2025年高职单招《数学(中职)》每日一练试题01月08日
<p class="introTit">单选题</p><p>1、不等式<img src="https://img2.meite.com/questions/202409/2166ee7fc694b60.png" />的解集是()
</p><ul><li>A:<img src='https://img2.meite.com/questions/202409/2166ee7fcda7764.png' /></li><li>B:<img src='https://img2.meite.com/questions/202409/2166ee7fd66b116.png' /></li><li>C:<img src='https://img2.meite.com/questions/202409/2166ee7fddbb351.png' /></li><li>D:<img src='https://img2.meite.com/questions/202409/2166ee7fe6c3187.png' /></li></ul><p>答 案:A</p><p>解 析:由<img src="https://img2.meite.com/questions/202409/2166ee7fc694b60.png" />得<img src="https://img2.meite.com/questions/202409/2166ee8335a2830.png" />,解得<img src="https://img2.meite.com/questions/202409/2166ee833e042dd.png" />,故不等式<img src="https://img2.meite.com/questions/202409/2166ee7fc694b60.png" />的解集为<img src="https://img2.meite.com/questions/202409/2166ee7fcda7764.png" />.</p><p>2、已知<img src="https://img2.meite.com/questions/202409/1266e28f272db9c.png" />,则<img src="https://img2.meite.com/questions/202409/1266e28f32123f7.png" /></p><ul><li>A:1</li><li>B:3</li><li>C:0</li><li>D:-3</li></ul><p>答 案:C</p><p>解 析:因为<img src="https://img2.meite.com/questions/202409/1266e28f272db9c.png" />,所以当x=-1时,<img src="https://img2.meite.com/questions/202409/1266e28f32123f7.png" /><img src="https://img2.meite.com/questions/202409/1266e2917424c3f.png" /></p><p>3、已知tanα=5,则<img src="https://img2.meite.com/questions/202409/1366e3dfbc60b53.png" />()</p><ul><li>A:<img src='https://img2.meite.com/questions/202409/1366e3dfc312001.png' /></li><li>B:1</li><li>C:<img src='https://img2.meite.com/questions/202409/1366e3dfc9a4979.png' /></li><li>D:<img src='https://img2.meite.com/questions/202409/1366e3dfd028fe3.png' /></li></ul><p>答 案:B</p><p>解 析:<img src="https://img2.meite.com/questions/202409/1366e3dfd68518c.png" /></p><p>4、不等式<img src="https://img2.meite.com/questions/202409/1066dfefe865045.png" />的解集为()</p><ul><li>A:<img src='https://img2.meite.com/questions/202409/1066dfefeddec32.png' /></li><li>B:<img src='https://img2.meite.com/questions/202409/1066dfeff29f1f7.png' /></li><li>C:<img src='https://img2.meite.com/questions/202409/1066dfeff804cae.png' /></li><li>D:<img src='https://img2.meite.com/questions/202409/1066dff002a7788.png' /></li></ul><p>答 案:C</p><p>解 析:<img src="https://img2.meite.com/questions/202409/1066dff00b2f1e2.png" /><img src="https://img2.meite.com/questions/202409/1066dff013ab106.png" /></p><p class="introTit">填空题</p><p>1、已知向量a=(6,2),b=(3,6),则a与b的夹角为()
</p><p>答 案:<img src="https://img2.meite.com/questions/202409/1966ebc6f967091.png" /></p><p>解 析:<img src="https://img2.meite.com/questions/202409/1966ebc511a7a4b.png" /><img src="https://img2.meite.com/questions/202409/1966ebc51778881.png" /><img src="https://img2.meite.com/questions/202409/1966ebc51cef086.png" /><img src="https://img2.meite.com/questions/202409/1966ebc5218a756.png" /></p><p>2、若事件A与事件B互为对立事件,且P(B)=P(A),则P(B) =____
</p><p>答 案:0.5</p><p>解 析:由于两个事件是对立事件, 因此两者的概率之和为1,
又两个事件的概率相等,因此概率均为0.5
</p><p>3、函数<img src="https://img2.meite.com/questions/202409/1466e53d4dd18be.png" />的最小正周期是()</p><p>答 案:π</p><p>解 析:<img src="https://img2.meite.com/questions/202409/1466e53d549721e.png" /><img src="https://img2.meite.com/questions/202409/1466e53d5b08234.png" /><img src="https://img2.meite.com/questions/202409/1466e53d600d7ea.png" /></p><p>4、已知函数<img src="https://img2.meite.com/questions/202501/06677b77d831dcc.png" />若f(a)=3,则实数a=____________</p><p>答 案:10</p><p>解 析:由<img src="https://img2.meite.com/questions/202501/06677b77dd55c16.png" />解得a=10</p><p class="introTit">简答题</p><p>1、若a>0,b>0,计算<img src="https://img2.meite.com/questions/202501/06677b7b28c2976.png" />
</p><p>答 案:解:<img src="https://img2.meite.com/questions/202501/06677b7b2d383d5.png" /></p><p>2、如图,在四棱锥P-ABCD中,E,F,G分别是PC,PD,BC的中点,且DC//AB,证明平面 PAB //平面 EFG.
<img src="https://img2.meite.com/questions/202409/1366e3a21d83281.png" />
</p><p>答 案:因为E,F分别是 PC,PD 的中点, 所以EF//DC.
又DC //AB,
所以 EF//AB.
又<img src="https://img2.meite.com/questions/202409/1366e3ab8bb7d43.png" />
所以EF//平面PAB.
因为E,G分别是 PC,BC的中点,
所以 EG //PB.
又<img src="https://img2.meite.com/questions/202409/1366e3adcc7d4fa.png" />
所以EG//平面PAB.
又<img src="https://img2.meite.com/questions/202409/1366e3ade91781a.png" />
所以平面 PAB //平面EFG.
</p>