2021-2022学年上海市浦东新区某中学高二（下）期末数学试卷（附答案详解）

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2021-2022
()ᦪᔁஹᓫ⌱⚪(ᜧ⚪ᐳ4⚪ᐳ20.0ᑖ)1.a,b,c%&ᦪᑣᑡ)⚪*+Ḅ-()A.a>b,ᑣGe?>be2B.4Q>b,ᑣ5<abC.4aab>b2D.4QVbV0,ᑣ:ab2.AḄஹஹBᐳᨵD1350Gᐸ500GBIJ50G%KLM᪥DᏉPQRSTᵨᑖVW᪵YZ[\]^ᙠW`Ḅ᪵ᨵD120GᑣM᪵ḄDGᦪ%()A.80B.96C.108D.1103.4de(a+l)(a+2)(a+3)(a+4)(a+5),ᑣdeiaḄjᦪkl()A.ᙠ1,2,3,4,5ᡠᨵn`opqrḄᦪḄstuvB.ᙠ1,2,3,4,5ᡠᨵn`BpqrḄᦪḄstuvC.ᙠ1,2,3,4,5ᡠᨵn`wpqrḄᦪḄstuvD.xyz{q|4.}ᦪy-y(x)Ḅ%1,0)U(0,1,ᐸnP(x,y)/+y2=,ᑣᑡ)⚪*+Ḅ-()A.}ᦪy=f(x)-Ꮤ}ᦪB.}ᦪy=f(x)-᜻}ᦪC.}ᦪy=/(x)-Ꮤ}ᦪᑣᐸ%(1,0ᡈ0,1)D.4}ᦪ%(1,1),ᑣ}ᦪy=-᜻}ᦪஹ⚪(ᜧ⚪ᐳ12⚪ᐳ54.0ᑖ)5.ᔠ4={-3,-1,0,1,2},B={x||x|>1),ᑣAnB=.6.qki>0ḄL%.7.⚗idei⚗Ḅjᦪ%.8.ᵬ¢£ᕒḄᢗ¦)᳛%0.7,¨¢£ᕒḄᢗ¦)᳛%0.9,4ᵬஹ¨ᔜᢗ¦ªᑣាᨵG)Ḅᭆ᳛-.9.}ᦪ/(x)=
+sinx+1.4/'(m)=4,ᑣ/'(-m)=.

110.A5ᔆ|ᢇ²[\W᪵³´᪷¶W᪵³´·Ḅ²¸¹(ᓫº»¼)ᦪ¶½ᑴḄ⚣᳛ᑖÀÁY᝞ᡠò¸¹ḄÅ-Æ[96,106],᪵¸¹ᙠÆ[96,100)Ḅ²pᦪ-24,ᑣ᪵¸¹ᙠÆ[100,104)Ḅ²pᦪ-♦⚣᳛0.1500.1250.1000.0750.05006oxinnin,ind10611./(x)=(x+l)/nx,ᑣ/''প=.12.|ᑗ&ᦪx,ÉÊ%qᜧlxḄᨬᜧ᦮ᦪ.Í[3.25]=3,[0.36]=0.4[|x-3|]=2,ᑣ&ᦪ%Ḅ`Å-.13.Ïrᨵ4qrḄᦪÐ3qrḄᱥᳮÐv3qrḄᓄÐÔn`2,ᑣÕ2ÐÖlqr×Ḅᭆ᳛-(yØᵨᑖᦪ⊤Ã).14.4ᐵlxḄqki|2x-3|+|2x+5|

219.ᐰ{/=/?,ùᔠ4={ú;—ý<஺}8={x|þCO}.x-{3a+i)i1x-aJ(1)a=Bn4(2)pxeA,qxEB,pqḄᐙᑖᩩᦪaḄ".20.$%&'()*+,-ᐵ/0ᐭ2345⁚789ᜧ;45<=〉├@A5BḄCDE+F-G&ᑁ<=185K〉├LMBN42KO├5BḄPὃRS.TUVWXYZ[5BḄ\├]9(^_`5BḄ├abPd(e5bf├abgh)f\├iᵨxdᐗmnP=3-q(ᐸs0

3½ᫀN¿᪆1.ூ½ᫀ௃Cூ¿᪆௃¿@/4,c=0ac2=be2,mn஺஺2>Å2,⌱⚗A┯Ê@/8,Q>O>b->0>^,mnL—b>0,ᡠÏ(—a)?>(—a)(—fe)>(—b)2>0,ᓽÒ>ab>b2,⌱⚗Cv©@/D,Ôa=-2,b=-l,ᑣ2=,Õ=2,mn⌱⚗஺┯Ê.a2babᦑ⌱c.᪷ØhÙḄÚ}ឋÜ@⌱⚗sḄÝ⚪ßZᑖ᪆ஹᑨâvÊᓽã.}⚪ὃä-hÙḄÚ}ឋÜfåᵨæ⚪ÚẠ⚪.2.ூ½ᫀ௃Cூ¿᪆௃ூᑖ᪆௃}⚪è⌕ὃäᑖêë᪵Ḅåᵨ᪷Øíîᐵï¿ð}⚪Ḅᐵñò/ÚẠ⚪.ᵫ⚪ºã,ôVஹôõஹôÕḄöᦪᑖ÷T500,450,400,ᓽãø,`᪵}sḄôõùeöᦪ.ூ¿½௃¿ú`᪥ôõᐳᨵùeLöWijx+x-50+500=1350,=450,ᡠஹஹḄᦪᑖ500,450,400,2=50025ᡠ᪵"#$%ᦪ450X^=108,ᦑ⌱C.3.ூ-ᫀ௃Aூ᪆௃ூᑖ᪆௃14⚓ᐳ12⚓

4"⚪ὃ6Ḅ78⌕:⚗<=ᳮḄ?ᵨA⌕ὃ6$%ḄBCDEFGᣚDEIJKDELMNẠ⚪.ᑭᵨ⚗1}={x\x>1ᡈx<—1),AC\B={-3,2}.ᦑ-ᫀ{-3,2}.

5°V¯ᔠA,B,ᵫgD°VAnB."⚪ὃ6´¯Ḅ°µὃ6´¯=uiNẠ78ὃ6BC°DEyNẠ⚪.6.ூ-ᫀ௃(8,0)¸1,+8)ூ᪆௃ni

0,º»m¼oxe1)2,:.x(x-1)>0,x<஺ᡈ%>1,ᦑ-ᫀ(ߟ8,0)u(L+8).᪷Ãᑖ5(_/)=6/ᡠ᮱Ḅhᦪ-6,ᦑ-ᫀ—6.ᑭᵨ⚗<=ᳮ°VQR<#[᮱Ḅ⚗ᵫgᓽ]°."⚪ὃ6¨⚗<=ᳮḄ?ᵨὃ6¨$%ḄBCDELMNẠ⚪.8.ூ-ᫀ௃0.34ூ᪆௃ËᵬBÍᕒÏ#ÐÑ4ÒBÍᕒÏ#ÐÑB,ᑣP(A)=0.7,P&=0.9,ᡠាᨵÖÏ#Ḅᭆ᳛P=P(A)P(B)+P(A)P(B)=0.7x0.1+0.3x0.9=0.34.ᦑ-ᫀ0.34.ᑭᵨÙÚÐÑḄᭆ᳛eµÛ<°."⚪A⌕ὃ6ÙÚÐÑḄᭆ᳛eµÛ

6ᓽ/'(m)+/(—m)=2f(—m)=-2ᦑ-ᫀ-2.Üg(x)=/(x)-1Bᵨtᦪ᜻ᏔឋḄ=u]g(-x)=-g(x)éê]g(-m)=-g(m),ᓽ/(-m)-1=-[/(m)-1],éê°Vf(m)+f(-m)Ḅ,ᓽ]°Vf(-m)Ḅ."⚪✌ᐜᑭᵨ᪀⌼ĵ᪀⌼ðḄtᦪᯠòBᵨtᦪḄ᜻ᏔឋḄ=uᑨ§tᦪḄ᜻Ꮤឋ,ᵨ᦮ôJ«°Vf(m)+/(-õ)=⚪x⌕öb᦮ôJ«ḄBᵨ.10.ூ-ᫀ௃44ூ᪆௃ᵫ⚪b]7᪵"#÷øᙠ[96,100)ḄùúḄ⚣᳛=(0.05+0.1)X2=0.3,.•.᪵"üý=,=80,᪵"#÷øᙠ[100,104)Ḅùú`ᦪ=(0.15+0,125)x2X80=44.ᦑ-ᫀ44.᪷Ã⚣᳛ᑖþÿ
Ḅᵫ᪵ᙠ[96,100)Ḅᦪ24᪵!᪵ᙠ[100,104)Ḅᦪ.⚪$⚣᳛ஹ⚣ᦪᮣ)*ᵨḄ,ᔠὃ/.⚣᳛ஹ⚣ᦪḄᐵ12⚣᳛=⚣ᦪ+ᦪ567.11.ூ:ᫀ௃2ூ=᪆௃=2•••/(x)=(x+l)/nx,ᑣ/''(%)=Inx+~~>f(l)=/nl+.=2.ᦑ:ᫀJ22.᪷5LᔠMᦪNOP!/'(%)Q((1).⚪R⌕ὃ/NᦪḄT*UVWTẠ.12.ூ:ᫀ௃(0,1]U[5,6)ூ=᪆௃=2᪷5⚪!224|x-3|<3,ᑣ2Wx-3<3ᡈb3

7⚪ὃ/᪷5MᦪghiTẠ⚪.13.ூ:ᫀ௃ᢈூ=᪆௃=2klmnᨵ4dmḄᦪnp3dmḄᱥᳮp73dmḄᓄnptuv2Twx6ᦪn=%)=45,y2pz{dmn|ᒹ~ḄTwxᦪm=C2-d-Cl-Cl=33,0ᑣy2pz{dmn|Ḅᭆ᳛p=2="=*ᦑ:ᫀJ2ᢈ.tuv2Twx6ᦪn=C/°=45,y2pz{dmn|ᒹ~ḄTwxᦪ=஺bb—=33,ᵫy2pz{dmn|Ḅᭆ᳛.⚪ὃ/ᭆ᳛Ḅὃ/ᐺᭆஹ᣸ᑡᔠeTẠὃ/*U=TẠ⚪.14.ூ:ᫀ௃m4ூ=᪆௃=2y=|2x-3|+|2x+5|ᑣMᦪy=\2x-3|+|2x+5>|2x-3-2%-5|=8,Mᦪ|ḄgiJ8,+8)deP|2x—3|+\2x+5|8,•••m<-2ᡈm>4ᦑ£ᦪaḄvg¦m<-2ᡈm>4.ᦑ:ᫀJ2m<-2ᡈm>4.ᡃ¨©᪀⌼¬$gMᦪ᪷5¬$gḄ®ᡃ¨᧕$°Mᦪy=|2x-3|+|2x+5|Ḅgi!ᑮ£ᦪrnḄvg¦.⚪ὃ/Ḅ³¬$g´µdePᐸ᪀⌼¬$gMᦪ·᪷5¬$gḄ®ᑨ¹Mᦪy=|2ºb3|+|2%+5|Ḅgi=:⚪Ḅᐵ».15.ூ:ᫀ௃(b8,2¼ூ=᪆௃=2᪷5⚪!:(/(XiDminÁ(g(X2))min•••/(X)=X+2ᙠEl¼ÄᓫÆ⌴Èᑣf(x)>/(I)=5,Ê••g(x)=2%+a-1ᙠ2,3¼ÄᓫÆ⌴Ëᑣg(x)>g(2)=a+3,8⚓ᐳ12⚓

85>a+3,ᑣaS2ᦑ:ᫀJ2(-00,2¼.᪷5⚪!2(f^>((x)),ᑖÏ᪷5ᓫÆឋᨬgÒᐭ*U=.min52min⚪ὃ/ÔMᦪḄឤᡂ×Ø⚪ÙᓄJMᦪḄᨬgÚḄᐵ1=⚪ᐵ»z{᫏⚪.16.ூ:ᫀ௃0,Üூ=᪆௃=2Q=0Þᑣ/(%)=/ßᔠ⚪Q=0ᡂ×àQH0Þᵫ⚪!Ô(%)Ḅâ³Ja,3a,ᑣ0f(2a),•••f(x)ᙠ0,2¼ÄḄᨬᜧgJ/(2),çIJ4a<2,=!a<,Äᡠê20WaW1ᦑ:ᫀJ20ëᐜíî/Q)â³Ḅᦪïð!a=0ᡂ×àña*஺Þ/(%)ᨵòâ³óᔠ
ô᪷5ᨬkgJ0,!0/(2a),ᑣ᪷5/(x)ḄᨬᜧgJ/(2),ᑣ4aW2,ᑖ᪆*U=.⚪ὃ/~õᦪMᦪõᦪvg¦ḄØ⚪᫏⚪.17.ூ:ᫀ௃=2(1)÷tuv2xøùJwx2,ᑣtuv2xøùḄᭆ᳛JP(4)=û=C1015(2)÷tüùv5xាᨵ2xùJwxB,ᑣtüùv5xាᨵ2xùḄᭆ᳛JP(B)=ÿ=
.(3)ᨵḄᨵ1C,

9♦.•ᨵḄ;ᑮḄᭆ᳛ᔁ=|,"ᨵḄᨵ1Ḅᭆ᳛#P(C)=1-ᡈஹ(1(|)3=ᑶூ+᪆௃(1)ᑭᵨ0ᐺᭆ2ஹ᣸ᑡ5ᔠ789+:(2)ᑭᵨ<=>ᑖ@9+.(3)ᑭᵨ"⚗ᑖ@9ᭆ᳛BCD9EᨵḄᨵ1Ḅᭆ᳛.F⚪ὃI0ᐺᭆ2ஹ<=>ᑖ@ஹ"⚗ᑖ@JKẠMNὃIOP9+DQRKẠ⚪.18.ூTᫀ௃+#(1)V(%)=ex{ax+a+b)-2%-4,,•\]y=/(%)ᙠa(0J(0))ᜐḄᑗ]fgy=4x4-4,.i:+k…(2)ᵫ(1)nM#/(%)=4ex(x+1)—%2—4%,ff(x)=4e"(%+2)—2%—4=4(%+2)(ex-ᵫ/'(%)>0+txV-2,x>-ln2,vwxᦪf(%)ᓫ|⌴~;ᵫ/'(%)<0+t(2V%V-)2,vwxᦪ/(X)ᓫ|⌴.ᦑ=-2wxᦪf(%)t᩽ᜧ,/(-2)=4(1-e-2).ூ+᪆௃(1)1(%)=ex(ax+Q+b)-2%-4,ᵫ\]y=f(%)ᙠa(0)(0))ᜐḄᑗ]fgy=4x+4,ntᐵQ,ᓃḄfg5+tᓽn.(2)ᵫ(1)nM#/(%)=4ex(x+1)—x2—4%,('(%)=4ex(x4-2)—2%—4=4(x+2)(∑-ᑖᵫ஺)>0:ᵫ/'(x)<0+txᦪ/(x)ᓫ|.tᑮxᦪḄ᩽ᜧ.F⚪ὃIᑭᵨᦪẆxᦪḄᓫ|ឋஹ᩽ஹᑗ]fgJKẠMNKFᢈDf,᫏⚪.19.ூTᫀ௃+#(1)a=:w4={R<0}=[x\2:ᡈxQ,ᡠªB={x\a<%2,ᓽa>wA={x|2

10¬pRqḄᐙᑖᩩᡠª4UB,ᡠª{Ḝ+1´2+2,+tµ¶·#ঝ3a+l=2,ᓽa=wᓽ4=஺¹ᔠ⚪º:ঞ3a+l<2,ᓽa<#wA={x|3a+1

11I×PDQ᫏⚪.21.ூTᫀ௃+#পøG(X)=2X2-(4K—1)=2(X-1)2-1,xe[0,2]ᑣ|G(x)|Ḅᨬᜧ1ÝG(0)=l,G(l)=-1,G(2)=l,ᦑy=4x-1Rg(x)=2/,[0,2]Ḅ“úûxᦪ”.(2)F(x)=((ax+b)ᵫ-M(a,b)'45M(a6b)=b,a=\,ýᙠ&6(0,4)ÿ
(2)=M(a,b),ᓽF(a,b)max=
()=b,ᓽF(x)=Vx—|x—b=—|(Vx—l)2+1—b,ᦑ=1,ᵫFপ=[-b=b,b=jஹ௄maxmax(3):M(a,b)=0<%<4|Vx—ax-b\=0|/>|+|2-4a-b|>|2-4a|>1,ᦑM(a,b)N,ூ᪆௃⚪ὃᦪḄᓫ#ឋஹᑖ'()*+ஹᣚᐗ*+ஹ./0Ḅឋ12ᐸ4ᵨὃ6ᳮ89:;<89=>?⚪.(1)AG(x)=2/_(4x-1)=2(X-1)2-1,X6[0,2].ᑭᵨᦪḄᓫ#ឋ|G(x)|Ḅᨬᜧ0F1,GG(0)=l,Gপ=-1,G(2)=l,(2)F(x)=H-(ax+b),ᵫ[2)741I^)'2_”(1,ᑗ'ᵨ3/?)=ᓃ,&=OP££ᙠae(0,4)R
(&)=M(a,b),ᓽ
(a,b)mg=FQ2)=b,ᓽS;maxmax(3)M(a,b)=0<%<4|Vx—ax—b\=0