2025年成考高起点《数学(理)》每日一练试题02月05日

聚题库

02/05

单选题1、在△ABC中，若b=<img src="https://img2.meite.com/questions/202303/2864228792c7c59.png" />，c=<img src="https://img2.meite.com/questions/202303/286422879bef613.png" /><img src="https://img2.meite.com/questions/202303/28642287a3c143e.png" />则a等于（）<ul><li>A：2</li><li>B：<img src='https://img2.meite.com/questions/202303/28642287b3e4835.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/28642287b8ca84c.png' /></li><li>D：无解</li></ul>答案：B解析：此题是已知两边和其中一边的对角,解三角形时,会出现一解、两解、无解的情况,要注意这一点.用余弦定理<img src="https://img2.meite.com/questions/202303/286422888d98016.png" />可得<img src="https://img2.meite.com/questions/202303/28642288b870fd3.png" /><img src="https://img2.meite.com/questions/202303/28642288bcdcd26.png" /><img src="https://img2.meite.com/questions/202303/28642288cb0279a.png" /><img src="https://img2.meite.com/questions/202303/28642288d358a96.png" /><img src="https://img2.meite.com/questions/202303/28642288e0d440f.png" />解出<img src="https://img2.meite.com/questions/202303/28642288f8ec133.png" /><img src="https://img2.meite.com/questions/202303/286422890103ec2.png" /><img src="https://img2.meite.com/questions/202303/286422890874181.png" /><img src="https://img2.meite.com/questions/202303/2864228911473af.png" />2、已知全集U=R，A={x|x≥1}，B={x|-1<x≤2},则<img src="https://img2.meite.com/questions/202303/2864229bae18781.png" /><ul><li>A：{x|x≤2}</li><li>B：{x|x<2}</li><li>C：{x|-1<x≤2}</li><li>D：{x|-1<x<1}</li></ul>答案：A解析：补集运算应明确知道是否包括端点.A在U中的补集是x<1， <img src="https://img2.meite.com/questions/202303/2864229c436e804.png" /> <img src="https://img2.meite.com/questions/202303/2864229c50ac610.png" /><img src="https://img2.meite.com/questions/202303/2864229c574ae01.png" /><img src="https://img2.meite.com/questions/202303/2864229c5e8c7e7.png" /> 3、14@@如图<img src="https://img2.meite.com/questions/202408/1666bef011bd0ff.png" />，中直线l1、l2、l3的斜率分别为k1、k2、k3，则（）。<ul><li>A：k1<k2<k3</li><li>B：k1<k3<k2</li><li>C：k3<k1<k2</li><li>D：k3<k2<k1</li></ul>答案：B解析：根据直线的位置、倾斜角，可得出斜率的大小关系，故选B。 4、从椭圆与x轴额右交点看短轴两端点的视角为60°的椭圆的离心率（） <ul><li>A：<img src='https://img2.meite.com/questions/202303/28642287ed710eb.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/28642287f182bba.png' /></li><li>C：1</li><li>D：<img src='https://img2.meite.com/questions/202303/28642287f85287f.png' /></li></ul>答案：A解析：求椭圆的离心率,先求出a,c.(如图) <img src="https://img2.meite.com/questions/202303/286422892bd4fb5.png" /><img src="https://img2.meite.com/questions/202303/286422893b50a35.png" />，由椭圆定义知<img src="https://img2.meite.com/questions/202303/2864228950523ff.png" /> <img src="https://img2.meite.com/questions/202303/286422895c76294.png" />主观题1、已知直线l的斜率为1，l过抛物线C：<img src="https://img2.meite.com/questions/202303/156411660ae04fb.png" />的焦点，且与C交于A,B两点.(I）求l与C的准线的交点坐标； (II）求|AB|.答案：(I）C的焦点为<img src="https://img2.meite.com/questions/202303/1564116c40cf40a.png" />，准线为<img src="https://img2.meite.com/questions/202303/1564116c45024f5.png" />由题意得l的方程为<img src="https://img2.meite.com/questions/202303/1564116c5cf0409.png" />因此l与C的准线的交点坐标为<img src="https://img2.meite.com/questions/202303/1564116c7901a26.png" />(II）由<img src="https://img2.meite.com/questions/202303/1564116c9294ce9.png" />，得<img src="https://img2.meite.com/questions/202303/1564116c9d411f3.png" />设A（x1,y1），B（x2,y2），则<img src="https://img2.meite.com/questions/202303/1564116cd0bfaf7.png" />因此<img src="https://img2.meite.com/questions/202303/1564116ce1375a9.png" />2、已知数列<img src="https://img2.meite.com/questions/202303/286422511c19556.png" />的前n项和<img src="https://img2.meite.com/questions/202303/2864225128dc6e0.png" /> 求证：<img src="https://img2.meite.com/questions/202303/286422513318bbb.png" />是等差数列，并求公差和首项。 答案：<img src="https://img2.meite.com/questions/202303/286422514f41b7b.png" /> <img src="https://img2.meite.com/questions/202303/28642251563e39b.png" /> 3、cos20°cos40°cos80°的值。答案：<img src="https://img2.meite.com/questions/202408/1666bef0eb172e9.png" />4、已知一组数据9.9；10.3；9.8；10.1；10.4；10；9.8；9.7，计算这组数据的方差。 答案：<img src="https://img2.meite.com/questions/202408/1566bda99290da3.png" />填空题1、已知sin2θ+1=cos2θ，则<img src="https://img2.meite.com/questions/202408/1966c2ba37bb500.png" />的值等于______。 答案：<img src="https://img2.meite.com/questions/202408/1966c2ba3b015d6.png" />解析：由已知，cos2θ-sin2θ=1，即cos2θ-（1-cos2θ）=1，cos2θ=1，所以cosθ=±1。而当cosθ=±1时，sinθ=0。 <img src="https://img2.meite.com/questions/202408/1966c2ba407a648.png" /> 2、若平面向量a=(x,1),b=(1,-2),且a//b,则x=（） 答案：<img src="https://img2.meite.com/questions/202303/286422508f0554f.png" />解析：由于a//b，故<img src="https://img2.meite.com/questions/202303/286422509cd5c14.png" />