2024年成考高起点《数学(理)》每日一练试题06月17日
聚题库
06/17
<p class="introTit">单选题</p><p>1、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>2、从椭圆与x轴额右交点看短轴两端点的视角为60°的椭圆的离心率（）
</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/28642287ed710eb.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/28642287f182bba.png' /></li><li>C：1</li><li>D：<img src='https://img2.meite.com/questions/202303/28642287f85287f.png' /></li></ul><p>答 案：A</p><p>解 析：求椭圆的离心率,先求出a,c.(如图) <img src="https://img2.meite.com/questions/202303/286422892bd4fb5.png" /><img src="https://img2.meite.com/questions/202303/286422893b50a35.png" />，由椭圆定义知<img src="https://img2.meite.com/questions/202303/2864228950523ff.png" />
<img src="https://img2.meite.com/questions/202303/286422895c76294.png" /></p><p>3、<img src="https://img2.meite.com/questions/202303/2864225b891ad2c.png" />展开式中,末3项的系数(a,x 均未知) 之和为()
</p><ul><li>A：22</li><li>B：12</li><li>C：10</li><li>D：-10</li></ul><p>答 案：C</p><p>解 析：<img src="https://img2.meite.com/questions/202303/2864225bbb4b976.png" /><img src="https://img2.meite.com/questions/202303/2864225bc299c02.png" /><img src="https://img2.meite.com/questions/202303/2864225bcaa8096.png" />末三项数之和为<img src="https://img2.meite.com/questions/202303/2864225bdfc7788.png" /><img src="https://img2.meite.com/questions/202303/2864225beaa0cc1.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>2、已知函数f(x)=(x-4)(x<sup>2</sup>-a)
（I）求f"(x)；
(Ⅱ)若f"(-1)=8，求f(x)在区间[0，4]的最大值与最小值</p><p>答 案：<img src="https://img2.meite.com/questions/202404/1966222f3f733cc.png" /><img src="https://img2.meite.com/questions/202404/1966222f47c8e62.png" /></p><p>3、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>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、函数<img src="https://img2.meite.com/questions/202303/28642285dd68e2c.png" />的定义域是（）</p><p>答 案：<img src="https://img2.meite.com/questions/202303/28642285f367786.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/28642285fcec513.png" /><img src="https://img2.meite.com/questions/202303/2864228601aa2da.png" />所以函数<img src="https://img2.meite.com/questions/202303/286422860d8135c.png" />的定义域是<img src="https://img2.meite.com/questions/202303/286422861644b62.png" /></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>
