2021-2022学年辽宁省沈阳市五校协作体高二（下）期中数学试卷（附答案详解）

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2021-2022
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Ḅn⚗V^n°n18.20222ᨴ4ᓅᝍᜧ9ᐰᐵḄ¡¢ᜩᨵ¥¦§¨©ªஹᵯ¬YZ®¯2ᐵ.°ª᪀²¢ᜩᦈ¯2ᐵḄ?ᙠ2^7BḄ´$“µ¶·¸᰿ºὅ”ᔲᑣ´$“½µ¶·¸᰿ºὅ”ª᪀¨D¾sg¿D¾ḄÀRÁªÂ,Ã100ÄÅᑖ᪆ᑮ᝞⊤(ᓫÊ8):µ¶·¸᰿ºὅ½µ¶·¸᰿ºὅᔠÍ᝕ឋ2050ᵱឋ15ᔠÍ100(1)²B⊤RḄᦪÑᑏÓ᦮sᑨÖ×ᔲᙠØ┯ÚḄᭆ᳛XÛ¨0.005ḄÜhÝ$ឋÞ9ᔲ$“µ¶·¸᰿ºὅ”ᨵᐵT(2)²⚣᳛¬$ᭆ᳛àg¿D¾Ḅ᝕ឋÀRᵨÁªÂ᪵Ḅã¢#Â,1,ᐳÂ,3#äåÂ,Ḅ3R“µ¶·¸᰿ºὅ”Ḅᦪ$X,:¢#Â,Ḅ192345ḄXḄᑖæᑡஹᦪçèE(X)VéO(X).n(ad-bc)2▬8K2=ᐸRTi=a+b+c+d.(a+b)(c+d)(a+c)(b+c)'

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a,+iḄ¯⚗ᡠ°=±•ᓽ+i=(3N61)(3*+2),n,11i,i1)nᑣᡂ=(3n-l)(3n+2)-3^3n-l3n+2)'.,rr,X,1.X.±X.±±■>•ஹflᵫᦇ•89=-X(--------+----------+…+---------------------)=-(--------------)=-------------.'µn3ஹ25583n-l3n+23ஹ23n+272(3n+2)ூ᪆௃(1)⌱জ·¸¹eᦪᑡ0ᦪᑡº»¼ᦪᑡḄ✌⚗pᓽ·dᦪᑡ¦Ḅz⚗#i⌱ঝ·¸¹ean+i+am=2M,·vᦪᑡaᦪᑡ,º»¼ᦪᑡḄ✌⚗pnᓽ·dᦪᑡ%JḄz⚗#i⌱ঞᑖ᪆·vᦪᑡ¾ᦪᑡᦪᑡº»¼ᦪᑡḄ✌⚗p·d¿,Àᵫa=22·dᦪᑡm"Ḅz⚗#in(2)d°=(3n-l)(3n+2),·ea="ÁÂ6⊤)ᑭᵨÄ⚗dp{·dÅLfjlO>5«i-Aᓝ4s⚪ὃuÆᦪᑡḄ⌴¸#pÄ⚗ÇÈdp4᫏⚪.18.ூZᫀ௃(1)2x2ᑡὶ⊤:ËÌÍ᰿ÏὅÑËÌÍ᰿ÏὅᔠÒ᝕ឋ203050ᵱឋ351550ᔠÒ5545100n(ad-bc)2_100x(20x15-30X35)2ᡠK2=«9.091>7.879,(a+b)(c+d)(a+c)(b+c)50x50x55x45ᡠᙠÖ┯ØḄᭆ᳛"ÛÜ0.005ḄÝÞßàឋᮓËÌÍ᰿Ïὅ”ᨵᐵ.(2)ᵫ⚪ã·XäB(3,|),XḄᡠᨵ·PS0,1,2,3,ᡠP(X=0)=ᘊ(|)஺(|)3=3:P(X=1)=0(|>(|)2=ញP(X=2)=ᡈ(èé=êP(X=3)=ëèì஺=ⅉᡠXḄᑖîᑡ:714⚓ᐳ19⚓

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Ḅᑖᑡ᫏⚪.19.ூᫀ௃(I)a=1f(x)=Inx+x,ᑣ/(%)=+1,/(1)=1,r(1)=2,ᦑᑗ!"y-1=2(x—1),ᓽ2x—y—1=0.(%)'ᦪ/'(%)=Inx+ax(aGR)Ḅ./0"(0,+8),f'(x')=জ2a20/(3=4>0,ᑣ'ᦪ/(x)=Inx+ax(aGR)ᙠ(0,+8)7ᓫ9⌴;ঝ2a<0xe(0,-=f(x)>0,ᑣ'ᦪf(x)=Inx+ax(aGR)ᙠ(0,7ᓫ9⌴;xe(>?,+8)/(%)<0,ᑣ'ᦪf(x)=Inx+ax(aGR)ᙠ(-+8)7ᓫ9⌴BC7ᡠE2a20'ᦪ“X)Ḅᓫ9⌴;FG"(0,+8),2a<0'ᦪf(x)Ḅᓫ9⌴;FG"(0,-=ᓫ9⌴BFG"(>1+8).ூ᪆௃(I)IᐭaḄKLM'ᦪḄNᦪOP/(I),Q(1),LMᑗ!ᓽRS(II)LM'ᦪḄNᦪTUVWaḄYᑨ[N'ᦪḄ\]LM'ᦪḄᓫ9FGᓽR.^⚪ὃ`aLᑗ!b⚪ὃ`'ᦪḄᓫ9ឋdeNᦪḄfᵨὃ`ᑖhVWij,k᫏⚪.

1620.ூᫀ௃(1)2nN2A=n2/l-i=(n-I)2,n9nlmnBa=A—A_=2n—1Snnn12oi=1Ḅ=&=1,p〉ᔠs=2n—1,ᦑᦪᑡQ
ḄT⚗um"=2n-1Sn(2)ᵫ⚪wx0=y=z{C=c+c+-+c,nx2n_1.352"-lrḄ=77+*+…+4=,+|+M+…+}lmnBR~=/+≶++…+ᝅ>ᓽB=[++*+≶+…+ᜓ)ߟ1+(1—+)-2n+3oCn=3--(3p=£S+,ᯠ+>22zi—12n+13------------------=L2TI+12n—1ᓽb“>2>B=+Z>2+…+b">2n:n%ᵫ2n-l,2n+l2,,,,2,22>☢,+ᨴ=d1-n+1+n=2n+>u₹ᓽ=2+-|,ᵯ=2+|>|,…=2+2(⊤>),2222222fi„=(2+--)+(2+---)+-+(2+—--)=2n+2--<2n+2,Tᓽ2n2}=2,R~2=++…+b>2nS¬ᵫᓃ=◤+᝼=1-½+1+-Z=2+¾>ᗩ£¤RÀ=n2222222(2-|)(2|--)...(2—--)=2n2--<2n2,+7+++++++kR®Á2n<%Ã<2n+2(nGN*).Ä16⚓ᐳ19⚓

1721.ூᫀ௃(1)ÇÈÉ4Ḅᭆ᳛"PG4),ÌÍᑮḄÏÐÑᦪ"Òᑣᵫ⚣᳛ᑖÔÕR~ÖÍ1É×ÑkÐÑḄᭆ᳛"5(0.04+0.02)=0.3,¸kÐÑḄᭆ᳛"1-0.3=0.7,ØWÙB(2,0.7),ᑣP(4)=©0.7x0.3+Ð0.7x0.7=0.42+0.49=0.91S(2)ᵫ⚣᳛ᑖÔÕ~ᢣ᪗Kᜧᡈ485Ḅ×Ñm6[85,90)Ḅ⚣᳛"0.08x5=0.4,me[90,95)Ḅ⚣᳛"0.04x5=0.2,mG[95,100)Ḅ⚣᳛"0.02x5=0.1,•ᑭᵨᑖßÌ᪵ÌÍḄ7É×Ñrn€[85,90)Ḅᨵ4Ém€[90,95)Ḅᨵ2Ém6[95,100)Ḅᨵ1Éâã7É×ÑÖÍ3É,äᢣ᪗Kme[90,95)Ḅ×ÑÉᦪxḄᡠᨵR§ÍK"0,1,2,ØUP(X=0)=|=|,P(X=1)=4=P(X=2)=å=i,.XḄᑖᑡ":X01224iP777416•xḄᦪç"F(X)=Ox|+l-7-7-7(3)ᵫ⚣᳛ᑖÔÕR~è×ÑḄäᢣ᪗Kéᑭêy(ᐗ)Ḅᐵí᝞⊤ᡠï(1

18õö'(t)=-0.5ef+2.5=0,~t=ln5,ý2te(1,ln5),h'(t)>0,ᦪh(t)=—0.5et+2.5tᓫ⌴te(bi5,4)'(t)<0,ᦪ(t)=-0.5e+2.5tᓫ⌴,.•.t="5h(t)#ᨬᜧ&'("5)=-0.5e,n5+2.5xln5«1.5,•••,-.-/01234ᑭ1=m5x1.689-/Ḅ;ᙳᑭ=>ᑮᨬᜧ.ூA᪆௃(1)DEFG#H9IJ/Ḅᭆ᳛'0.3,ᵫ⚪PQRST⚗ᑖWXAᓽZ[(2)᪷]ᑖ^G᪵Z`8^ᑖaG#4,2,19᪷]bcdᑖWXᑖWᑡஹghᓽZ;(3)DE89-/Ḅ;ᙳᑭ=ᑭᵨkᦪXFᨬᜧ&ᓽZlA.m⚪ὃop⚣᳛ᑖWrstuᦣwxyz{ḄᑖWᑡ|gh}~ᭆ᳛ᙠ2▭⚪Ḅᵨ᫏⚪.22.ூᫀ௃Aপ'g'(x)=e,ᡠ}g(x)ᙠx=0ᜐᑗ᳛k=g'(0)=1,ᑗy=x+l,((=H1,|/(x)ᑗḄᑗ'Qo,xoln*),ᑣ᳛k=f(%)=In5-1,0ᑣᑗ1Ḅs¥Z⊤§'Q=On—l)(x-x)+xln^-=l)x+x,oo0ᑍ0XQXQᵫn«1HI,A¬la=2.elx=10(2)(x+x)4>a2xx,ᳮᵫ᝞°:x212ᵫ⚪r(x)=ln£-l,ᵫ´(x)=0lx=£,?0)ᓫ⌴'K<%1+x/(%1+%2)2ᓽxpn>(x+x)lnXix2Xj~rX2ᡠ}lnº>@Mn+,জXjX]X+XJ712ÁᳮÂ>ÃÄÅঝজ+ঝlᕶ+1È>(Ã+ÃÉÊ'Ë+5=2+Ì+ÍÎ4,Xix%22ᵫX1+Ï0,Ñ18⚓ᐳ19⚓

19ᡠ}InÔ+InÕ>4)=,ᓽ\>(H)4,X1x2X±XXXXi+X12t22ᡠ}(%i+x)4>a2xx-212ூA᪆௃(1)ᑭᵨkᦪḄcdP×XFᑗḄ᳛ØᐭÚs¥ᓽZ[(2)ᑨÜ᜜ḄᓫឋlFfQi),/(©)/(à+&)Ḅᜧ«ᐵã᪷]kᦪḄäEឋåæçèÚḄឋålFéê.m⚪ë⌕ὃoᑭᵨkᦪẆîᑗ⚪ᑭᵨkᦪẆîïz{⚪è`ðè⚪.