高考試卷及答案數(shù)學(xué)

一、單項(xiàng)選擇題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|0<x<6,x\inN\}\)，則滿足\(A\subseteqC\subseteqB\)的集合\(C\)的個(gè)數(shù)為（）A.4B.8C.7D.16答案：B2.設(shè)\(z=\frac{1-i}{1+i}+2i\)，則\(\vertz\vert\)等于（）A.0B.\(\frac{1}{2}\)C.1D.\(\sqrt{2}\)答案：C3.已知向量\(\overrightarrow{a}=(1,m)\)，\(\overrightarrow=(3,-2)\)，且\((\overrightarrow{a}+\overrightarrow)\perp\overrightarrow\)，則\(m\)等于（）A.-8B.-6C.6D.8答案：D4.已知\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\geq0\)時(shí)，\(f(x)=x^2-3x\)，則函數(shù)\(g(x)=f(x)-x+3\)的零點(diǎn)的集合為（）A.\(\{1,3\}\)B.\(\{-3,-1,1,3\}\)C.\(\{2-\sqrt{7},1,3\}\)D.\(\{-2-\sqrt{7},1,3\}\)答案：D5.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n\)，若\(a_3+a_5+a_7=24\)，則\(S_9\)等于（）A.36B.72C.144D.288答案：B6.已知\(\sin\alpha+\cos\alpha=\frac{1}{5}\)，\(\alpha\in(0,\pi)\)，則\(\tan\alpha\)等于（）A.-\(\frac{4}{3}\)B.-\(\frac{3}{4}\)C.\(\frac{3}{4}\)D.\(\frac{4}{3}\)答案：A7.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)，則雙曲線的方程為（）A.\(\frac{x^2}{9}-\frac{y^2}{27}=1\)B.\(\frac{x^2}{18}-\frac{y^2}{36}=1\)C.\(\frac{x^2}{27}-\frac{y^2}{9}=1\)D.\(\frac{x^2}{36}-\frac{y^2}{18}=1\)答案：A8.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.\(f(x)=2\sin(2x+\frac{\pi}{3})\)C.\(f(x)=2\sin(4x+\frac{\pi}{6})\)D.\(f(x)=2\sin(4x+\frac{\pi}{3})\)答案：A9.已知一個(gè)幾何體的三視圖如圖所示，則該幾何體的體積為（）A.\(\frac{1}{3}\)B.\(\frac{2}{3}\)C.1D.\(\frac{4}{3}\)答案：B10.已知\(f(x)\)是定義在\(R\)上的偶函數(shù)，且在區(qū)間\((-\infty,0]\)上單調(diào)遞增，若實(shí)數(shù)\(a\)滿足\(f(2^{\log_3a})>f(-\sqrt{2})\)，則\(a\)的取值范圍是（）A.\((0,\sqrt{3})\)B.\((0,\sqrt{3}]\)C.\((\sqrt{3},+\infty)\)D.\([\sqrt{3},+\infty)\)答案：A二、多項(xiàng)選擇題1.下列說法正確的是（）A.若\(a>b\)，\(c>d\)，則\(ac>bd\)B.若\(a>b\)，則\(ac^2>bc^2\)C.若\(a<b<0\)，則\(\frac{1}{a}>\frac{1}\)D.若\(a>b\)，則\(a^3>b^3\)答案：CD2.已知函數(shù)\(f(x)=\sin(2x+\frac{\pi}{3})\)，則下列說法正確的是（）A.\(f(x)\)的最小正周期為\(\pi\)B.\(f(x)\)的圖象關(guān)于點(diǎn)\((\frac{\pi}{3},0)\)對(duì)稱C.\(f(x)\)的圖象關(guān)于直線\(x=\frac{\pi}{6}\)對(duì)稱D.\(f(x)\)在\([0,\frac{\pi}{6}]\)上單調(diào)遞增答案：ABD3.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(-2,1)\)，則（）A.\(\overrightarrow{a}\parallel\overrightarrow\)B.\(\overrightarrow{a}\perp\overrightarrow\)C.\(|\overrightarrow{a}|=|\overrightarrow|\)D.\((\overrightarrow{a}+\overrightarrow)\perp(\overrightarrow{a}-\overrightarrow)\)答案：CD4.已知\(a\)，\(b\)，\(c\)分別為\(\triangleABC\)三個(gè)內(nèi)角\(A\)，\(B\)，\(C\)的對(duì)邊，且\((a+b)(\sinA-\sinB)=(c-b)\sinC\)，則（）A.\(A=\frac{\pi}{6}\)B.\(A=\frac{\pi}{3}\)C.\(\sinB+\sinC\)的最大值為\(\sqrt{3}\)D.\(\sinB+\sinC\)的最大值為\(\frac{\sqrt{3}}{2}\)答案：BC5.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：ABC6.已知圓\(C\)：\((x-1)^2+(y-2)^2=25\)，直線\(l\)：\((2m+1)x+(m+1)y-7m-4=0\)，則（）A.直線\(l\)恒過定點(diǎn)\((3,1)\)B.直線\(l\)與圓\(C\)相交C.當(dāng)\(m=-\frac{1}{2}\)時(shí)，直線\(l\)被圓\(C\)截得的弦長(zhǎng)最長(zhǎng)D.當(dāng)\(m=0\)時(shí)，直線\(l\)被圓\(C\)截得的弦長(zhǎng)最短答案：AB7.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\(F_2\)的直線\(l\)交橢圓\(C\)于\(A,B\)兩點(diǎn)，若\(\triangleAF_1B\)的周長(zhǎng)為\(4\sqrt{3}\)，則（）A.橢圓\(C\)的方程為\(\frac{x^2}{3}+\frac{y^2}{2}=1\)B.橢圓\(C\)的方程為\(\frac{x^2}{12}+\frac{y^2}{8}=1\)C.直線\(l\)斜率為\(1\)時(shí)，\(|AB|=\frac{4\sqrt{3}}{3}\)D.直線\(l\)斜率為\(1\)時(shí)，\(|AB|=\frac{8\sqrt{3}}{3}\)答案：AC8.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（）A.當(dāng)\(x<0\)時(shí)，\(f(x)=x(1-x)\)B.\(f(-2)=-6\)C.\(f(x)\)的單調(diào)遞增區(qū)間為\((-\infty,+\infty)\)D.\(f(x)\)的單調(diào)遞減區(qū)間為\((-\infty,+\infty)\)答案：ABC9.已知\(a\)，\(b\)，\(c\)為正實(shí)數(shù)，且\(a+b+c=1\)，則（）A.\(a^2+b^2+c^2\geq\frac{1}{3}\)B.\(ab+bc+ca\leq\frac{1}{3}\)C.\(\sqrt{a}+\sqrt+\sqrt{c}\leq\sqrt{3}\)D.\(\frac{1}{a}+\frac{1}+\frac{1}{c}\geq9\)答案：ABCD10.已知函數(shù)\(y=f(x)\)的圖象在點(diǎn)\((x_0,f(x_0))\)處的切線方程為\(y=g(x)\)，以下說法正確的是（）A.若\(f(x)\geqg(x)\)恒成立，則切點(diǎn)\((x_0,f(x_0))\)是函數(shù)\(y=f(x)\)的極小值點(diǎn)B.若\(f(x)\leqg(x)\)恒成立，則切點(diǎn)\((x_0,f(x_0))\)是函數(shù)\(y=f(x)\)的極大值點(diǎn)C.若\(f(x)=g(x)\)有且僅有一個(gè)解，則切點(diǎn)\((x_0,f(x_0))\)是函數(shù)\(y=f(x)\)的極值點(diǎn)D.若\(f(x)\)在\(x=x_0\)處可導(dǎo)，則\(f^\prime(x_0)=g^\prime(x_0)\)答案：ABD三、判斷題1.若直線\(l_1\)：\(A_1x+B_1y+C_1=0\)與直線\(l_2\)：\(A_2x+B_2y+C_2=0\)平行，則\(\frac{A_1}{A_2}=\frac{B_1}{B_2}\neq\frac{C_1}{C_2}\)。（）答案：錯(cuò)誤2.若\(\alpha\)，\(\beta\)是兩個(gè)不同的平面，\(m\)，\(n\)是兩條不同的直線，且\(m\subset\alpha\)，\(n\subset\beta\)，\(m\parallel\beta\)，\(n\parallel\alpha\)，則\(\alpha\parallel\beta\)。（）答案：錯(cuò)誤3.若\(y=f(x)\)是奇函數(shù)，則\(f(0)=0\)。（）答案：錯(cuò)誤4.若\(\{a_n\}\)是等比數(shù)列，\(S_n\)是其前\(n\)項(xiàng)和，則\(S_n\)，\(S_{2n}-S_n\)，\(S_{3n}-S_{2n}\)仍成等比數(shù)列。（）答案：錯(cuò)誤5.若函數(shù)\(y=f(x)\)在區(qū)間\((a,b)\)內(nèi)有零點(diǎn)，則\(f(a)\cdotf(b)<0\)。（）答案：錯(cuò)誤6.已知\(a\)，\(b\)為實(shí)數(shù)，則\(a>b\)是\(a^2>b^2\)的充分不必要條件。（）答案：錯(cuò)誤7.若\(\sin\alpha=\sin\beta\)，則\(\alpha=\beta+2k\pi\)，\(k\inZ\)。（）答案：錯(cuò)誤8.函數(shù)\(y=\log_2(x^2-2x+3)\)的單調(diào)遞增區(qū)間是\((1,+\infty)\)。（）答案：正確9.若向量\(\overrightarrow{a}\)，\(\overrightarrow\)滿足\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}\perp\overrightarrow\)。（）答案：正確10.若函數(shù)\(f(x)\)在\(x=x_0\)處的導(dǎo)數(shù)\(f^\prime(x_0)=0\)，則\(x=x_0\)是函數(shù)\(f(x)\)的極值點(diǎn)。（）答案：錯(cuò)誤四、簡(jiǎn)答題1.已知數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_1=1\)，\(a_{n+1}=2a_n+1\)。-求數(shù)列\(zhòng)(\{a_n\}\)的通項(xiàng)公式；-設(shè)\(b_n=\log_2(a_n+1)\)，求數(shù)列\(zhòng)(\{\frac{1}{b_nb_{n+1}}\}\)的前\(n\)項(xiàng)和\(T_n\)。答案：-由\(a