2021-2022学年山西省部分学校高二（下）期中数学试卷（附答案详解）

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2021-2022
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1A.56B.84C.96D.12611.efᦪᑡ¨ᓽª«¬=2,a-a=®Uᑣ=()n+1nA2328¯2932RnA•±B.$C,-D,-12.ᵬஹ²7³´µ¶·ᎷQ¹¶·ºḄᭆ᳛»ᔜ¹¶·½¾¿ÀḄ,Áᵨ4¹3ºᑴ.ᎷQ¶·ÃᨵĹᑣ²ᡊºᵬḄᭆ᳛R()ஹÆÇ⚪(ᜧ⚪ᐳ4⚪ᐳ20.0ᑖ)13.ÈfÉÊ/(x)=a(x+1)-☜ᙠE(0J(0))ᜐḄᑗÊÎÊx-2y+3=0ᚖÎᑣÐᦪaḄ>R.14.ÑÒÓÔÕÖ×70Ø“Ú0M☢”RÜY4,“Ú0Ý☢”RÜYB,ᑣP(B|A)=.15.?ᱥᳮ$àn04$á4$lmḄÄᙳ>âRãᱥᳮ$Ḅᨬålm.efᨬålmḄv;N(0,æR)v஺ᙠ(—050.5)ᑁḄᭆ᳛Uè0.6827.éê⌕4$_0(IX;NQd),ᑣp(஻-?@AB29᥎ᑮ3ᳫḄᭆ᳛.18.GHᦪᑡJ%LḄMn⚗5%ᐜ,QR=1,S=2+Aa_i(n>28%Uᦪ).nn(1)VḄ,a,ᡂXYᦪᑡA4ḄZ[2(2)V[1=4,b=a-2a,A\ᦪᑡb
%X]ᦪᑡ^Aᦪᑡa
Ḅ_⚗nn+1nn`a.B2⚓ᐳ13⚓

219.cᖪe%ff(ghḄiᱥkl:;ᙠᖪeᦈnf200oghiᱥḄᐵᦪq᝞⊤:9iᱥu(ᓫ[0,100)[100,200)[200,300)[300,400)[400,4-oo)o\ᐗ)ghxᦪ20a5060CL+10(1)AaḄZ[(2)%fyzᖪe├|}~9iᱥ300ᐗḄghx?.ᨵ5xMᖪeiᱥᵨ⚣᳛ᭆ᳛AḄᦪfḄᑖᑡᦪ.20.(1)7x᣸ᡂ᣸᯿ᱏV⌕Aᵬஹஹ3xᨵ᣸#(2)e¡¢ᐗ£¤¥ᨵ4ᖛ§⁚©52ª⁚©⌕A᣸=⁚©ᓫB⁚©5ᨬ¬⁚©®ᖛ§⁚©ᨵ᣸#(3)14ᵱ☘±ᦟ³55᝕☘±ᦟ³⌱=4¶ᦟ³·z¸ᦟᩞº»⌕A¼ᨵ2¶ᵱᦟ³51¶᝕ᦟ³·zᨵ⌱#21.±Ḅ4ᨴ23¾®ὶᔠÁᦟÂᦻÄÅÆḄ“ÈÉÊ˾”ÍΓÈÉË5᱐ᩗ¾”%f(cᙢÒÓ▅ÊÕÖḄᑖ×ØÙ1ᙢ:;ÚÛf1000¶ÒÓÜÝᙠÞßàᑮfá1000¶ÓḄ¾âᙳ▅ÊÕÖ(ᓫo\Õ)^ä᪵,ᦪqᑖᡂ=2],(2,4],(4,6],(6,8],(8,10],(10,12],(12,14],(14,16],(16,18]æÄçᑴᡂ᝞ᡠḄ⚣᳛ᑖê".(2)%Üëf(á1000¶Óᦪìíî▅ÊÕÖ5ïðË▅ÊÕÖḄᑖ×ØÙ,1¾âᙳ▅ÊÕÖᙠ(8,10],(10,12]ñÄᑁḄÓóᵨᑖôÚ᪵Ḅ"#ÚÛf10x,1á10x:;ÚÛ3x,õ¾âᙳ▅ÊÕÖᙠ(10,12]ᑁḄÓxᦪ%X,AXḄᑖᑡ5ᦪ.

322.GHöᦪf(x)=(x2-x+1)•e-x+^x2-ax+|(ae/?).(1)Va=0,÷\g(x)=/(x)-2ᙠø—2,1úûᙠüḄýþ;(2)a
x21/(%)>4⚓ᐳ13⚓

4ᫀ᪆1.ூᫀ௃Bூ᪆௃4ᵯḄᵨ!"#$%&'(ᐸ*+,,ᑡ./ᩭᦑA23⚪56B,7891:9;<᪗Ḅ>ᦪX"#$@ᐸ*+A0,1,2,…10,ᦑXACᦣEFG#$ᦑB3ᔠ⚪56C,I$,ᢇᵯKLMḄᵯNᙠ10V20WPQḄᵯN+X"#$%&',,ᑡ./XḄᡠᨵ*+ᦑX2"CᦣEFG#$ᦑC23⚪56D,,TᙠyUVFGWXḄYZ[ᙠyUVḄ\]X"#$%&',,ᑡ./ᐸᡠᨵ*+ᦑX2"CᦣEFG#$ᦑ஺23⚪5.ᦑ⌱:B.#$Ḅ*+"FG/a@b,,ᑡ./ᩭḄFG#$cACᦣEFG#$de⌲⚗ᑨiᓽb.k⚪ὃmFGnopqẠ⚪.2.ூᫀ௃Dூ᪆௃:•••t+2=w6,3x+2=x+6ᡈ3x+2+x+6=20,•••x—2ᡈx—3,ᦑ⌱D.ᑭᵨzᔠᦪ{|ᓽb}.k⚪ὃm~zᔠᦪ{|Ḅᵨ⚪"qẠ⚪.3.ூᫀ௃Cூ᪆௃FG#$X8(10,0.4),D(X)=10x0.4x(1-0.4)=2.4.ᦑ⌱C.ᑭᵨ⚗ᑖḄ{|}ᓽb.

5k⚪ὃmCᦣEFG#$Ḅ}'"qẠ⚪.4.ூᫀ௃Bூ᪆௃Aᵯoᨵ4〈'᪷dᑖ'ᦪᳮ(52Ḅᵯo〈ᑮ4Tᵯ;ᑣ2Ḅ〈'ᐳᨵ45,ᦑ⌱B.ᑭᵨᑖ'ᦪᳮ}.k⚪⌕ὃm~ᑖ'ᦪᳮpqẠ⚪.5.ூᫀ௃Dூ᪆௃f(x)=xsinx—cosx,••f'(x)=sinx+xcosx+sinx=2sinx+xcosx,•••A-7)=2sin(-j)-jcos(-j)=-2,ᦑ⌱D./■(%)}¡¢£r(,)Ḅ+ᓽb.k⚪⌕ὃm¡ᦪḄqkW£¤¥qẠ.6.ூᫀ௃Bூ᪆௃ᵫ§᝱ᑖḄ©ªឋY¬P(f<2)=P(1<6<2)+0,5=P(04,஺6=®11S7=2SII.♦.=!6⚓ᐳ13⚓

61c"=´=µz=1x2=1.a1sI1S41122244ᦑ⌱C.ᵫ¶ᓽ·"ᦪᑡb¬S7=7a4,5=lla,¢}/¸Ḅ+.n6u4k⚪ὃmᦪᑡḄឋYὃm¹ºqkḄW£»¼pqẠ⚪.8.ூᫀ௃Cூ᪆௃AFG#$X½¾LZᑖ@PQ=1)=1,ᡠ¿P(x=0)=|,ᦑA§À6E(X)=Oxi+lxi=iᦑB§À6E(2X)=2E(X)=2x2=1,ᦑC2§À6D(X)=ix(0-1)2+|x(l-|)2=i,ᦑ஺§Àᦑ⌱C.k⚪ὃmLZᑖḄᳮ¿ÁE(X)=2NIUP"D(X)=2ᓃO-E(X))2p"E(aX+b)=aE(X)+bḄ£Wᵨ.k⚪ὃm⚗ᑖὃm¹ºḄW£»¼p;᫏⚪.9.ூᫀ௃Dூ᪆௃ᙠᜓ⌱Ḅ8⍝Æ⚪;ᵬ»ᐸ;Ḅ4⍝⚪ᑣ¾ᜓ⌱⚪;FGÈ/4⍝⚪ÉÊIÆ3⍝⚪Ḅᭆ᳛P(X=3)==£.ᦑ⌱D.ÎdÏᐺᭆEÑ}X=3Ḅᭆ᳛.k⚪ὃm~ÏᐺᭆEḄᭆ᳛{|pqẠ⚪.10.ூᫀ௃Dூ᪆௃(1+#)3+(1+*)4+.“+(1+4)8ḄÒÓ|;*3ḄÔᦪAÕ+Ö+...+×=(b+;)+Ø+...+×=(CJ+CR+...+Ö=+=C=126,ᦑ⌱D.

7ÙÚᑭᵨ⚗|ÔᦪḄឋYc$+C1=41ᓽb}¬ᫀ.k⚪ὃm⚗|ÛᳮḄᵨḼÝὃm⚗|ÔᦪḄឋYÞ+C7T=஺ß1ḄᵨὃmW£}»¼p;᫏⚪.11.ூᫀ௃Cூ᪆௃••an+i-an=|=6-Wᑣᵫ஺=%+(a-&)+…+(a,஺9)=2+(1—©,á+…+(W)=3-2101_29io-10ᦑ⌱C.ᵫa“+i=âã=6,äᑭᵨa஺=%+(஺2-%)+…+(%0—&9)ᓽb¬/åæ.k⚪ὃm~ᦪᑡ⌴èᐵÔஹë⚗}'ὃm~èᳮ»¼ì£»¼p;᫏⚪.12.ூᫀ௃Bூ᪆௃ᵫ⚪5í¤îïᨵ3ð3ð"µñḄᭆ᳛APi=(|)3=5¤îᨵ4ðò3ðµñ2ð4ðµñḄᭆ᳛AP2=C/X(|)3X=*óVíµᡊñᵬḄᭆ᳛AP=5+Ö=ᢴᦑ⌱B.ᑖA¤îïᨵ3ð3ð"µñ¤îᨵ4ðò3ðµñ2ð4ðµñᑖö}/ᭆ᳛¢}.k⚪ὃm~÷øùúnoḄᭆ᳛'£⚪"qẠ⚪.13.ூᫀ௃-1ூ᪆௃"/(x)=a(x+1)-f'fx}=a-ex,ᑣ(0)=a-l,ûüý/(x)ᙠZ(0,f(0))ᜐḄᑗ
x-2y+3=0ᚖa-1=-2,a=-1.ᦑᫀ—1.ᦪḄᦪᵫ⚪f(0)=a-l=-2,ᵫa.8⚓ᐳ13⚓

8⚪ὃ!ᦪḄ"#$%&ᵨὃ!(ᚖ
)᳛Ḅᐵ,-.Ạ⚪.14.ூᫀ௃j1-1==-ூ᪆௃67P(B\A)24-:4ᒹ9Ḅ.:;<==>,<=1-@>,ABᒹ9Ḅ.:;<=@>,2“஺ভF.᪷Hᩩ;ᭆ᳛KLMNᓽKL.⚪ὃ!Pᩩ;ᭆ᳛ḄKLQR.Ạ⚪.15.ூᫀ௃12ூ᪆௃᪷H=᝱VḄWXឋZ⌕\]^஺ᙠ(-050.5)ᑁḄᭆ᳛efR0.6827,ᑣ(஻7l7,4+஺)n(-050.5)o“=0,0=,ᡠr0.52snN12,nஹ/nᦑᫀ12.᪷H=᝱ᑖyZz{ᔠḄᒹ}ᐵ,~eᐵ,.⚪ὃ!=᝱ᑖyQ.Ạ⚪.16.ூᫀ௃72ூ᪆௃ᐜC,ᨵ=46ᐳᨵ⁐ᦑA
E,8
Dᨵ7W⁐ᑣḄ⁐6ᐳᨵ+6•⚪=186ᦑᐳᨵ4X18=726.ᦑᫀ72.ᑭᵨKᦪᳮᐜCḄ⁐ᯠᢥ᯿4
E,B
஺-ᔲ⁐r%⁐ḄWᦪ⁐6ᦪᨬᢥ¤6Kᦪᳮ.⚪ὃ!KᦪᳮḄ&ᵨ¥ὃ!¦§Ḅ¨©ªᳮ«¬QR᫏⚪.17.ூᫀ௃ᵨ⊤¯7°᥎ᑮ³ᳫ¬⊤¯°᥎ᑮ³ᳫµ⊤¯7°᥎ᑮ¶ᳫ·2⊤¯°᥎ᑮ¶ᳫᑣP(4)=P(AAUBI4)=PGMz)+P(Bi4)=PG4i)P(4Mi)+T2P(BI)P(42|BI)=—x+—X'"'ziLJ43+4-13+43+4-173+

9ூ᪆௃ᑭᵨÀÁ:;Ḅᭆ᳛MN
ᩩ;ᭆ᳛MNKL.⚪ὃ!PÀÁ:;Ḅᭆ᳛MN
ᩩ;ᭆ᳛MNQR.Ạ⚪.18.ூᫀ௃(l);ai=l=Si5=2+4Â-1522,/1Ãᦪ)71Q2=S?_S]=4+1,Q3=S3_S?=ᐭ2,ÅÆ,a,%ᡂ^ᦪᑡ2Ê2%=2(2+1)=14-A2,.%A=1±V2;(2)ËÌÍÎ1=4¥S=2+4Â_1(n>2),n•*,S+i=2+4a,:.QÏ+i=4a—4a_,nnzint•a—2a=2(a—2a_i)(n>2),Åa2=4+1=5%=1a—2al=3,n+1nnn2ᓽb=2b_],Ð=3,nn•.ᦪᑡ<Ï>-r3✌⚗2MÓḄÓᦪᑡ•b=3x2n,na-2a=3x2n-1,(Ô¥◀r2n+1n+1na஻+iÖ=3Å3,22n+12n4’22f<×>-r5✌⚗r:M^Ḅ^ᦪᑡ⌶=Ú73•,•an=(H),2%ூ᪆௃(1)᪷HḄ,஺2,ᡂ^ᦪᑡÎIḄÛÎ(2)᪷HÓᦪᑡḄ$ËÌÜᵫÓᦪᑡÝ⚗MNᦪᑡ&JḄ⌴ªMNᨬᵫ⌴ªMNß.⚪ὃ!^ᦪᑡḄ$ஹÝ⚗MNÓᦪᑡ$ஹÝ⚗MNᵫ⌴ªMNÝ⚗Q᫏⚪.19.ூᫀ௃(1)ᵫ⚪ᨵ20+a+50+60+a+10=200,Q=30,ᦑaḄ30Î(2)ᵫ(1)Z1àáᱥãäåæḄ⚣᳛ᓽᭆ᳛p=è=pᦑ5àáᱥãäåæḄᦪéfê~⚗ᑖyfëB(5,5,ᑣPì=0)=C«6(|)°•(Ú5=p(í=1)=i,(l)i-(1)4=A,P(f=2)=î.©2C┐=ᔁ%=ᑓ=fò,(1=A,%=4)=ó.V•ô=a%=5)=)210⚓ᐳ13⚓

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ḄᑖᑡḄὃẠ⚪.20.ூᫀ௃পᵬ!"3#$%&'ᐳᨵ“+=720.(2)/01⁚34ᨬ601⁚37ᖛ9⁚3ᐳᨵ:*=288.(3)⌱2=ᵱᦟ@A2=᝕ᦟ@ᐳᨵC/=60.⌱3=ᵱᦟ@A1=᝕ᦟ@ᐳᨵDE=20.ᡠᐳᨵ60+20=80..ூ᪆௃(1)ᑭᵨᣊLᓽNO(2)ᐜ᣸/01Aᨬ601R᣸ᒕTḄ⁚3ᓽNO(3)ᑖ⌱2=ᵱᦟ@A2=᝕ᦟ@A⌱3=ᵱᦟ@A1=᝕ᦟ@ᵫVᓽN.W⚪ὃX᣸ᑡYᔠḄ[ᓫᦪ^⚪Ḅ_ᵨὃX`aḄbcdẠ⚪.21.ூᫀ௃(1)ᵫ⚣᳛ᑖghij2(0.02+0.03+0.05+0.05+0.15+a+0.05+0.04+0.01)=1,ja=0.10.(2)ᵫ⚣᳛ᑖghijk1000=`almnᙳ▅qrsᙠ(8,10
,(10,12
uYᑁḄ`a#ᦪwxy0.150.1=32,z{ᵨᑖ|}᪵Ḅh}X10#ᑣmnᙳ▅qrsᙠ(8,10
ᑁḄ`al}10=6(#)ᙠmnᙳ▅qrsᙠ(10,12
ᑁḄ`al}4#k10#l3#ᑣXḄNDy0,1,2,3,

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ᑖᑡḄὃ²³cdẠ⚪.22.ூᫀ௃¹º(1)Q=0r/(%)=(%20%+1)•e~x,g(x)—/(%)-2=(x2-%+1)-e~x—2,xG[—2,1],g'(x)=9ÃÄ0,g(0)=1—2=—1<0,.•.ÏᙠÐ0&e(-1,0)u[-2,1],Ójg(3)=0,ᓽa=0,g(x)=/(x)-2ᙠÉÏᙠÐ0ḄÕÖ.(2)a>⌕¹º×x21rØ%)=1+#Aw25Ú⌕¹ºÛÜ+Ý•ÞwwßᓽN.exe32eàá+2.ᔖXG[l,+co),__(ä_1)஺_2)X-l_(XT)[eX-e3(x-2)]å(%)ߟᡃ'e3~ex+3à—/(ß02),xG[1,4-oo),஻'(x)=ex-e3=u(x)ᙠêG[1,+8)ᓫÊ⌴ìv(3)=0,•xE[1,3),î(x)<0,VrÇᦪ஻(x)ᓫÊ⌴ÌOxG(3,4-oo),î(%)>0,VrÇᦪ“(X)ᓫÊ⌴ì/12⚓ᐳ13⚓

12x=3r”(%)j᩽òDᓽᨬòDu(3)=0,•u(x)>u(3)=0,,.Ø'(%)>0,•Ø(%)ᙠ[1,+8)ÉᓫÊ⌴ì•h(x)>h(l)=%ó×x>1r/(x)==%+a-ôH>2ᡂ÷.&,ex2eூ᪆௃(1)Q=0r/(%)=(%2—%+1)-e~xg஺)=f(x)—2=(%2-%+1)-e~x—f2,xw[-2,l],ᑭᵨøᦪẆúÇᦪg(x)ḄᓫÊឋRᑭᵨÇᦪÕÖÏᙠªᳮᓽNj¯§ü.(2)a>4-⌕¹º×x21r/0)=ýþ+#ÿ
.⌕+3e6J\yx2eexe3e2:ᓽ./i(x)=++'”xe+8)ᑭᵨᦪẆᦪ(x)Ḅᓫ!ឋ᩽$%ᨬ$ᓽ'(.)⚪ὃ,-ᑭᵨᦪẆᦪḄᓫ!ឋ᩽$%ᨬ$ஹ/01ᓄ34ὃ,-5ᳮ78%9:78;<=⚪.