2024年成考高起点《数学(文史)》每日一练试题03月12日

聚题库

03/12

单选题1、已知<img src="https://img2.meite.com/questions/202303/296423e580b835d.png" />成等差数列，且<img src="https://img2.meite.com/questions/202303/296423e58b478b7.png" />为方程<img src="https://img2.meite.com/questions/202303/296423e5978a20a.png" />的两个根，则<img src="https://img2.meite.com/questions/202303/296423e5a3a2171.png" />的值为（） <ul><li>A：<img src='https://img2.meite.com/questions/202303/296423e5afbd31c.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/296423e5b427e6e.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/296423e5b93c781.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/296423e5bd84cbf.png' /></li></ul>答案：D解析：由根与系数的关系得<img src="https://img2.meite.com/questions/202303/296423e65c0bb98.png" />由等差数列的性质得<img src="https://img2.meite.com/questions/202303/296423e66c81d64.png" />2、点P(-5,12)到y轴的距离（） <ul><li>A：12</li><li>B：7</li><li>C：-5</li><li>D：5</li></ul>答案：D解析：由点P的坐标（-5,12）知，点P到y轴的距离为|x|=53、已知<img src="https://img2.meite.com/questions/202303/14641027b0e9511.png" />，则sin2α=（）<ul><li>A：<img src='https://img2.meite.com/questions/202303/14641027d7193ea.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/14641027dcded6f.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/14641027e2be0ff.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/14641027e75615d.png' /></li></ul>答案：D解析：<img src="https://img2.meite.com/questions/202303/1464102b8ba4635.png" />两边平方得<img src="https://img2.meite.com/questions/202303/1464102bb0eb6cc.png" /><img src="https://img2.meite.com/questions/202303/1464102bb4c5429.png" />，故<img src="https://img2.meite.com/questions/202303/1464102bc8067d1.png" />4、已知点M(-2,5),N(4,2),点P在<img src="https://img2.meite.com/questions/202303/296423a916ad36e.png" />上，且<img src="https://img2.meite.com/questions/202303/296423a924de9aa.png" />=1:2，则点P的坐标为（）<ul><li>A：<img src='https://img2.meite.com/questions/202303/296423a9375cb17.png' /></li><li>B：(0,4)</li><li>C：(8,2)</li><li>D：(2,1)</li></ul>答案：B解析：由题意得： <img src="https://img2.meite.com/questions/202303/296423a997be381.png" /> 主观题1、在△ABC中，AB=2，BC=3,B=60°，求AC及△ABC的面积答案：<img src="https://img2.meite.com/questions/202303/296423a37bd555e.png" />2、设函数<img src="https://img2.meite.com/questions/202303/1564111c65679ad.png" /> (I）求f'(2)； (II）求f(x）在区间[一1,2]的最大值与最小值．答案：(I）因为<img src="https://img2.meite.com/questions/202303/1564111dd4eb139.png" />，所以f'(2)=3×22-4=8.(II）因为x＜-1，f(-1)=3.<img src="https://img2.meite.com/questions/202303/1564111ea39de57.png" />f(2)=0. 所以f(x）在区间[一1,2]的最大值为3，最小值为<img src="https://img2.meite.com/questions/202303/1564111eb99e49a.png" />3、在△ABC中，B=120°,C=30°,BC=4，求△ABC的面积．答案：因为A= 180°-B-C=30°，所以AB = BC=4.因此△ABC的面积<img src="https://img2.meite.com/questions/202303/1564111c8c97743.png" />4、已知直线l的斜率为1，l过抛物线C：<img src="https://img2.meite.com/questions/202303/1564111c54b8a1f.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/202303/1564111ce1ece45.png" />，准线为<img src="https://img2.meite.com/questions/202303/1564111cf077c15.png" />由题意得l的方程为<img src="https://img2.meite.com/questions/202303/1564111d17b9087.png" />因此l与C的准线的交点坐标为<img src="https://img2.meite.com/questions/202303/1564111d41e334d.png" />(II）由<img src="https://img2.meite.com/questions/202303/1564111d60deac4.png" />得<img src="https://img2.meite.com/questions/202303/1564111d70ccff6.png" />设A（x1,y1）.B（x2,y2），则<img src="https://img2.meite.com/questions/202303/1564111da85efe1.png" />因此<img src="https://img2.meite.com/questions/202303/1564111db86701f.png" />填空题1、点（4,5)关于直线y=x的对称点的坐标为（）答案：(5,4)解析：点(4,5)关于直线y=x的对称点为（5,4).2、设<img src="https://img2.meite.com/questions/202303/2964239c3b4ac2f.png" />则<img src="https://img2.meite.com/questions/202303/2964239c42d80d7.png" />答案：-1解析：<img src="https://img2.meite.com/questions/202303/2964239ca8a1cc9.png" /> <img src="https://img2.meite.com/questions/202303/2964239cb367f80.png" /> <img src="https://img2.meite.com/questions/202303/2964239cc4f078f.png" />