山西高考真題及答案

一、單項選擇題（共10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(shè)\(i\)是虛數(shù)單位，若復數(shù)\(z=\frac{a-i}{1+i}(a\inR)\)的實部與虛部相等，則\(a=（）A.-1B.0C.1D.2答案：B3.執(zhí)行如圖所示的程序框圖，若輸入的\(x=2\)，則輸出的\(y\)的值為（）A.2B.5C.11D.23答案：D4.已知\(\sin(\alpha+\frac{\pi}{6})=\frac{1}{3}\)，則\(\cos(2\alpha-\frac{2\pi}{3})\)的值是（）A.\(\frac{7}{9}\)B.\(\frac{1}{3}\)C.-\(\frac{1}{3}\)D.-\(\frac{7}{9}\)答案：A5.已知\(a=\log_20.2\)，\(b=2^{0.2}\)，\(c=0.2^{0.3}\)，則（）A.\(a<b<c\)B.\(a<c<b\)C.\(c<a<b\)D.\(b<c<a\)答案：B6.已知雙曲線\(C\)：\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a>0,b>0)\)的一條漸近線方程為\(y=\frac{\sqrt{5}}{2}x\)，且與橢圓\(\frac{x^2}{12}+\frac{y^2}{3}=1\)有公共焦點，則\(C\)的方程為（）A.\(\frac{x^2}{8}-\frac{y^2}{10}=1\)B.\(\frac{x^2}{4}-\frac{y^2}{5}=1\)C.\(\frac{x^2}{5}-\frac{y^2}{4}=1\)D.\(\frac{x^2}{4}-\frac{y^2}{3}=1\)答案：B7.函數(shù)\(f(x)=\frac{\sinx+\cosx}{\sinx-\cosx}\)的最小正周期為（）A.\(\frac{\pi}{4}\)B.\(\frac{\pi}{2}\)C.\(\pi\)D.\(2\pi\)答案：C8.已知\(a\)，\(b\)為單位向量，且\(a\cdotb=0\)，若\(c=2a-\sqrt{5}b\)，則\(\cos\langlea,c\rangle=（）A.\(\frac{\sqrt{5}}{3}\)B.\(\frac{\sqrt{5}}{5}\)C.\(\frac{2\sqrt{5}}{5}\)D.\(\frac{\sqrt{5}}{9}\)答案：C9.已知三棱錐\(P-ABC\)的四個頂點在球\(O\)的球面上，\(PA=PB=PC\)，\(\triangleABC\)是邊長為\(2\)的正三角形，\(E\)，\(F\)分別是\(PA\)，\(AB\)的中點，\(\angleCEF=90^{\circ}\)，則球\(O\)的體積為（）A.\(8\sqrt{6}\pi\)B.\(4\sqrt{6}\pi\)C.\(2\sqrt{6}\pi\)D.\(\sqrt{6}\pi\)答案：D10.已知函數(shù)\(f(x)=\begin{cases}x^2+2x+a-1,x\leq0\\-x^2+2x-2a,x>0\end{cases}\)，若對任意\(x\in[-3,+\infty)\)，\(f(x)\leq|x|\)恒成立，則\(a\)的取值范圍是（）A.\(\left[\frac{1}{8},1\right]\)B.\(\left[\frac{1}{8},\frac{3}{4}\right]\)C.\(\left[0,\frac{3}{4}\right]\)D.\(\left[0,1\right]\)答案：B二、多項選擇題（共10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.已知向量\(\vec{a}=(1,2)\)，\(\vec=(-2,1)\)，則（）A.\(\vec{a}\parallel\vec\)B.\(\vec{a}\perp\vec\)C.\(|\vec{a}|=|\vec|\)D.\((\vec{a}+\vec)\perp(\vec{a}-\vec)\)答案：CD3.對于函數(shù)\(f(x)=\sin(2x+\frac{\pi}{6})\)，下列說法正確的是（）A.函數(shù)\(f(x)\)的最小正周期為\(\pi\)B.函數(shù)\(f(x)\)圖象關(guān)于點\((\frac{\pi}{6},0)\)對稱C.函數(shù)\(f(x)\)圖象關(guān)于直線\(x=-\frac{\pi}{6}\)對稱D.函數(shù)\(f(x)\)在\([0,\frac{\pi}{3}]\)上單調(diào)遞增答案：AD4.已知\(a\)，\(b\)，\(c\)為三條不重合的直線，\(\alpha\)，\(\beta\)，\(\gamma\)為三個不重合的平面，則下列說法正確的是（）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\(\alpha\parallela\)，\(\beta\parallela\)，則\(\alpha\parallel\beta\)答案：AC5.已知橢圓\(C\)：\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的左、右焦點分別為\(F_1,F_2\)，離心率為\(\frac{\sqrt{3}}{3}\)，過\(F_2\)的直線\(l\)交\(C\)于\(A\)，\(B\)兩點，若\(\triangleAF_1B\)的周長為\(4\sqrt{3}\)，則下列說法正確的是（）A.\(a=\sqrt{3}\)B.\(b=\sqrt{2}\)C.\(c=1\)D.橢圓\(C\)的方程為\(\frac{x^2}{3}+\frac{y^2}{2}=1\)答案：ACD6.已知函數(shù)\(f(x)\)是定義在\(R\)上的奇函數(shù)，當\(x\geq0\)時，\(f(x)=x(1+x)\)，則下列說法正確的是（）A.\(f(-1)=-2\)B.當\(x<0\)時，\(f(x)=x(1-x)\)C.\(f(x)\)的單調(diào)遞增區(qū)間是\((-\infty,+\infty)\)D.不等式\(f(x)>0\)的解集為\((-1,0)\cup(1,+\infty)\)答案：ABC7.已知數(shù)列\(zhòng)(\{a_n\}\)為等差數(shù)列，\(S_n\)為其前\(n\)項和，若\(a_3=6\)，\(S_3=12\)，則（）A.\(a_1=0\)B.\(d=2\)C.\(a_n=2n-2\)D.\(S_n=n^2-n\)答案：ABCD8.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\(C\)可能相離C.直線\(l\)被圓\(C\)截得的最短弦長為\(4\sqrt{5}\)D.當直線\(l\)被圓\(C\)截得的弦長最短時，直線\(l\)的方程為\(2x-y-5=0\)答案：ACD9.已知函數(shù)\(f(x)=x^3-3x^2+2\)，則（）A.函數(shù)\(f(x)\)有兩個極值點B.\(f(x)\)在區(qū)間\((-\infty,0)\)上單調(diào)遞增C.\(f(x)\)在區(qū)間\((0,2)\)上單調(diào)遞減D.\(f(x)\)在區(qū)間\((2,+\infty)\)上單調(diào)遞增答案：ABCD10.已知\(x\)，\(y\)滿足約束條件\(\begin{cases}x+y\geq1\\x-y\leq1\\y\leq1\end{cases}\)，則（）A.\(z=x+2y\)的最大值為\(3\)B.\(z=x^2+y^2\)的最大值為\(2\)C.\(z=\frac{y}{x+1}\)的最大值為\(\frac{1}{2}\)D.\(z=2^{x-y}\)的最大值為\(2\)答案：ABD三、判斷題（共10題）1.若\(y=f(x)\)是奇函數(shù)，則\(y=f(x+2)\)也是奇函數(shù)。（×）2.直線\(l\)：\(Ax+By+C=0\)（\(A\)，\(B\)不同時為\(0\)）的斜率\(k=-\frac{A}{B}\)。（×）3.若\(\sin\alpha=\frac{1}{2}\)，則\(\alpha=\frac{\pi}{6}\)。（×）4.已知向量\(\vec{a}=(x_1,y_1)\)，\(\vec=(x_2,y_2)\)，若\(\vec{a}\cdot\vec=x_1x_2+y_1y_2=0\)，則\(\vec{a}\perp\vec\)。（√）5.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\(y=\pm\frac{a}x\)。（√）6.若\(a\)，\(b\)，\(c\)成等比數(shù)列，則\(b^2=ac\)。（√）7.函數(shù)\(y=\log_ax(a>0,a\neq1)\)在\((0,+\infty)\)上單調(diào)遞增。（×）8.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\(\frac{A_1}{A_2}=\frac{B_1}{B_2}\neq\frac{C_1}{C_2}\)。（√）9.對于函數(shù)\(y=A\sin(\omegax+\varphi)(A\neq0,\omega>0)\)，其最小正周期\(T=\frac{2\pi}{\omega}\)。（√）10.若\(a>b\)，則\(a^2>b^2\)。（×）四、簡答題（共4題）1.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和為\(S_n\)，\(a_1=1\)，\(S_5=25\)。求數(shù)列\(zhòng)(\{a_n\}\)的通項公式及\(S_n\)。答案：設(shè)等差數(shù)列\(zhòng)(\{a_n\}\)的公差為\(d\)，由\(S_5=5a_1+\frac{5\times4}{2}d=25\)，\(a_1=1\)，代入可得\(5+10d=25\)，解得\(d=2\)。則\(a_n=a_1+(n-1)d=1+2(n-1)=2n-1\)。\(S_n=na_1+\frac{n(n-1)}{2}d=n+n(n-1)=n^2\)。2.已知函數(shù)\(f(x)=x^2-2ax+1\)，\(x\in[0,2]\)，求\(f(x)\)的最小值。答案：函數(shù)\(f(x)=x^2-2ax+1\)的圖象開口向上，對稱軸為\(x=a\)。當\(a\leq0\)時，\(f(x)\)在\([0,2]\)上單調(diào)遞增，\(f(x)_{\min}=f(0)=1\)；當\(0<a<2\)時，\(f(x)_{\min}=f(a)=1-a^2\)；當\(a\geq2\)時，\(f(x)\)在\([0,2]\)上單調(diào)遞減，\(f(x)_{\min}=f(2)=5-4a\)。3.已知橢圓\(C\)：\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的離心率為\(\frac{\sqrt{2}}{2}\)，且過