高考數(shù)學仿真題庫及答案

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.設\(z=\frac{1-i}{1+i}+2i\)，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\(m\)的值為（）A.-8B.-6C.6D.8答案：D4.函數(shù)\(y=\log_{a}(x+3)-1\)（\(a>0\)且\(a\neq1\)）的圖象恒過定點\(A\)，若點\(A\)在直線\(mx+ny+1=0\)上，其中\(zhòng)(mn>0\)，則\(\frac{1}{m}+\frac{2}{n}\)的最小值為（）A.2B.4C.8D.10答案：C5.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和為\(S_n\)，若\(a_3+a_4+a_5=12\)，則\(S_7\)的值為（）A.28B.42C.56D.14答案：A6.已知\(\sin\alpha+\cos\alpha=\frac{1}{5}\)，\(\alpha\in(0,\pi)\)，則\(\tan\alpha\)的值為（）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\(y=\frac{3}{4}x\)，則雙曲線的離心率為（）A.\(\frac{5}{3}\)B.\(\frac{5}{4}\)C.\(\frac{4}{3}\)D.\(\frac{3}{2}\)答案：B8.一個四面體的三視圖如圖所示，則該四面體的表面積是（）A.\(1+\sqrt{3}\)B.\(2+\sqrt{3}\)C.\(1+2\sqrt{3}\)D.\(2\sqrt{3}\)答案：B9.執(zhí)行如圖所示的程序框圖，輸出的\(S\)值為（）A.1B.\(\frac{2}{3}\)C.\(\frac{13}{21}\)D.\(\frac{34}{55}\)答案：C10.已知函數(shù)\(f(x)=\begin{cases}2^x-1,x\leq0\\f(x-1)+1,x>0\end{cases}\)，把函數(shù)\(g(x)=f(x)-x\)的零點按從小到大的順序排列成一個數(shù)列\(zhòng)(\{a_n\}\)，則該數(shù)列的通項公式為（）A.\(a_n=\frac{n(n-1)}{2}\)B.\(a_n=n(n-1)\)C.\(a_n=n-1\)D.\(a_n=2^n-2\)答案：C二、多項選擇題1.下列函數(shù)中，既是偶函數(shù)又在\((0,+\infty)\)上單調(diào)遞增的是（）A.\(y=x^3\)B.\(y=x^2+1\)C.\(y=\vertx\vert\)D.\(y=2^{-x}\)答案：BC2.已知\(a,b,c\)是實數(shù)，下列命題正確的是（）A.若\(a>b\)，則\(ac^2>bc^2\)B.若\(ac^2>bc^2\)，則\(a>b\)C.若\(a<b<0\)，則\(\frac{1}{a}>\frac{1}\)D.若\(a<b<0\)，則\(a^2>ab>b^2\)答案：BCD3.已知直線\(l\)：\(y=kx+m\)與圓\(C\)：\((x-1)^2+(y-2)^2=25\)相交于\(A\)，\(B\)兩點，下列說法正確的是（）A.若\(\vertAB\vert=10\)，則\(m^2+2km=24-k^2\)B.若\(\vertAB\vert=10\)，則\(m^2+2km=24\)C.若\(k=0\)，則\(\vertAB\vert=2\sqrt{25-m^2}\)D.若\(m=0\)，則\(\vertAB\vert=2\sqrt{\frac{25(1+k^2)-1}{1+k^2}}\)答案：ACD4.已知函數(shù)\(f(x)=\sin(\omegax+\varphi)\)（\(\omega>0\)，\(\vert\varphi\vert<\frac{\pi}{2}\)）的部分圖象如圖所示，則（）A.\(\omega=2\)B.\(\varphi=\frac{\pi}{6}\)C.函數(shù)\(f(x)\)的單調(diào)遞增區(qū)間為\([k\pi-\frac{\pi}{3},k\pi+\frac{\pi}{6}]\)，\(k\inZ\)D.函數(shù)\(f(x)\)的圖象關(guān)于點\((\frac{k\pi}{2}+\frac{\pi}{12},0)\)，\(k\inZ\)對稱答案：ABC5.已知\(F_1,F_2\)是橢圓\(C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的兩個焦點，\(P\)為橢圓\(C\)上一點，且\(\overrightarrow{PF_1}\perp\overrightarrow{PF_2}\)，若\(\trianglePF_1F_2\)的面積為\(9\)，則（）A.\(b=3\)B.\(a-c=3\)C.\(\trianglePF_1F_2\)的周長為\(6+2\sqrt{a^2-b^2}\)D.點\(P\)的縱坐標為\(\pm\frac{9}{c}\)答案：AC6.已知函數(shù)\(f(x)=x^3-3x\)，則（）A.\(f(x)\)的單調(diào)遞增區(qū)間為\((-\infty,-1)\)和\((1,+\infty)\)B.\(f(x)\)的單調(diào)遞減區(qū)間為\((-1,1)\)C.\(f(x)\)的極大值為\(2\)，極小值為\(-2\)D.方程\(f(x)=k\)有三個不同的實根，則\(-2<k<2\)答案：ABCD7.已知\(\{a_n\}\)是等比數(shù)列，公比\(q\neq1\)，其前\(n\)項和為\(S_n\)，下列說法正確的是（）A.若\(a_3a_4=a_{11}\)，則\(a_1=q^4\)B.若\(a_1a_2a_3=a_8\)，則\(a_1=q\)C.若\(S_3=3a_1\)，則\(q=-2\)D.若\(S_4=2S_2\)，則\(q=\pm\sqrt{2}\)答案：ABC8.已知拋物線\(y^2=2px(p>0)\)的焦點為\(F\)，準線為\(l\)，過點\(F\)的直線與拋物線交于\(A\)，\(B\)兩點，\(A(x_1,y_1)\)，\(B(x_2,y_2)\)，設\(\overrightarrow{AF}=\lambda\overrightarrow{FB}\)（\(\lambda>0\)），則（）A.\(y_1y_2=-p^2\)B.\(x_1x_2=\frac{p^2}{4}\)C.\(\frac{1}{x_1}+\frac{1}{x_2}=\frac{2}{p}\)D.\(\vertAB\vert=x_1+x_2+p\)答案：ABCD9.已知函數(shù)\(f(x)=\cosx\sin2x\)，則（）A.\(f(x)\)是奇函數(shù)B.\(f(x)\)的最大值為\(\frac{4\sqrt{3}}{9}\)C.\(f(x)\)的最小正周期為\(2\pi\)D.\(f(x)\)在區(qū)間\([-\frac{\pi}{2},\frac{\pi}{2}]\)上有\(zhòng)(3\)個零點答案：ABD10.已知函數(shù)\(f(x)=e^x-ax-1\)（\(a\inR\)），則（）A.當\(a=1\)時，\(f(x)\)在\((0,+\infty)\)上單調(diào)遞增B.當\(a=0\)時，\(f(x)\)的圖象與\(x\)軸有兩個交點C.當\(a<0\)時，\(f(x)\)在\(R\)上單調(diào)遞增D.當\(a>0\)時，\(f(x)\)在\((-\infty,\lna)\)上單調(diào)遞減，在\((\lna,+\infty)\)上單調(diào)遞增答案：ACD三、判斷題1.若\(a,b\inR\)，且\(a+b>4\)，則\(a>2\)且\(b>2\)。（×）2.命題“\(\forallx\inR\)，\(x^2+1>0\)”的否定是“\(\existsx\inR\)，\(x^2+1\leq0\)”。（√）3.若直線\(l_1:ax+2y+6=0\)與直線\(l_2:x+(a-1)y+a^2-1=0\)平行，則\(a=-1\)或\(a=2\)。（×）4.若\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，則\(\tan\alpha=-\frac{3}{4}\)。（√）5.已知\(\{a_n\}\)是等差數(shù)列，\(S_n\)是其前\(n\)項和，若\(S_7=S_11\)，則\(S_{18}=0\)。（√）6.函數(shù)\(y=\log_{0.5}(x^2-2x-3)\)的單調(diào)遞增區(qū)間是\((-\infty,-1)\)。（√）7.若向量\(\overrightarrow{a},\overrightarrow\)滿足\(\vert\overrightarrow{a}\vert=1\)，\(\vert\overrightarrow\vert=2\)，且\(\overrightarrow{a}\)與\(\overrightarrow\)的夾角為\(60^{\circ}\)，則\(\vert\overrightarrow{a}-\overrightarrow\vert=\sqrt{3}\)。（√）8.橢圓\(\frac{x^2}{25}+\frac{y^2}{9}=1\)上一點\(P\)到焦點\(F_1\)的距離為\(6\)，則\(P\)到焦點\(F_2\)的距離為\(4\)。（√）9.函數(shù)\(f(x)=x^3+ax^2+bx+c\)，若\(f(x)\)在\(x=1\)處有極值，則\(3+2a+b=0\)。（√）10.已知函數(shù)\(y=A\sin(\omegax+\varphi)\)（\(A>0\)，\(\omega>0\)）的圖象過點\(P(\frac{\pi}{12},0)\)，圖象上與點\(P\)最近的一個最高點是\(Q(\frac{\pi}{3},5)\)，則\(A=5\)，\(\omega=2\)，\(\varphi=-\frac{\pi}{6}\)。（√）四、簡答題1.已知函數(shù)\(f(x)=x^2-2x+2\)，\(x\in[t,t+1]\)，\(t\inR\)，求\(f(x)\)的最小值\(g(t)\)。答案：函數(shù)\(f(x)=x^2-2x+2=(x-1)^2+1\)，其對稱軸為\(x=1\)。當\(t+1\leq1\)即\(t\leq0\)時，\(f(x)\)在\([t,t+1]\)上單調(diào)遞減，\(g(t)=f(t+1)=t^2+1\)；當\(t<1<t+1\)即\(0<t<1\)時，\(g(t)=f(1)=1\)；當\(t\geq1\)時，\(f(x)\)在\([t,t+1]\)上單調(diào)遞增，\(g(t)=f(t)=t^2-2t+2\)。2.已知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