2025年八省聯(lián)考文科試卷及答案

一、單項(xiàng)選擇題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|0<x<6,x\inN\}\)，則\(A\capB\)等于（）A.\(\{1,2\}\)B.\(\{2,3\}\)C.\(\{3,4\}\)D.\(\{4,5\}\)答案：A2.復(fù)數(shù)\(z=\frac{1+2i}{1-i}\)（\(i\)為虛數(shù)單位），則\(z\)的共軛復(fù)數(shù)\(\overline{z}\)為（）A.\(-\frac{1}{2}+\frac{3}{2}i\)B.\(-\frac{1}{2}-\frac{3}{2}i\)C.\(\frac{1}{2}+\frac{3}{2}i\)D.\(\frac{1}{2}-\frac{3}{2}i\)答案：B3.命題“\(\forallx\inR\)，\(x^2+2x+3\geq0\)”的否定是（）A.\(\forallx\inR\)，\(x^2+2x+3<0\)B.\(\existsx\inR\)，\(x^2+2x+3\leq0\)C.\(\existsx\inR\)，\(x^2+2x+3<0\)D.\(\forallx\inR\)，\(x^2+2x+3\leq0\)答案：C4.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(m,-1)\)，若\(\overrightarrow{a}\parallel(\overrightarrow{a}+\overrightarrow)\)，則\(m\)的值為（）A.\(-\frac{1}{2}\)B.\(\frac{1}{2}\)C.2D.-2答案：A5.函數(shù)\(y=\log_2(x^2-1)\)的定義域?yàn)椋ǎ〢.\((-1,1)\)B.\((-\infty,-1)\cup(1,+\infty)\)C.\((-1,1]\)D.\((-\infty,-1]\cup[1,+\infty)\)答案：B6.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n\)，若\(a_3=5\)，\(S_4=16\)，則\(a_9\)等于（）A.17B.19C.21D.23答案：A7.若\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，則\(\tan(\alpha+\frac{\pi}{4})\)的值為（）A.\(\frac{1}{7}\)B.7C.\(-\frac{1}{7}\)D.-7答案：C8.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\(y=\pm\frac{3}{4}x\)，則雙曲線的離心率為（）A.\(\frac{5}{4}\)B.\(\frac{5}{3}\)C.\(\frac{7}{4}\)D.\(\frac{7}{3}\)答案：A9.已知函數(shù)\(f(x)=A\sin(\omegax+\varphi)\)（\(A>0\)，\(\omega>0\)，\(|\varphi|<\frac{\pi}{2}\)）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.\(f(x)=2\sin(2x-\frac{\pi}{6})\)C.\(f(x)=2\sin(x+\frac{\pi}{6})\)D.\(f(x)=2\sin(x-\frac{\pi}{6})\)（題目中雖沒(méi)圖，但不影響本題選項(xiàng)設(shè)置及答案，這里不涉及圖相關(guān)內(nèi)容）答案：A10.若函數(shù)\(f(x)=x^3-3x+a\)有三個(gè)不同的零點(diǎn)，則實(shí)數(shù)\(a\)的取值范圍是（）A.\((-2,2)\)B.\([-2,2]\)C.\((-\infty,-2)\cup(2,+\infty)\)D.\((-\infty,-2]\cup[2,+\infty)\)答案：A二、多項(xiàng)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.已知向量\(\overrightarrow{a}=(1,1)\)，\(\overrightarrow=(-1,2)\)，則下列向量與\(2\overrightarrow{a}+\overrightarrow\)共線的是（）A.\((1,3)\)B.\((3,1)\)C.\((-1,-3)\)D.\((-3,-1)\)答案：CD3.已知\(a\)，\(b\)，\(c\)滿足\(c<b<a\)，且\(ac<0\)，那么下列選項(xiàng)中一定成立的是（）A.\(ab>ac\)B.\(c(b-a)<0\)C.\(cb^2<ab^2\)D.\(ac(a-c)<0\)答案：AD4.對(duì)于函數(shù)\(f(x)=\sin(2x+\frac{\pi}{3})\)，下列說(shuō)法正確的是（）A.函數(shù)\(f(x)\)的圖象關(guān)于直線\(x=\frac{\pi}{12}\)對(duì)稱(chēng)B.函數(shù)\(f(x)\)的圖象關(guān)于點(diǎn)\((\frac{\pi}{3},0)\)對(duì)稱(chēng)C.函數(shù)\(f(x)\)在區(qū)間\([-\frac{\pi}{6},\frac{\pi}{6}]\)上單調(diào)遞增D.把函數(shù)\(f(x)\)的圖象向右平移\(\frac{\pi}{6}\)個(gè)單位長(zhǎng)度可得到\(y=\sin2x\)的圖象答案：ACD5.已知橢圓\(C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的左、右焦點(diǎn)分別為\(F_1,F_2\)，離心率為\(\frac{\sqrt{3}}{3}\)，過(guò)\(F_2\)的直線\(l\)交\(C\)于\(A\)，\(B\)兩點(diǎn)，若\(\triangleAF_1B\)的周長(zhǎng)為\(4\sqrt{3}\)，則下列說(shuō)法正確的是（）A.\(a=\sqrt{3}\)B.\(b=\sqrt{2}\)C.橢圓\(C\)的方程為\(\frac{x^2}{3}+\frac{y^2}{2}=1\)D.\(\triangleAF_1B\)面積的最大值為\(2\sqrt{3}\)答案：ABC6.已知數(shù)列\(zhòng)(\{a_n\}\)是等比數(shù)列，下列結(jié)論正確的是（）A.若\(a_1a_2>0\)，則\(a_2a_3>0\)B.若\(a_1+a_3<0\)，則\(a_4+a_6<0\)C.若\(a_2>a_1\)，則\(a_3>a_2\)D.若\(a_1a_2<0\)，則\(\frac{a_4}{a_2}>0\)答案：ABD7.下列關(guān)于基本不等式的說(shuō)法正確的是（）A.對(duì)任意\(a\)，\(b\inR\)，都有\(zhòng)(a+b\geq2\sqrt{ab}\)B.若\(a>0\)，\(b>0\)，則\(\frac{a+b}{2}\geq\sqrt{ab}\)當(dāng)且僅當(dāng)\(a=b\)時(shí)等號(hào)成立C.已知\(x>0\)，則函數(shù)\(y=2x+\frac{1}{x}\)的最小值為\(2\sqrt{2}\)D.已知\(x>0\)，則函數(shù)\(y=x+\frac{1}{x+1}\)的最小值為\(1\)答案：BC8.已知函數(shù)\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\geq0\)時(shí)，\(f(x)=x^2-2x\)，則下列說(shuō)法正確的是（）A.\(f(-1)=1\)B.當(dāng)\(x<0\)時(shí)，\(f(x)=-x^2-2x\)C.函數(shù)\(f(x)\)的單調(diào)遞增區(qū)間是\((-\infty,-1)\)和\((1,+\infty)\)D.函數(shù)\(f(x)\)的圖象與直線\(y=1\)有\(zhòng)(2\)個(gè)交點(diǎn)答案：AB9.已知圓\(C:x^2+y^2-2x-4y+1=0\)，直線\(l:y=kx\)，則下列說(shuō)法正確的是（）A.直線\(l\)與圓\(C\)相交B.若直線\(l\)將圓\(C\)分成的兩段弧長(zhǎng)之比為\(1:2\)，則\(k=2\pm\sqrt{2}\)C.若直線\(l\)與圓\(C\)相交于\(A\)，\(B\)兩點(diǎn)，則弦長(zhǎng)\(|AB|\)的最小值為\(2\sqrt{2}\)D.若點(diǎn)\(M(x_0,y_0)\)在圓\(C\)上運(yùn)動(dòng)，則\(x_0^2+y_0^2\)的最大值為\(2+2\sqrt{5}\)答案：ACD10.已知函數(shù)\(f(x)\)的導(dǎo)函數(shù)為\(f^\prime(x)\)，且滿足\(f(x)=2xf^\prime(1)+\lnx\)，則下列說(shuō)法正確的是（）A.\(f^\prime(1)=-1\)B.\(f(x)\)在\(x=1\)處取得極大值\(-2\)C.\(f(x)\)在\((0,+\infty)\)上單調(diào)遞減D.不等式\(f(x)<-x-1\)的解集為\((1,+\infty)\)答案：ACD三、判斷題1.若\(a>b\)，則\(a^2>b^2\)。（×）2.函數(shù)\(y=\cosx\)的圖象關(guān)于點(diǎn)\((\frac{\pi}{2},0)\)對(duì)稱(chēng)。（√）3.若直線\(l_1:y=k_1x+b_1\)與直線\(l_2:y=k_2x+b_2\)平行，則\(k_1=k_2\)且\(b_1\neqb_2\)。（√）4.若\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)。（×）5.等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=na_1+\frac{n(n-1)}{2}d\)（\(d\)為公差）。（√）6.函數(shù)\(y=a^x\)（\(a>0\)且\(a\neq1\)）在\(R\)上一定是單調(diào)函數(shù)。（√）7.橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的離心率\(e=\frac{c}{a}\)（\(c\)為半焦距），且\(0<e<1\)。（√）8.若函數(shù)\(f(x)\)在區(qū)間\([a,b]\)上的圖象是連續(xù)不斷的，且\(f(a)\cdotf(b)<0\)，則函數(shù)\(f(x)\)在區(qū)間\((a,b)\)內(nèi)至少有一個(gè)零點(diǎn)。（√）9.對(duì)于任意兩個(gè)向量\(\overrightarrow{a}\)，\(\overrightarrow\)，都有\(zhòng)((\overrightarrow{a}+\overrightarrow)^2=\overrightarrow{a}^2+2\overrightarrow{a}\cdot\overrightarrow+\overrightarrow^2\)。（√）10.若\(f(x)\)是奇函數(shù)，則\(f(0)=0\)。（×）四、簡(jiǎn)答題1.求函數(shù)\(y=\sin^2x+\sqrt{3}\sinx\cosx\)的最小正周期及單調(diào)遞增區(qū)間。答案：先化簡(jiǎn)函數(shù)，\(y=\sin^2x+\sqrt{3}\sinx\cosx=\frac{1-\cos2x}{2}+\frac{\sqrt{3}}{2}\sin2x=\sin(2x-\frac{\pi}{6})+\frac{1}{2}\)。最小正周期\(T=\frac{2\pi}{2}=\pi\)。令\(2k\pi-\frac{\pi}{2}\leq2x-\frac{\pi}{6}\leq2k\pi+\frac{\pi}{2}