2025年廣東高考試題及答案

一、單項(xiàng)選擇題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|0<x<5,x\inN\}\)，則滿足條件\(A\subseteqC\subseteqB\)的集合\(C\)的個(gè)數(shù)為（）A.1B.2C.3D.4答案：D2.若復(fù)數(shù)\(z\)滿足\((1+i)z=1-i\)（\(i\)是虛數(shù)單位），則其共軛復(fù)數(shù)\(\overline{z}\)為（）A.\(i\)B.\(-i\)C.\(1+i\)D.\(1-i\)答案：A3.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(m,-1)\)，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：A4.函數(shù)\(y=\log_2(x^2-1)\)的定義域?yàn)椋ǎ〢.\((-1,1)\)B.\((-1,1]\)C.\((-\infty,-1)\cup(1,+\infty)\)D.\((-\infty,-1]\cup[1,+\infty)\)答案：C5.已知\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，則\(\tan(\alpha+\frac{\pi}{4})\)的值為（）A.\(\frac{1}{7}\)B.7C.\(-\frac{1}{7}\)D.-7答案：C6.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n\)，若\(a_3+a_5+a_7=15\)，則\(S_9\)的值為（）A.60B.45C.36D.27答案：B7.拋物線\(y^2=4x\)的焦點(diǎn)到雙曲線\(x^2-\frac{y^2}{3}=1\)的漸近線的距離是（）A.\(\frac{1}{2}\)B.\(\frac{\sqrt{3}}{2}\)C.1D.\(\sqrt{3}\)答案：B8.已知\(a=\log_20.3\)，\(b=2^{0.3}\)，\(c=0.3^{2}\)，則（）A.\(a<c<b\)B.\(a<b<c\)C.\(c<a<b\)D.\(b<c<a\)答案：A9.若函數(shù)\(f(x)=\sin(\omegax+\varphi)(\omega>0,|\varphi|<\frac{\pi}{2})\)的圖象的相鄰兩條對(duì)稱軸之間的距離為\(\frac{\pi}{2}\)，且\(f(-\frac{\pi}{6})=0\)，則\(f(x)\)的解析式為（）A.\(f(x)=\sin(x+\frac{\pi}{6})\)B.\(f(x)=\sin(x-\frac{\pi}{6})\)C.\(f(x)=\sin(2x+\frac{\pi}{6})\)D.\(f(x)=\sin(2x-\frac{\pi}{6})\)答案：C10.已知三棱錐\(P-ABC\)的所有頂點(diǎn)都在球\(O\)的球面上，\(PA\perp\)平面\(ABC\)，\(PA=2\sqrt{3}\)，\(AB=1\)，\(AC=2\)，\(\angleBAC=60^{\circ}\)，則球\(O\)的體積為（）A.\(\frac{32\pi}{3}\)B.\(\frac{8\pi}{3}\)C.\(8\pi\)D.\(4\pi\)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\(a\)，\(b\)，\(c\)為非零實(shí)數(shù)，且\(a>b\)，則下列不等式一定成立的是（）A.\(a^2>b^2\)B.\(ac^2>bc^2\)C.\(\frac{1}{a}<\frac{1}\)D.\(a-c>b-c\)答案：BD3.已知直線\(l\)過(guò)點(diǎn)\((1,0)\)且垂直于\(x\)軸，若\(l\)被拋物線\(y^2=4ax\)截得的線段長(zhǎng)為\(4\)，則拋物線的焦點(diǎn)坐標(biāo)為（）A.\((1,0)\)B.\((2,0)\)C.\((0,1)\)D.\((0,2)\)答案：AB4.已知函數(shù)\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\geq0\)時(shí)，\(f(x)=x(1+x)\)，則下列結(jié)論正確的是（）A.\(f(-1)=-2\)B.當(dāng)\(x<0\)時(shí)，\(f(x)=x(1-x)\)C.\(f(x)\)的圖象關(guān)于原點(diǎn)對(duì)稱D.\(f(x)\)的單調(diào)遞增區(qū)間是\((-\infty,+\infty)\)答案：ACD5.已知\(\{a_n\}\)是等比數(shù)列，公比\(q>1\)，前\(n\)項(xiàng)和為\(S_n\)，則下列說(shuō)法正確的是（）A.數(shù)列\(zhòng)(\{a_n\}\)的偶數(shù)項(xiàng)構(gòu)成的數(shù)列一定是等比數(shù)列B.若\(a_2+a_4=20\)，\(a_3+a_5=40\)，則\(S_5=31\)C.\(S_n\)不可能是\(n\)的一次函數(shù)D.若\(a_n>0\)，則\(\lga_1+\lga_2+\cdots+\lga_{20}=10\lg(a_1a_{20})\)答案：ABD6.已知圓\(C\)：\((x-1)^2+(y-2)^2=25\)，直線\(l\)：\((2m+1)x+(m+1)y-7m-4=0\)，則以下說(shuō)法正確的是（）A.直線\(l\)恒過(guò)定點(diǎn)\((3,1)\)B.直線\(l\)與圓\(C\)一定相交C.當(dāng)直線\(l\)被圓\(C\)截得的弦長(zhǎng)最短時(shí)，直線\(l\)的方程為\(2x-y-5=0\)D.直線\(l\)被圓\(C\)截得的最長(zhǎng)弦長(zhǎng)為\(10\)答案：ABCD7.已知\(\alpha\)，\(\beta\)是兩個(gè)不同的平面，\(m\)，\(n\)是兩條不同的直線，則下列說(shuō)法正確的是（）A.若\(m\parallel\alpha\)，\(n\subset\alpha\)，則\(m\paralleln\)B.若\(m\perp\alpha\)，\(m\paralleln\)，\(n\subset\beta\)，則\(\alpha\perp\beta\)C.若\(\alpha\cap\beta=n\)，\(m\parallel\alpha\)，\(m\parallel\beta\)，則\(m\paralleln\)D.若\(\alpha\perp\beta\)，\(\alpha\cap\beta=m\)，\(n\perpm\)，則\(n\perp\alpha\)答案：BC8.已知函數(shù)\(f(x)=\frac{1}{3}x^3-x^2-3x+1\)，則（）A.函數(shù)\(f(x)\)有兩個(gè)極值點(diǎn)B.函數(shù)\(f(x)\)在\((-\infty,-1)\)上單調(diào)遞增C.函數(shù)\(f(x)\)在\(x=3\)處取得極小值D.函數(shù)\(f(x)\)在\([-2,2]\)上的最大值為\(\frac{19}{3}\)答案：ABC9.已知\(a\)，\(b\)，\(c\)分別為\(\triangleABC\)內(nèi)角\(A\)，\(B\)，\(C\)的對(duì)邊，\(\sin^2B=2\sinA\sinC\)，則（）A.當(dāng)\(a=b\)時(shí)，\(\cosB=\frac{3}{4}\)B.當(dāng)\(a=b\)時(shí)，\(\cosB=\frac{1}{4}\)C.當(dāng)\(B=90^{\circ}\)時(shí)，\(a=c\)D.當(dāng)\(B=90^{\circ}\)時(shí)，\(a\neqc\)答案：AC10.已知函數(shù)\(f(x)=\cos(\omegax+\varphi)(\omega>0,0<\varphi<\pi)\)的部分圖象如圖所示，則（）A.\(\omega=2\)B.\(\varphi=\frac{\pi}{3}\)C.\(f(x)\)的單調(diào)遞減區(qū)間為\([k\pi-\frac{\pi}{6},k\pi+\frac{\pi}{3}],k\inZ\)D.\(f(x)\)的圖象關(guān)于點(diǎn)\((\frac{\pi}{12},0)\)對(duì)稱答案：ABD三、判斷題1.若\(a\)，\(b\)為實(shí)數(shù)，則\(a^2+b^2\geq2ab\)，當(dāng)且僅當(dāng)\(a=b\)時(shí)等號(hào)成立。（）答案：對(duì)2.直線\(Ax+By+C=0\)（\(A\)，\(B\)不同時(shí)為\(0\)）的斜率為\(-\frac{A}{B}\)。（）答案：錯(cuò)（當(dāng)\(B=0\)時(shí)，直線斜率不存在）3.若函數(shù)\(y=f(x)\)在區(qū)間\((a,b)\)內(nèi)有\(zhòng)(f^\prime(x)>0\)，則函數(shù)\(y=f(x)\)在區(qū)間\((a,b)\)上單調(diào)遞增。（）答案：對(duì)4.若向量\(\overrightarrow{a}\)，\(\overrightarrow\)滿足\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}\perp\overrightarrow\)。（）答案：對(duì)（前提是\(\overrightarrow{a}\)，\(\overrightarrow\)為非零向量，本題默認(rèn)按此理解）5.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\(y=\pm\frac{a}x\)。（）答案：對(duì)6.若\(a>b>0\)，\(c<d<0\)，則\(ac<bd\)。（）答案：對(duì)7.函數(shù)\(y=\sinx\)的圖象向左平移\(\frac{\pi}{2}\)個(gè)單位長(zhǎng)度后得到\(y=\cosx\)的圖象。（）答案：對(duì)8.若\(\{a_n\}\)是等差數(shù)列，\(S_n\)是其前\(n\)項(xiàng)和，則\(S_n\)，\(S_{2n}-S_n\)，\(S_{3n}-S_{2n}\)仍成等差數(shù)列。（）答案：對(duì)9.已知\(a\)，\(b\)，\(c\)為\(\triangleABC\)的三邊，若\(a^2+b^2>c^2\)，則\(\triangleABC\)一定是銳角三角形。（）答案：錯(cuò)（只能說(shuō)明\(C\)為銳角，不能判定三角形一定是銳角三角形）10.若函數(shù)\(y=f(x)\)是偶函數(shù)，則\(f(x)\)的圖象關(guān)于\(y\)軸對(duì)稱。（）答案：對(duì)四、簡(jiǎn)答題1.已知函數(shù)\(f(x)=\sin(2x+\frac{\pi}{3})+\sin(2x-\frac{\pi}{3})+2\cos^2x-1\)，\(x\inR\)。-求函數(shù)\(f(x)\)的最小正周期；-求函數(shù)\(f(x)\)在區(qū)間\([-\frac{\pi}{4},\frac{\pi}{4}]\)上的最大值和最小值。答案：化簡(jiǎn)\(f(x)\)得\(f(x)=\sin2x+\cos2x=\sqrt{2}\sin(2x+\frac{\pi}{4})\)。最小正周期\(T=\frac{2\pi}{2}=\pi\)。在區(qū)間\([-\frac{\pi}{4},\frac{\pi}{4}]\)上，\(2x+\frac{\pi}{4}\in[-\frac{\pi}{4},\frac{3\pi}{4}]\)，當(dāng)\(2x+\frac{\pi}{4}=\frac{\pi}{2}\)即\(x=\frac{\pi}{8}\)時(shí)，\(f(x)\)取最大值\(\sqrt{2}\)；當(dāng)\(2x+\frac{\pi}{4}