2024年成考高起点《数学(文史)》每日一练试题02月25日

聚题库

02/25

单选题1、若函数f(x)=1+<img src="https://img2.meite.com/questions/202303/296423a8d0db03d.png" />在(0,+∞)上是减函数，则（）<ul><li>A：a>1</li><li>B：a>2</li><li>C：1<a<2</li><li>D：0<a<1</li></ul>答案：D解析：由已知条件函数f(x)=1+<img src="https://img2.meite.com/questions/202303/296423a8d0db03d.png" />在(0,+∞)上是减函数，及对数函数<img src="https://img2.meite.com/questions/202303/296423a9706abcb.png" />的性质可得底数0<a<12、下列函数为奇函数的是 ( )。<ul><li>A：<img border="0" style="width: 58px; height: 28px;" src="https://img2.meite.com/zzpuce/2023-04/643679c4979df72105.jpeg"></li><li>B：<img border="0" style="width: 87px; height: 28px;" src="https://img2.meite.com/zzpuce/2023-04/643679c4a2e3413730.jpeg"></li><li>C：<img border="0" style="width: 60px; height: 31px;" src="https://img2.meite.com/zzpuce/2023-04/643679c4a9e5831050.jpeg"></li><li>D：<img border="0" style="width: 60px; height: 25px;" src="https://img2.meite.com/zzpuce/2023-04/643679c4b014127406.jpeg"></li></ul>答案：D解析：本题主要考查的知识点为函数的奇偶性．【应试指导】f(z)=sinx=-sin(-x)=-f(-x)，所以y=sinx为奇函数． 3、命题甲:x>y且xy>0,命题乙：<img src="https://img2.meite.com/questions/202303/296423aa88de569.png" />则（） <ul><li>A：甲是乙的充分条件,但不是必要条件</li><li>B：甲是乙的必要条件，但不是充分条件</li><li>C：甲是乙的充分必要条件</li><li>D：甲不是乙的必要条件也不是乙的充分条件</li></ul>答案：A解析：<img src="https://img2.meite.com/questions/202303/296423aabe64820.png" /><img src="https://img2.meite.com/questions/202303/296423aac4c7280.png" /><img src="https://img2.meite.com/questions/202303/296423aacbc46fc.png" /><img src="https://img2.meite.com/questions/202303/296423aacfe951a.png" />4、设M=<img src="https://img2.meite.com/questions/202303/286422a42729326.png" />那么（）<ul><li>A：<img src='https://img2.meite.com/questions/202303/286422a43031e0b.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/286422a433cfa72.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/286422a4397f784.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/286422a43e0967d.png' /></li></ul>答案：D解析：<img src="https://img2.meite.com/questions/202303/286422a4b8b4342.png" /> M是集合，a为元素，{a}为集合，元素与集合的关系是<img src="https://img2.meite.com/questions/202303/286422a4d2b7178.png" />集合与集合的关系是<img src="https://img2.meite.com/questions/202303/286422a4dc161c3.png" /><img src="https://img2.meite.com/questions/202303/286422a4e20a711.png" /><img src="https://img2.meite.com/questions/202303/286422a4e6eebab.png" /> 主观题1、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" /> 2、已知三角形的一个内角是<img src="https://img2.meite.com/questions/202303/296423b4bf816f0.png" />，面积是<img src="https://img2.meite.com/questions/202303/296423b4cd02d83.png" />周长是20,求各边的长. 答案：设三角形三边分别为a,b,c,∠A=60°， <img src="https://img2.meite.com/questions/202303/296423b55f6ab61.png" /> 3、已知等差数列<img src="https://img2.meite.com/questions/202303/296423eaf9717d6.png" />前n项和<img src="https://img2.meite.com/questions/202303/296423eb032d219.png" /> （Ⅰ）求通项<img src="https://img2.meite.com/questions/202303/296423eb1a4ebf5.png" />的表达式（Ⅱ）求<img src="https://img2.meite.com/questions/202303/296423eb26c2214.png" />的值 答案：（Ⅰ）当n=1时，由<img src="https://img2.meite.com/questions/202303/296423eb432a645.png" />得<img src="https://img2.meite.com/questions/202303/296423eb5068b03.png" /> <img src="https://img2.meite.com/questions/202303/296423eb59a45cd.png" /> <img src="https://img2.meite.com/questions/202303/296423eb6100c03.png" /> 也满足上式，故<img src="https://img2.meite.com/questions/202303/296423eb755b7df.png" />=1-4n（n≥1）（Ⅱ）由于数列<img src="https://img2.meite.com/questions/202303/296423eb93e2df0.png" />是首项为<img src="https://img2.meite.com/questions/202303/296423eba5a3367.png" />公差为d=-4的等差数列，所以<img src="https://img2.meite.com/questions/202303/296423ebc29c045.png" />是首项为<img src="https://img2.meite.com/questions/202303/296423ebe5ba947.png" />公差为d=-8，项数为13的等差数列，于是由等差数列前n项和公式得： <img src="https://img2.meite.com/questions/202303/296423ec1ac9811.png" /><img src="https://img2.meite.com/questions/202303/296423ec20a013e.png" /> 4、在△ABC中,已知三边 a、b、c 成等差数列,且最大角∠A是最小角的2倍, a: b :c. 答案：<img src="https://img2.meite.com/questions/202303/296423b0ae0659d.png" />填空题1、不等式<img src="https://img2.meite.com/questions/202303/286422a55aeabe3.png" />的解集是（） 答案：<img src="https://img2.meite.com/questions/202303/286422a56c78cca.png" />解析：<img src="https://img2.meite.com/questions/202303/286422a578989db.png" />或<img src="https://img2.meite.com/questions/202303/286422a57faa8bc.png" />或<img src="https://img2.meite.com/questions/202303/286422a58777039.png" />2、<img src="https://img2.meite.com/questions/202303/1464102a1d5eac7.png" />（）答案：3解析：<img src="https://img2.meite.com/questions/202303/14641031bbc80a1.png" />