2024年成考高起点《数学(文史)》每日一练试题01月24日

聚题库

01/24

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、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" />3、已知函数f(x)的定义域为R，且满足f(2x)=<img src="https://img2.meite.com/questions/202303/296423a4f003da6.png" />,则f(x)的反函数为（）<ul><li>A：<img src='https://img2.meite.com/questions/202303/296423a506c2ca4.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/296423a50aa8fc5.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/296423a51284df7.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/296423a516a6101.png' /></li></ul>答案：B解析：令2x=t，则x=<img src="https://img2.meite.com/questions/202303/296423a5d090a18.png" /> <img src="https://img2.meite.com/questions/202303/296423a5d7d5daa.png" /> 4、若函数y=f(x)在[-1,1]上是单调函数,则使得y=f(sinx)必为单调函数的区间是() <ul><li>A：R</li><li>B：[-1,1]</li><li>C：<img src='https://img2.meite.com/questions/202303/296423ae7c91c8e.png' /></li><li>D：[-sin1 ,sin1]</li></ul>答案：C解析：y=f(x)在[-1,1]上是单调函数,所以y=f(x)的单调区间为[-1,1] <img src="https://img2.meite.com/questions/202303/296423af59555b2.png" /> 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、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" />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、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棵填空题1、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 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" />