2024年成考高起点《数学(理)》每日一练试题05月09日
聚题库
05/09
<p class="introTit">单选题</p><p>1、对满足a>b的任意两个非零实数，下列不等式成立的是（）
</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/2864228b1f8efca.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/2864228b2567c86.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/2864228b2a86110.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/2864228b30e50d4.png' /></li></ul><p>答 案：D</p><p>解 析：A错误，例如-2>4,而<img src="https://img2.meite.com/questions/202303/2864228ba68a732.png" /> B错误，例如：-10>100,而<img src="https://img2.meite.com/questions/202303/2864228bbe163a2.png" />
C错误，例如：-1>-2,而<img src="https://img2.meite.com/questions/202303/2864228bd9de925.png" />
<img src="https://img2.meite.com/questions/202303/2864228be175c60.png" /></p><p>2、函数<img src="https://img2.meite.com/questions/202303/15641164b43c663.png" />的反函数是（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/15641164d78e1fc.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/15641164de92884.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/15641164e5206d4.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/15641164e93e32e.png' /></li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202303/15641168660282b.png" />，由于x≤0，故<img src="https://img2.meite.com/questions/202303/1564116881a60a4.png" />把x与y互换，得所求反函数为<img src="https://img2.meite.com/questions/202303/15641168ab18774.png" /></p><p>3、设函数<img src="https://img2.meite.com/questions/202303/15641163f4b1b54.png" />，则f(x+1)=（）</p><ul><li>A：x<sup>2</sup>+2x+1</li><li>B：x<sup>2</sup>+2x</li><li>C：x<sup>2</sup>+1</li><li>D：x<sup>2</sup></li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202303/15641167631a1eb.png" /></p><p>4、设集合M={x∈R|x2=1}，N={x∈R|x3=1}，则M∩N=（）。</p><ul><li>A：{1}</li><li>B：{-1}</li><li>C：{-1，1}</li><li>D：<img src='https://img2.meite.com/questions/202404/1966222e09c92b0.png' /></li></ul><p>答 案：A</p><p>解 析：本题主要考查的知识点为集合的运算
由题意M={-1，1}，N={1}，所以M∩N={1}</p><p class="introTit">主观题</p><p>1、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>2、已知数列<img src="https://img2.meite.com/questions/202303/286422511c19556.png" />的前n项和<img src="https://img2.meite.com/questions/202303/2864225128dc6e0.png" />
求证：<img src="https://img2.meite.com/questions/202303/286422513318bbb.png" />是等差数列，并求公差和首项。
</p><p>答 案：<img src="https://img2.meite.com/questions/202303/286422514f41b7b.png" /> <img src="https://img2.meite.com/questions/202303/28642251563e39b.png" />
</p><p>3、在正四棱柱ABCD-A'B'C'D'中，<img src="https://img2.meite.com/questions/202303/2864229a3bc3098.png" />
（Ⅰ）写出向量<img src="https://img2.meite.com/questions/202303/2864229a57ba174.png" />和<img src="https://img2.meite.com/questions/202303/2864229a5e46ac8.png" />关于基底{a,b,c}的分解式;
（Ⅱ）求证：<img src="https://img2.meite.com/questions/202303/2864229a76ba56d.png" />
（Ⅲ）求证：<img src="https://img2.meite.com/questions/202303/2864229a7fdd541.png" />
</p><p>答 案：（Ⅰ）由题意知(如图所示) <img src="https://img2.meite.com/questions/202303/2864229af6b1567.png" />
<img src="https://img2.meite.com/questions/202303/2864229afe90f50.png" />
<img src="https://img2.meite.com/questions/202303/2864229b08314c5.png" />
</p><p>4、已知a,b,c成等差数列，a,b,c+1成等比数列．若b=6，求a和c．</p><p>答 案：由已知得<img src="https://img2.meite.com/questions/202303/1564116c009cc19.png" />解得<img src="https://img2.meite.com/questions/202303/1564116c0e039c1.png" /></p><p class="introTit">填空题</p><p>1、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><p>2、不等式<img src="https://img2.meite.com/questions/202303/28642289d6ca884.png" />的解集为（）
</p><p>答 案：<img src="https://img2.meite.com/questions/202303/28642289e5c9bcc.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/28642289efc4ba4.png" /><img src="https://img2.meite.com/questions/202303/28642289fa37c87.png" /><img src="https://img2.meite.com/questions/202303/2864228a0077853.png" /></p>
