黑龙江省鸡西市鸡东县2022-2023学年高三上学期二模数学试题（含答案解析）

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ḕ2022-2023ᦪ⚪᪥:.::ὃ:ஹᓫ⌱⚪1.ᔠ4=x|logK«x-l0,#leA,ᑣaḄ)*,-.A.(8,2)B.0C.(1,2)D.(2,+oo)2.78ᦪ=cosx+

16.xe.O,M{8ᦪy=.—ߟ1/ᔙ3@8ᦪ{ᑣzᦪ%Ḅ*@.A.tn=2B.tn=-\C.m=-lᡈ/=2D.21.#“=10°{=lg..8,c=log3.5,ᑣ.5A.a>b>cB.b>a>cC.c>a>bD.a>c>b8.8ᦪ஻-bᙠRḄ8ᦪ=l.#lḄᨵ2W>3Kᵨ¢.3x-2£<1ᔩ16-3¥.3£-2Ḅ¦@4A.D.,+003¨sin2acos/?=2cos2a.l+sin/?,ᑣVᑡYZvwḄ9.-A.2a-B.2a+=ynjrC.a-\-/3=—D.a—P=—10.8ᦪ{.x=2sin.0x+sM>O,«¬{ᐸ®¯°Ḅᨬ±²³´Ḅµ¶@{·8ᦪy=/.xḄ®ᔣ¹º»¼Xᓫ½¾¿¬Àᑮ8ᦪg.xḄ®{g.x@᜻8ᦪ{ᑣ.A.ÃḄ®ᐵm²Å0bÇÈB.n”Ḅ®ᐵm²É?ÊlÈC.஻xᙠWᓫË⌴ÍÎ.஻xᙠÉᓝᓫË⌴Í11.8ᦪ/.x=2sin.0x+e,.ty>O,-1^

2Õ-()---x>012.8ᦪx'#8ᦪg(x)=஻x)TᨵØXÙ²{ᑣ()l-x12,x<0A.lv¹l1E.“Ḅ.15.cosl—+aÛIjcosØஹÞß⚪16.#8ᦪ“X)Ḅàᦪá(Êâᙠàᦪ{ãr(x)Ḅàᦪ@r(x).᝞/(Êlxe(a^),åᨵá(x)<0ᡂç,ᑣ“ᨵ᝞VឋéêK+஽;..+ì4)+/(?+...+/(íᐸu“î,o/…{”(M).#஻x)=sinx,ᑣ/஻(x)=q᪷ñòឋéóôêᜩ+஽+W=ᐔ᳝,ì,ìe(O,7T){sinx,+sinx+sinwḄᨬᜧ*@.2øஹ¦ù⚪

317.1ᦪ/(x)=(2M+9,஻-4)x"ᙠ(-8,0)78ᦪ.প:;ᦪAx)=᪆?@(2)ᑨBᦪAx)Ḅ᜻ᏔឋFᑏHᐸᓫKLM.18.ᦪ/(x)="e"-Inx-e.(1)Q஺=1RSTᦪ“X)ḄVWXᙠYZ@(2)Q“>1R[\]Qx>0R/(x)>2-e.19.ᦪ/(x)=sin(]-x)sinx-Gcos2x.(1);/(x)Ḅᨬbcᕜefᨬᜧ@TT2஻(2)STAx)ᙠ7ḄᓫKឋ.OJ20.ᦪ=cos2x+sᔊ(x+-g(xeR).(1);/(x)ᙠLM-],()7Ḅᨬᜧfᨬb@ফ#/m-n)=ᜓ;ainlaḄ.21.ᦪf(x)=-x|x—a|+l(xwR).পQa=2R:ᑏHᦪg(x)=/(x)-xḄᓫKLM;ফQR,;ᦪf(x)ᙠ[1,3]7Ḅᨬᜧ.22.ᦪ,/'(x)=e*sinx-&asin(x-2),xe[O,7t].প#a41,ᑨBᦪf(x)ḄᓫKឋ@(2)[\]ev(n-x)+1>sinx-cosx.

4zὃ|ᫀ]1.Cூ=௃-.-l&A,••l°gi(«-1)>0,ᓽ2ᑣᦪ஻Ḅ(L2),ᦑ⌱:C.2.Cூᑖ᪆௃᪷RḄᦪ•/'(x)Ꮤᦪ/(-x)=/(x)ᑨB.ூ=௃b=0Rf(x)=cosx+bsinx=cosx,/(x)Ꮤᦪ@/(x)ᏔᦪR./Ḅxឤᡂ
/(-%)=cos(-x)+bsin(-x)=cosx-Z?sinxcosx+Z?sinx=cosx-&sinx,inr=0Ḅxឤᡂ
ᓃ=0.“6=0”“f(x)Ꮤᦪ”Ḅᐙᑖ⌕ᩩᦑ⌱C.ூW¡௃¢⚪¤᧕¦§§⌕¨ஹ1Ạ¨ஹ«¬ᳮ¯°Ḅὃ±.3.Bூᑖ᪆௃᪷ᐰ³´µ¶⚪ḄᔲXᙠ´µ¶⚪Xᙠ´µ¶⚪Ḅᔲᐰ³´µ¶⚪¸ᑨBজঝ@ᑭᵨ1¢½?ᑨBঞ;¿ᔠÁÂᦪឤÃᣚÅÆឋÇᑨBট¸|ᫀ.ூ=௃᪷ᐰ³´µ¶⚪ḄᔲXᙠ´µ¶⚪Xᙠ´µ¶⚪Ḅᔲᐰ³´µ¶⚪জ½cÉ^^ll3xeR,cosx+^->2,,fi2./tanxx------=2,V2)tanxVtanxi7T\7T1QÌÍQtanx=——ᓽX=0,ÎRÏঞcÉ@tanx4I2)ᵫsinx+cosx=>/2sine[-72,,Ñ᝞xR,0sin(x+F)=&,ᦑHrwR,Ó$m+85%=⊈টcÉᦑ⌱]B4.D2121ூᑖ᪆௃ÖS+°×஺+ᓃØÙÚÛÜᑭᵨ1¢½?¸;S+°Ḅᨬb.3a4b3a4஺ூ=௃ᵫᩩ¸|ᫀÝ1⚓ᐳ13⚓

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.Êàg+LḄᨬb“+ᳮ3a4b123ᦑ⌱]D.5.Dூᑖ᪆௃ᑨBᦪḄ᜻Ꮤឋ¸᣸◀B,C@ᑭᵨᱯä¸ᑨBA,D,ᓽ|ᫀ.ூ=௃Êᦪf(x)=±jlḄ(YO,0)U(0,”O),Ji/(-x)=~4v~—=/(x)42x2xᦑ஻x)=£tlᏔᦪ᣸◀⌱⚗B,C@2xQx=2R/(2)=æ<0,çWᙠÝèé▲ᦑ᣸◀A,ᦑ⌱]D.6.Aூᑖ᪆௃᪷ëᦪḄfᓫKឋ¸|ᫀ.ூ=௃Êᦪì=(/-஻-1)"3íîᦪï(0,)Ḅ8ᦪ,m1—m—\=1ᡠÅ=:tn=2.53<0ᦑ⌱]A.7.Dூᑖ᪆௃᪷ᢣᦪᦪÅÆᦪᦪḄឋÇᑨB஺°,cḄᓽ¸Ñ¤ᜧb¸|ᫀ.ூ=௃ᵫᦪy=10ஹòᦪ¸a=10°'>1,ᵫy=lgxòᦪ¸b=lg0-8<஺ᵫᵫy=log5*òᦪ¸01>c=log3.5>0>=lg0.8,5'.a>c>hfᦑ⌱:D8.C|ᫀÝ2⚓ᐳ13⚓

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%+3X1FxJ,ᔠ?@ᦪ0ὃBCDᓄFGHᑖ᪆FG,LMN᫏⚪.9.Aூᑖ᪆௃ᵨPQRSஹURVḄWXSHYZSᓄ[sin2acos/?=2cos2a
1+sinব0ᵫ]^W_`.ூa௃ᨵsin2acos/7=2cos2a
l+sin/7,2sinacosacos஻=2cos2a
l+sin/7,sinacos-cosasin/7=cosa,sin
a-^=cosa=sin——a,ᵫMdᫀf3⚓0ᐳ13⚓

7᜛€(0ᔁ]ᓛ(0pqᡠsc-ᡈ-aac-Sஹ0ᦑ⌱A.ூ'(௃z{⚪|⌕ὃB~Rឤᣚ0ὃBPQRSஹURVḄWXSHYZS0LMN᫏⚪.10.Cூᑖ᪆௃᪷5ᦪf(x)/Ḅᨬ"'Ḅ0ᑮT=0᧕/(x)=2sin(2x+e).ᦪy=/(x)Ḅ/ᔣ¡ᓫ¢£¤¥0g(x)=2sin(2x+?+00¨᪷5g(x)᜻ᦪ0ªIJ/(x)=2sin(2x-?),ᯠ¥⌲⚗°±ᓽ.ூa௃²ᦪf(x)/Ḅᨬ"'Ḅ³0ᡠsᐸᨬ{Wᕜ¶7=³0ᑣ஺=º=2.ᡠs/(»)=2sin(2x+>).ᦪy=஻x)Ḅ/ᔣ¡ᓫ¢£¤¥0g(x)=2sin[2[x+1]+e=2sin(2x+7+”Ḅ/,²g(x)᜻ᦪ0£+e=%r(keZ),6ᡠs9=ᐔ_?(eZ).Ç62ᡠs஺=£.6ᦑ{)=2$É(2%-".Êx=?Ë0/(x)=l,ᦑ஻x)Ḅ/ᐵM'Í0):Î0ᦑA┯ÐÑÊx=-gË0f(x)=-2,ᦑ/(x)Ḅ/ᐵMÒÓx=-J:Î0ᐵM':Î,o6\v7ᦑB┯Ð;f.fj.f(x)ᓫ=⌴0ᦑCW_;f(x)ᓫ=⌴Ú0ᦑD┯Ð.ᦑ⌱ÛCdᫀf4⚓0ᐳ13⚓

8ூ'(௃z⚪|⌕ὃB~RᦪḄ/Hឋ-Þᐸ/ᣚ0ßὃBCàá@ḄFG,LMN᫏⚪.11.Aூᑖ᪆௃᪷5f(x)Ḅ/@7=/0@ᑗ=2,¨᪷5/(1)=2,@oË0஻G=õ0ᑣ(G=ö÷0.•.ᙠ(O,e)Çx)>0,/(x)⌴0ᙠ(3))<0,⌴Ú,Px>0Ë0஻ù)=ᜐᨵᨬᜧã/üý0þᙠ(O,e)/(x)e(—8,1)0ᙠ(e,+=o)xeef(x)e(Oý).eÊxWOË0/(*)=32+1ᓫ=⌴0•♦./(X)/᝞
ᫀ5⚓ᐳ13⚓

9ᦑ⌱c.13.4ூᑖ᪆௃᪷ᐗ£ឤᡂA=l-4(a-2)«(),ᓽ"
ᫀ.9$%&௃Qx2+x+a—220xwRឤᡂ/.'=l-4(a-2)0,/.«-,9ᦑ
ᫀ(0'4ூ&᪆௃ᑖ)஺0+,)஺-0+./ᑖ012"&34
ᫀ.ூ%&௃)஺0+1஺-1,1+஺51,ᡠ7/(1஺)=/(1+/20_a)+a=_(l+a)ߟ2a,&4=_<0,=>?@A)஺-0+l-«l,l+al,ᡠ7(1—a)—2a=2(l+a)+a,&a=-0,=>._,3ᦑ
ᫀ(-D.4ூEF௃G⚪ὃJ&ᑖKLᦪḄ34ᙠᑖKLᦪ"LᦪPḄ+᎛⌕STUVWᐭᑮᡠZḄ&᪆[\&G⚪Ḅᐵ^_`aẠ⚪.ூᑖ᪆௃ᵫdeᩩgᑭᵨjklᓄncos(^-a)=cosᓽ"&.ூ%&௃&o(cosp+a1
ᫀ6⚓ᐳ13⚓

10ᦑ
ᫀ(16.-sinx---2ூᑖ᪆௃/'(x)=cosx"k_f(x)=-sinx,ᵫ~LᦪḄe/(x)<0ᡂ᪷LᦪḄឋsin᳝+sinx+sinx<3sin$ஹ+A+,ᓽ"sin᳝+sinx,+sinx?Ḅᨬ23ᜧP.ூ%&௃஻x)=sinx,xw(O,7t),ᑣ/"(x)=cosx,ᑣ/"(x)=—sinx,xe(O,7t),ᵫ`/஻(x)<0ឤᡂᦑF(X)ᨵ᝞ឋ(+%-+ᔥ&)+*2+…+fম=3xsif=¥JsinX]+sinᓰ+sin&<3sin[32□/a/.sinx,+sin+sinḄᨬᜧP(-yߟ,2ᦑ
ᫀ(-sinx,¨217.(l)/(x)=x-5(2)᜻Lᦪᐸᓫ®¯°((-8,0),(0,-KO)ூᑖ᪆௃(1)᪷³LᦪḄ´µ,¶2/+9஻?-4=1,"&ᓽA(2)᪷aLᦪḄឋᑨºLᦪḄᓫ®ឋ»¼ᐸᓫ®°.(1)ᵫ⚪½2¾+9,”-4=1,&m=1ᡈ"=-5,2ÂÃÄ)"=g+Lᦪ/(x)=jᙠ°(-8,0)ÇȽµᡠ7É=5,M/(x)=x~5•(2)•••/(X)=XT=3⌕ÎLᦪᨵ½µᑣXW0,ᓽ´µÐ((F0)U(0,+8),ᐸᐵ`ÒEÓ.
ᫀ7⚓ᐳ13⚓

11•••/(T)=ᓰ=->-/(X),ÕÖLᦪ(᜻Lᦪ.)x>0+᪷aLᦪḄឋe/஺)=ᔆ5ᙠ(0,+8)Ç(¯Lᦪ•••Lᦪ"X)\᜻Lᦪᙠ(y,0)ÇÙ(¯Lᦪᦑᐸᓫ®¯°((—,0),(0,-K»).18.(1).ÛÜEA(2)ÝÞß&᪆.ூᑖ᪆௃(1)à஺=1Wᐭ/প=0,"âLᦪ/*)Ḅkᦪᑭᵨkᦪã1LᦪḄᓫ®ឋäåæÜEçᙠឋ´ᳮᓽ"&A(2)᪷éeᩩg᪀⌼Lᦪg(x)=e'-lnx-2,ÝÞg(x)>0ᙠx>0+ឤᡂᓽ&.ூ%&௃প)஺=1+,f(x)=e-

12x-e,ìᯠî)=(),ᓽ1\/পḄÛÜE"kr(x)=e--,ðপᙠ(0,+8)Çᓫ®⌴òó-[)=£3<0,r(D=e-l>0ᑣð(x)ᙠ(')ÇçᙠõÜE¼)0cx<᳝)+f\x)<0,)x>/+f\x)>0,oöLᦪAx)ᙠ(0,)Çᓫ®⌴¯ᙠ((ø))Çᓫ®⌴ò¼஻/)0,û¼ᙠ(0,)ÇLᦪf(x)çᙠÛÜEᡠ7Lᦪ/“)çᙠ.ÛÜEAফ¶g(x)=e*-lnx-2,x>0,ᑣg'(x)=e*-—ᵫ(1)eg'(x)ᙠ(0,1)Çᓫ®⌴òóᙠXþ,1)ÇçᙠõÜEÿᓽ*=,xe(O,x0)g(x)ᓫ⌴,»)g(x)ᓫ⌴^W>^(x)=e''>-lnx-2=e'''-ln^--2=—+x-2>0,ᓽe*-lnx>2,ᑣ000ex஺e-Inx—e>2-e>&a>l,ᨵae>e"*+,/(x)=ae'-Inx—e>e'-lnx-e>2—e,ᡠ/x>0/(x)>2-e.1ᫀ38⚓ᐳ13⚓

1319.(1)ᨬ;<ᕜ>?@ᨬᜧB?1-3C(2)ᙠ஽6ᓫ⌴ᙠEFᓫ⌴.ூᑖ᪆௃(1)ᵫᩩMᑭᵨPQឤSTᣚᓄWXᦪZᑭᵨ<[XᦪḄᕜ>ឋ^ᨬB_,f(x)Ḅᨬ;<ᕜ>^ᨬᜧBC(2)᪷b2x-ce[0,eᑭᵨ<[XᦪḄᓫឋᑖfgh_,f(x)Ḅᓫឋ.ூij௃(1)/(x)=sin^y-Ac^sinx->/3cos2x=sinxcosx-A/3cos2x1.crr1+cos2x=—sin2x-73--------22=sin2x——----7I3J224ᑣ/(X)Ḅᨬ;<ᕜ>?T=C=@€Z,ᓽX=+᝕x&£Z/(X){,ᨬᜧB?1—XEC32122(2)}~]2x-ye[0^],7T-JT7T§77"ᑣ2x-ge0,g,ᓽxeg,3f(x)?XᦪCj2JTFTT§TT22%-ὡ€@,@ᓽxe—஻x)?Xᦪ•57r27r••;)ᙠiifᓫ⌴ᙠ—yᓫ⌴.ூ௃⚪ὃ<[XᦪḄឋj⚪Ḅᐵ+ᑭᵨPQឤSTᣚᓄWXᦪ.20.(1)/uu=1,w*ফflூᑖ᪆௃ᑭᵨQZᵫQᓄ.পᵫXḄ_,¡ḄᑣXᦪᨬB¢_C(2)ᵫ£¤_,sin(᜛-?)=(,Zᵫ§¨©Q_sin2aḄB.ூij௃jc/(^)=cos2x+sin|x+co.y|x+|1ᫀ39⚓ᐳ13⚓

141+coslx1-fcos2x+-cos2x+—sin2x\'---------------4-«=2222227—1—3cos஺2x+=----sin2x+ὡ஺?2x+222J222~2nf-72171(1)VXG~,2x+—GT~333µI2x+—3JG—1,~Tᑣ/(°”“³´%"=ߟ_~2325ூ௃⚪ὃPQXᦪḄឤSTᣚ¶ᵨὃy=As·(5+9)¸XᦪḄ¹ºEឋ,ὃ»¼½¾¿*À᫏⚪.21.(1)ᓫ⌴ÂÃ?(-8,g3^Ä2,+8),ᓫ⌴ÂÃ?(1,221(1<«<3)ফ/(x)Å10-3஻(3<஺<4)2-a(a>4)x2-3x+l(x<2)ூᑖ᪆௃(1)4=2_Èg(x)=/(x)-X=<*+É("2)’ᑭᵨËÌXᦪḄឋÍÎXᦪḄᓫÂÃ;(2)ÐÈXᦪ73ḄᜧѹºᦪÒÓᔠᑖfghÕÖᙠÄ1,3×ØḄXᦪB/প,/(3),/(஻)Ḅᜧ;ᐵÙᓽ¢_,1ᫀ.(1)x2-2x+l(x<2)a=2y(x)=-x|x-2|+l=-X?+2x+1(xN2)'x2-3x4-l(x<2)ᡠ/g(ᐗ)=/(¾-Ü=,—x?+x+l(x>2)1ᫀ310⚓ᐳ13⚓

153xv2^(x)=x2-3x+l,ᐸ¹ºßàᔣØâãäåæ?x=ᡠ/g(x)ᙠç8,|Øᓫ⌴ᙠè,2)Øᓫ⌴CXN2g(x)=-x?+X+1,ᐸ¹ºßàᔣéâãäåæ?X=g,ᡠ/g(x)ᙠÄ2,M)Øᓫ⌴.ëØ¢¤g(x)Ḅᓫ⌴ÂÃ?ç8,|^Ä2,+8),ᓫ⌴ÂÃ?(1,2(2)ᵫ⚪ì¤஺>1,/(X)*cÐÈᜧѹº᝞¹c@X-ax+\(x3f*)ᙠl,yØᓫ⌴ᙠô,3Øᓫ⌴,ᡠ/,õ3<஺<4,ᑣ/(0=/(3)=10-3஺Cõ“W4,ᑣ/(÷“᧜=/(1)=2³ëØ¢¤ᙠÂÃÄ1,3×Ø1(1<஻43)/(x)max=/°—3஻(3<஻<4).2-a(a>4)22.(1)ᙠÄ0,Ø஻x)?XᦪCᙠÄúᐔ×Øf(x)?Xᦪ.441ᫀ3II⚓ᐳ13⚓

16ü2ýþÿ
᪆.ூᑖ᪆௃1ᦪḄᦪᑨᦪᑨᦪᓫឋ;2஺=1!ᔠI$%e*sinx--sinx-£/-1᦮ᳮ2evsinx+1>sinx-cosx,ᯠ:᪀⌼ᦪgx=Ax-sinx,ᑭᵨᐸᦪBC!D.(1)G2/(x)=e*sinx-V26rsin(LXG[O,TC],ᡠMfXx)=e"sinx+eAcosx-41acos(x-O)=e"(sinx+cosx)-஽(cosx+sinx)=(ev-^)(sinx+cosx),G2a«l,ᡠMᙠ0ಘXe*-aY0,ᵫ,3=0,
%ᵪ].40_x_`rxY0,ᦑ/Xᙠc0,X2dᦪe44f_x_ᐔrx_o,/XᙠchiX2jᦪ.442BCOᵫ1k஺=1,”m=n:o--᝞n-£qᙠc0,X2dᦪᙠcr,ᐔqX2jᦪ.k4e44G2/0="©=-1,ᡠM/xu/ᐔ,nᦑexsinx-V2sinx~~NT,ᡠMe'sin'usinx-cosx-1,ᡠMevsinx+1>sinx-cosx.wgx=7c-x-sinx,g'x=-1-cosx_0,ᡠMgxᙠc0,ᐔqX2jᦪ.yg7t=0,ᑣgx2g7t=o,ᡠMn-xWsinx,ᡠMe”it-x+12e*sinx+1YsinJC-cosx.ூ}~௃⚪ὃᑭᵨᦪᑨᦪḄᓫឋMᑭᵨᦪBC⚪
⌕CᦪᦪḄᓫឋuḄᐵ
Ḅᐵ᪷⚪⌕BCḄᔠᳮ᪀⌼ᦪᑭᵨᦪᑨᓫឋBC.ᫀ12⚓ᐳ13⚓

17ᫀ13⚓ᐳ13⚓