ'Ḅ:;<+ᩩ-./=⚪Ḅᐵ?.2.ூᫀ௃3ூ᪆௃$
2=“:.+%2=—2b—3,X.X=3c=m67n,t2A2b=-3,3c=-m2+6mf4•y=%2_3%+3(2_6m),mAx=0,y—\(m2—6m),••(m2—6m)),vAB1yB•48஻%B•8EḄFᙶ᪗I(K2L6m),+y=1(m?-6m)2ᐭy=/-3%+((K2-6m),0;(——6m),=%2—3%+(m2—6m),0%i=0,N=3,:.AB=3.ᦑᫀ$3.᪷P᪷QᦪḄᐵQSTcḄUVSWNXᦪḄ᪆'Ax=0,0Y=i(m2-6m),᪷PABIyB04B஻yB08EḄFᙶ᪗I(ZL6m),UVSBEḄᙶ᪗[VSABḄ.4⚪ὃ78\ᱥ^xBḄEஹ᪷QᦪḄᐵQஹWNXᦪḄឋaஹWNXᦪbcde4⚓ᐳII⚓

4EḄᙶ᪗ᱯijklmnopEḄqᔠsᵨ᪷QᦪḄsᵨ=⚪ᐵ?.3.ூᫀ௃uூ᪆௃$•.•m/A8CO=w/.AB=CD,AD=BC=3,x4=NO=90°,•••E=90°,••xEFG+4EGy=90°,•AFB+DGC=90°,4AFB+4ABF=90஺,:.Z.ABF=Z.DGC,•AFB^L.DCG,AF_AB**CDߟ⁰’ABCD=AFDG,ᓽ~5=•DG,AF-AFFGGD=321,31AAF=FG=1,DG=i,22c313AB2=AF-DG=-x-=~,224ᦑᫀ$.ᵫw/Ḅឋa0~B=CD,AD=BC=3,x4=ND=90஺DCG,0AB2=AF-DG,=0ᑮ.4⚪ὃ78/Ḅᑨឋaw/Ḅឋajkw/Ḅឋa/=⚪Ḅᐵ?.4.ூᫀ௃y=-x2+18X-80ூ᪆௃$ᵫ⚪0AO/liBiஹ&81482ஹ…ᙳῪ/,1-'OB௃=B$2=BB,,'B_B=2,23nin.•.E4(1,9),42(3,3)*…4'2n-l,),271—114Bn=/nBn-iAMnῪ/•9_1••-±,2n-lAn=5,(9,1),A^4(8,0),85(10,0),

5\ᱥ^Ḅ᪆'y=a(x-8)(x-10),E4(9,1)2ᐭ᪆'0La=1,•a=—1,W\ᱥ^Ḅ᪆'y=-(x-8)(x-10)=-x2+18%-80.ᦑᫀ$y=-x2+18x-80.ᐜ0E¡2,…ArḄᙶ᪗ᯠ¥ᵫῪ/Ḅឋa0/=/¦\ᱥ^⚔EḄᙶ᪗ᯠ¥0sḄ\ᱥ^᪆'.4⚪ὃ78Ὺ/Ḅឋa\ᱥ^Ḅ᪆'¨©ªXᦪbcdEḄᙶ᪗ᱯi⚪Ḅᐵ?=oῪ/Ḅឋa0QᑡEAḄᙶ᪗¬.5.ூᫀ௃36ூ᪆௃$ᵫ±+3+2=0,²ᑖ³0Q+lb+2c+3(b+2)(c+3)+(a+l)(c+3)+(a+l)(b+2)=0,ᑣ(Q+l)2+(b+2)2+(c+3)2=[(Q+1)+(b+2)+(c+3)]2—2[(b+2)(c+3)+(a+l)(c+3)+(Q+l)(b+2)]=(a+ᓃ+c+6»=(0+6)2=36.ᦑᫀ$36.ᑭᵨ½ᐰ¿ÀÁ'(a+b+c)2=a2+b2+c2+2ab+2bc+2ac,0a?+᮱+c?=(a+b+c)2—2ab—2bc—2ac,Ä᯿lnÁ'ᓽÆ.4⚪Ç⌕ὃ7½ᐰ¿ÀÁ'ÉÁ'ḄÊn./Á'⚪ᜧᨵÍÎ.6.ூᫀ௃18ூ᪆௃$Xy/y+yVx-V2022x-,2022y+j2022xy=2022,./¥(2+Ñ)-72022(Vx+¥)+,2022xy-V20227,ᡠÔ(Õ+À+Ö×)(ÖL/Ù)=0,ᡠÔÖLÚẚ=0,xy=2022=2x3x337,x,yᙳ᦮ᦪx-y-7>0,:.JßLy-7ᨬZ¦x=337,y=6,Jx-y-7ᨬZV337-6-7=V324=18.ᦑᫀ$18.&'Æ./+y/y)-72022(Vx+5)+y/2022xy-V20222,ᡠÔ++V2022)(7xy-V2022)=0,ᡠÔáLᶭã=0,᪷PäæÆ0x=337,y=6.e6⚓ᐳII⚓

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]x96=60x12-5
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——
#°DE2a23a2vXa3a7a=3k--k--k—-k=9,223O3k=jᦑ.ᫀD3445஺7஺F஻x:!;BE<58!;y:<5G,=>8E;x:<5“!?@O஺,᪷\]DECḄ☢ID3,]0DEḄ☢I!S஺5ᙶ᪗DG^B!ᑣE5ᙶ᪗D3a,Q᪷\☢Iᑡ_`ᓽbkḄc.⚪ὃdefgᦪ&Ḅijkl!⚪ᐵ+*᪷\mnᩩp!S5Ḅᙶ᪗!ᑭᵨqrs%ḄឋuஹLMEK%Ḅឋuஹrs%Ḅ☢Iwxᑡᐵ{<5L,?@OL,7DK1CF<5K,•••EK%ACFG}EK%BCDE~*_%!•CF=AC=3,BC=CD=2,UCF=BCD=90°,ACB=120°,♦DCF=360°-90°-90°-120°=60°,•CKD=FKD=90°,DK.V3CK6஺1—=sin6rA0O=——"——=cos60=CD2CD2.DK=^X2=^,CK=1X2=1,FK=3-1=2,•DF=+22=V7,••CHABஹH,•AAHC=90°,•Z.FCL=90°-ACH=CAB,vZ.CFL=180°-60°=120°=ACB,•••]CLF]4BCG4SA),LF=BC=CD,•EK%LFCO*LMEK%!8⚓!ᐳII⚓

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9•EK%AMGD¥%!•BG=AF=2k,AG=BF=4k,1R*•EG=AE+AG=—k29BE=y/BG2+EG2=—k,2BE__V37'8==T'ᦑ.ᫀD3-Y~.SAC,BD%&'F,45B7BG1E4;E4Ḅ=>{<5G,ᑭᵨsrs%ḄKsᐵOᑮcos·4cB=¸=30CF=3k,ᑣCB=5k,ᑭᵨᳮ!;»BC5ᳮ!LM{ᑖ{¼ᡂfgᳮOBF,DF,AE,ᑭᵨᳮO{¼CE¿ᑭᵨ¥%Ḅᑨឋu}ᳮOBE!ᑣ&ÀbO.⚪Á⌕ὃd¥%Ḅឋu!srs%ḄKsᐵᳮ!ᳮ!;»ᳮ!ÂÃÄÅᙊḄᐵឋu!ᑭᵨᳮOÇḄ>È*⚪Ḅᐵ+.II.ூ.ᫀ௃3Ê_`bᓄD2/Î3x-(k+3)=0,জ(1)Ö4=0!k=—1■,=%2=3ØÙᩩp¿84(2)^x=1*_`জḄ᪷!O2xÚÎ3x1-(A+3)=0,k=-4¿_`জḄÛÎÜ᪷D5ᦑÊ_`ÝÞᨵÎ᪷x=(3)Ö_`জᨵàáâ᪷!=r)<0ä%#1ᓽæ#-4,$k>-3,Ê_`ÝÞᨵÎÜâᦪ᪷¿(4)Ö_`জᨵÎÜ᪷D0!k=-3,ÛÎÜ᪷Dç=|,Ê_`ÝÞᨵÎÜâ᪷.éêᡠë!ØÙᩩpḄìḄcî*k=Δᡈk=-4ᡈk>-3.8ூ᪆௃ᐜòÊ_`ᓄD2/-3x-(k+3)=0,Î*ÎÜÎᐗJô_`!ᙠâᦪîᑁ!Þ÷ᙠÎÜᦪ*ᐵ::?ᓽ.@⌕ὃCDEḄFGHᑖIḄJKLM⚪NḄᱯP⌕ᑖ%&'(.Q10⚓ᐳII⚓

1012.ூUᫀ௃(1)E)ᵫYA஺BE,CF^YP0,.__S4OBC0E_S-o4cOF_SAOஹODOEOF.xᐭ+{+k=1,(1_}+(1-~+(1-1,R,RR•**----------------------=29ADBECF1,1,124-H----------------=—=ADBECFRdூE᪆௃(1)᪷S-BC=S&ABO+S.4C0+S&BCO,E⚪;(2)ghAD^஺஺YM,ᵫYAO,BE,CᐳP0.ᯠ9ᵫ஺஺=R-DMஹAM=2/?,:(.⚪ὃCD᜜pᙊ᜜ᑖIḄE⚪Ḅᐵ᜜pᙊ᜜.