2024年成考高起点《数学(文史)》每日一练试题03月10日

聚题库

03/10

单选题1、设α是三角形的一个内角，若<img src="https://img2.meite.com/questions/202303/1464102637baabc.png" />，则sinα=（）<ul><li>A：<img src='https://img2.meite.com/questions/202303/146410277c73796.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/14641027838231f.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/1464102788b3139.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/146410278d24d10.png' /></li></ul>答案：D解析：由题知0＜α＜兀，而<img src="https://img2.meite.com/questions/202303/1464102b0581dad.png" />，故<img src="https://img2.meite.com/questions/202303/1464102b0b41884.png" />，因此<img src="https://img2.meite.com/questions/202303/1464102b0fe7c88.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、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}.4、已知向量i,j为互相垂直的单位向量，向量a=2i+mj，若|a|=2，则m=（）<ul><li>A：-2</li><li>B：-1</li><li>C：0</li><li>D：1</li></ul>答案：C解析：由题可知a=(2,m),因此<img src="https://img2.meite.com/questions/202303/1464102be29a7c0.png" />，故m=0.主观题1、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" />2、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3、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" />4、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" /> 填空题1、<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" />2、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" />