2023年成考高起点《数学(理)》每日一练试题06月09日

聚题库
06/09
<p class="introTit">单选题</p><p>1、袋中有6个球,其中4个红球,2个白球,从中随机取出2个球,则其中恰有1个红球的概率为()</p><ul><li>A:<img src='https://img2.meite.com/questions/202303/15641165c5e79d0.png' /></li><li>B:<img src='https://img2.meite.com/questions/202303/15641165cb7ed67.png' /></li><li>C:<img src='https://img2.meite.com/questions/202303/15641165d0b1aa2.png' /></li><li>D:<img src='https://img2.meite.com/questions/202303/15641165d3de24c.png' /></li></ul><p>答 案:A</p><p>解 析:<img src="https://img2.meite.com/questions/202303/1564116ab1b1548.png" /></p><p>2、5名高中毕业生报考3所院校,每人只能报一所院校,则有()种不同的报名方法  </p><ul><li>A:<img src='https://img2.meite.com/questions/202303/28642253cbeb828.png' /></li><li>B:<img src='https://img2.meite.com/questions/202303/28642253cf87ee2.png' /></li><li>C:<img src='https://img2.meite.com/questions/202303/28642253d82d2a0.png' /></li><li>D:<img src='https://img2.meite.com/questions/202303/28642253d319585.png' /></li></ul><p>答 案:C</p><p>解 析:将院校看成元素,高中生看成位置,由重复排列的元素、位置的条件口诀: “元素可挑剩,位置不可缺”,重复排列的种数共有<img src="https://img2.meite.com/questions/202303/286422548fe3345.png" />种,即将元素的个数作为底数,位置的个数作为指数.即:元素(院校)的个数为 3,位置(高中生)的个数为5,共有<img src="https://img2.meite.com/questions/202303/28642254ad8b5e0.png" />种。  </p><p>3、方程<img src="https://img2.meite.com/questions/202303/286422844e41cfc.png" />的图像是下图中的()  </p><ul><li>A:<img src='https://img2.meite.com/questions/202303/286422845f870bc.png' /></li><li>B:<img src='https://img2.meite.com/questions/202303/2864228467a7899.png' /></li><li>C:<img src='https://img2.meite.com/questions/202303/286422847066eef.png' /></li><li>D:<img src='https://img2.meite.com/questions/202303/286422847761b5b.png' /></li></ul><p>答 案:D</p><p>解 析:本题属于读图题型,在寻求答案时,要着重讨论方程的表达式 <img src="https://img2.meite.com/questions/202303/28642284efc983b.png" /> <img src="https://img2.meite.com/questions/202303/286422851faebf4.png" /> <img src="https://img2.meite.com/questions/202303/2864228526ccc03.png" />  </p><p>4、已知<img src="https://img2.meite.com/questions/202303/15641164fa2237c.png" />,则sin2α=()</p><ul><li>A:<img src='https://img2.meite.com/questions/202303/1564116517f1106.png' /></li><li>B:<img src='https://img2.meite.com/questions/202303/156411651ce8f2e.png' /></li><li>C:<img src='https://img2.meite.com/questions/202303/15641165224b184.png' /></li><li>D:<img src='https://img2.meite.com/questions/202303/1564116525c6916.png' /></li></ul><p>答 案:D</p><p>解 析:<img src="https://img2.meite.com/questions/202303/1564116928359d5.png" />两边平方得<img src="https://img2.meite.com/questions/202303/156411693780841.png" />,故<img src="https://img2.meite.com/questions/202303/156411694945042.png" /></p><p class="introTit">主观题</p><p>1、在△ABC中,B=120°,BC=4,△ABC的面积为<img src="https://img2.meite.com/questions/202303/15641165ec55404.png" />,求AC.</p><p>答 案:由△ABC的面积为<img src="https://img2.meite.com/questions/202303/15641165ec55404.png" />得<img src="https://img2.meite.com/questions/202303/1564116bba3c98d.png" />所以AB =4.因此<img src="https://img2.meite.com/questions/202303/1564116be4bebd5.png" />所以<img src="https://img2.meite.com/questions/202303/1564116be967e8f.png" /></p><p>2、建筑一个容积为8000<img src="https://img2.meite.com/questions/202303/2864224b406cbf6.png" />,深为6m的长方体蓄水池,池壁每<img src="https://img2.meite.com/questions/202303/2864224b5cac16d.png" />的造价为15元,池底每<img src="https://img2.meite.com/questions/202303/2864224b60ac28e.png" />的造价为30元。(I)把总造价y(元)表示为长x(m)的函数;(Ⅱ)求函数的定义域  </p><p>答 案:<img src="https://img2.meite.com/questions/202303/2864224be4311f4.png" /><img src="https://img2.meite.com/questions/202303/2864224bee67713.png" /></p><p>3、已知等差数列前n项和<img src="https://img2.meite.com/questions/202303/2864228a3204a03.png" /> (Ⅰ)求这个数列的通项公式;(Ⅱ)求数列第六项到第十项的和</p><p>答 案:<img src="https://img2.meite.com/questions/202303/2864228a568855e.png" /> <img src="https://img2.meite.com/questions/202303/2864228a63bc5a4.png" />  </p><p>4、在正四棱柱ABCD-A'B'C'D'中,<img src="https://img2.meite.com/questions/202303/28642255fa50503.png" /> (Ⅰ)写出向量<img src="https://img2.meite.com/questions/202303/286422561b1d145.png" />关于基底{a,b,c}的分解式 (Ⅱ)求证:<img src="https://img2.meite.com/questions/202303/286422563d58cde.png" /> (Ⅲ)求证:<img src="https://img2.meite.com/questions/202303/28642256478aacd.png" />  </p><p>答 案:(Ⅰ)由题意知(如图所示) <img src="https://img2.meite.com/questions/202303/286422566983935.png" /> <img src="https://img2.meite.com/questions/202303/28642256740213a.png" /><img src="https://img2.meite.com/questions/202303/286422567c06c5d.png" /> (Ⅱ)<img src="https://img2.meite.com/questions/202303/2864225695c5fbd.png" /><img src="https://img2.meite.com/questions/202303/286422569cdc533.png" /> (Ⅲ)<img src="https://img2.meite.com/questions/202303/28642256a537b6d.png" /> 由已知,a,c是正四棱柱的棱,a,b,c两两垂直 <img src="https://img2.meite.com/questions/202303/28642256d1c4379.png" />  </p><p class="introTit">填空题</p><p>1、长方体的长、宽、高分别为2,3,6,则该长方体的对角线长为()</p><p>答 案:7</p><p>解 析:由题可知长方体的底面的对角线长为<img src="https://img2.meite.com/questions/202303/1564116b1132166.png" />,则在由高、底面对角线、长方体的对角线组成的三角形中,长方体的对角线长为<img src="https://img2.meite.com/questions/202303/1564116b3811959.png" /></p><p>2、lg(tan43°tan45°tan47°)=()  </p><p>答 案:0</p><p>解 析:lg(tan43°tan45°tan47°)=lg(tan43°tan45°cot43°)=lgtan45°=lg1=0</p>
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