文科數(shù)學(xué)試卷及答案

一、單項(xiàng)選擇題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|0<x<5,x\inN\}\)，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.函數(shù)\(y=\log_2(x^2-4x+3)\)的定義域?yàn)椋ǎ〢.\((1,3)\)B.\((-\infty,1)\cup(3,+\infty)\)C.\((0,1)\cup(3,+\infty)\)D.\((-\infty,1)\cup(2,+\infty)\)答案：B3.已知\(\overrightarrow{a}=(1,-2)\)，\(\overrightarrow=(x,4)\)，且\(\overrightarrow{a}\parallel\overrightarrow\)，則\(\vert\overrightarrow{a}-\overrightarrow\vert\)等于（）A.\(5\)B.\(2\sqrt{5}\)C.\(\sqrt{5}\)D.\(5\sqrt{5}\)答案：A4.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.\(7\)C.\(-\frac{1}{7}\)D.\(-7\)答案：C5.若拋物線\(y^2=2px(p>0)\)的焦點(diǎn)與雙曲線\(\frac{x^2}{6}-\frac{y^2}{3}=1\)的右焦點(diǎn)重合，則\(p\)的值為（）A.\(4\)B.\(6\)C.\(8\)D.\(12\)答案：B6.執(zhí)行如圖所示的程序框圖，若輸入\(n=10\)，則輸出\(S=\)（）（程序框圖內(nèi)容：開(kāi)始，輸入\(n\)，\(S=0\)，\(i=1\)，判斷\(i\leqn\)，是則\(S=S+\frac{1}{i(i+1)}\)，\(i=i+1\)，循環(huán)；否則輸出\(S\)，結(jié)束）A.\(\frac{9}{10}\)B.\(\frac{10}{11}\)C.\(\frac{11}{12}\)D.\(\frac{12}{13}\)答案：B7.已知直線\(l\)過(guò)點(diǎn)\((1,2)\)，且在\(x\)軸和\(y\)軸上的截距相等，則直線\(l\)的方程為（）A.\(x+y-3=0\)B.\(x-y+1=0\)C.\(x+y-3=0\)或\(2x-y=0\)D.\(x-y+1=0\)或\(2x-y=0\)答案：C8.已知函數(shù)\(f(x)=\sin(2x+\frac{\pi}{6})\)，將其圖象向右平移\(\frac{\pi}{6}\)個(gè)單位長(zhǎng)度后得到函數(shù)\(g(x)\)的圖象，則\(g(x)\)的一個(gè)單調(diào)遞增區(qū)間是（）A.\([-\frac{\pi}{12},\frac{5\pi}{12}]\)B.\([\frac{5\pi}{12},\frac{11\pi}{12}]\)C.\([-\frac{\pi}{6},\frac{\pi}{3}]\)D.\([\frac{\pi}{3},\frac{5\pi}{6}]\)答案：A9.已知\(x\)，\(y\)滿足約束條件\(\begin{cases}x+y\geq1\\x-y\leq1\\y\leq1\end{cases}\)，則\(z=3x-y\)的最大值為（）A.\(1\)B.\(2\)C.\(3\)D.\(4\)答案：C10.已知函數(shù)\(f(x)=\begin{cases}2^x,x\leq0\\\log_3x,x>0\end{cases}\)，則\(f(f(\frac{1}{9}))\)的值為（）A.\(\frac{1}{4}\)B.\(4\)C.\(-4\)D.\(-\frac{1}{4}\)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.\(y=x^2\)B.\(y=\frac{1}{x}\)C.\(y=\lgx\)D.\(y=2^x\)答案：ACD2.已知\(a\)，\(b\)，\(c\)為三條不重合的直線，\(\alpha\)，\(\beta\)，\(\gamma\)為三個(gè)不重合的平面，則下列說(shuō)法正確的是（）A.若\(a\parallelc\)，\(b\parallelc\)，則\(a\parallelb\)B.若\(a\parallel\alpha\)，\(b\parallel\alpha\)，則\(a\parallelb\)C.若\(\alpha\parallel\gamma\)，\(\beta\parallel\gamma\)，則\(\alpha\parallel\beta\)D.若\(a\parallel\alpha\)，\(\alpha\parallel\beta\)，則\(a\parallel\beta\)答案：AC3.已知數(shù)列\(zhòng)(\{a_n\}\)是等差數(shù)列，其前\(n\)項(xiàng)和為\(S_n\)，若\(a_3=6\)，\(S_3=12\)，則（）A.\(a_n=2n\)B.\(a_n=3n-3\)C.\(S_n=n^2+n\)D.\(S_n=\frac{3n^2-3n}{2}\)答案：AC4.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（）A.\(f(-1)=2\)B.函數(shù)\(g(x)=f(x)-x+3\)有\(zhòng)(3\)個(gè)零點(diǎn)C.\(f(x)\)的解析式為\(f(x)=\begin{cases}x^2-3x,x\geq0\\-x^2-3x,x<0\end{cases}\)D.方程\(f(x)=x\)有\(zhòng)(3\)個(gè)不同的實(shí)數(shù)根答案：ABCD5.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\(l\)交橢圓\(C\)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.橢圓\(C\)的方程為\(\frac{x^2}{3}+\frac{y^2}{2}=1\)B.橢圓\(C\)的焦距為\(2\)C.直線\(l\)斜率為\(1\)時(shí)，\(\vertAB\vert=\frac{4\sqrt{3}}{3}\)D.點(diǎn)\(F_1\)到直線\(AB\)距離的最大值為\(\sqrt{2}\)答案：ABD6.已知函數(shù)\(f(x)=\sin(2x+\varphi)(-\frac{\pi}{2}<\varphi<\frac{\pi}{2})\)，將函數(shù)\(f(x)\)的圖象向左平移\(\frac{\pi}{6}\)個(gè)單位長(zhǎng)度后得到函數(shù)\(g(x)\)的圖象，且\(g(x)\)是偶函數(shù)，則（）A.\(\varphi=\frac{\pi}{6}\)B.\(f(x)\)在\((0,\frac{\pi}{3})\)上單調(diào)遞增C.\(f(x)\)的圖象關(guān)于點(diǎn)\((\frac{5\pi}{12},0)\)對(duì)稱D.\(f(x)\)在\([-\frac{\pi}{6},\frac{\pi}{6}]\)上的最大值為\(1\)答案：ACD7.已知\(a\)，\(b\)，\(c\)滿足\(a>b>c\)，且\(ac<0\)，則下列不等式一定成立的是（）A.\(ab>ac\)B.\(c(b-a)>0\)C.\(cb^2<ab^2\)D.\(ac(a-c)<0\)答案：ABD8.已知圓\(C:x^2+y^2-2x-4y+1=0\)，直線\(l:y=kx\)，則（）A.直線\(l\)與圓\(C\)相交B.若\(k=0\)，則直線\(l\)被圓\(C\)截得的弦長(zhǎng)為\(2\sqrt{3}\)C.若直線\(l\)被圓\(C\)截得的弦長(zhǎng)最短，則\(k=\frac{1}{2}\)D.直線\(l\)被圓\(C\)截得的弦長(zhǎng)最長(zhǎng)為\(4\)答案：ABC9.已知函數(shù)\(f(x)=\frac{1}{3}x^3-x^2-3x+1\)，則（）A.函數(shù)\(f(x)\)的單調(diào)遞增區(qū)間為\((-\infty,-1)\)和\((3,+\infty)\)B.函數(shù)\(f(x)\)的單調(diào)遞減區(qū)間為\((-1,3)\)C.\(f(x)\)的極大值為\(\frac{8}{3}\)D.\(f(x)\)的極小值為\(-8\)答案：ABCD10.已知函數(shù)\(f(x)=\cos(2x+\frac{\pi}{3})+\sin^2x\)，則（）A.\(f(x)\)的最小正周期為\(\pi\)B.\(f(x)\)的最大值為\(\frac{3}{2}\)C.\(f(x)\)在\((-\frac{\pi}{6},\frac{\pi}{6})\)上單調(diào)遞減D.\(f(x)\)的圖象關(guān)于點(diǎn)\((\frac{\pi}{6},\frac{1}{4})\)對(duì)稱答案：ACD三、判斷題1.若\(a>b\)，則\(a^2>b^2\)。（）答案：×2.函數(shù)\(y=\sinx\)的圖象的對(duì)稱軸方程為\(x=k\pi+\frac{\pi}{2}(k\inZ)\)。（）答案：√3.若向量\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)。（）答案：×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\(y=\pm\frac{a}x\)。（）答案：√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：×6.等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=\frac{n(a_1+a_n)}{2}\)。（）答案：√7.函數(shù)\(y=\log_ax(a>0,a\neq1)\)在\((0,+\infty)\)上單調(diào)遞增。（）答案：×8.直線\(Ax+By+C=0\)（\(A\)，\(B\)不同時(shí)為\(0\)）的斜率\(k=-\frac{A}{B}\)。（）答案：×9.若\(a\)，\(b\)，\(c\)成等比數(shù)列，則\(b^2=ac\)。（）答案：√10.已知\(A\)，\(B\)，\(C\)是平面內(nèi)不共線的三點(diǎn)，若\(\overrightarrow{AB}=\lambda\overrightarrow{AC}(\lambda\inR)\)，則\(A\)，\(B\)，\(C\)三點(diǎn)共線。（）答案：×四、簡(jiǎn)答題1.已知數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=n^2+2n\)。求數(shù)列\(zhòng)(\{a_n\}\)的通項(xiàng)公式。答案：當(dāng)\(n=1\)時(shí)，\(a_1=S_1=1^2+2\times1=3\)；當(dāng)\(n\geq2\)時(shí)，\(a_n=S_n-S_{n-1}=n^2+2n-[(n-1)^2+2(n-1)]=2n+1\)。當(dāng)\(n=1\)時(shí)，\(a_1=3\)滿足\(a_n=2n+1\)。所以數(shù)列\(zhòng)(\{a_n\}\)的通項(xiàng)公式為\(a_n=2n+1\)。2.已知函數(shù)\(f(x)=\sinx\cosx+