2025高考真題及答案

一、單項選擇題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|0<x<5,x\inN\}\)，則滿足條件\(A\subseteqC\subseteqB\)的集合\(C\)的個數(shù)為（）A.1B.2C.3D.4答案：D2.設(shè)復(fù)數(shù)\(z\)滿足\((1+i)z=2i\)，則\(\vertz\vert\)=（）A.\(\frac{1}{2}\)B.\(\frac{\sqrt{2}}{2}\)C.\(\sqrt{2}\)D.2答案：C3.已知向量\(\overrightarrow{a}=(1,m)\)，\(\overrightarrow=(3,-2)\)，且\((\overrightarrow{a}+\overrightarrow)\perp\overrightarrow\)，則\(m\)=（）A.-8B.-6C.6D.8答案：D4.函數(shù)\(f(x)=\frac{1-x}{1+x}\)的圖象關(guān)于（）A.\(y\)軸對稱B.直線\(y=x\)對稱C.直線\(y=-x\)對稱D.坐標(biāo)原點(diǎn)對稱答案：D5.已知\(\sin\alpha+\cos\alpha=\frac{1}{5}\)，\(\alpha\in(0,\pi)\)，則\(\tan\alpha\)=（）A.\(-\frac{4}{3}\)B.\(-\frac{3}{4}\)C.\(\frac{3}{4}\)D.\(\frac{4}{3}\)答案：A6.已知雙曲線\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a>0,b>0)\)的一條漸近線方程為\(y=\sqrt{3}x\)，且與橢圓\(\frac{x^2}{100}+\frac{y^2}{64}=1\)有相同的焦點(diǎn)，則該雙曲線的方程為（）A.\(\frac{x^2}{9}-\frac{y^2}{27}=1\)B.\(\frac{x^2}{27}-\frac{y^2}{9}=1\)C.\(\frac{x^2}{16}-\frac{y^2}{48}=1\)D.\(\frac{x^2}{48}-\frac{y^2}{16}=1\)答案：A7.執(zhí)行如圖所示的程序框圖，若輸入的\(a=1\)，則輸出的\(k\)=（）A.2B.3C.4D.5答案：C8.已知函數(shù)\(f(x)=A\sin(\omegax+\varphi)(A>0,\omega>0,\vert\varphi\vert<\frac{\pi}{2})\)的部分圖象如圖所示，則\(f(x)\)的解析式為（）A.\(f(x)=2\sin(2x+\frac{\pi}{6})\)B.\(f(x)=2\sin(2x+\frac{\pi}{3})\)C.\(f(x)=2\sin(x+\frac{\pi}{6})\)D.\(f(x)=2\sin(x+\frac{\pi}{3})\)答案：A9.已知直三棱柱\(ABC-A_1B_1C_1\)中，\(\angleABC=90^{\circ}\)，\(AB=BC=BB_1=2\)，則異面直線\(A_1C\)與\(AB_1\)所成角的余弦值為（）A.\(\frac{\sqrt{10}}{5}\)B.\(\frac{\sqrt{15}}{5}\)C.\(\frac{\sqrt{5}}{5}\)D.\(\frac{2\sqrt{5}}{5}\)答案：B10.已知函數(shù)\(f(x)\)是定義在\(R\)上的偶函數(shù)，且在\([0,+\infty)\)上單調(diào)遞增，則滿足\(f(2x-1)<f(\frac{1}{3})\)的\(x\)的取值范圍是（）A.\((\frac{1}{3},\frac{2}{3})\)B.\([\frac{1}{3},\frac{2}{3})\)C.\((\frac{1}{2},\frac{2}{3})\)D.\([\frac{1}{2},\frac{2}{3})\)答案：A二、多項選擇題1.下列函數(shù)中，在區(qū)間\((0,+\infty)\)上單調(diào)遞增的是（）A.\(y=x^{\frac{1}{2}}\)B.\(y=2^x\)C.\(y=\log_{\frac{1}{2}}x\)D.\(y=\frac{1}{x}\)答案：AB2.已知\(a\)，\(b\)，\(c\)為三條不重合的直線，\(\alpha\)，\(\beta\)，\(\gamma\)為三個不重合的平面，則下列說法正確的是（）A.若\(a\parallelb\)，\(b\parallelc\)，則\(a\parallelc\)B.若\(a\parallel\alpha\)，\(b\parallel\alpha\)，則\(a\parallelb\)C.若\(\alpha\parallel\beta\)，\(\beta\parallel\gamma\)，則\(\alpha\parallel\gamma\)D.若\(\alpha\parallel\gamma\)，\(a\parallel\alpha\)，則\(a\parallel\gamma\)答案：AC3.已知\(a\)，\(b\)是正實數(shù)，且\(a+b=1\)，則下列說法正確的是（）A.\(ab\)有最大值\(\frac{1}{4}\)B.\(\frac{1}{a}+\frac{1}\)有最小值\(4\)C.\(\sqrt{a}+\sqrt\)有最大值\(\sqrt{2}\)D.\(a^2+b^2\)有最小值\(\frac{1}{2}\)答案：ABCD4.已知函數(shù)\(f(x)=\sin(2x+\varphi)(-\frac{\pi}{2}<\varphi<\frac{\pi}{2})\)的圖象關(guān)于直線\(x=\frac{\pi}{6}\)對稱，則（）A.\(\varphi=\frac{\pi}{6}\)B.\(f(x)\)在\([0,\frac{\pi}{6}]\)上單調(diào)遞增C.\(f(x)\)的圖象向左平移\(\frac{\pi}{6}\)個單位長度得到\(y=\cos2x\)的圖象D.若\(x\in[-\frac{\pi}{6},\frac{\pi}{3}]\)，則\(f(x)\)的值域為\([-\frac{1}{2},1]\)答案：ABD5.已知數(shù)列\(zhòng)(\{a_n\}\)是等差數(shù)列，\(S_n\)是其前\(n\)項和，若\(a_1+a_3+a_5=15\)，\(S_4=16\)，則（）A.\(a_1=1\)B.\(d=2\)C.\(a_n=2n-1\)D.\(S_n=n^2\)答案：ABCD6.已知\(F_1\)，\(F_2\)是橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的兩個焦點(diǎn)，\(P\)為橢圓上一點(diǎn)，且\(\angleF_1PF_2=60^{\circ}\)，則下列說法正確的是（）A.當(dāng)\(a=2b\)時，滿足條件的點(diǎn)\(P\)有且只有兩個B.當(dāng)\(a>2b\)時，滿足條件的點(diǎn)\(P\)有四個C.\(\triangleF_1PF_2\)的面積為\(\frac{\sqrt{3}}{3}b^2\)D.\(\overrightarrow{PF_1}\cdot\overrightarrow{PF_2}\)的取值范圍是\([b^2,2b^2)\)答案：ABCD7.已知函數(shù)\(f(x)=x^3-3x\)，則（）A.\(f(x)\)是奇函數(shù)B.\(f(x)\)在\(x=1\)處取得極大值\(-2\)C.\(f(x)\)在\((-\infty,-1)\)上單調(diào)遞增D.曲線\(y=f(x)\)在點(diǎn)\((0,0)\)處的切線方程為\(y=-3x\)答案：ACD8.已知\(a\)，\(b\)，\(c\)分別為\(\triangleABC\)內(nèi)角\(A\)，\(B\)，\(C\)的對邊，\(\sin^2B=2\sinA\sinC\)，且\(a>c\)，\(\cosB=\frac{1}{4}\)，則（）A.\(a\)，\(b\)，\(c\)成等比數(shù)列B.\(a\)，\(b\)，\(c\)成等差數(shù)列C.\(\sinA=\frac{\sqrt{10}}{4}\)D.\(\sinA=\frac{\sqrt{6}}{4}\)答案：AC9.已知函數(shù)\(f(x)=\begin{cases}2^x,x\leq0\\\log_2x,x>0\end{cases}\)，則下列說法正確的是（）A.\(f(f(\frac{1}{4}))=\frac{1}{4}\)B.方程\(f(x)=-1\)的解為\(x=\frac{1}{2}\)C.函數(shù)\(f(x)\)的值域為\(R\)D.函數(shù)\(y=f(x)-\frac{1}{2}\)有兩個零點(diǎn)答案：ACD10.已知圓\(C\)：\((x-1)^2+(y-2)^2=25\)，直線\(l\)：\((2m+1)x+(m+1)y-7m-4=0(m\inR)\)，則（）A.直線\(l\)恒過定點(diǎn)\((3,1)\)B.直線\(l\)與圓\(C\)相交C.直線\(l\)被圓\(C\)截得的弦長最短時，直線\(l\)的方程為\(2x-y-5=0\)D.直線\(l\)被圓\(C\)截得的弦長最長時，直線\(l\)的方程為\(3x-y-8=0\)答案：ABC三、判斷題1.若\(a>b\)，則\(ac^2>bc^2\)。（×）2.函數(shù)\(y=\sin^2x\)的最小正周期為\(\pi\)。（√）3.若向量\(\overrightarrow{a}\)，\(\overrightarrow\)滿足\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)。（×）4.雙曲線\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a>0,b>0)\)的漸近線方程為\(y=\pm\frac{a}x\)。（√）5.若函數(shù)\(y=f(x)\)在區(qū)間\((a,b)\)內(nèi)有零點(diǎn)，則\(f(a)\cdotf(b)<0\)。（×）6.已知\(a\)，\(b\)，\(c\)為實數(shù)，若\(a>b\)，則\(a^3>b^3\)。（√）7.直線\(x+\sqrt{3}y-1=0\)的傾斜角為\(120^{\circ}\)。（√）8.若\(S_n\)是等比數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和，則\(S_n\)，\(S_{2n}-S_n\)，\(S_{3n}-S_{2n}\)仍成等比數(shù)列。（×）9.函數(shù)\(y=\log_2(x^2+1)\)的值域為\([0,+\infty)\)。（√）10.若\(m\)，\(n\)是兩條不同的直線，\(\alpha\)，\(\beta\)是兩個不同的平面，且\(m\subset\alpha\)，\(n\subset\beta\)，\(m\parallel\beta\)，\(n\parallel\alpha\)，則\(\alpha\parallel\beta\)。（×）四、簡答題1.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和為\(S_n\)，\(a_3=5\)，\(S_4=16\)。求數(shù)列\(zhòng)(\{a_n\}\)的通項公式。答案：設(shè)等差數(shù)列\(zhòng)(\{a_n\}\)的公差為\(d\)。由\(a_3=5\)可得\(a_1+2d=5\)；由\(S_4=16\)可得\(4a_1+\frac{4\times3}{2}d=16\)，即\(4a_1+6d=16\)。聯(lián)立方程組\(\begin{cases}a_1+2d=5\\4a_1+6d=16\end{cases}\)，解得\(\begin{cases}a_1=1\\d=2\end{cases}\)。所以\(a_n