杭州市重点2023年高三（最后冲刺）数学试卷含解析

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2023
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15...ᵫ!"#$ᙠ&᪵Ḅ(MN,ᑣMN//1,)(0ᑮMNḄ*+0D=5-3=2,27r47rNMON=0,τa|=«ூ(-௃/0⚪2⌕ὃ5ᙶ᪗6ᣚὃ58ᙊḄ9:ᐵ<ὃ5᩽ᙶ᪗8ᙶ᪗=>?ᓄὃ5AᦪᓄCDὃ5ᦪEFᔠḄᦪHIJKLMN᫏⚪.20.(1)PQ=300sin஺P^—

16TTZOAP^——0,2OPAPᵫ[\]ᳮ.Asin26,(2)AP=300sin0,QH5072AQ=——1-----r-=-------.|71C)COS0,sin——0(2).PQ=AP-AQ=300si”6-,COS஺PQ=300sin3->0,cos8>0,COS஺ᓄᙠ021(6)=0,ᓽtan”+tan஺—3p=0,/.(tanO-\[2)(tan20+\[2tan0+3)=0,஻஻2஺0=>/5,6()Gf0,—

17ovev%¬(e)>o,/(e)ᓫ"⌴>/(e)ீo,/(஺)ᓫ"⌴$2.—ஹ4¯*/°=—-—>3+•••tan0=41/য²ᨬᜧ4´sing9,cos0=3,P஺=50¶(3yf2sin0--·=507633Icos0JP஺Ḅᨬᜧ4¸50¹º.ூ5¼௃¾⚪À⌕ὃÂÃÄÅ.ᦪᙠÆ▭ÈḄÉᵨ◤⌕᪷@⚪ÌÍÎÅÏ+zÏÐḄᐵaÑÒvÓᑖ᪆.ᦪḄᓫ"ឋ,᪷@ÄÅ.ᦪ4v{ÖÉḄᨬ4ᓽb.×YØ⚪.2r21.(I)—+y2=l(D)4.4'ூ{᪆௃(I)ÙᔠÛSbÜ=Îoc=ÝvÞ“ßḄ4ᓽbàᙊ<âa2(II)ᵫ⚪ÌbSãäḄå᳛ᙠçÞãä<âὶÎãä<â+àᙊ<âᑭᵨᑨëìíY0bᑭ2=4î+1,ὶÎãä<â+ᙊḄ<âÙᔠ᪷+aᦪḄᐵavS^CO+SMN஺ᑭᵨïzîìð5ᑮãäḄòóîìvÞSIMON»ᑮ^ACMN=^tMON+^AMCO+^SANO,᦮ᳮqᑭᵨô¾õíìvᨬ4.ூö{௃{>(I)b£=÷ø?=6Ùᔠ/=஻+/,a2{a=2,c=Ýb=\,àᙊ<âÜ+y2=i4(II)᧕SãäMNḄå᳛ᙠçMN>y=kx+m,'2>>7>44ú2+1*+8û+4"—1=0,ᵫᵫA=64îüýþ164î+lm2-1=0,"=4+1,

18**,SACMN=SAA/ON+5AAyco+NOç5஺ᑮãäMN>Ax-y+m=0Ḅòó¸d,|MN|=2yl\OMf-d2=24--[y=kx+mᵫ“22A,(Z?+1*+2/7nr+஻z2-4=0,xz+y=4-2kmm2-4Xj+x2FTP:.y+)5=8+++=(+஽)+22km]2m=k+2"/k2+l•••S&wco+SANA஺=JXG(|X|+1%I)=4(Ix+%I)=#??Kτ1SACMNQq&MON2_l&m2=4/+I#(=)*£,᧕-220,.ᑭ221,ᑣ011,2_8.0_804856789ACM7VḄ☢@A6B_*CA+3-Jiߟ-2J3-+1|/n|+H3HIJHK=|"Mᓽ=±PKQ

19ூST௃V⚪ὃYZᵫa,b,c[\ᙊḄ᪗_`a#bcd\ᙊḄefᐵh#ὃYZijḄklm5#nᔠឋqrs#tuv⚪.22.(1)-(2)wxyz21{᧕ὑ}ூ᪆௃(1)ᵫ~k⊤ᦪᑖA,஺ᙠ6ᨴᵨ᧕ὑ}Ḅ{ᦪ6,7,8KḄᭆ᳛#xᓫeᜓ6ᨴᵨ᧕ὑ}Ḅ{ᦪᦪX,ᑣP(X>21)=%*=22)+%=23),ᑭᵨ{ᭆ᳛(¡&[¢ᓽ£(2)ᵫ⚪XᡠᨵmḄQ¦19,20,21,22,23,ᓽ[¨wḄᭆ᳛#©ᑖª«xᓫeᙠyzᜓKw0Kyz20{᧕ὑ}¬21{᧕ὑ}KᵨḄmQ¦®¯°#ᓽᑖ᪆[¢.ூ௃(1)ᵫ⚪Ḅ⊤²-301AḄᜓ6ᨴᵨ᧕ὑ}Ḅ{ᦪ6¬7Ḅ⚣᳛ᙳµ=-£602BḄᜓ6ᨴᵨ᧕ὑ}Ḅ{ᦪ6,7,8Ḅ⚣᳛ᑖ¶=1·=!#2=!£6036026஺6CḄᜓ6ᨴᵨ᧕ὑ}Ḅ{ᦪ7¬8Ḅ⚣᳛ᑖ^1=7(11=75xᓫe6ᨴA,B,஺ᜓᵨ᧕ὑ}Ḅ{ᦪᑖ»V#z#ᑣ¼(x=6)=P(x=7)=2#P(y=6)=!#P(y=7)=(#P(y=8)=!#P(z=7)=1,P(z=8)=*#232644xᓫeᜓ6ᨴᵨ᧕ὑ}Ḅ{ᦪᦪX,ᑣP(X>21)=P(X=22)+P(X=23)&P(X=22)=P(x=6,y=8,z=8)+P(x=7,y=7,z=8)+P(x=7,y=8,z=7)1111111137=—X—X—+—X—X—+—X—X—=—,26422426448P(X=23)=P(x=7,y=8,z=8)=—x—x—=—,26448ᓽxᓫe6ᨴA,8,CᜓᵨḄ᧕ὑ}ᦪ¿À21{Ḅᭆ᳛(2)Á⚪Â-,XᡠᨵmḄQ¦19,20,21,22,23,11111311317P(X=20)=P(x=6,y=6,z=8)+(x=6,y=7,z=7)+P{x=7,y=6,z=7)=—x-x—■F—x—x—■F—x—x—=——£23422423448P(X=21)=P(x=6,y=7,z=8)+(x=6,y=8,z=7)+P(x=7,y=6,z=8)+P(x=7,y=7,z=7)

20111317—X—X—+—X—X—+—X—XPᓝPx-x—=2242642342244871ᵫ(1)^,P(X=22)=—,P(X=23)=—,ÅxᓫeᙠyzᜓḄ0KyzZ20{᧕ὑ}#xᓫe6ᨴyz᧕ὑ}ᡠ◤ḄᵨXᐗ#ᑣXḄᡠᨵmQ¦2000,2200,2400,2600,11723P(1£=2000)=P(X=19)+P(X=20)=-+—=—£o4o4o17C(É=2200)=P(X=21)=—£487¼(X=2400)=¼(X=22)=—£P(X=2600)=¼(X=23)=—£48231771=2000x—+2200x—+2400x—+2600x—«2142£148484848ÅxᓫeᙠËzᜓḄ0KyzZ21{᧕ὑ}#xᓫe6ᨴyz᧕ὑ}ᡠ◤ḄᵨÌ?ᐗ#ᑣ5ḄᡠᨵmQ¦2100,2300,2500,117175P(Y=2100)=P(X=19)+P(X=20)+P(X=21)=-+—+—=-28484867P(Y=2300)=P(X=22)=—£2P(Y=2500)=¼(X=23)=*£2571EY,=2100x-+2300x—+2500x—«2138£264848EY