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）

上有且僅有一個(gè)零點(diǎn)，當(dāng)ω最大時(shí)f(x(在區(qū)間[-100π,100π[上的零點(diǎn)個(gè)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.A.-7A.B.C.2D.2f(n((n∈N,n≥2(，記數(shù)列{cn{的前n項(xiàng)積為Tn，數(shù)列{Tn{的前n項(xiàng)和為Sn，則A.≤Sn<2D.≤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?yàn)镽的函數(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(xiàng)錯(cuò)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(，滿足則稱函數(shù)y=f(x(是在區(qū)間[a,b]上的一個(gè)雙中值函數(shù)。已知函數(shù)f是區(qū)間[0,t]上的雙中值函數(shù)，則實(shí)數(shù)t的取值范圍是A.,B.,C.,D.(1,都有f(—x(—f+x(=0，f(2024(=。若f(x(+f/(—x(>0，則不等式的解集是A.(3,+∞(C.(1,+∞(PC，二面角P-AC-B的大小為150°,若三棱錐P-ABC外接球的表面積為84π,則該三棱錐P-ABC體積的最大值等于2C.2EQ\*jc3\*hps21\o\al(\s\up8(—→),B)EQ\*jc3\*hps21\o\al(\s\up8(—→),A)EQ\*jc3\*hps21\o\al(\s\up8(—→),C)EQ\*jc3\*hps21\o\al(\s\up8(—→),C)EQ\*jc3\*hps21\o\al(\s\up8(—→),C)643A.643B.πC.πD.πEQ\*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)A.(,1)B.(,1)C.(1,2)D.(1,)A.4514.（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(=ax(a>0,a≠1(，若存在x使得f(x+1(，f(ax(，f(x+2(依次成等差數(shù)列，則實(shí)數(shù)a的取值范圍為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(gè)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.-πB.-πD.π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(gè)零點(diǎn)D.f(2x(=f(x(y=f(x((x≠0(滿足f(xy(=f(x(+f(y(-1，當(dāng)x>1時(shí)，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.[,1)C.(0,)D.(34,2]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月綜測數(shù)列{an{的前n項(xiàng)和為Sn，且滿足則下列有關(guān)數(shù)列{an{的敘述正確的是()A.a7>a6B.a9<1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(函數(shù)，f,(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(gè)不同的解，則稱f(x(為[a,b[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,+∞(C.[-2,1[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(gè)零點(diǎn)，則實(shí)是A.(-12,4)B.(-12,-4]C.(-4,8]D.[-4,4)A.B.A.B.C.D.1C.4+27D.2+7A.2B.6D.2031.（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.60A.{-20,21}B.{-20,20}C.{-29,11}D.{-20,19}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.B.C.D.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.B.D.A.a<b<cB.b<c<aC.c<a<bD.c<b<aA.-7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\up9(—→),O)若向量BEQ\*jc3\*hps21\o\al(\s\up8(—→),A)在向量BEQ\*jc3\*hps21\o\al(\s\up8(—→),C)上的投影向量為BEQ\*jc3\*hps21\o\al(\s\up8(—→),C)，則cosB的值為()R-2,6]內(nèi)函數(shù)g(x)=f(x)-loga(x+2)(a>1)有三個(gè)不同的零點(diǎn)，則實(shí)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(gè)粽子體積的比為(A.πππππD.πA.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(diǎn)(m,n)在曲線y=f(x(上，則f(m(-f(n(A.2B.D.A.B.(0,+∞(C.D.(0,2]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)≤2A.3B.4C.5D.6EQ\*jc3\*hps21\o\al(\s\up8(—→),B)EQ\*jc3\*hps21\o\al(\s\up8(—→),E)EQ\*jc3\*hps21\o\al(\s\up8(—→),E)EQ\*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)A.3B.24cA.6B.9R)為奇函數(shù)，且f(x)在區(qū)間(t-1,tA.(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)AA1=3BE上一動(dòng)點(diǎn)Q滿足EEQ\*jc3\*hps21\o\al(\s\up9(—→),Q)·AEQ\*jc3\*hps21\o\al(\s\up9(—→),Q)=0，P是該長A.長方體ABCD-A1B1C1D1外接球的半徑為B.點(diǎn)A到平面A1BE的距離為3f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<的A.f(x)=2sin(2x+B.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[t,t+,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<1D.d+a>0中，M是AC上A.過點(diǎn)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|+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(gè)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)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)22nA.當(dāng)0<q<1時(shí)，數(shù)列{dn{單調(diào)遞減C.當(dāng)d1>d2n{單調(diào)遞減D.當(dāng)d1<d2n{單調(diào)遞增定義域?yàn)镽，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(gè)交點(diǎn)-A.函數(shù)f(x(的最大值為C.當(dāng)m<0時(shí)，方程f(x(=m有且只有一個(gè)實(shí)根D.若f(x1(=f(x2((x1≠x2(，則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?yàn)镽，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)A.|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(shí)數(shù)解x0，則稱點(diǎn)(x0,A.f(x(的拐點(diǎn)為B.f(x(有極值點(diǎn)，則b2-3c>0C.過f(x(的拐點(diǎn)有三條切線D.若b=-3，c=1，則f(2-x(+f(x(=-2內(nèi)兩定點(diǎn)M(0,-2(和N(0,2(與一動(dòng)點(diǎn)P(x,y(，滿足若動(dòng)點(diǎn)P的軌跡為曲C.若P,M,N三點(diǎn)不共線，則△PMN周長最小值為D.曲線E上與M,N不共線的任意一點(diǎn)G關(guān)于原點(diǎn)對稱的點(diǎn)為H，則四邊形GMHN的面積不大于m21.（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A.f(x(在(0,上是增函數(shù)B.f(x(的圖象關(guān)于點(diǎn),0(中心對稱C.f(x(在(0,π(上有兩個(gè)極值點(diǎn)D.若x0為f(x(的一個(gè)極小值點(diǎn)，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)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.[++…+]=18C.當(dāng)x+y≠0時(shí)，y-x>2D.當(dāng)x+y≠0時(shí)，-1<xy<0B.若f(x(有三個(gè)不同的零點(diǎn)x1,x2,x3，則x1.x2.x3=-D.當(dāng)x0≠時(shí)，f(x(在x=x0處的切線與函數(shù)y=f(x(的圖象有且僅有兩個(gè)交點(diǎn),y1),N(x2,y2)是函數(shù)的圖象上的兩點(diǎn)，對坐標(biāo)平面內(nèi)的任一點(diǎn)P，f(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B.f(x)的圖象關(guān)于點(diǎn)Q中心對稱C.若f(t)+f(t2-1)≥1，則實(shí)數(shù)t的取值范圍為(-∞,-2]∪[1,+∞)D.f()+f()+f()+…+f()=(n∈N*)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(diǎn)，拋物線C在點(diǎn)A處的切線與直線y=-2交于點(diǎn)N，作NM⊥AP交AB于點(diǎn)M，則A.OEQ\*jc3\*hps21\o\al(\s\up8(—→),A)?OEQ\*jc3\*hps21\o\al(\s\up8(—→),B)=-5B.直線MN恒過定點(diǎn)B.點(diǎn)I的運(yùn)動(dòng)軌跡為雙曲線的一部分EQ\*jc3\*hps21\o\al(\s\up9(—→),F)EQ\*jc3\*hps21\o\al(\s\up9(—→),F)，則y-x=3+bx2+cx+1<x2<x3)，函數(shù)g(x)=f(x)-1也有三個(gè)零點(diǎn)t1，t2，t3(t1<t2<t3)，A.b2>3acC.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)<1D.關(guān)于x的方程f(x)=有兩個(gè)實(shí)數(shù)解滿足：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(diǎn)，則點(diǎn)F在球D.C1D與平面ABED所成角的正弦值的最大值為A.f(x)=2sin(2x+B.將f(x)圖象向右平移后得到函數(shù)y=2A.當(dāng)a=3，b=1時(shí)，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2D.Γ的面積大于2e-4A.對任意實(shí)數(shù)x，f2(x(-g2(x(=1C.對任意實(shí)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(gè)交點(diǎn)，設(shè)這三個(gè)交點(diǎn)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(diǎn)(-4,0)在C上在C上，則2<yEQ\*jc3\*hps12\o\al(\s\up3(2),0)<3C.Tn=2n+2-2n-4A.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(gè)交點(diǎn)f(x(滿足f(x(=f，其中a為實(shí)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xB.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的體積為域?yàn)镽，若2[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為周期為坐標(biāo)原點(diǎn)，點(diǎn)A(2,1(在拋物線C:x2=2py(p>0(上，拋物線的焦點(diǎn)為F，過點(diǎn)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(diǎn)，則2|PF|=|QF|則()B.AB⊥PCC.平面PDE⊥平面PADD.l被球O截得的弦長為1A.A1D.截面四邊形BED1F的周長的最小值為10)A.f(2(+f(4(<0*)。則下列選項(xiàng)正確的是()B.數(shù)列{an{是單調(diào)遞增數(shù)列5+…+b2n—1<2—A.當(dāng)a<0時(shí)，函數(shù)f(x(為單調(diào)遞增函數(shù)B.點(diǎn)(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(gè)零點(diǎn)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(shí)數(shù)構(gòu)成的數(shù)列{an{滿足an+1=-aEQ\*jc3\*hps12\o\al(\s\up3(2),n)+k=2______f(x(f(x+1(<0，則正整數(shù)a的最小值為.__點(diǎn)處的切線方程為，且函數(shù)g(x(=f(ax((a>0(在區(qū)間(π,2π)上沒有零點(diǎn)，則實(shí)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(shí)，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.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)-m，若f(x)與g(x)的零點(diǎn)構(gòu)成的集合的元素個(gè)數(shù)為3，則m的取值范圍是.________ni(b1,n)的曼哈頓距離為|a1-b1|+|a2-b2|+…+|an-bn|。在5維“立方體”的頂點(diǎn)中任取兩個(gè)不同的頂點(diǎn)，記隨機(jī)變量X為所取兩點(diǎn)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(gè)交點(diǎn)，則a=.________n+t}也成等差FEQ\*jc3\*hp