高考数学难点突破_难点21-30

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61(4)ᑡ$%&'().+᣸ᑡ-.ᔠ0ᵨ⚪1ᵨḄ34ᨵ678'4-98'4ᑖ4-ᑖ4ᐗ;ᑖ᪆4<=ᑖ᪆4>?4ᣊA4BCD.E1
ᵨḄᦪFGH6জᑖJKGHঝMᓄGHঞPQGH.RSTUVWXஹZ?⚪1.(ਭਭਭਭ)]^ᔠ_0,1,2,3,5,7,11cde3gᐗ;ᑖh(i7j3kAr+&y+C=0dḄAஹ8ஹC,ᡠuḄEvᙶ᪗UḄ7jᨵᩩ(ᵨᦪy⊤{).2.(*****)ᙊᕜᨵ2஻gBᑖUᐸdgUi⚔UḄ7Ḅgᦪi.ஹ+)⚪3.(*****)dᨵ5ᡫᐸd2i⁐Ḅ2,3i⁐ḄA,ᨵ5$$XDUᦪḄᦪ▲ᨵDḄ$344.(ਭਭਭਭ)¡ᦪ)=2+4+¢Ḅ£ᦪ4ஹbஹc,ᙠ^ᔠ_-3,—2,—1,0,1,2,3,4cd⌱3gḄyᑣ¨©ᙶ᪗UᙠªᱥjᑁḄªᱥjᩩ5.(*****)ᨵ3®ᵱ°4®᝕°ᙠ²ᑡ⌕´²´Ḅ᣸ᑡ34µᦪ.(1)ᐰ·᣸ᡂX¹ᐸdᵬᙠd9ᡈὅ½¾<=.(2)ᐰ·᣸ᡂX¹ᐸdᵬᙠᨬÀ¾Áᙠᨬ¾.(3)ᐰ·᣸ᡂX¹ᐸdᵱ°ÃÄ᣸ᙠXÅ.(4)ᐰ·᣸ᡂX¹ᵱஹ᝕ᔜÇÈ.(5)ᐰ·᣸ᡂX¹ᵱ°᣸ᙠXÅ.(6)ᐰ·᣸ᡂX¹ᐸdᵬஹÁஹÊ]ÀËÂḄÌÍÎ.(7)᣸ᡂÏÐ᣸Ï᣸3Ð᣸4.(8)ᐰ·᣸ᡂX¹ᵬஹÁ½d9ÃÄᨵ3.6.(*****)20gÑÒhḄÓᳫÕᐭ×Øi1ஹ2ஹ3ḄgÙ&d⌕´gÙᑁḄᳫᦪÓÚÛḄ×Øᦪ´ḄÕ4Dᦪ.7.(****)ᵨÜDḄÝ⁐ÞßdḄপ(2)(3)(4)Ḅᔜᑖá⁐ᑖáX⁐ÇÈᑖá⁐ᑣá⁐Ḅ34ᐳᨵãD8.(****)ᵬஹÁஹÊyᕜXËᕜäḄåy½ᜩåçᵬyᕜXஹÁyᕜäᑣ¨᣸$Ḅyå⊤ᦪièὃ)ᫀTUëì+6(984)6eᓱᱏ¨.ᡂ<ᦪC•23•A“g)ᐸd0ᙠð<ḄᨵC0ñ6(g)òᔠ⚪óḄᦑᐳᨵ<ᦪ:C6᮱÷6Xø᮱ñ=432(g).RSTUVW

62Xஹ1.+᪆6ùi7jvUᡠC=0,]1,2,3,5,7,11ò6gᦪde2g(iAஹB½ᦪḄÌÍ⊤{Ḅ7jᡠ7jḄᩩᦪiA6=30.)ᫀ6302.+᪆62”gBᑖU¨($஻ᩩ7ú]de⌱•ᩩ7úᐳᨵC6D34û]²Ḅ(2஻-2)gBᑖUde⌱XgUᐳᨵC[_2D34᪷ýþ4ᳮ67Ḅgᦪi6C6•g.)ᫀ62n(n—1)ஹ3.+6H1Ḅ34¨ᑖi²ã6(1)5ᐰᑖÿ
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3A
ᨵA(3)22
3A
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3A
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3Aᑖ
ᨵCA.
ᐳᨵḄA+A+A+AA+A+CA=860.4.ᵫᱯᑖ᪆
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ᐸa6bᐰ᣸ᑡ,ᨵ.ᵫe(ᳮgAA=2160.(2)\]ᑖ᪆.ᐜ᣸ᨬXi
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a-Ḅ6[\]ᐰ᣸ᨵA
mnᒆ◀pᙠᨬXiḄ᣸ᦪAA.ᑣrᔠᩩtḄ᣸ᐳᨵAA*AA=3720.(3)ᣊv.wᵱyzᡂ[᦮},~ᐰ᣸ᑡ.DᐸᐗP~ᐰ᣸ᑡ.ᐳᨵAA=720.(4).ᐜ᣸ᵱy
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ᐳᨵAA=1440.

63(6);᣸ᑡ.
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ᵬஹpCᐸa2b᣸ᡂ᣸ᵬஹpḄ᣸ᨵAA1ᨬD¡⌱Ḅ3bḄ᣸ᑡᐭᑮᵬஹp£ᓽ>.ᐳᨵAXAXA=720.6.✌ᐜᢥ§[¨©Ḅª«¬ᐭ1[ஹ2[ஹ3[ᳫ
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64)---0-0-0-ᵨ—0—ᫀ[1](ਭਭਭਭਭ)ᨵ"#$50Ḅ᪵(ᦪ*Ḅᑖ+,ᔜ+Ḅ⚣᳛ᦪ᝞01[10,15]4[30,35)9[15,20)5135,40)8120,25)10[40,45)3125,30)11(1)ᑡ9᪵(Ḅ⚣᳛ᑖ:⊤(<=>⚣᳛)1(2)?9⚣᳛ᑖ:@ABC=>⚣᳛Ḅᑖ:B.E⚪GB1(⚪H⌕ὃK⚣᳛ᑖ:⊤⚣᳛ᑖ:@ABC=>⚣᳛Ḅᑖ:BḄ?L.MNᡲ1⚣᳛ஹ=>⚣᳛ḄᭆPQ,⚣᳛ᑖ:⊤ஹ@ABC=>⚣᳛ᑖ:BḄ?L.┯Sᑖ᪆1SU(⚪VWX#᧕9Zᜫ\]⌕^G⚣᳛ᑖ:_=>⚣᳛ᑖ:Ḅ`.ᢈb_AL1(⚪ᐵdᙠfghij⊤kḄ`_ὶ.S1(1)ᵫᡠoᦪ*WXp᝞0⚣᳛ᑖ:⊤ᦪs*[10,15)[15,20)[20,25)[25,30)[30,35)[35,40)[40,45)Wr⚣45101198350ᦪ⚣0.080.100.200.220.180.160.061᳛=>0.080.180.380.600.780.941⚣᳛(2)⚣᳛ᑖ:@AB_=>⚣᳛ᑖ:B᝞0:[2](ਭਭਭਭਭ)vᵯᘤᖪz{|}Ḅz~Z(ᨴ9ḄᵯḄᑖᦪ4"$Ḅᑖ:ᑡ᝞01123......121111P......121212129"ᵯᵯᘤᖪᑭ300ᐗ᝞├9>fᑣᨴ◤ᵨ100ᐗᵯᘤᖪᨴ|ᵯ¡¢£¤¥ᨴ¦ᙳᦈ©ᨬᜧ¬E⚪GB1(⚪ὃKᑭᵨᭆ᳛Ḅv®MN᝞¯°ᩭS²³▭⚪.MNᡲ1¯°ḄᭆP,µᦪḄᨵᐵMN.

65┯Sᑖ᪆1ᙠ(⚪Ey"¸¹ºᨵ»¼½¾¿ᜫ\.ᢈb_AL1ÀÁÂᭆ᳛ᑖ:ஹ¯°ஹAÃÄMNᩭS²Å¿¾¿ÆḄ³▭⚪.S1xᨴᵯᘤᖪḄᦪÈÉὃ⇋ḄËÌᵯᘤᖪᨴḄᦈ©yᐗᑣy$4Ḅµᦪ]Íᵯᘤᖪ¦ᙳᨴ©300x-100(x-7)¬234᪗Ḅᭆ23᳛9LBᙠDEFG014᪗;ᑣ4᪗I13Ḅᭆ᳛J()42.(***MNOPQRS4ḄᑖTᑡJP(4=k)=Lk=l,2,3,ᑣP(3C+5)^_()3A.6B.9C.3D.4eஹfg⚪3.(****)1h3ᨵ9ijk3ilk;mno1ipk;oqrstuv;ᙠowjkxNoqḄlkᦪ4Ḅz{E4=.4.(ਭਭਭਭ)}~ᨵ52E;ᵱ᝕ᔜ;ᵱ᝕ᔜᙳᑖᡂ;i~3⌱q4E}⚗;4EាᩭsFḄᭆ᳛9.Dஹ⚪5.(*****)ᵬஹ2

66(1)¯°ᦪaḄ±;²³q´Ḅᭆ᳛¥¦µ¶3(2)¯P(l´·5)•7.(*****)¸Pᙠ[0,5]¹PQᙢo±;¯»/+᝞+/+J.=oᨵ¼᪷Ḅᭆ᳛.8.(*****)¸¾QᘤᙠᜩᑁÂÃᦑÅḄᭆ᳛J0.2,QᘤÂÃᦑÅGᐰᜩÇÈ:É.Êᕜ5i:ÉÌÍᙳÎᦑÅ;ÏÐᑭÒ10ÓᐗÂÃnᦑÅÏÐᑭÒ5Óᐗ;ÕÂÃnᦑÅÏÐᑭÒ0Óᐗ;ÂÃDnᡈDn×¹ᦑÅØ⌕ÙÚ2Óᐗ஺¯ᕜᑁz{ᑭÒ9Ü¡Ýὃᫀ%&àáâᐗãAஹ8ஹCj°:ÉḄäãᑖJAஹBஹC,ᵫNOᩩãP(A)=0.80,P(B)=0.90,P(C)=0.90.(1)çJäãAஹB.C9èéêëḄ;ᡠ×;íîMj°:ÉḄᭆ᳛P=P(A;C)=P(A)ï(8)P(C)=0.648,ᦑíîMj°:ÉḄᭆ᳛J0.648t(2)íîMj°:ÉḄᭆ᳛P=P(A)•[l-P(BC)]2=P(A)•E1-P(5)P(C)]=0.80X[1-(1-0.90)(1-0.90)]=0.792ᦑíîNj°:ÉḄᭆ᳛J0.7922#$%&'(ஹ1.᪆¸ᵬ234᪗JäãA,<234᪗Jäã8,>234᪗JäãC,ᑣ4᪗I13ḄäãÏ×⊤ñJA+B+C,ᓽ134᪗⊤ñäãAஹBஹC3¡ᨵiÂÃ.P(ABC)=P(A)-P(B\P(C)=(1-P(A)]-[1-P(B)]-[1-P(C)]———13ᦑ4᪗I13Ḅᭆ᳛J1—P(A•B•C)=1——=—44ᫀA2.᪆Ef=(1+2+3)--=2,Ef2=(l2+22+32)•-=—333-o14o2D.DS=Ef2-(£f)2=—-22=-.33O(3f+5)=9Ef=6.ᫀAc1aeஹ3.᪆ᵫᩩãO;§Ḅo±J0,1,2,3,²ôᨵï($=())=—=—,C14J2,

67P(L1)_C©_9CC_9c©_1.1)-2a44'ï(1)2G220'k3)2ü2203991••þ=0x+lx+2x+3x=0.3444220220ᫀ0.34.᪆:
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13,,⌱1ᨵC3ᡠᡠᭆ᳛
=%-.C52©ᫀ:C4~52ஹ5.(1)ᡃ$%“ᵬ()*+),-᪗”0123A,“6()*+),-᪗”01238.8ᯠ23AஹB:;<=ᡠ>ᔜ()*+@),-᪗Ḅᭆ᳛BP(AB)=P(A)•P(B)=0.6X0.6=0.36H>@),-᪗Ḅᭆ᳛B0.36(2)Jᳮ>ᔜ()*+ᵬ),ஹ6L),Ḅᭆ᳛BP(A•N)=P(A)•P(N)=0.6X(1—0.6)=0.6X0.4=0.24ᵬL),ஹ6),Ḅᭆ᳛BP(ᐭ•B)=P(A)P(B)=0.24,8ᯠ“ᵬ),ஹ6L),”R“ᵬL),ஹ6),”BSTUJVWXᓽ234•NZᐭ;[ᡠាᨵ*),-᪗Ḅᭆ᳛B(4•B)+P(A•8)=0.24+0.24=0.48Hᐸ,ាᨵ*),-᪗Ḅᭆ᳛B0.48.(2)>ᔜ()*+_`ᨵ*),-᪗Ḅᭆ᳛P=P(AB)+[(A•B)+P(A)•B]=0.36+0.48=0.84H_`ᨵ*),-᪗Ḅᭆ᳛B0.84.6.প
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1,ᡠj(l—a+2—a)•1=1,2.1•,a=—2ᭆ᳛mnop᝞r

6831133(2)P(1<^<7)=7(7+l)-^=x222297.*ᐗt+uᨵvᦪ᪷Q420.,Pl,y4=P-*4(*+-)=p2-p-2=(P+l)(P-2)42zPW-1ᡈP22[0.5]A{(—8,—l]U[2,+8)}Ḅ}n3ᦑᡠᭆ᳛
P=[0,5]Ḅ}n58.X⊤*ᕜ5ᜩᑁᘤWXᦑḄᜩᦪᑣX—8(5,0.2),BXᨵᭆ᳛ᑖP(X=k)=C50,2A0.85-t,Jt=0,l,2,3,4,5.y⊤*ᕜᑁᡠᑭᑣ10X=05X=1y=g(x)=ீ0«X=2-2X>3Ḅᭆ᳛ᑖ
P(r=l0)=P(X=0)=0.85=0.328p(y=5)=(X=l)=C0.2•0.84=0.410P(y=0)=P(X=2)=C•0.22•00=0.205(y=—2)=P(X3)=1—P(X=0)*(X=I)—P(X=2)=0.057ᦑ*ᕜᑁḄᑭ
£7=10X0.328+5X0.410+0X0.205-2X0.057=5.216(Nᐗ)