2025年新高考地區(qū)數(shù)學(xué)名校地市選填壓軸題好題匯編（九）（原卷版）

1.（2025屆河北省啄名小漁高三11月階段調(diào)研（二已知函數(shù)f(x上有且僅有一個零點，當(dāng)ω最大時f(x(在區(qū)間[-100π,100π[上的零點個數(shù)為Asin(ωx+φ((A>0,ω>0,0<φ<2π(的部分圖象如圖所示，若所在平面不等式f2(x(+f(x(-a≥0A.B.C.D.時，f(x(=x2-4x，則f(k(=A.-7f(x(=log4-a|-b是奇函數(shù)，則ab=1A.B./2B.2C.2D.2f(n((n∈N,n≥2(，記數(shù)列{cn{的前n項積為Tn，數(shù)列{Tn{的前n項和為Sn，則B.1<Sn≤ C.<Sn≤D.≤Sn<27.（安徽省合肥市第一中學(xué)2024-2025學(xué)年高三上學(xué)期第三次素質(zhì)拓展）已知定義域為R的函數(shù)f(x(，滿足f(1?x(f(1?y(+f(x+y(=f(x(f(y(，且f(0(≠0，f(?1(=0，則以下選項錯誤的是A.f(1(=0B.f(x(圖象關(guān)于(2,0)對稱C.f(x(圖象關(guān)于(1,0)對稱D.f(x(為偶函數(shù)間[a,b]上存在x1,x2(a<x1<x2<b(，滿足f’(x1(=，f’(x2(f(x(是在區(qū)間[a,b]上的一個雙中值函數(shù)。已知函數(shù)f(x(=x3-x2是區(qū)間[0,t]上的雙中值函數(shù)，A.,B.,C.,D.(1,都有f(?x(?f(EQ\*jc3\*hps21\o\al(\s\up7(3),2)+x(=0，f(2024(=EQ\*jc3\*hps21\o\al(\s\up7(1),e)。若f(x(+f’(?x(>0，則不等式f(x+1(>的解集是ABC體積的最大值等于A.A.2C.2D.2EQ\*jc3\*hps21\o\al(\s\up8(—→),A)EQ\*jc3\*hps21\o\al(\s\up8(—→),B)EQ\*jc3\*hps21\o\al(\s\up8(—→),C)EQ\*jc3\*hps21\o\al(\s\up8(—→),M)EQ\*jc3\*hps21\o\al(\s\up8(—→),B)EQ\*jc3\*hps21\o\al(\s\up8(—→),C)EQ\*jc3\*hps21\o\al(\s\up5(1),2)EQ\*jc3\*hps21\o\al(\s\up5(2),3)EQ\*jc3\*hps21\o\al(\s\up5(5),2)1=214.（福建省福州市八縣（市）協(xié)作校2024-2025學(xué)年高三上學(xué)期期中聯(lián)考）已知函數(shù)f(x(=A.a<-1B.a>1C.0<a<1D.<a<1(f(x(+x2(=x(f'(x(+x(，f(1(=-，則f(x(的最小值為A.-eB.eC.-e2D.-數(shù)f(x(=(x2-aex)ln(x+1)的圖象經(jīng)過四個象限，則a的取值范圍為A.(0,e)B.(0,e-1)C.(4e-2,e)D.(0,4e-2)A.-B.-C.D.義在R上的函數(shù)f(x(滿足2f(x+y(f(x-y(=f(x(+f(y(，且f(0(≠0，則下列結(jié)論正確的是A.f(0(=-1B.函數(shù)f(x(為奇函數(shù)C.函數(shù)f(x(有2個零點D.f(2x(=f(x(y=f(x((x≠0(滿足f(xy(=f(x(+f(y(-1，當(dāng)x>1時，f(x(<1，則A.f(x(為奇函數(shù)B.若f(2x+1(>1，則-1<x<0C.若f(2(=，則f(1024(=-4A.21.（廣東省華南師范大學(xué)附屬中學(xué)2024-2025學(xué)年2025屆高三上學(xué)期11月綜測述正確的是()A.a7>a6B.a9<1C.S10<12D.S13>16數(shù)f(x(在區(qū)間[0,2[上單調(diào)遞減，且滿足f(4+x(+f(x(=2f(?2(，函數(shù)y=f(x?2(的對稱中心為A.f(2024(=0C.f(3(>f(2log248(x(為f(x(的導(dǎo)函數(shù)，若方程f(x(=f′(x(在[a,b[上至少有3個不同的解，則稱f(x(為[a,b[C.?4≤m<D.?7≤m<?4f(x(=ex?1?e1?x+sin(x?1(，則關(guān)于x的不等式f(x2?x?2(+f(?2x(≥0的解集為()A.[?1,4[B.(?∞,?1]∪[4,+∞(D.(?∞,?2]∪[1,+∞(=f(?x(，x∈R，f(5.5(=1，函數(shù)g(x(=(x?1(?f(x(，若g(x+1(為偶函數(shù)，則g(?0.5(的值為()A.3C.2f(x(=x|x|-4x，若函數(shù)F(x(=[f(x(]2-(2a+8)f(x(+a(a+8)有4個零點，則實A.(-12,4)B.(-12,-4]C.(-4,8]D.[-4,4)A.9B.C.D.D.1D.2+731.（湖南省長沙市雅禮中學(xué)2024-2025學(xué)年高三上學(xué)期月考（三設(shè)集合A={(x1,x2,x3,x4,x5)|xi∈A.{-20,21}B.{-20,20}C.{-29,11}D.{-20,19}f(x(=2sin(ωx+φ((ω>0,0<φ<的部分圖象如圖所示，若函數(shù)f(x+θ(的圖象關(guān)于y軸對稱，A.C.8D.34.（江蘇省2025屆南京一中、金陵中學(xué)、南通海安中學(xué)高三上期中考聯(lián)）在正四棱柱ABCD-A1B1C1D1B.2D.335.（江蘇省常州市2024-2025學(xué)年高三第一（上）學(xué)期期中質(zhì)量調(diào)研考試）已知函數(shù)f(x(=A.D.A.a<b<cB.b<c<aC.c<a<bD.c<b<a且f(x+6(=2f(x(，當(dāng)x∈時，f(xA.-7A.上的函數(shù)f(x(滿足f(xy(=xf(y(+yf(x(，且f(e(=e，則C.f(x(是增函數(shù)EQ\*jc3\*hps21\o\al(\s\up8(—→),A)EQ\*jc3\*hps21\o\al(\s\up8(—→),C)R-2,6]內(nèi)函數(shù)g(x)=f(x)-loga(x+2)(a>1)有三個不同的零點，則實數(shù)a的取值范圍為()A.(1,2]D.(2,+∞)A.lnb>aB.alnb>1D.a(1+lnb)<1A.-2B.-1截面中均恰好看不見肉餡。則肉餡與整個粽子體積的比為(A.B.C.A.B.C.D.π93ππ3πA.B.C.5D.47.（山東省菏澤市2025屆高三上學(xué)期期中考）已知函數(shù)f(x(=x(1-ex(，點(m,n)在曲線y=f(x(上，則f(m(-f(n(EQ\*jc3\*hps21\o\al(\s\up5(1),e)EQ\*jc3\*hps21\o\al(\s\up5(1),e)EQ\*jc3\*hps21\o\al(\s\up6(1),e)A.29B.49D.2A.A.3B.3A.,+∞(B.(0,+∞(C.D.(0,2]義域為為奇函數(shù)，設(shè)g(x)是f(x)的導(dǎo)函數(shù)，若g(2x+1)為奇函數(shù)則A.的連續(xù)函數(shù)，若f(x+y)+f(x-y)=f(x)f(y)，f(1)=0，則A.f(0)=1B.f(x)為奇函數(shù)C.f(x)的周期為2D.-2≤f(x)≤2D.6EQ\*jc3\*hps21\o\al(\s\up8(—→),B)EQ\*jc3\*hps21\o\al(\s\up8(—→),E)2+BEQ\*jc3\*hps21\o\al(\s\up8(—→),E)?EEQ\*jc3\*hps21\o\al(\s\up8(—→),D)，EQ\*jc3\*hps21\o\al(\s\up8(—→),B)EQ\*jc3\*hps21\o\al(\s\up8(—→),B)EQ\*jc3\*hps21\o\al(\s\up8(—→),D)B.2A.(3,4)EQ\*jc3\*hps21\o\al(\s\up8(灬),AC)EQ\*jc3\*hps21\o\al(\s\up8(灬),CB)EQ\*jc3\*hps21\o\al(\s\up8(—→),M)EQ\*jc3\*hps21\o\al(\s\up8(—→),C)EQ\*jc3\*hps21\o\al(\s\up8(—→),N)EQ\*jc3\*hps21\o\al(\s\up8(—→),B)A.當(dāng)λ=時，直線AM與BC所成角的余弦值為AA1=3A.長方體ABCD-A1B1C1D1外接球的半徑為B.點A到平面A1BE的距離為3B.將f(x)圖象向右平移后得到函數(shù)y=2sin2x的圖象C.f(x)在區(qū)間上單調(diào)遞增D.f(x)在區(qū)間上的最大值與最小值之差的取值范圍為[1,23]A.m<0B.m>0C.xEQ\*jc3\*hps12\o\al(\s\up3(2),1)+xEQ\*jc3\*hps12\o\al(\s\up3(2),2)>e2D.lnx2+x1<1x)=,x>-1，g(x)=(1-x)ex,x<1，且f(ac中，M是AC上A.過點M有四條直線與AB，BC所成角均為B.BB1⊥平面AB1C7.（安徽省合肥市第一中學(xué)2024-2025學(xué)年高三上學(xué)期第三次素質(zhì)拓展）已知函數(shù)f(x(=|sinx|+|cosx|-則A.f(x(的圖象關(guān)于直線x=π對稱B.f(x(是周期函數(shù)，且其中一個周期是C.f(x(的值域是[、2-1,1[D.f(x(在,上單調(diào)遞增B.log2x+log2y的最大值為C.y-x-xy的最小值為-1EQ\*jc3\*hps18\o\al(\s\up3(Γ),L)A.B.C.D.f(x+y(f(x-y(=f2(x(-f2(y(，且f(1(=2，函數(shù)f(3x+1(為偶函數(shù)，則A.f(0(=0B.f(4-x(+f(x(=0C.f(x(為偶函數(shù)f(k(=222C.當(dāng)d1>d2n{單調(diào)遞減D.當(dāng)d1<d2n{單調(diào)遞增定義域為R，函數(shù)F(x(=f(1+x(-(1+x(為偶函數(shù)，函數(shù)G(x(=f(2+3x(-1為奇函數(shù)，則下列說B.f(0(=-1D.f(0(+f(1(+f(2(+f(3(+f(4(=5P(x0B.xEQ\*jc3\*hps12\o\al(\s\up3(2),0)+yEQ\*jc3\*hps12\o\al(\s\up3(2),0)的最大值為22D.直線y=x+2與曲線C有且僅有3個交點-A.函數(shù)f(x(的最大值為C.當(dāng)m<0時，方程f(x(=m有且只有一個實根D.若f(x1(=f(x2((x1≠x2(，則x1+x2>D1B.三棱錐P-EFG體積的最大值為C.若A1P//平面EFG數(shù)f(x(的定義域為R，滿足f(x+y(=f(x(f(1-y(+f(y(f(1-x(，f(1(=1，則A.f(0(=0B.f(x(=f(2-x(C.f(x(是偶函數(shù)f(k(=1A.|a-b|=42C.|a-c|的最小值為D.|a-c|的最大值為18.（甘肅省白銀市靖遠(yuǎn)縣第一中學(xué)2024-2025學(xué)年高三上學(xué)期11月新高考模擬卷暨期中考）設(shè)f'(x(是三次函數(shù)y=f(x(的導(dǎo)數(shù)，f''(x(是f'(x(的導(dǎo)數(shù)，若方程f''(x(=0有實數(shù)解x0，則稱點(x0,A.f(x(的拐點為B.f(x(有極值點，則b2-3c>0C.過f(x(的拐點有三條切線D.若b=-3，c=1，則f(2-x(+f(x(=-2內(nèi)兩定點M(0,-2(和N(0,2(與一動點P(x,y(，滿足||=m(m≥4(，若動點P的軌跡為曲C.若P,M,N三點不共線，則△PMN周長最小值為2m+4D.曲線E上與M,N不共線的任意一點G關(guān)于原點對稱的點為H，則四邊形GMHN的面積不大于mC.|AC|的最小值大于221.（廣東省華南師范大學(xué)附屬中學(xué)2024-2025學(xué)年2025屆高三上學(xué)期11月綜測D.若x0為f(x(的一個極小值點，且a<e-cosxf(x(+tanx0恒成立，則a<-122.（湖北省2024年秋季鄂東南省級示范高中教育教學(xué)改革聯(lián)盟學(xué)校期中聯(lián)考）已知函數(shù)f(x(=EQ\*jc3\*hps21\o\al(\s\up7(-x),x)EQ\*jc3\*hps21\o\al(\s\up7(≤),x)EQ\*jc3\*hps21\o\al(\s\up7(0),x)>0，若不等式f(x-1(≥f(x(對任意x∈R都成立，則實數(shù)a的值可以為A.-B.-C.-2D.-1是世界上偉大數(shù)學(xué)家。用他名字定義的函數(shù)f(x(=[x]（[x]表示不超過x的最大整數(shù)）稱為高斯函A.an=n(n∈N*)B.Sn=n2+?+b63]=6D.[++?+]=18A.當(dāng)y<0時，x+y=0B.當(dāng)x<0時，x+y=0C.當(dāng)x+y≠0時，y-x>2D.當(dāng)x+y≠0時，-1<xy<02x3-3ax2+1A.當(dāng)a=0時，直線y=1是曲線y=f(x(的切線D.當(dāng)x0f(x(在x=x0處的切線與函數(shù)y=f(x(的圖象有且僅有兩個交點EQ\*jc3\*hps21\o\al(\s\up9(—→),M)EQ\*jc3\*hps21\o\al(\s\up9(—→),N)EQ\*jc3\*hps21\o\al(\s\up9(—→),Q)A.f(x)在R上單調(diào)遞減D.f()+f()+f()+?+f()=(n∈N*)A.<B.Sn<-4C.Rn<A.a1>a2-2B.an≥n+1C.f(an)>f(n)D.an+m>an+amC.直線x+y=t截第一象限花瓣的弦長的最大值為C:x2=4y交于A(x1,y1),B(x2,y2)兩點，拋物線C在點A處的切線與直線y=-2交于點N，作NM⊥AP交AB于點M，則—→—→A.OA?OB=-5B.直線MN恒過定點B.點I的運(yùn)動軌跡為雙曲線的一部分EQ\*jc3\*hps21\o\al(\s\up6(—→),F)EQ\*jc3\*hps21\o\al(\s\up6(—→),F)，則y-x=3+bx2+cx+1<x2<x3)，函數(shù)g(x)=f(x)-1也有三個零點t1，t2，t3(t1<t2<t3)，A.b2>3ac2=-C.x1+x3<t1+t3D.xEQ\*jc3\*hps12\o\al(\s\up3(2),1)+xEQ\*jc3\*hps12\o\al(\s\up3(2),2)+xEQ\*jc3\*hps12\o\al(\s\up3(2),3)=tEQ\*jc3\*hps12\o\al(\s\up3(2),1)+tEQ\*jc3\*hps12\o\al(\s\up3(2),2)+tEQ\*jc3\*hps12\o\al(\s\up3(2),3)A.f(x)是周期函數(shù)B.-1<f(x)<1滿足：f(1+x)+f(1-x)=2，f(2+x)+f(2-x)=4，則A.f(3)=3B.f(x)為奇函數(shù)f(x0)=x0+1x+1)-f(x)≥2A.a=2A.函數(shù)f(x)為單調(diào)減函數(shù)C.若對?x>0，f(x)>f(-x)+a恒成立，則a≤2C.若F為線段AC1的中點，則點F在球D.C1D與平面ABED所成角的正弦值的最大值為B.將f(x)圖象向右平移后得到函數(shù)y=2C.f(x)在區(qū)間上單調(diào)遞增A.當(dāng)a=3，b=1時，有f(-2-x)+f(x)=0恒成立x-e+1與y=ln(x+e-1)的部分圖象可得一條封閉曲線Γ,則A.Γ有對稱軸C.直線x+y=t被Γ截得弦長的最大值為2A.對任意實數(shù)x，f2(x(-g2(x(=1C.對任意實數(shù)x，y，g(x+y(g(x-y(=g2(x(+g2(y(D.若直線y=t與函數(shù)y=f(x(和y=g(x(的圖象共有三個交點，設(shè)這三個交點的橫坐標(biāo)分別為x1，x21+x2+x3>ln(1+、2(a,0((a>0(的距離之積為定值a2。則下列說法正確的是()(參考數(shù)據(jù)：，則點(-4,0)在C上在C上，則2<yEQ\*jc3\*hps12\o\al(\s\up3(2),0)<3-=183A.a2=C.Tn=2n+2-2n-4D.-<Sn≤1-A.f(x(是非奇非偶函數(shù)D.f(x(的圖象與y=-|x|的圖象恰有6個交點f(x(滿足f(x(=f，其中a為實數(shù)，其值域是M。若對于任何滿足上述條件的f(x(都有{y|y=f(x(,x∈[0,1]}=M，則()A.方程f(x(=f(0(可以有無數(shù)多解x弧度(0<x<記表面積增加量為S=f(x(，則()B.f(x(的圖象關(guān)于直線對稱D.S≤6-42A1BA.異面直線EF與CD所成角的余弦值是C.三棱錐P?AA1C的體積為[f(x+y(+f(x-y([=f(x(f(y(，f(1(=2，則()A.f(2(=-2B.f(x(是偶函數(shù)C.f(x(以4為周期f(k(=-4為坐標(biāo)原點，點A(2,1(在拋物線C:x2=2py(p>0(上，拋物線的焦點為F，過點B(0,-1(的直線l交A.直線AB與拋物線C相切C.若P是線段BQ的中點，則2|PF|=|QF|則()B.AB⊥PCC.平面PDE⊥平面PADA.A1D.截面四邊形BED1F的周長的最小值為10)A.f(2(+f(4(<0B.當(dāng)0<x<6時，f(x(≤C.當(dāng)3<x<4時，f(x(>f(D.當(dāng)0<x<2時，f(x(<f(*)。則下列選項正確的是()a2n?1-是等比數(shù)列B.數(shù)列{an{是單調(diào)遞增數(shù)列+b3+b5+?+b2n?1<2D.若cn=，則c2+c4+c6+?+c2n=A.當(dāng)a<0時，函數(shù)f(x(為單調(diào)遞增函數(shù)B.點(0,-2)為函數(shù)y=f(x(圖象的對稱中心D.函數(shù)f(x(有三個零點的充要條件是a>356（重慶市巴蜀中學(xué)2025屆高考適應(yīng)性月考卷（三已知由實數(shù)構(gòu)成的數(shù)列{an{滿足an+1=-aEQ\*jc3\*hps12\o\al(\s\up3(2),n)+n*n{是遞增數(shù)列D.若a1=n=，{bn{的前n項和為Sn，則Sn>-2 2.（2025屆湖北省名校圓創(chuàng)聯(lián)盟高三11月第二次聯(lián)考）對任意x>0，都有xlnx?kx+2k+1?f(x(f(x+1(<0，則正整數(shù)a的最小值為.<在原點處的切線方程為y=x+，且函數(shù)g(x(=f(ax((a>0(在區(qū)間(π,2π)上沒有零點，則實數(shù)a在(0,+∞)上的函數(shù)f(x(滿足f(x+1(=f(x(?x，當(dāng)0<x≤1時，f(x(=x?x，若f(x(在區(qū)間(0,7.（安徽省合肥市第一中學(xué)2024-2025學(xué)年高三上學(xué)期第三次素質(zhì)拓展）已知函數(shù)f(x(=ex-e-x-2sinx+1，不等式f(2023a-x2ex(+f(2lnx+x(≤2對任意的x∈(0,+∞(恒成立，則a的最大值為. |a-b||b-c|3|c-a|的最大值是.kx(kx-1( EQ\*jc3\*hps12\o\al(\s\up3(m),n)EQ\*jc3\*hps12\o\al(\s\up3(m),n)EQ\*jc3\*hps12\o\al(\s\up3(m),n)EQ\*jc3\*hps12\o\al(\s\up3(m),n)R，若f(2x+1(為奇函數(shù)，f(x+2(為偶函數(shù)，且f(0(=1，則f(k(=.________整數(shù)n，函數(shù)f(x(=+lnx-(an+2(x均存在兩個極值點xn1,xn2，且滿足|xn2-xn1|=(n+1(an，則Sn=.-m，若f(x)與g(x)的零點構(gòu)成的集合的元素個數(shù)為3，則m的取值范圍是.i,?,bn)的曼哈頓距離為|a1-b1|+|a2-b2|+?+|an-bn|。在5維“立方體”的頂點中任取兩個不同的頂點，記隨機(jī)變量X為所取兩點間的曼哈頓距離，則E(X)=.圖象如圖②,若圓x2-4x+3+y2=0與該蔓葉線恰有兩個交點，則a=.n+t}也成等差