高考真題山東試卷及答案

一、單項(xiàng)選擇題1.設(shè)集合\(A=\{x|1\leqx\leq3\}\)，\(B=\{x|2\ltx\lt4\}\)，則\(A\cupB=\)（）A.\(\{x|2\ltx\leq3\}\)B.\(\{x|2\leqx\leq3\}\)C.\(\{x|1\leqx\lt4\}\)D.\(\{x|1\ltx\lt4\}\)答案：C2.已知\(i\)是虛數(shù)單位，若復(fù)數(shù)\(z\)滿足\(z(1+i)=2i\)，則\(z=\)（）A.\(-1+i\)B.\(1-i\)C.\(1+i\)D.\(-1-i\)答案：C3.設(shè)\(a=\log_{0.2}0.3\)，\(b=\log_{2}0.3\)，則（）A.\(a+b\ltab\lt0\)B.\(ab\lta+b\lt0\)C.\(a+b\lt0\ltab\)D.\(ab\lt0\lta+b\)答案：B4.函數(shù)\(y=\frac{\sinx+x}{\cosx+x^{2}}\)在\([-\pi,\pi]\)的圖象大致為（）（選項(xiàng)略）答案：D5.已知三棱錐\(S-ABC\)中，\(\angleSAB=\angleABC=\frac{\pi}{2}\)，\(SB=4\)，\(SC=2\sqrt{13}\)，\(AB=2\)，\(BC=6\)，則三棱錐\(S-ABC\)的體積是（）A.\(4\)B.\(6\)C.\(4\sqrt{3}\)D.\(6\sqrt{3}\)答案：A6.已知\(P\)是雙曲線\(C\)：\(\frac{x^{2}}{2}-y^{2}=1\)右支上一點(diǎn)，直線\(l\)是雙曲線\(C\)的一條漸近線，\(P\)在\(l\)上的射影為\(Q\)，\(F_{1}\)是雙曲線\(C\)的左焦點(diǎn)，則\(|PF_{1}|+|PQ|\)的最小值為（）A.\(1\)B.\(2\)C.\(\sqrt{2}+1\)D.\(2\sqrt{2}+1\)答案：A7.已知\(a\gt0\)，\(b\gt0\)，且\(a+b=1\)，則（）A.\(a^{2}+b^{2}\geq\frac{1}{2}\)B.\(2^{a-b}\gt\frac{1}{2}\)C.\(\log_{2}a+\log_{2}b\geq-2\)D.\(\sqrt{a}+\sqrt\leq\sqrt{2}\)答案：ABD8.已知函數(shù)\(f(x)=\sin(\omegax+\varphi)(\omega\gt0,|\varphi|\lt\frac{\pi}{2})\)的最小正周期為\(\pi\)，將其圖象向左平移\(\frac{\pi}{6}\)個(gè)單位長度后得到的圖象關(guān)于\(y\)軸對(duì)稱，則\(f(x)\)的一個(gè)對(duì)稱中心為（）A.\((-\frac{\pi}{12},0)\)B.\((\frac{\pi}{6},0)\)C.\((\frac{\pi}{3},0)\)D.\((\frac{\pi}{2},0)\)答案：A9.已知\(a=3^{0.2}\)，\(b=\log_{6}4\)，\(c=\log_{3}2\)，則\(a\)，\(b\)，\(c\)的大小關(guān)系為（）A.\(c\ltb\lta\)B.\(b\ltc\lta\)C.\(a\ltb\ltc\)D.\(c\lta\ltb\)答案：A10.已知\(F_{1}\)，\(F_{2}\)是橢圓\(C\)：\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)的兩個(gè)焦點(diǎn)，\(P\)為橢圓\(C\)上一點(diǎn)，且\(\angleF_{1}PF_{2}=60^{\circ}\)，若\(\triangleF_{1}PF_{2}\)的面積為\(9\sqrt{3}\)，則\(b=\)（）A.\(3\)B.\(6\)C.\(3\sqrt{3}\)D.\(2\sqrt{3}\)答案：A二、多項(xiàng)選擇題1.下列關(guān)于向量的說法正確的是（）A.若\(\vec{a}\parallel\vec\)，\(\vec\parallel\vec{c}\)，則\(\vec{a}\parallel\vec{c}\)B.若\(\vec{a}\)，\(\vec\)都是單位向量，則\(\vec{a}=\vec\)C.若\(|\vec{a}+\vec|=|\vec{a}|+|\vec|\)，則\(\vec{a}\)與\(\vec\)同向D.若\(\vec{a}\perp\vec\)，則\(\vec{a}\cdot\vec=0\)答案：CD2.已知函數(shù)\(f(x)=2\sin(2x-\frac{\pi}{6})\)，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)\((\frac{\pi}{12},0)\)對(duì)稱C.\(f(x)\)在\([0,\frac{\pi}{2}]\)上的最大值為\(2\)D.\(f(x)\)在\((\frac{\pi}{3},\frac{5\pi}{6})\)上單調(diào)遞減答案：ACD3.已知\(m\)，\(n\)是兩條不同的直線，\(\alpha\)，\(\beta\)是兩個(gè)不同的平面，則下列說法正確的是（）A.若\(m\parallel\alpha\)，\(n\parallel\alpha\)，則\(m\paralleln\)B.若\(m\parallel\alpha\)，\(m\parallel\beta\)，則\(\alpha\parallel\beta\)C.若\(m\perp\alpha\)，\(n\perp\alpha\)，則\(m\paralleln\)D.若\(m\perp\alpha\)，\(m\perp\beta\)，則\(\alpha\parallel\beta\)答案：CD4.已知數(shù)列\(zhòng)(\{a_{n}\}\)是等差數(shù)列，\(S_{n}\)是其前\(n\)項(xiàng)和，若\(a_{3}+a_{9}=2a_{5}+2\)，則下列結(jié)論正確的是（）A.\(S_{10}=10\)B.\(S_{10}=50\)C.\(a_{5}=5\)D.\(a_{1}+a_{10}=10\)答案：BD5.已知函數(shù)\(f(x)=\begin{cases}x^{2}-2x+3,x\leq2\\\log_{2}x,x\gt2\end{cases}\)，則下列說法正確的是（）A.\(f(x)\)在\((-\infty,1]\)上單調(diào)遞減B.\(f(x)\)的值域?yàn)閈([2,+\infty)\)C.\(f(4)=2\)D.若\(f(a)=3\)，則\(a=2\)或\(a=8\)答案：ACD6.已知\(F\)是拋物線\(y^{2}=2px(p\gt0)\)的焦點(diǎn)，\(A\)，\(B\)是拋物線上的兩點(diǎn)，滿足\(\overrightarrow{AF}=3\overrightarrow{FB}\)，則直線\(AB\)的斜率可能為（）A.\(\sqrt{3}\)B.\(-\sqrt{3}\)C.\(\frac{\sqrt{3}}{3}\)D.\(-\frac{\sqrt{3}}{3}\)答案：AB7.已知函數(shù)\(f(x)=\frac{1}{3}x^{3}-x^{2}-3x+1\)，則下列說法正確的是（）A.\(f(x)\)的極大值為\(\frac{10}{3}\)B.\(f(x)\)的極小值為\(-8\)C.\(f(x)\)在\((-\infty,-1)\)上單調(diào)遞增D.\(f(x)\)在\((3,+\infty)\)上單調(diào)遞減答案：ABC8.已知\(a\)，\(b\)，\(c\)分別為\(\triangleABC\)三個(gè)內(nèi)角\(A\)，\(B\)，\(C\)的對(duì)邊，且\(a\cosC+\sqrt{3}a\sinC-b-c=0\)，則下列說法正確的是（）A.\(A=\frac{\pi}{3}\)B.\(B=\frac{\pi}{6}\)C.若\(a=2\)，則\(\triangleABC\)的面積最大值為\(\sqrt{3}\)D.若\(a=2\)，則\(\triangleABC\)的周長最大值為\(6\)答案：ACD9.已知函數(shù)\(f(x)=\cos^{2}x-\sin^{2}x+2\sqrt{3}\sinx\cosx\)，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)\((\frac{\pi}{6},0)\)對(duì)稱C.\(f(x)\)在\([0,\frac{\pi}{2}]\)上的最大值為\(2\)D.\(f(x)\)的單調(diào)遞增區(qū)間為\([k\pi-\frac{\pi}{3},k\pi+\frac{\pi}{6}]\)，\(k\inZ\)答案：ACD10.已知\(x\)，\(y\)滿足約束條件\(\begin{cases}x+y\geq2\\x-y\leq2\\y\leq2\end{cases}\)，則下列說法正確的是（）A.\(z=x+2y\)的最小值為\(4\)B.\(z=x^{2}+y^{2}\)的最大值為\(8\)C.\(z=\frac{y}{x+1}\)的最大值為\(1\)D.\(z=3x-y\)的最大值為\(4\)答案：BC三、判斷題1.若\(a\gtb\)，則\(ac^{2}\gtbc^{2}\)。（）答案：×2.函數(shù)\(y=\sinx\)在區(qū)間\([0,\pi]\)上是單調(diào)遞增的。（）答案：×3.若向量\(\vec{a}\)與\(\vec\)的夾角為\(60^{\circ}\)，\(|\vec{a}|=2\)，\(|\vec|=1\)，則\(\vec{a}\cdot\vec=1\)。（）答案：√4.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：×5.數(shù)列\(zhòng)(\{a_{n}\}\)滿足\(a_{n+1}=2a_{n}\)，則\(\{a_{n}\}\)是等比數(shù)列。（）答案：×6.函數(shù)\(y=\log_{2}(x^{2}-4)\)的定義域?yàn)閈((-\infty,-2)\cup(2,+\infty)\)。（）答案：√7.橢圓\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)的離心率\(e=\frac{c}{a}\)，其中\(zhòng)(c^{2}=a^{2}-b^{2}\)。（）答案：√8.若\(f(x)\)是奇函數(shù)，則\(f(0)=0\)。（）答案：×9.函數(shù)\(y=2^{x}\)與\(y=\log_{2}x\)的圖象關(guān)于直線\(y=x\)對(duì)稱。（）答案：√10.若\(x\gt0\)，\(y\gt0\)，且\(x+y=1\)，則\(\frac{1}{x}+\frac{1}{y}\geq4\)。（）答案：√四、簡答題1.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)的前\(n\)項(xiàng)和為\(S_{n}\)，\(a_{3}=5\)，\(S_{6}=36\)。求數(shù)列\(zhòng)(\{a_{n}\}\)的通項(xiàng)公式\(a_{n}\)。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\(S_{6}=36\)，根據(jù)等差數(shù)列求和公式\(S_{n}=na_{1}+\frac{n(n-1)d}{2}\)，可得\(6a_{1}+\frac{6\times5d}{2}=36\)，即\(6a_{1}+15d=36\)。聯(lián)立方程組求解，將\(a_{1}=5-2d\)代入\(6a_{1}+15d=36\)，得\(6(5-2d)+15d=36\)，解得\(d=2\)，進(jìn)而得\(a_{1}=1\)。所以\(a_{n}=a_{1}+(n-1)d=1+2(n-1)=2n-1\)。2.已知函數(shù)\(f(x)=x^{3}-3x^{2}+2\)。求函數(shù)\(f(x)\)的單調(diào)區(qū)間。答案：對(duì)函數(shù)\(f(x)=x^{3}-3x^{2}+2\)求導(dǎo)，得\