2024年成考高起点《数学(文史)》每日一练试题03月26日

聚题库

03/26

单选题1、函数f(x)=<img src="https://img2.meite.com/questions/202303/296423e87e65604.png" />当x∈[-2,+∞)时是增函数，当x∈(-∞,-2]时是减函数，则f(1)=() <ul><li>A：-3</li><li>B：13</li><li>C：7</li><li>D：由m而定的常数</li></ul>答案：B解析：由题意知抛物线的对称轴为x=-2， <img src="https://img2.meite.com/questions/202303/296423e91d09887.png" /> 2、设<img src="https://img2.meite.com/questions/202303/296423e8404792c.png" />成等比数列,则x等于 <ul><li>A：0或-2</li><li>B：1或-1</li><li>C：0或-2</li><li>D：-2</li></ul>答案：C解析：由已知条件的得<img src="https://img2.meite.com/questions/202303/296423e8f3e39ea.png" /><img src="https://img2.meite.com/questions/202303/296423e8f926be1.png" />3、任选一个两位数,它恰好是10的倍数的概率是（）<ul><li>A：<img src='https://img2.meite.com/questions/202303/2964239a9b1203b.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/2964239a9f21f1c.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/2964239aa80509d.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/2964239aa374c5f.png' /></li></ul>答案：C解析：由已知条件可知此题属于等可能事件.两位数(正整数)从10~99共有90个,则n=90,是10的倍数的两位数共有9个，则m=9，<img src="https://img2.meite.com/questions/202303/2964239b50cf34a.png" />故任选一个两位数(正整数),它恰好是10的倍数的概率是<img src="https://img2.meite.com/questions/202303/2964239b6932ff5.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，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" />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、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、已知向量a=(3,2),b=(-4,x),且a⊥b，则x=（） 答案：6解析：∵a⊥b， ∴3×(-4)+2x=0 ∴x=6. 2、函数f(x)=<img src="https://img2.meite.com/questions/202303/296423b497a799f.png" />在区间[-3,3]上的最大值为（） 答案：4解析：这题考的是高次函数的最值问题，可用导数来求函数在区间[-3,3]上的最值。<img src="https://img2.meite.com/questions/202303/296423b5082e922.png" /> 列出表格<img src="https://img2.meite.com/questions/202303/296423b517619c0.png" /> 由上表可知函数在[-3,3]上，在x=1点处有最大值为4.