2024年成考高起点《数学(文史)》每日一练试题02月06日

聚题库

02/06

单选题1、设集合M={x||x-2||＜2}，N={0,1,2,3,4}，则M∩N=（）<ul><li>A：{2}</li><li>B：{0,1,2}</li><li>C：{1,2,3}</li><li>D：{0,1,2,3,4}</li></ul>答案：C解析：解得M={x||x-2||＜2}={x|-2＜x-2＜2}={x|0＜x＜4}，故M∩N={1,2,3}.2、已知向量a=(3,4),b=(0,-2),则cos=() <ul><li>A：<img src='https://img2.meite.com/questions/202303/296423b170c2f95.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/296423b17508b91.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/296423b17967146.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/296423b17e2de84.png' /></li></ul>答案：B解析：因为a=(3,4),b=(0,-2), <img src="https://img2.meite.com/questions/202303/296423b1f8241e7.png" /> 3、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、函数<img src="https://img2.meite.com/questions/202303/14641028ec3037a.png" />的图像与直线y=4的交点坐标为（）<ul><li>A：(0,4)</li><li>B：(4,64)</li><li>C：(1,4)</li><li>D：(4,16)</li></ul>答案：C解析：令y=4x=4，解得x=1，故所求交点为（1,4).主观题1、如图：已知在△ADC中，∠C=90°，∠D=30°，∠ABC=45°，BD=20，求AC(用小数表示，保留一位小数) <img src="https://img2.meite.com/questions/202303/296423e7b58f8d3.png" /> 答案：如图 <img src="https://img2.meite.com/questions/202303/296423e7cbcb7ab.png" /> <img src="https://img2.meite.com/questions/202303/296423e7dd72c9c.png" /> 2、设函数f(x)<img src="https://img2.meite.com/questions/202303/296423a66bbdb95.png" />且f'(-1)=-36 (Ⅰ)求m (Ⅱ)求f(x)的单调区间答案：(Ⅰ)由已知得f'=<img src="https://img2.meite.com/questions/202303/296423a74f41b7f.png" /> 又由f'(-1)=-36得 6-6m-36=-36 故m=1. (Ⅱ)由(Ⅰ)得f'(x)=<img src="https://img2.meite.com/questions/202303/296423a792d1aff.png" /> 令f'(x)=0，解得<img src="https://img2.meite.com/questions/202303/296423a7b14cf3f.png" /> 当x<-3时，f'(x)>0; 当-3<x<2时，f'(x)<0; 当x>2时，f'(x)>0; 故f(x)的单调递减区间为(-3,2)，f(x)的单调递增区间为(-∞,-3),(2,+∞) 3、每亩地种果树20棵时,每棵果树收入90元,如果每亩增种一棵,每棵果树收入就下降3元,求使总收入最大的种植棵数. 答案：设每亩增种x棵,总收入味y元，则每亩种树(20+x)棵，由题意知增种x棵后每棵收入为（60-3x）则有y=(90-3x)(20+x) 整理得y=<img src="https://img2.meite.com/questions/202303/286422a66eea349.png" />+30x+1800 配方得y=<img src="https://img2.meite.com/questions/202303/286422a688a5af1.png" />+1875 当x=5时，y有最大值，所以每亩地最多种25棵4、设椭圆的中心是坐标原点,长轴在x轴上,离心率<img src="https://img2.meite.com/questions/202303/2964239c71aeb01.png" />已知点P<img src="https://img2.meite.com/questions/202303/2964239c7e7d039.png" />到圆上的点的最远距离是<img src="https://img2.meite.com/questions/202303/2964239c8cba609.png" />求椭圆的方程 答案：由题意，设椭圆方程为<img src="https://img2.meite.com/questions/202303/2964239cdfdcc2f.png" /> 由<img src="https://img2.meite.com/questions/202303/2964239cef23e00.png" /><img src="https://img2.meite.com/questions/202303/2964239cf5cc660.png" /> 设P<img src="https://img2.meite.com/questions/202303/2964239d01ba1aa.png" />点到椭圆上任一点的距离为 d, <img src="https://img2.meite.com/questions/202303/2964239d0dd8af6.png" /> <img src="https://img2.meite.com/questions/202303/2964239d1e44fb3.png" />则在y=-b时，<img src="https://img2.meite.com/questions/202303/2964239d2c1a969.png" />最大，即d也最大。 <img src="https://img2.meite.com/questions/202303/2964239d43183b3.png" /><img src="https://img2.meite.com/questions/202303/2964239d48e58c6.png" /> <img src="https://img2.meite.com/questions/202303/2964239d5187168.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、从某班的一次数学测试卷中任意抽出10份,其得分情况如下:81,98,43,75,60,55,78,84,90,70,则这次测验成绩的样本方差是（） 答案：252.84解析：<img src="https://img2.meite.com/questions/202303/296423a0854ced5.png" /> <img src="https://img2.meite.com/questions/202303/296423a08a3c5bd.png" /> <img src="https://img2.meite.com/questions/202303/296423a0a201208.png" /><img src="https://img2.meite.com/questions/202303/296423a0b18ce79.png" /><img src="https://img2.meite.com/questions/202303/296423a0c014f0f.png" /><img src="https://img2.meite.com/questions/202303/296423a0ca81d80.png" /><img src="https://img2.meite.com/questions/202303/296423a0d0c2d44.png" />=252.84