洛阳市强基联盟2023届高三数学（理）7月摸底大联考答案解析卷

《洛阳市强基联盟2023届高三数学（理）7月摸底大联考答案解析卷》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

□ὶ2023ᦪᳮ7ᨴ᥎ᜧὶὃᔁὃ1.ᔁᑖ⌱⚪⌱⚪!"ᑖ.$ᑖ150ᑖ%ὃ&'120ᑖ(.2.)⚪*%ὃ+,ᵨ./0.5012⁐456789:;<ᑁ⚗?@ᑏBC.3.ὃD)&%E9)ᫀ)ᙠ)⚪ᓱI.⌱⚪JK⚪⌱L)ᫀM%ᵨ2BN8O)⚪ᓱIPQ⚪?Ḅ)ᫀ᪗TU2⌱⚪Eᵨ./0.50ᩭ2⁐45678ᙠ)⚪ᓱIᔜ⚪Ḅ)⚪XYᑁD)%ZL)⚪XY[ᑏḄ)ᫀ\ᦔ%ᙠ⚪ᔁஹ₝`aID)\ᦔ.bஹ⌱⚪⚪ᐳ12K⚪%JK⚪5ᑖ%ᐳ60ᑖ.ᙠJK⚪dLḄef⌱⚗g%hᨵb⚗jkᔠ⚪?⌕nḄ.1.bfᵯrgsᨵ12!fuv%uv1sᨵ4,B!fᐗv%uv2sᨵC,D,Efᐗv%Jfuvgᨵbfᐗv}~Dᑣuv}~D%ᑣᵯr}~DḄ

13.☢ᳮᳮḄA.ᵫ“ᕜḄḄ☢ᨬᜧ”,!“ᙠ⊤☢Ḅ$$Ḅ$ᨬᜧ'B.&'ᜧ'(ᜧ)*A/BCNABC>ZBAC,ᑣ/C>BCC.ᵫr+23=32,F+23+T=62,…,,ᑮ.+23+33+43+53+6,=2/D.0ᑗᏔᦪ3452᦮◀228Ꮤᦪᡠ:22022452᦮◀ூ<ᫀ௃Aூ?᪆௃ூᑖ᪆௃ᵫᳮஹCDᳮஹEFᳮḄGHIᑨKᓽM.ூO?௃(PA,ᵫQ☢RḄឋT!UVWX$ḄឋTᳮAYZ(PB,CDᳮB┯\](PC,EFᳮC┯\](PD,CDᳮD┯\.ᦑ⌱ZA.4,`abcdeX~N5,b*PX28=0.36,ᑣPXு2=A.0.36B.0.18C.0.64D.0.82ூ<ᫀ௃Cூ?᪆௃ூᑖ᪆௃᪷h᝱ᑖjḄ(kឋᓽMl?.ூO?௃mX~N5,CT2,ᡠ:PXV2=PX28=0.36,ᡠ:nX>2=0.64.ᦑ⌱:C.5."<”"lna

26.ᙠAaBCg%ᑁÄ4B,CḄPÅᑖÆ஺%b,c,É4=27%%cos^t=--,sinB=2sinC»ᑣ஺=4A.1B.2C.3D.4ூ)ᫀ௃Bூ᪆௃ூᑖ᪆௃ᵫsinB=2sinC,ᑭᵨ~ÑÒᳮb=2c,ᯠM¬ᔠÔÕᩩvᑭᵨÖÑÒᳮnLcூ௃sinB=2sinC.ᵫ~ÑÒᳮb=2c.,:a=2y[6%cosA---,ᵫÖÑÒᳮ/=c2+b2-2c6cosA>24=/+b2^-j=4c2+஺2+gx2c2,c=2ᡈc=-2ÚÛ.ᦑ⌱B.x>l,7.Ô᝞ÝᦪK,J%$àáâᩩv•x+yW2,,ᑣ2x+yḄᨬKçjx-3^<0.77A.—B.3C.—D.223ூ)ᫀ௃Cூ᪆௃ூᑖ᪆௃ᵫáâᩩvDLèY%ᓄ?᪗êᦪ.<ëìḄíîï%ᦪð¬ᔠᑮᨬò%OᨬòḄᙶ᪗ôᐭ?᪗êᦪ)ᫀ.x>l,ூ௃DL$àáâᩩvö+yW2,ḄèY᝞÷▢ù"ᑖᡠûx-3y<03

3ὶüᨴö,ý%þz=2x+y,y=-2x+z,ᵫ÷Õ%ÿ
y=-2x+z.«L
ᙠyḄᨬᜧzᨵ17ᨵᨬᡠz=2x+y=2x1+,=1,ᦑ⌱C.8.&3x-3=Ḅ()*+ᔜ-⚗*/ᦪ12364,ᑣ()*+Ḅ7ᦪ⚗3&A.-540B.135C.18D.1215ூ;ᫀ௃Bூ?᪆௃ூᑖ᪆௃ᵫ⚪DE2"=64,GH"=6,IJKGH-⚗()*ḄL⚗M*ᯠOPxḄQᦪ3RGHIJKGHSTூU?௃ᵫ⚪DE2"=64,ᡠ஻=6,ᡠ&3W-ᓝ()*ḄL⚗&=C&3x>„2'3P6—r=0Er-4,2ᡠ()*+Ḅ7ᦪ⚗3&-l'ca-3-=135.ᦑ⌱aB.9.ᡃd+ef⌱HḄ“hfhi”klᶭnopqᙳᨵs℉ᦔT“hf”ᑖv3wxyz⚩|ஹ~xyஹ⊈“hi”ᑖv3yp᣸ஹᓄiஹpi.eI“hfhi”+⌱Hhfi4⊤⌱HḄhfi+ᨵfB⊤⌱HḄhfi+ᨵiᑣ&8=&199918A.—B.—C.-D.—20101919ூ;ᫀ௃Dூ?᪆௃ூᑖ᪆௃ᑭᵨ¡ᐺᭆ¤M*GHP&82P&/3,§ᑭᵨᩩᭆ᳛M*ª«ᓽKEᑮ®⚪;ᫀ.4

4ூU?௃ᵫ⚪KE(B)=lf஺P(ᨴ8)=²³´Lµ/>UL61Uᡠ*")=¸¹ᦑ⌱aD10.kº»ᦪḄhQiᡃ¼Kᑖ?3½»ᦪ¾Ḅ2af=],r=3+5,33=7+9+lbᵬ=13+15+17+19,…᪷ÁÂÃÄ25,Ḅᑖ?*+ÅÆÇÈḄᡠᨵᦪ+ᨬᜧḄᦪ3()A.325B,323C,649D.647ூ;ᫀ௃Cூ?᪆௃ூᑖ᪆௃Éᵫ⚪ÊᡠËᦪÁÌSÃÄᢥ᯿ÃÄᓽKG?.ூU?௃ÏÐKÑÅÆÇÈḄᡠᨵᦪ+ᨬᜧḄᦪÒQ31,5,11,19,ÓÔÕ,22+1,3?+2,4?+3,ᵫÃÄKÑ253Ḅᑖ?*+ÅÆÇÈḄᡠᨵᦪ+ᨬᜧḄᦪ3252+24=649•ᦑ⌱aC.11.Ö×fḄᭆ᳛ᑖØᑡ3Ú=Û)=£%4=1,2,3,ᐸ+cß7ᦪᑣ஺(à-3)Ḅ3()KTKA10B.117C.38D.35ூ;ᫀ௃Cூ?᪆௃ூᑖ᪆௃᪷ÁᑖØᑡឋâGH§ª«Ö×JḄãäiåᑭᵨiåឋ⪫஺(94-3).ூU?௃•••P(f=%)=^,k=l,2,3,7Tk+k—=1,?Ec=±,26123.••^)=lx|+2x|+3x|=^,.••^)=(l-j)2xj+(2-^)2x|+(3-^)2x|=|1,.-.Z)(9^-3)=92Z)(^)=81Z)(^)=38.ᦑ⌱ac1Q12.æÑçᦪ/(x)=]f_3x2+8x-],g(x)=x-lnx,Vx௃xe(0,3),g(%)+A2/(è)ឤᡂ25

5}ᑣᦪḄ()A.[2+In2,+oo)B.[-3,+s)C.-,-H»ID.[3,+00)ூ<ᫀ௃Dூ?᪆௃ூᑖ᪆௃ᑭᵨᦪᑨKᓫឋ᪷hᓫឋl?ᨬ᪷hᦪᨬWḄᐵᓽMl?.ூO?௃/'(x)=x2_6x+8=(x-2)(x-4),~xe(0,2){/'(x)>0,/(x)ᓫ⌴~xw(2,3){/'(x)<0,/(x)ᓫ⌴,ᡠ:/(x)ᙠ(0,3)Ḅᨬᜧ"2)=4./\11X—1g(x)=l-=0'XX~xe(0,l){g'(x)<0,g(x)ᓫ⌴~xe(l,3){g'(x)>0,g(x)ᓫ⌴ᡠ:g(x)ᙠ(0,3)Ḅᨬgপ=1,*H2£(0,3),g(xj+k”(w)ឤᡂ},ᑣ[g(x)+],2/)ᓽ1+ᐭ4,1Mxᡠ:¤23,ᡠ:ᦪkḄ[3,+Q0).ᦑ⌱:D.-ஹÿ⚪⚪ᐳ4⚪⚪5ᑖᐳ20ᑖ.13.¥¦y=xe*+2x-2ᙠx=0ᜐḄᑗ¦¨.ூ<ᫀ௃3x-y-2=0ூ?᪆௃ூᑖ᪆௃ᑭᵨᦪḄX©Gl?ᓽMூO?௃ᵫy=xe"+2x-2,,y'=e*+xe*+2,~x=0{y=-2,yᱏ3,ᡠ:ᑗ¦¨y-(-2)=3x,ᓽ3x-y-2=0.6

6ᦑᫀ3x-y-2=014.᝘ₐ!ὁ#$!ᙠ2021&12ᨴ()*+,Ḅ.ᦪy01ᜩḄ3ᙳ56x/࠷789ឋ;<ᑖ᪆>?ᦈABCᨴD4ᜩḄEᐵᦪG(᝞I⊤)KᵫᨬNOPQR;?X~2(4,p),y(X21)=ᑣDX=_____81Oூᫀ௃X9ூe᪆௃ூᑖ᪆௃X3(4,p),N⚗ᑖḄឋ)p=,ᙠᵨOX=஻p(l-p)ᓽr.ூse௃X8(4,p),P(X21),ᡠ{p(x=o)=l-=”''81817

7ᡠ:CpO(l-p)2olᡠ:l-p=j,ᡠ:p=;,ᡠ:஺X=4xkh-”=§.3I3j9Q<ᫀZ0916.`aF«ᙊG[+£=1(஺>6ு0)Ḅ®ᯖ°±«ᙊGḄ⚔°³¥¦஺2:-ᓃ=1a2b2m2n2(¶>0,”>0)·«ᙊGᐳᯖ°*¹¦"·³¥¦C?Ḅ0ᩩ»¼¦Q½q,C2Ḅ¾¿᳛ᑖÁ12q஺2,ᑣ0+0Ḅᨬ.0%ூ<ᫀ௃2&ூ?᪆௃hYIூᑖ᪆௃᪷h¹¦"·GḄ0ᩩ»¼¦Q½,ᑮ0=0ÃÄᔠ³¥¦·«ᙊᐳᯖ°,ᑮeR=l,cmÃᑭᵨÆÇqÈÉl?.ூO?௃?ZÊ஺ḄËᯖÌc(c>0),ᑣF(c,0),Í4(0,-b),ᡠ:ÎF=2,͹¦"·GḄ0ᩩ»¼¦Q½Cᡠ:2=2ᡠ:t=2ª,Cmclw2a2-c2c2-m2ᡠ:mᡠ:j=Ïc~in"ᡠ:e©=1,ÍÐ+2=+-4=e,+2q>2,2ὡ᜜=2,eie2"28

8~ÓÔ~e2=2q,ᓽ4=Õ{ÈÖᡂ}11ᔆᓽ0+0Ḅᨬ2Ø.e\e2ᦑ<ᫀZ2¶®ஹe⚪ᐳ70ᑖ.e°ᑏ)ᦻ³´µஹ¶µhTᡈ¸¹º.»17~21⚪xὃ⚪,Y½⚪ὃ¾¿xÀÁ.»22ஹ23⚪⌱ὃ⚪ὃ¾᪷G⌕QÁ.(X)xὃ⚪ᐳ60ᑖ.17.ÊÈÙᦪᑡÆ4ÇḄÛ஻⚗Þ5“ÓS6=9S2,3%-4=%.(1)lᦪᑡÆ4ÇḄß⚗àÉ]2(2)Ê”=——,lᦪᑡwâḄÛ஻⚗ÞananAூ<ᫀ௃(1)a=2n-\,(«eN).n+(2)T=-^—,(neN).n+"2n+lூe᪆௃ூᑖ᪆௃(1)ᵫÈÙᦪᑡḄß⚗àÉÞÛ"⚗ÞÄᔠ`aᩩuὶ}¨MlUqÞd,ᓽMlUß⚗àÉ.(2)⊤äUᢌ“â,æ⚗çzlÞᓽM.ூè1O?௃5=9⎃J2%—d=0?Zᵫ⚪Maëríí?,q=l,d=2,3%-4=%2%+d=4ᡠ:(=2஻-1,(neN).+ூè2O?௃,2211î(1)ab=---=--------=--------“(%(2஻—1)(2஻+1)2w+lᡠ:ᓅ=4+·+…4_]+4=i_+ª_g+…+1-1-----1----14-----------2஻-32n-l2n-l2஻+1=i——ð=ñ0,ᡠ:ᓅ=2(neN).+2஻+12஻+12஻+19

918.᝞ÙᙠfÚÛÜ/BCD-44G஺V48஻q),ADLCD,AD=CD=DD=2,AB=1.1á1âQ¶4"14Gá2âQN☢äA-4C-4Ḅæçb.ூᫀ௃á1ⶵèe᪆ªá2â63ூe᪆௃ூᑖ᪆௃á1ⶵD4,DCééᚖfëìífäᙶ᪗ðQ)ñòᵫó•ò=0ᓽr¶µá2âQ)3☢4C4õ3☢NCB1ḄPᔣᵫᔣᜳäøùQ)æçbᓽr.ூú1se௃13☢ABCD.AD,CDu3☢/BCD.ᡠ{1"J_C஺.üý_LCD,ᡠ{D4,DC,ééᚖf{k஺ᙶ᪗ÿ
D4,DCᡠᙠᑖx
,
z᝞ᡠḄᙶ᪗,10

10ᑣ4(2,0,0),C(0,2,0),D,(0,0,2),4(2,1,2).ᡠ&=(-2,0,2),)=(-2,1,-2).ᡠ*.)=(-2)x(-2)+0xl+2x(-2)=0,ᡠ4஺114c.ூ01223௃rn^AC=0-2C+2%=0,ᐗ=(-2,2,0),6ᔣ89=(4%,zj<☢4cAḄ?@Aᔣ8
ᑣ.
ᓽm-A“=0-2Xj+24=0,n-AC=0Eᓰ=1,GH=(1,1,1),6ᔣ8஻=(4%/2)<☢NOB1Ḅ?@Aᔣ8
ᑣN?ᓽOᵫ஺=0-2X+2y=0,22-2x+y-2z=0,222tn-n1X2+1X2-1_73EQ=2,G஻=(2,2,-1).ᡠcos8஻.x3P6U☢4-zc-4Ḅᜧ0Wᵫ*X0,g,ᡠcos஺=Z.ᡠU☢A-/c-q3Ḅ]^_`.319.bcᙠdefgᵨicjkAl
mnᙠopḄqᐰ◚t
ᓻvwxyz{Ḅ|}.~ẆbcdefgᵨicḄ
c~100bc
Gᑮᙠ55ᵱឋbc
defgᵨicḄᨵ40{
defgᵨicḄᨵ15{ᙠ45᝕ឋbc
defgᵨicḄᨵ20{
defgᵨicḄᨵ25{.(1)ᡂ☢Ḅ2x2ᑡὶ⊤
ᑨjᔲᨵ99.5%Ḅ¡¢£defgᵨic¤bcḄឋᨵᐵdefgᵨicdefgᵨicᔠᵱឋbc{ᦪ᝕ឋbc{ᦪᔠ(2)¨ᵨᑖ©ª᪵¬defgᵨicḄ{ª8{
C¬®8{cª3{
¯XdefgᵨicḄᵱឋbc{ᦪ
°XḄᑖ±ᑡyᦪ²³´.µὃᦪ·11

11¸পº0.150.100.050.0250.0100.0050.001k2.0722.7063.8415.0246.6357.87910.828µὃ»¼/2=-----ஹ:8b஺)——-,ᐸ஻=a+b+c+d(a+b)(c+d)(o+c)(6+d)ூ¿ᫀ௃(1)Á⊤Â3᪆ᨵ99.5%Ḅ¡¢£defgᵨic¤bcḄឋᨵᐵ9(2)ᑖ±ᑡÂ3᪆³´§ூ3᪆௃ூᑖ᪆௃(1)᪷·⚪Ç⊡ᐰᑡὶ⊤
ÉᓱOËÌᓽ*(2)᪷·ÍÎÏᑖ±ÐᐵXÑᓽ*°GXḄᑖ±ᑡyᦪ²³´.ூ01123௃ᵫÒXᦪ·*G2x2ᑡὶ⊤᝞:defgᵨicdefgᵨicᔠᵱឋbc{ᦪ401555᝕ឋbc{ᦪ202545ᔠ6040100ÔÕᎷ6defgᵨic¤bcḄឋ×ᐵ,Ø4,100x(40x25-15x20)"Ùx=----------------------n8.249>7.87960x40x55x45ᡠᨵ99.5%Ḅ¡¢£defgᵨic¤bcḄឋᨵᐵ.ூ01223௃defgᵨicḄᵱឋbc{ᦪ8x3—=3{15+2525defgᵨicḄ᝕ឋbc{ᦪ8x----------=5{.15+25ᵫ⚪Ç*XXḄᡠᨵ*Ú_0,12,3,C35C'C215C2Cl15C31Ù¸(X=0)===3¸(X=l)=*=2¸(X=2)=*=BP(X=3)=^=-.IJC28I/C28I)C56ஹ/C56ᑣXḄᑖ±ᑡ12

129-820.`aòᱥ¦CḄ⚔°ᙶ᪗ΰᯖ°ᙠyöÓòᱥ¦C÷ø°P(2,l).(1)lòᱥ¦CḄ¨](2)4Bòᱥ¦CùP°nḄú°û¹¦nüÞ¹¦Ḅý᳛ᑖÁþ,(¤ÿ#0)

11c—+~=2,43.Kk2ூᫀ௃পx2=4y(2)᪆ூ᪆௃ூᑖ᪆௃(1)ᵫ⚪ᱥCḄ=2(peR),!ᐭP(2,l)ᓽ$(2)ᵫ⚪%.48Ḅு='+6,ᑭᵨ,-ᳮ/ᩩ1%26=-1,ᓽ.ூ3415௃ᵫ⚪67ᱥCḄ#=20
(peR).8ᱥ9P(2,l),ᡠ;2?=2p,2p=2.ᡠ;ᱥCḄf=4y.ூ3425௃/2\(.2\ᵫ⚪6%<748Ḅ=᳛?@ᙠ7BCḄ^='+7,4x,A,B7F.I4JI4JὶHI
“'
2--4'-46=0.y=kx+b,ᐸLAM16p+166>0,ᓽN+6>0,x,+x=4k,x,x=-4b.2213

13111=/?21è_2_4τ4_4(ê+஽)+16J2•*,k,kxxx.+2x+2x.x+2(x+X)+42222444x4"16cᓽ--------------=2,xx+2x4k+4i2ᡠᓰì=-46=4,3G஺=-l.ᡠ43ḄOíî=ï?1,ឤñò(0,-1).21.ÒXóᦪ/(x)=±+41nx-or(4<0).x(1)ôõóᦪ/(X)Ḅᓫឋ(2)÷஺=-1f
øù¼/(x)?£+x-6(x-l)ᱏᙠxe[L+s)ûឤᡂ
°üᦪbḄ_þ.Xூ¿ᫀ௃(1)/(X)ᙠ(0,1)ûᓫ⌴
ᙠ(L+8)ᓫ⌴,ஹ11(2)—,+8Iூ᪆௃ூᑖ᪆௃(1)

ᦪᜧ00Ḅ
ᓫឋ(2)!"#lnx«b(x-l)e'ᙠxw[l,+e)ឤᡂ&
᪀⌼g(x)=Mx-6(x-l)e',
Ẇ*ᐸᓫឋ
,bᑖ-./
0ᑮ6,e234⚪6
ᐸ789ᙳ;ᔠ⚪6
=ᫀ.ூ@1A௃/(X)#(஺,+8),eஹex(x-l)a(xT)”ಘf(x)=----~-+——a=------------------(«<0)'XXXF#e'-ox>0ឤᡂ&
ᡠHI0l2
/'(x)>0,ᡠHf(x)ᙠ(0,1)ᓫ⌴
ᙠ(1,+8)ᓫ⌴ூ@2A௃14

14I4L-12
/(x)=---lnx+x,---lnx+x>—+x-ft(x-l)ex,᦮ᳮ0[lnxW6(x-l)e\X--------------------XᓽInX<6(x-l)exᙠXw0,+e)ឤᡂ&
fg(6=hi_6(i_1)k
xe[l,+8),n640,ᑣg(K)=lnx-b(x-l)eXN0ឤᡂ&,;ᔠ⚪6,bு0,ᑣg'(x)=l-fere",x^A(x)=--fexex,xe[l,-H»),xᑣ/f(x)=--y-6(x+l)er<0ᙠX£|,+8)ឤᡂ&
ᡠH஻(x)=L-bxe*ᙠxe[l,+e)ᓫ⌴
I62,A(x)e<0,ᓽg'(x)40eᡠHg(x)=lnx-6(x-l)e*ᙠxe[l,+s)ᓫ⌴
ᦑg(x)=lnx-b(x-l)e*0=b-eb1,g'(%)=0
Ixe஺,)2,g'(x)>0,Ixc(xoZ)2
g'(x())<0,0ᡠHg(x)ᙠxe(l,%)ᓫ⌴
ᙠxc(Xo
*o)ᓫ⌴
ᡠHᙠxe(l,x0)0g(x)>gপ=0,;ᔠ⚪6
[ᦪbḄ[,+8)ூ௃ᦪᦪḄ@⚪
⌕ᔠᦪᦪḄᱯ
,ᦪᑖ-./
ᔠᓫឋ
᩽ᨬ.(L)⌱ὃ⚪[ᐳ10ᑖ.¤ὃ¥ᙠ¦22ஹ23§⚪¨©⌱ª⚪«=.᝞®¯
ᑣᢥᡠ¯Ḅ15

15¦ª⚪±ᑖ.⌱²4-4ᙶ᪗µᦪ¶·22.ᙠO☢Qᙶ᪗Tx0
L7UCḄVᦪ".ºaVᦪY.;஺᩽7x\Ḅ]y=2+sina^\᩽\_H᩽ᙶ᪗T.º1½CḄ`a$º2½b

16ᡠ;ᑗḄ᩽ᙶ᪗pcos(e+j=_Q_#ᡈ0cos⌱4?5[B⌱23.b<ᦪ/(x)=k+4+k-a|(aeR).(1)
a=2,B/(x)29Ḅ$(2)
VxeR,B7(x)2/-2aឤᡂH7ᦪaḄ.(2)[0,4]ூ᪆௃ூᑖ᪆௃(1)᪷k⚪67ᑖxW-2,-29,2F2¤7ᡠ;F2¥.¦§7B/(x)Z9Ḅ|1TO,-.ூ3425௃8/(F)=+«+?«2+஺)-_஺)|=2«7¡®¡-R¯xS«¢°ᡂH,
VxeR,Bf(x)2/-2஺ឤᡂH7±◤242ᱏ-2஺.¡Q20¢7ZaN/—2஺7204஺44¡஺<0¢7-2a>a2-2a
´¢µ¶ᩩ1Ḅ஺B@ᙠ.¦§7ᦪaḄ|[0,4].17