高中月考卷题库及答案

高中月考卷题库及答案

一、单项选择题(每题2分,共10题)1.已知集合\(A=\{x|x^2-3x+2=0\}\),\(B=\{x|0<x<6,x\inN\}\),则\(A\capB=(\)\)A.\(\{1,2\}\)B.\(\{2,3\}\)C.\(\{1,2,3\}\)D.\(\{2,4,5\}\)2.函数\(y=\sqrt{x-1}+\frac{1}{x-2}\)的定义域为\((\)\)A.\([1,2)\cup(2,+\infty)\)B.\((1,+\infty)\)C.\([1,2)\)D.\([1,+\infty)\)3.已知\(a=\log_20.3\),\(b=2^{0.1}\),\(c=0.2^{1.3}\),则\(a,b,c\)的大小关系是\((\)\)A.\(a<b<c\)B.\(c<a<b\)C.\(a<c<b\)D.\(b<c<a\)4.已知向量\(\overrightarrow{a}=(1,2)\),\(\overrightarrow{b}=(3,1)\),则\(\overrightarrow{a}+\overrightarrow{b}\)的坐标为\((\)\)A.\((4,3)\)B.\((3,4)\)C.\((2,3)\)D.\((3,2)\)5.若\(\sin\alpha=\frac{3}{5}\),且\(\alpha\)为第二象限角,则\(\cos\alpha=(\)\)A.\(-\frac{4}{5}\)B.\(\frac{4}{5}\)C.\(-\frac{3}{5}\)D.\(\frac{3}{5}\)6.圆\((x-2)^2+y^2=4\)的圆心坐标和半径分别为\((\)\)A.\((0,2)\),\(2\)B.\((2,0)\),\(2\)C.\((-2,0)\),\(4\)D.\((2,0)\),\(4\)7.已知直线\(l_1:2x+y-3=0\),\(l_2:x-y+6=0\),则\(l_1\)与\(l_2\)的交点坐标为\((\)\)A.\((-1,4)\)B.\((1,2)\)C.\((-2,5)\)D.\((2,-1)\)8.等差数列\(\{a_n\}\)中,\(a_2=3\),\(a_5=9\),则公差\(d=(\)\)A.\(1\)B.\(2\)C.\(3\)D.\(4\)9.函数\(y=\sin2x\)的最小正周期为\((\)\)A.\(\pi\)B.\(2\pi\)C.\(\frac{\pi}{2}\)D.\(\frac{\pi}{4}\)10.从\(1\),\(2\),\(3\),\(4\),\(5\)中任取\(2\)个不同的数,事件\(A\)为"取到的\(2\)个数之和为偶数",事件\(B\)为"取到的\(2\)个数均为偶数",则\(P(B|A)=(\)\)A.\(\frac{1}{8}\)B.\(\frac{1}{4}\)C.\(\frac{2}{5}\)D.\(\frac{1}{2}\)二、多项选择题(每题2分,共10题)1.下列函数中,是偶函数的有\((\)\)A.\(y=x^2\)B.\(y=\cosx\)C.\(y=\sinx\)D.\(y=|x|\)2.下列命题中,正确的有\((\)\)A.若\(a>b\),\(c>d\),则\(a-c>b-d\)B.若\(a>b\),\(c>d\),则\(ac>bd\)C.若\(a>b\),则\(a^2>b^2\)D.若\(a>b\),\(c>0\),则\(ac>bc\)3.已知向量\(\overrightarrow{a}=(1,1)\),\(\overrightarrow{b}=(-1,1)\),则下列向量与\(2\overrightarrow{a}-\overrightarrow{b}\)平行的有\((\)\)A.\((1,0)\)B.\((0,1)\)C.\((-1,1)\)D.\((1,-1)\)4.下列函数中,在\((0,+\infty)\)上单调递增的有\((\)\)A.\(y=x^3\)B.\(y=\lnx\)C.\(y=2^x\)D.\(y=\cosx\)5.已知\(\triangleABC\)中,角\(A,B,C\)所对的边分别为\(a,b,c\),则下列结论正确的有\((\)\)A.\(a^2=b^2+c^2-2bc\cosA\)B.\(b^2=a^2+c^2-2ac\cosB\)C.\(c^2=a^2+b^2-2ab\cosC\)D.\(\cosA=\frac{b^2+c^2-a^2}{2bc}\)6.已知圆\(C:x^2+y^2-2x-4y+1=0\),则下列说法正确的有\((\)\)A.圆心坐标为\((1,2)\)B.圆心坐标为\((-1,-2)\)C.半径为\(2\)D.半径为\(4\)7.已知直线\(l:y=kx+b\),则下列说法正确的有\((\)\)A.当\(k>0\)时,直线\(l\)单调递增B.当\(k<0\)时,直线\(l\)单调递减C.直线\(l\)恒过定点\((0,b)\)D.直线\(l\)与\(x\)轴交点坐标为\((-\frac{b}{k},0)\)8.已知数列\(\{a_n\}\)的前\(n\)项和\(S_n=n^2\),则下列说法正确的有\((\)\)A.\(a_1=1\)B.\(a_n=2n-1\)C.\(a_n=n^2\)D.数列\(\{a_n\}\)是等差数列9.已知函数\(y=\sinx\),则下列说法正确的有\((\)\)A.函数\(y=\sinx\)的最大值为\(1\)B.函数\(y=\sinx\)的最小值为\(-1\)C.函数\(y=\sinx\)的周期为\(2\pi\)D.函数\(y=\sinx\)是奇函数10.从装有\(2\)个红球和\(2\)个黑球的口袋内任取\(2\)个球,则下列事件中是互斥事件的有\((\)\)A.至少有一个黑球与都是黑球B.至少有一个黑球与至少有一个红球C.恰有一个黑球与恰有两个黑球D.至少有一个黑球与都是红球三、判断题(每题2分,共10题)1.空集是任何集合的子集。()2.若\(a>b\),则\(\frac{1}{a}<\frac{1}{b}\)。（)3.函数\(y=\sqrt{x^2}\)与\(y=x\)是同一个函数。()4.向量的模一定是非负实数。()5.若\(\sin\alpha=0\),则\(\alpha=0\)。（)6.圆的标准方程可以确定圆的圆心和半径。()7.直线的斜率不存在时,直线垂直于\(x\)轴。（)8.等差数列的通项公式是唯一的。()9.函数\(y=\cosx\)是奇函数。()10.互斥事件一定是对立事件。(）四、简答题(每题5分,共4题)1.已知\(f(x)=x^2-2x+3\),求\(f(0)\),\(f(1)\),\(f(2)\)的值。答案：\(f(0)=3\),\(f(1)=2\),\(f(2)=3\)。2.求过点\((1,2)\)且斜率为\(3\)的直线方程。答案:由点斜式得\(y-2=3(x-1)\),即\(3x-y-1=0\)。3.在\(\triangleABC\)中,\(A=60^{\circ}\),\(a=\sqrt{3}\),\(b=1\),求角\(B\)。答案:由正弦定理\(\frac{a}{\sinA}=\frac{b}{\sinB}\),得\(\sinB=\frac{1}{2}\),又\(b<a\),所以\(B=30^{\circ}\)。4.已知等比数列\(\{a_n\}\)中,\(a_1=2\),\(a_4=16\),求公比\(q\)和通项公式\(a_n\)。答案：\(q^3=\frac{a_4}{a_1}=8\),得\(q=2\),\(a_n=2\times2^{n-1}=2^n\)。五、讨论题(每题5分,共4题)1.讨论函数\(y=x^2-4x+3\)的单调性。答案:对称轴为\(x=2\),在\((-\infty,2)\)上单调递减,在\((2,+\infty)\)上单调递增。2.讨论直线\(y=kx+1\)与圆\(x^2+y^2=4\)的位置关系。答案:圆心到直线距离\(d=\frac{1}{\sqrt{k^2+1}}\)。当\(d<2\)即\(k>\frac{\sqrt{3}}{3}\)或\(k<-\frac{\sqrt{3}}{3}\)时相交;\(d=2\)即\(k=\pm\frac{\sqrt{3}}{3}\)时相切;\(d>2\)即\(-\frac{\sqrt{3}}{3}<k<\frac{\sqrt{3}}{3}\)时相离。3.讨论在等差数列\(\{a_n\}\)中,若\(a_n=2n-1\),求其前\(n\)项和\(S_n\)的表达式。答案：\(S_n=\fr