海南數(shù)學(xué)高考真題及答案

一、單項選擇題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|0<x<6,x\inN\}\)，則滿足\(A\subseteqC\subseteqB\)的集合\(C\)的個數(shù)為（）A.4B.8C.7D.16答案：B2.復(fù)數(shù)\(z=\frac{1+2i}{1-i}\)，則\(\vertz\vert\)等于（）A.\(\frac{1}{2}\)B.\(\frac{\sqrt{10}}{2}\)C.\(\frac{5}{2}\)D.\(\frac{3\sqrt{2}}{2}\)答案：B3.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(m,-1)\)，且\(\overrightarrow{a}\perp(\overrightarrow{a}+\overrightarrow)\)，則\(m\)的值為（）A.-1B.-3C.-7D.-9答案：C4.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：A5.函數(shù)\(y=\log_2(1-x)\)的圖象大致為（）A.B.C.D.答案：C6.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和為\(S_n\)，若\(a_3=5\)，\(S_9=81\)，則\(a_7\)等于（）A.18B.13C.9D.7答案：B7.已知\(a=\log_32\)，\(b=\ln2\)，\(c=5^{-\frac{1}{2}}\)，則\(a\)，\(b\)，\(c\)的大小關(guān)系為（）A.\(a<b<c\)B.\(c<a<b\)C.\(b<c<a\)D.\(c<b<a\)答案：B8.某幾何體的三視圖如圖所示（單位：\(cm\)），則該幾何體的體積（單位：\(cm^3\)）是（）A.\(\frac{1}{3}\)B.\(\frac{2}{3}\)C.1D.\(\frac{4}{3}\)答案：D9.已知拋物線\(y^2=4x\)的焦點為\(F\)，準(zhǔn)線為\(l\)，點\(P\)為拋物線上一點，且在第一象限，\(PA\perpl\)，垂足為\(A\)，\(\vertPF\vert=4\)，則直線\(AF\)的斜率為（）A.\(-\sqrt{3}\)B.\(-\frac{\sqrt{3}}{3}\)C.\(\sqrt{3}\)D.\(\frac{\sqrt{3}}{3}\)答案：A10.已知函數(shù)\(f(x)=\sin(\omegax+\varphi)(\omega>0,\vert\varphi\vert<\frac{\pi}{2})\)的圖象的相鄰兩條對稱軸之間的距離為\(\frac{\pi}{2}\)，且\(f(-\frac{\pi}{12})=0\)，則下列說法正確的是（）A.\(f(x)=\sin(x+\frac{\pi}{6})\)B.\(f(x)\)在區(qū)間\((-\frac{\pi}{6},\frac{\pi}{3})\)上單調(diào)遞增C.\(f(x)\)的圖象關(guān)于點\((\frac{5\pi}{12},0)\)對稱D.\(f(x)\)的圖象關(guān)于直線\(x=\frac{\pi}{3}\)對稱答案：B二、多項選擇題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\(a>b\)，則\(\frac{1}{a}<\frac{1}\)D.若\(a>b\)，\(c>d\)，則\(a+c>b+d\)答案：D2.已知向量\(\overrightarrow{a}=(1,1)\)，\(\overrightarrow=(-1,1)\)，則下列向量與\(\overrightarrow{a}+\overrightarrow\)共線的是（）A.\((2,0)\)B.\((0,2)\)C.\((-1,-1)\)D.\((1,-1)\)答案：AC3.已知函數(shù)\(f(x)=\sin(2x+\varphi)(\vert\varphi\vert<\frac{\pi}{2})\)，將函數(shù)\(f(x)\)的圖象向左平移\(\frac{\pi}{6}\)個單位長度后得到\(g(x)\)的圖象，\(g(x)\)是偶函數(shù)，則（）A.\(\varphi=\frac{\pi}{6}\)B.\(f(x)\)在區(qū)間\((-\frac{\pi}{3},\frac{\pi}{6})\)上單調(diào)遞增C.\(f(x)\)的圖象關(guān)于點\((\frac{5\pi}{12},0)\)對稱D.\(f(x)\)在區(qū)間\([0,\frac{\pi}{2}]\)上的值域為\([-\frac{1}{2},1]\)答案：ABCD4.已知雙曲線\(C\)：\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a>0,b>0)\)的離心率為\(2\)，則（）A.雙曲線\(C\)的漸近線方程為\(y=\pm\sqrt{3}x\)B.雙曲線\(C\)的漸近線方程為\(y=\pm\frac{\sqrt{3}}{3}x\)C.雙曲線\(C\)的實軸長與虛軸長相等D.雙曲線\(C\)的焦距是實軸長的\(2\)倍答案：AD5.已知函數(shù)\(f(x)=x^3-3x^2+2\)，則（）A.\(f(x)\)在\(x=1\)處取得極大值\(0\)B.\(f(x)\)在\(x=1\)處取得極小值\(0\)C.\(f(x)\)在\(x=2\)處取得極大值\(-2\)D.\(f(x)\)在\(x=2\)處取得極小值\(-2\)答案：AD6.已知\(a\)，\(b\)，\(c\)為正實數(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：ABCD7.已知函數(shù)\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\geq0\)時，\(f(x)=x^2-2x\)，則（）A.\(f(-1)=1\)B.當(dāng)\(x<0\)時，\(f(x)=-x^2-2x\)C.\(f(x)\)的單調(diào)遞增區(qū)間為\((-\infty,-1)\)和\((1,+\infty)\)D.\(f(x)\)的值域為\(R\)答案：BD8.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\((3,1)\)B.直線\(l\)與圓\(C\)恒相交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\(2x-y-5=0\)答案：ABC9.已知\(a\)，\(b\)是兩個不相等的正數(shù)，且\(a+b=2\)，則（）A.\(ab<1\)B.\(\frac{1}{a}+\frac{1}>2\)C.\(\sqrt{a}+\sqrt<2\)D.\(a^2+b^2>2\)答案：ABCD10.已知函數(shù)\(f(x)=\lnx-ax\)，則（）A.當(dāng)\(a>0\)時，\(f(x)\)在\((0,\frac{1}{a})\)上單調(diào)遞增B.當(dāng)\(a>0\)時，\(f(x)\)在\((\frac{1}{a},+\infty)\)上單調(diào)遞減C.當(dāng)\(a=1\)時，\(f(x)\)有最大值\(-1\)D.當(dāng)\(a=0\)時，\(f(x)\)在\((0,+\infty)\)上單調(diào)遞增答案：ABCD三、判斷題1.若\(A\)，\(B\)是互斥事件，則\(P(A\cupB)=P(A)+P(B)\)。（）答案：對2.若直線\(l\)與平面\(\alpha\)內(nèi)的無數(shù)條直線垂直，則\(l\perp\alpha\)。（）答案：錯3.若\(z=a+bi(a,b\inR)\)，則\(z\)為純虛數(shù)的充要條件是\(a=0\)。（）答案：錯4.若\(a>b\)，則\(a^2>b^2\)。（）答案：錯5.函數(shù)\(y=\sinx\)的圖象的一個對稱中心是\((\frac{\pi}{2},0)\)。（）答案：錯6.若數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和\(S_n=2n^2+3n\)，則\(a_n=4n+1\)。（）答案：對7.若向量\(\overrightarrow{a}\)，\(\overrightarrow\)滿足\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}\perp\overrightarrow\)。（）答案：對8.函數(shù)\(y=\log_ax(a>0\)且\(a\neq1)\)在\((0,+\infty)\)上單調(diào)遞增。（）答案：錯9.若橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的離心率為\(\frac{\sqrt{3}}{2}\)，則\(a=2b\)。（）答案：對10.若函數(shù)\(y=f(x)\)的圖象關(guān)于直線\(x=a\)對稱，則\(f(a+x)=f(a-x)\)。（）答案：對四、簡答題1.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和為\(S_n\)，\(a_3=5\)，\(S_6=36\)。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\(S_6=36\)可得\(6a_1+\frac{6\times5}{2}d=36\)，即\(6a_1+15d=36\)。聯(lián)立方程組\(\begin{cases}a_1+2d=5\\6a_1+15d=36\end{cases}\)，解方程組得\(a_1=1\)，\(d=2\)。所以\(a_n=a_1+(n-1)d=1+2(n-1)=2n-1\)。2.已知函數(shù)\(f(x)=\sin(2x+\frac{\pi}{6})+\frac{1}{2}\)。求函數(shù)\(f(x)\)的最小正周期及單調(diào)遞增區(qū)間。答案：對于函數(shù)\(f(x)=\sin(2x+\frac{\pi}{6})+\frac{1}{2}\)，其最小正周期\(T=\frac{2\pi}{\omega}\)（\(\omega=2\)），所以\(T=\pi\)。令\(2k\pi-\frac{\pi}{2}\leq2x+\frac{\pi}{6}\leq2k\pi+\frac{\pi}{2}(k\inZ)\)，解不等式得\(k\pi-\frac{\pi}{3}\leqx\leqk\pi+\frac{\pi}{6}(k\inZ)\)，所以函數(shù)\(f(x)\)的單調(diào)遞增區(qū)間為\([k\pi-\frac{\pi}{3},k\pi+\frac{\pi}{6}](k\inZ)\)。3.已知拋物線\(y^2=2px(p