人教版高中高二上册数学期末试卷后附答案

人教版高中高二上册数学期末试卷后附答案

一、填空题1.若直线经过\((1,2)\)和\((3,4)\)两点，则直线的斜率为______。2.已知椭圆\(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)，其长半轴长为______。3.双曲线\(\frac{x^{2}}{9}-\frac{y^{2}}{16}=1\)的渐近线方程为______。4.抛物线\(y^{2}=8x\)的焦点坐标是______。5.已知向量\(\vec{a}=(1,2)\)，\(\vec{b}=(3,-1)\)，则\(\vec{a}\cdot\vec{b}=\)______。6.若直线\(l\)的倾斜角为\(60^{\circ}\)，且过点\((0,-2)\)，则直线\(l\)的方程为______。7.已知点\(A(1,2)\)，\(B(3,4)\)，则线段\(AB\)的中点坐标为______。8.圆\((x-2)^{2}+(y+3)^{2}=16\)的圆心坐标是______。9.已知等差数列\(\{a_{n}\}\)中，\(a_{3}=5\)，\(a_{5}=9\)，则公差\(d=\)______。10.等比数列\(\{a_{n}\}\)中，\(a_{1}=2\)，\(a_{2}=4\)，则\(a_{3}=\)______。二、单项选择题1.直线\(x+y-3=0\)的倾斜角是（）A.\(30^{\circ}\)B.\(45^{\circ}\)C.\(135^{\circ}\)D.\(150^{\circ}\)2.椭圆\(\frac{x^{2}}{m}+\frac{y^{2}}{4}=1\)的焦距为\(2\)，则\(m\)的值为（）A.\(5\)B.\(3\)C.\(5\)或\(3\)D.\(8\)3.双曲线\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a\gt0,b\gt0)\)的离心率\(e=2\)，则其渐近线方程为（）A.\(y=\pm\sqrt{3}x\)B.\(y=\pm\frac{\sqrt{3}}{3}x\)C.\(y=\pm2x\)D.\(y=\pm\frac{1}{2}x\)4.抛物线\(y^{2}=-4x\)的准线方程是（）A.\(x=-1\)B.\(x=1\)C.\(y=-1\)D.\(y=1\)5.已知向量\(\vec{a}=(2,1)\)，\(\vec{b}=(x,-2)\)，若\(\vec{a}\parallel\vec{b}\)，则\(x\)的值为（）A.\(4\)B.\(-4\)C.\(1\)D.\(-1\)6.过点\((1,-1)\)且与直线\(x-2y+1=0\)垂直的直线方程为（）A.\(2x+y-1=0\)B.\(2x+y+1=0\)C.\(x-2y-3=0\)D.\(x-2y+3=0\)7.圆\(x^{2}+y^{2}-4x+6y=0\)的半径为（）A.\(\sqrt{13}\)B.\(13\)C.\(\sqrt{10}\)D.\(10\)8.在等差数列\(\{a_{n}\}\)中，\(a_{1}+a_{3}+a_{5}=105\)，\(a_{2}+a_{4}+a_{6}=99\)，则\(a_{20}\)等于（）A.\(-1\)B.\(1\)C.\(3\)D.\(7\)9.在等比数列\(\{a_{n}\}\)中，\(a_{3}=2\)，\(a_{7}=8\)，则\(a_{5}\)等于（）A.\(4\)B.\(-4\)C.\(\pm4\)D.\(5\)10.已知点\(P(x,y)\)在圆\((x-2)^{2}+(y+3)^{2}=1\)上，则\(x+y\)的最大值为（）A.\(\sqrt{2}-1\)B.\(\sqrt{2}+1\)C.\(-\sqrt{2}-1\)D.\(-\sqrt{2}+1\)三、多项选择题1.下列关于直线和圆的说法正确的是（）A.直线\(y=kx+1\)与圆\(x^{2}+y^{2}=1\)恒有公共点B.直线\(x-y+1=0\)与圆\((x-1)^{2}+(y+1)^{2}=4\)相交C.圆\(x^{2}+y^{2}-2x-4y=0\)的圆心坐标为\((1,2)\)D.圆\(x^{2}+y^{2}=4\)的半径为\(2\)2.对于椭圆\(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\)，下列说法正确的是（）A.焦点在\(x\)轴上B.长轴长为\(8\)C.离心率为\(\frac{\sqrt{7}}{4}\)D.焦点坐标为\((\pm\sqrt{7},0)\)3.关于双曲线\(\frac{y^{2}}{4}-\frac{x^{2}}{3}=1\)，下列说法正确的是（）A.焦点在\(y\)轴上B.渐近线方程为\(y=\pm\frac{2\sqrt{3}}{3}x\)C.离心率为\(\frac{\sqrt{7}}{2}\)D.实轴长为\(4\)4.抛物线\(y^{2}=2px(p\gt0)\)的性质有（）A.开口向右B.焦点坐标为\((\frac{p}{2},0)\)C.准线方程为\(x=-\frac{p}{2}\)D.对称轴为\(x\)轴5.已知向量\(\vec{a}=(1,2)\)，\(\vec{b}=(-2,3)\)，则（）A.\(\vec{a}+\vec{b}=(-1,5)\)B.\(\vec{a}-\vec{b}=(3,-1)\)C.\(\vec{a}\cdot\vec{b}=4\)D.\(\vert\vec{a}\vert=\sqrt{5}\)6.等差数列\(\{a_{n}\}\)中，\(a_{1}=1\)，\(d=2\)，则（）A.\(a_{n}=2n-1\)B.\(a_{20}=39\)C.前\(20\)项和\(S_{20}=400\)D.\(a_{n}=2n+1\)7.等比数列\(\{a_{n}\}\)中，\(a_{1}=1\)，\(q=2\)，则（）A.\(a_{n}=2^{n-1}\)B.\(a_{5}=16\)C.前\(5\)项和\(S_{5}=31\)D.\(a_{n}=2^{n}\)8.已知直线\(l_{1}:y=k_{1}x+b_{1}\)，\(l_{2}:y=k_{2}x+b_{2}\)，则\(l_{1}\parallell_{2}\)的条件是（）A.\(k_{1}=k_{2}\)B.\(b_{1}\neqb_{2}\)C.\(k_{1}=k_{2}\)且\(b_{1}\neqb_{2}\)D.\(k_{1}\neqk_{2}\)9.圆\((x-a)^{2}+(y-b)^{2}=r^{2}\)与直线\(Ax+By+C=0\)相切的条件是（）A.\(\frac{\vertAa+Bb+C\vert}{\sqrt{A^{2}+B^{2}}}=r\)B.圆心到直线的距离等于半径C.直线与圆有且只有一个公共点D.\(A^{2}+B^{2}=r^{2}\)10.已知点\(A(x_{1},y_{1})\)，\(B(x_{2},y_{2})\)，则线段\(AB\)的中点坐标为（）A.\((\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\)B.\((\frac{x_{1}-x_{2}}{2},\frac{y_{1}-y_{2}}{2})\)C.\((\frac{x_{1}+x_{2}}{2},y_{1}+y_{2})\)D.若\(M\)为\(AB\)中点，则\(\overrightarrow{AM}=\overrightarrow{MB}\)四、判断题1.直线\(y=2x+1\)的斜率为\(2\)。（）2.椭圆\(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\)的焦点在\(x\)轴上。（）3.双曲线\(\frac{x^{2}}{4}-\frac{y^{2}}{9}=1\)的渐近线方程为\(y=\pm\frac{3}{2}x\)。（）4.抛物线\(y^{2}=-4x\)的焦点在\(x\)轴负半轴上。（）5.若向量\(\vec{a}=(1,2)\)，\(\vec{b}=(2,4)\)，则\(\vec{a}\)与\(\vec{b}\)共线。（）6.直线\(x+y-1=0\)与圆\(x^{2}+y^{2}=1\)相离。（）7.等差数列\(\{a_{n}\}\)中，若\(a_{1}=1\)，\(d=2\)，则\(a_{5}=9\)。（）8.等比数列\(\{a_{n}\}\)中，若\(a_{1}=1\)，\(q=2\)，则\(a_{3}=4\)。（）9.点\((1,2)\)在圆\((x-1)^{2}+(y-2)^{2}=1\)上。（）10.若直线\(l_{1}:y=k_{1}x+b_{1}\)，\(l_{2}:y=k_{2}x+b_{2}\)，且\(k_{1}=k_{2}\)，则\(l_{1}\parallell_{2}\)。（）五、简答题1.求过点\((2,-3)\)且斜率为\(2\)的直线方程。2.求椭圆\(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)的焦点坐标和离心率。3.已知向量\(\vec{a}=(1,-2)\)，\(\vec{b}=(3,4)\)，求\(\vec{a}\cdot\vec{b}\)及\(\vert\vec{a}+\vec{b}\vert\)。4.求等差数列\(\{a_{n}\}\)中，\(a_{1}=3\)，\(d=2\)，求\(a_{10}\)和前\(10\)项和\(S_{10}\)。六、讨论题1.讨论直线\(y=kx+1\)与圆\(x^{2}+y^{2}=1\)的位置关系。2.讨论椭圆\(\frac{x^{2}}{m}+\frac{y^{2}}{4}=1\)的焦点位置与\(m\)的取值关系。3.讨论等比数列\(\{a_{n}\}\)中，公比\(q\)对数列单调性的影响。4.讨论直线\(Ax+By+C=0\)与圆\((x-a)^{2}+(y-b)^{2}=r^{2}\)的位置关系。答案一、填空题1.\(1\)2.\(5\)3.\(y=\pm\frac{4}{3}x\)4.\((2,0)\)5.\(1\)6.\(y=\sqrt{3}x-2\)7.\((2,3)\)8.\((2,-3)\)9.\(2\)10.\(8\)二、单项选择题1.C2.C3.A4.B5.B6.A7.A8.B9.A10.B三、多项选择题1.ACD2.ABCD3.ABCD4.ABCD5.ABD6.ABC7.ABC8.C9.ABC10.AD四、判断题1.√2.×3.√4.√5.√6.×7.√8.√9.√10.×五、简答题1.由点斜式\(y-y_{0}=k(x-x_{0})\)（其中\((x_{0},y_{0})=(2,-3)\)，\(k=2\)）可得\(y+3=2(x-2)\)，即\(2x-y-7=0\)。2.对于椭圆\(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)，\(a=5\)，\(b=4\)，则\(c=\sqrt{a^{2}-b^{2}}=3\)，焦点坐标为\((\pm3,0)\)，离心率\(e=\frac{c}{a}=\frac{3}{5}\)。3.\(\vec{a}\cdot\vec{b}=1\times3+(-2)\times4=3-8=-5\)，\(\vec{a}+\vec{b}=(4,2)\)，\(\vert\vec{a}+\vec{b}\vert=\sqrt{4^{2}+2^{2}}=\sqrt{20}=2\sqrt{5}\)。4.\(a_{n}=a_{1}+(n-1)d\)，则\(a_{10}=3+(10-1)\times2=21\)，\(S_{n