2023年新高考数学名校地市选填压轴题好题汇编（十三）（解析版）

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49%+3,,=53“-(gh+4i”+--+%+3ᔣ)◤cdᔠᳮᑖ᪆kUVNlmᜧoN⚪.46.(2022.rs.tᓅvwx᪥z{|})~ᦪ“X),g(x)ᑖRḄᏔ~ᦪk᜻~ᦪ/.(X)+g(x)=a*+ln(Jx?+1+x)-sinx(a0awl),SXfteR,~ᦪF(X)=/3-2O2_3i-2022)-2"ᨵᑣᦪ஻Ḅ%()A.—1B.—C.1D.—22ூᫀ௃ABூ᪆௃ூᑖ᪆௃ᑭᵨ~ᦪf(x),8(¡᜻Ꮤឋ%&஻*)=£/¤t(x)=▢-h1(x)-2஻2,ᵫ᜻Ꮤឋ§¨%&"X)©Ꮤ~ᦪ/(ª)=ᓡ"-23-(x-3—2022)-2¬ᐵP®¯x=3f+2022°~ᦪF(x)ᨵ%&F(3t+2022)=e°-///(0)-2//2=0,00±ᵫ/(0)=²-=1%³&ᫀ.ூ´௃~ᦪ/(x),g(X)ᑖRḄᏔ~ᦪk᜻~ᦪ,ᡠ~ᦪ/(-X)=/(x),g(-x)=-g(x),4஻x)+g(x)=µ++1+x)-sinx,/(-x)+g(-x)=/(x)-g(x)=a-t+ln^Vx2+l-xj+sinx,¹º»¼%&f(x)=",¤½¡=j_஻/(0_2஻2,f(-x)=▢-஻=M-஻/(X)-2஻2=r(x),ᡠf(x)©Ꮤ~ᦪ$¾ᐵP¿°ᡠÀ(x)=/Á-—஻3,—2022)-2¬ᐵP®¯X=3,+2022°,Vre/?,~ᦪF(x)ᨵ,ᡠÀব+2022)=0,ᓽx=3f+2022,

50F(3t+2022)=e஺-஻஻0)-2/?=0,4/(0)=Æ2=1,ᡠ1-஻-2஻2=O,&/z=gᡈ஻=-l,ᦑ⌱JAB.{ஹÊË⚪47.(2022•ÎᓭÐÑ•z{▤ÓÔÕ)Ö×~ᦪ/(x)=V,g(x)=2Ø-1],“Ùᦪ.ÚPÛÜᡭᵪß0,2],X/VX2,àᨵ/(M-/(X2)lF(x)=x2—2ax+2ax[0,1].48.(2022.AᓭCD.EFGH)IJK┵P-2BCDḄᔜ⚔STᙠUVWᳫ஺Ḅ⊤☢PB1D☢A8CD,PB=2,AB=CD=1,AD=2BC=2&BC//AD,ᑣᳫ஺Ḅ^_=.

51ூ;ᫀ௃23ᐔூc᪆௃ூᑖ᪆௃fᳫg0ᑮi☢A8c஺Ḅjk=஻AD,BCḄmSᑖn=oE,ᵫqrᩩtuJvwA8c஺ᡠᙠḄy☢ᙊḄᙊgG{ᙠ|}EFḄ~|OG_Li☢ABCDᯠᵫFwஹwmuᳫuᳫ^_.ூc௃fᳫg஺ᑮi☢A8COḄjk=/?,AD,8cḄmSᑖn=oE,ᵫqrᩩtuJvwABCDᡠᙠḄy☢ᙊḄᙊgG{ᙠ|}EFḄ~|0G1i☢ABC஺h=OG,=GA=GB,ᡠ+2=2+2GFBEEGt22ᡠ(1+G=()+(9+GF)cuGF=—»GA-yjAF24-GF2=⌲;22=஺P=04,ᡠVG42+0G2=+(PB-0G)2,=OB=OP,ᡠ஺G=^=l,ᡠᳫOḄ=/G42+OG»=J(3+12=",3ᡠᳫ஺Ḅ^_=()=.3\2J3ᐔᦑ;ᫀ=>X.7r3ᐔ

5249.2022ᓅᖆ•EFGHqrᦪfx=/Vaxa>0,b,cᑖn஻xḄ᩽ᜧ¢S£᩽¤¢S,Id>b8/'(d)=f(b),ᑣ,=ூ;ᫀ௃2ூc᪆௃ூᑖ᪆௃¨uᦪ/'Xᙠ98,—©ªQj,+8ᓫ⌴,ᙠHIᓫ⌴ᦑb=-᪷¯d>b8fd="±u@+5d_2.=0,ᦑd=2/³´u;ᫀ.ூc௃c>/(x)=%3—ax(a>0),ᡠ/''(%)=3x2—a,¶((%)=3x2—a=0ux=ᡠ6W(ߟ8,—u+8)/z(x)>0,xW,f(x)<09ᙠº/,/ᓫ⌴'=fd=/b,yo=oᡠd=2pᡠ5=2ᦑ;ᫀ=>2.50.2022.ᓅ¿ÀÁmÂEFGHf4,A2,8/ᑖnÃᙊc[+=la>b>0ḄÄஹÅஹ⚔S,஺=ᙶ᪗ÈS஺=|}஺8/ḄmSÉ|4஺Ḅᚖ|ᚖË=ÌI”ᑮx0Ḅjk=ⅉ|஺஺|,ᑣCḄkg᳛=ூ;ᫀ௃—##|V222ூc᪆௃

53ூᑖ᪆௃⊤ÓÔ|4஺ª|4”ḄÕÖὶØ⊤ÓÔ஺ᓽÔkg᳛.ூc௃|A/QḄÕÖ=y=%Ù+Ú|A2HḄÕÖ=Ù=Vx-a,y=/(X+a),4a2b16b8bὶØuy=•.Ü|0஺|—X-=Vy=-y(x-a),4a2+b2929?,a2=2b2,=11—=ᓉ=4a2+b29e7,Q22ᦑ;ᫀ=>8.251.2022•ᓅ¿ÀÁmÂEFGHJ☢^A8C£ÞḄ⚔SA,B,C,OᙠUVWᳫ☢,4B=BC=4C=6.IáᳫḄ⊤☢_=647r.ᑣJ☢^48co^_Ḅᨬᜧ¢=.ூ;ᫀ௃18gூc᪆௃ூᑖ᪆௃ᐜᵫᳫḄ⊟☢_=64æ,uᳫḄK,³´uFK┵஺-ABCḄE"ᯠᵫJ☢^ḄEᨬᜧ=h=R+»c.ூc௃=ᳫḄ⊤☢_=64ᐔᡠ4TTR2=64TT,cuᳫḄR=4,=AB=BC=AC=6,ᡠëABCḄE=3ìíJ☢^ABCD᜜ïᳫᳫg=O,ᑣFK┵஺-4BCḄE=J42—|x3g=2.ᡠJ☢^A8CO^_Ḅᨬᜧ¢=gxgx6x6xyX2+4=18ñᦑ;ᫀ=>18ò52.2022•óôḕö÷øVmÂEF▤}úûᙠFK┵P-4BCmAABCªëPBCTv=2gḄüFwPA=3&.IM=FK┵P-ABC᜜ïᳫḄþSᑣSMᑮi☢ABCjkḄᨬᜧ¢=

54ூ;ᫀ௃V5+1ூc᪆௃ூᑖ᪆௃f8cmS=7,ÿPTJ.AT,A4?CAPBCḄ᜜ᑖ஺1஺2஺2ᑖ☢Ḅᚖ஺ᓽ!"┵P—ABC᜜&ᳫḄᳫ()᜜&ᳫḄ*+R=0PḄ/Mᑮ☢ABCḄ23d7,AABCḄ᜜01APBCḄ᜜஺2஺1☢ABCḄᚖ஺2@☢PBCḄᚖᩩᚖḄ0ᓽ!"┵P-4BC᜜&ᳫḄᳫDAABCAPBCEFG/2gḄI!JK9LP7=A7=3,NPA=3ᡈᡠQAT2+PT2=ap2,ᡠQPTj.ar,qEAT1BC,BCDPT=T,ᡠQ47_LffifPBC,DATu☢ABC,ᡠQ☢PBCJ■☢ABC,[TO௃=(47=1,ᡠQ]GK஺஺"஺2FG/1ḄI_KᡠQ᜜&ᳫ*+R=0P=yjOOj+OP2=V1T4=V52Mᑮ☢ABCḄ23dSR+0஺1=c+1ᦑeᫀgV5+1.53.(2022•iᓅkl•m!no)qrᙊOḄ_t/+y2=1,pFᙊCg(%-2)2+ஹ2=16z{PᙊOḄᩩᑗᑗᑖAஹB,ᑣ_•~Ḅ.ூeᫀ௃ூ:᪆௃

55ூᑖ᪆௃ᵫᙊᑗḄឋ9rᙊᑗᑗᚖ@P8ḄᜳJ2a,:@J!JK()QPBḄ/;ᑭᵨᔣḄᦪ⊤),~ᑭᵨ!JᦪḄJᓄᦪᣚᐗ¡ᑭᵨ¢£ᦪ()ᨬ.ூ<:௃᝞¦QPBḄᜳJ2a,§"¨|=|ª8|=J-=2,tanasina/.PA-PB=IP411PSIcos2a_cosa.•cos2a-^c°s2a•cos2a.1111-sin2a-l-cos2a«FᙊC(%-2)2+y2=16z{2=4-\0C\<\P0\<\0C\+4=6,cosa=S==J-¬)2,21177•cos2a=2cosa-1=e]t=1—cosaeᑣ~-PB=®¯=|-3ᙠᓃ,³z⌴µt+ᡠQ¶t=·¸,(PA-PB)=p¹¸PḄᙶ᪗(-2,0),min¶t=2¸(¼•~)max=½¹¸PḄᙶ᪗(6,0),lo'lo

56.•.c•~ḄI,¾¿.ᦑeᫀgI,¾¿.54.(2022.iᓅkl.m!no)ᦪf(x)=|2À-1|-2xḄᨬÁ.ூeᫀ௃1ூ:᪆௃ூᑖ᪆௃ᑖÂÃÄÅᣵÇ¢ᑭᵨÈᦪẆÊᦪᓫÌឋ᩽Îc()ᨬÁ.ூ<:௃¶x>{ln2¸2x-l>0,¹¸f(x)=2x-l-2x,f'(x)=2x-2,/'(x)>0Lgx>0,/'(x)<0eeeL:-ln21·Òzgᦪ"x)=|2/-II-2%ḄᨬÁ1.ᦑeᫀg155.(2022iᓅ•ₚÔ>Õm!no)qrÖ×Cg!-g=1ḄØÙᯖᑖFB,PFCḄÙÛ169zḄ{(ÜF⚔)ª2/BPF2ḄJᑖḄᚖᚖÞFM,஺Fßᑣ|M஺ª.ூeᫀ௃4ூ:᪆௃ூᑖ᪆௃àᔠÖ×ḄâãQä!JKḄ>å(L|MO|.ூ<:௃æ/ª2MPç஺ᵫPMF4F/6ḄJᑖF2MLpM,ᡠQ!JKQPaFèῪ!JKᡠQ|PQ|=IPF2I[“F<2ëḄ>.᪷íÖ×Ḅâã9r|P0|—IPF2I=2a,ᓽIQFJ=2a,ᵫ஺Fª1ª2Ḅ>ᡠQ“0F!JKQ&FzḄ>åᡠQ|MO|=glQF/=a=4.ᦑeᫀg4

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58ᐵ_[\Z`⚪Ḅᐵ_bᑨdeᦪᑡf-Ḅ᜻ᦪ⚗LᡂM17✌⚗47OPḄQPᦪᑡ.57.2022•hᓅ•jk▤mno:pqrsLABCZ
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60ᡠMR2="+d2=1+ß=ᧅᡠM§¨©ª«☢¬᜜ᳫḄ⊤☢s=4nR2=â.looLᦑAᫀ7Zâ.ூ[\௃å[\ZR½¾¬᜜ᳫḄḄ⚪æçZb᪷ᳫḄ☢ḄឋᑭᵨᳫḄRஹ☢ᙊḄèÎᳫᑮ☢ᙊḄÌÍdkὅḄᐵêR2=N+d2RᐸëᳫḄìíbᐵ_îybï½¾¬⊡LᡂÂå¬ᑭᵨ½¾¬JÂå¬ᐳᨵḄ᜜ᳫḄᱯôᵫ᜜ᳫḄõQöÂå¬Ḅ¬÷tÂR.59.2022•hᓅ•¢£¤¥¦jk▤mno:“ᩰùkt”bûüýᦪ¦ᦻᓄḄᴮᨬᙠᓭᦪᩰ1261ᡠ℉Ḅ!"ᦪ#$ᓱᙠ1654&'()*+ᩰ⌕-./0.᝞3ᙠᵫ5⚗78ᦪᡠ᪀ᡂḄ“ᩰ<=''?@2AḄ@3BᦪCDE,@3AḄ@3BᦪCDG…@஺+1AḄ@3BᦪCDLᑣᵫ+஺2+஺3+…+.@஺A1@IA1I@2A121@3A1331@4A14641@5A15101051ூQᫀ௃220ூ᪆௃ூᑖ᪆௃ᐜᑭᵨ5⚗7Yᳮ[an=c'iabAcᔠᦪeᓽg.ூ௃ᵫ⚪i[anUcZ+i,ᡠjḄ+a?+CI3++an஺=Q2+c+C4+…+p2ii6x57x68x79x810x911x10=1+3+6+10+—+—+—+—+=1+3+6+10+15+21+28+36+45+55=220.ᦑQᫀDr220.60.2022stuv•x

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63AsinFsincsinyᡠjb=2sinB,c=2sinC,õ8+C=g,ᑣmb+nc=/w2sinB+M2sinC=2/77[sin(--C)+—sinC]G12=2m[T-2口n1-x)•n0-z=2m[2m2SIö“C)=3cosC+(---)sinC,ᑣ÷(C)=-3sinC+(--1)cosC,2m22m2ø÷(C)=0,ᑣùsinC+(--i)cosC=0,2m2n1ᓽtanC=%2£(0,),~2ᡠjúû(°,ýþᑣw2)-ᵫ⚪ᙠ4BCᵫᳮ==7===2,sir/sinFsincsmTᡠb=2sinB,c=2sinC,8+C=(ᑣmb+nc=/??2sinB+«2sinC=2/??[sin(--C)+—sinC]芭2cosC-5sinC+—sinC]2Z?西2/2cosC+(——-)sinC]m2/(C)=cosC+*᜛sinC]=2msin(C+(p),ᐸtancp=-j^-m2ᑣ"c+s=aᓽC=>3$%ᑮᨬᜧ),

64ᑣ+$tanC=tan«9)~=r-=Vs(°G)2*cos(9sin(jptan/>?ᡠ\_B(஺Dᑖᑣ(92).ᦑHᫀJC2)ூLM௃ᐵPLLM+⚪ὃRᳮḄTᵨὃRVWᦪឤZ[ᣚ]^ḄTᵨὃR_ᦪḄTᵨ`⚪ḄᐵPaᵫᳮbVWᦪឤZ[ᣚ]^ᑮc>+஻c=2gcosC+(--i)sinCJ,ᯠj᪀⌼Wᦪ/(C)2m/=@cosC+(--o)sinC,ᑭᵨ_ᦪᡈVWᦪḄឋstuᐸᨬ)vwtxyὃRᦪz{ᓄ}~2m2b⚪62.(2022•ᜧ•)Wᦪ/(x)=/-+(c0)ᨵL%1X2ᡝ3,ᨵ<ᑐ2<ᑣ(2-ᝅ)](2-¢(2-9Ḅ)J--------ூHᫀ௃12ூ`᪆௃ூᑖ᪆௃2¤xᵫ/(%)=0u(2—J)+(M+4)(2—J)—12=0,¨t=2ஹ,u/+(ni+4”—12=0,ᑭᵨ_ᦪug(x)=2-?Ḅ®ᵫLḄᦪxᔠ®t`ᓽ.ூ°`௃±/(²=0,ᑣ2^^%+=o,BP2-8x-x-mxx+2mx2=0eeQ"x=0$e஺=0,·ᡂgᦑH0º•Z^»¼½◀£ÀÁ+2m=0XXᓽ(2-£)2+(m+4)(2--12=0¨t=2—9ᑣt?+(m+4)t-12=0A=[(m+4)2-4x1x(-12)=(m+4)2+48>0ÅÆᨵ»·ZḄÇ᪷JIti-t=-12<02¨t௃>0,ᑣt2>0,¨g(x)=2-“(x)=ËÌ

65"xe(l,+oo)$g'(x)<0,"xe(0,1)ᡈxe(-8,0)$g'(x)>0ᓽWᦪg(x)ᙠ(L+8)ÏᓫÑ⌴Óᙠ(0,1),(-8,0)ÏᓫÑ⌴Ôg(l)=2-e<0᝞Öᡠ×1-,Wᦪf(X)ᨵL1Ù2%!<%<Ù32ÅLMLḄᦪtÛᦪḄÝÞ}ßᑭᵨ_ᦪuWᦪḄàᵫËLḄᦪxᔠ®uÛᦪḄÝ.63.(2022.áᓅãäz᪥)±Wᦪ/'(x)=ç᮱+nM+px+q(mê0,nK0)ÏìíḄL(Xi/(x))(i=1,234,5,6),ïð᝞Öᩩòজ/()=f3)=/(x)=0ঝWᦪ஻x)ᐵL(õ)ç஺)ö(3÷oঞWᦪ“X)ᙠL(ù)ú))ᜐḄᑗýᐸìËL஺6/(0))oᑣ+þ+ÿ+2X+5X)=------------6ூᫀ௃6ூ᪆௃ூᑖ᪆௃᪷ᩩজᑮ++3=-᪷ᩩঝᑮ=᪷ᩩঞᑮ"6+2&=2ᨵ!"#$ᓽ&'.ூ)௃*+/O1)=/(%2)=f(X3)=0,ᡠ56,⊈83+f(x)=஺Ḅ!"=>Ḅ,ᡠ5f(x)=m(x—x)(x—x~)(x—x)123

66=mx3-m(%i+B+x)x2+m(xx+xx+Xi%)x-mxxx312233123=mx3+nx2+px+q,ᡠ5—7n(%i+᜜+x3)=ᓽ+x4-x=—23*+/(%)=3mx2+2nx+p,J*+K(X)ᐵMN(X4JG4))QRᡠ5x=M+/'(%)=3mx2+2nx+pḄQRUᡠ5%4=2./(85)=3mx2+2nx+p,5s/'(x)ᙠ(X5,f(&))ᜐḄᑗZ+y=(3mx2+2nx+p)(x—x)+mx3+nx2+px+q,555s53*+\ᦪ/")ᙠN(^/(%5))ᜐḄᑗZᐸ`aMN(%6/(b6))ᡠ5(%6/(%6))ᑗZcᓽ(3mxs2+2nx+p)(x-%)+mx3+nx2+px+q=mx3+nx2+px+q,565353666efᓄh(36i52+2nx+p)(x-x)s65=m(%6-X)(x2+xx+%52)+(x-x)(x+x)+p(x&)566sn65656*+H%5ᡠ53mk2+2nx+p=mx2+mxx+mx2+nx+nx+p,s665565ᓽ2-27nx52+mxx+nx—nx=0=>m(x—x)(x+2x)+n(x—x)=0,6s65656565mn&X6+2X=᜼5,..,n.rnnoc%1+x+x=-->x+2x=-x=--.23654ᡠ5+^+*3+2X+X)=_rst)=6.56ᦑᫀ+v6

67