2025年高职单招《数学(中职)》每日一练试题05月15日

<p class="introTit">单选题</p><p>1、下列大小关系不正确的是（）  </p><ul><li>A：<img src='https://img2.meite.com/questions/202409/2166ee7856c8426.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/2166ee785db7471.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/2166ee7864dfe1a.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/2166ee786a7ca9c.png' /></li></ul><p>答 案：C</p><p>解 析：A选项，因为<img src="https://img2.meite.com/questions/202409/2166ee7be1cb31b.png" />,指数函数y=2.5^x在R上单调递增，所以<img src="https://img2.meite.com/questions/202409/2166ee7beac0d2b.png" />,故A不符合题意；B选项，<img src="https://img2.meite.com/questions/202409/2166ee7bf40b8fb.png" />，因为<img src="https://img2.meite.com/questions/202409/2166ee7bfd6201e.png" />，指数函数<img src="https://img2.meite.com/questions/202409/2166ee7c061f811.png" />在R上单调递减，所以<img src="https://img2.meite.com/questions/202409/2166ee7c0f3a46a.png" />,即<img src="https://img2.meite.com/questions/202409/2166ee7c181e16d.png" /><img src="https://img2.meite.com/questions/202409/2166ee7c201080c.png" />,故B不符合题意；C选项，因为函数<img src="https://img2.meite.com/questions/202409/2166ee7c297c0c0.png" />在(0,+∞)上单调递减，且<img src="https://img2.meite.com/questions/202409/2166ee7c303f8c7.png" />，所以<img src="https://img2.meite.com/questions/202409/2166ee7c3e3bffa.png" />,故C符合题意；D选项，因为指数函数y=2.5^x在R上单调递增，所以<img src="https://img2.meite.com/questions/202409/2166ee7c4f65342.png" />,因为指数函数y=2^x在R上单调递增，所以<img src="https://img2.meite.com/questions/202409/2166ee7c5dc7c68.png" />,所以<img src="https://img2.meite.com/questions/202409/2166ee7c6709727.png" />,故D不符合题意.</p><p>2、不等式<img src="https://img2.meite.com/questions/202409/1066dff0ff28aad.png" />的解集为（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202409/1066dff1071585c.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/1066dff10da314e.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/1066dff113ed7a8.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/1066dff11bb58e7.png' /></li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202409/1066dff126109db.png" /><img src="https://img2.meite.com/questions/202409/1066dff12b0a449.png" /><img src="https://img2.meite.com/questions/202409/1066dff12f7d187.png" /><img src="https://img2.meite.com/questions/202409/1066dff13602619.png" /><img src="https://img2.meite.com/questions/202409/1066dff13b61225.png" /></p><p>3、若指数函数y=(a+1)^x是增函数，则a的取值范围是（）</p><ul><li>A：(-1,0]</li><li>B：(-1,0)</li><li>C：(0,+∞)</li><li>D：[0,+∞)</li></ul><p>答 案：C</p><p>解 析：<img src="https://img2.meite.com/questions/202411/0467288efc6f4b2.png" /><img src="https://img2.meite.com/questions/202409/1266e24e737f078.png" /></p><p class="introTit">主观题</p><p>1、已知<img src="https://img2.meite.com/questions/202501/1167822ff243cf5.png" /></p><p>答 案：方法一：矢量图表示法 矢量图表示法如图所示。<img src="https://img2.meite.com/questions/202501/1167822ff89fe55.png" /><img src="https://img2.meite.com/questions/202501/1167822ffb0aba3.png" /> 方法二：矢量表示法<img src="https://img2.meite.com/questions/202501/116782300184954.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202409/1366e3aff07aaa2.png" /><img src="https://img2.meite.com/questions/202409/1366e3affb6a19c.png" /><img src="https://img2.meite.com/questions/202409/1366e3affff2ae2.png" /></p><p class="introTit">填空题</p><p>1、在平行四边形ABCD中，AC与BD交于点M<img src="https://img2.meite.com/questions/202409/1966ebc5501e669.png" />（）</p><p>答 案：<img src="https://img2.meite.com/questions/202409/1966ebc7d8e7462.png" /></p><p>解 析：在平行四边形ABCD中，因为AC与BD交于点M,所以M为AC的中点，<img src="https://img2.meite.com/questions/202409/1966ebc557362cc.png" /></p><p>2、<img src="https://img2.meite.com/questions/202409/1266e2a03ea8d89.png" />的展开式中,含x⁵的项是第()项.  </p><p>答 案：11</p><p>解 析：易得<img src="https://img2.meite.com/questions/202409/1266e2a03ea8d89.png" />的展开式的通项<img src="https://img2.meite.com/questions/202409/1266e2a7648567f.png" />令15-k=5,解得k=10,则含x⁵的项是展开式中的第 11 项.</p><p>3、不等式(x-4)(x+5)>0的解集是______________</p><p>答 案：{x|x>4或x<-5}</p><p>解 析：方程的根为x=4或x=-5， 所以不等式的解集为{x|x>4或x<-5}</p><p class="introTit">简答题</p><p>1、在等比数列{an}中，a₁a₂a₃=8,a₂+a₄=10. (1)求首项a₁及公比q; (2)求该数列的前8项和S₈</p><p>答 案：<img src="https://img2.meite.com/questions/202409/1866ea94201acf1.png" /> <img src="https://img2.meite.com/questions/202409/1866ea9426e98ec.png" /> <img src="https://img2.meite.com/questions/202409/1866ea942fe1293.png" /> <img src="https://img2.meite.com/questions/202409/1866ea943b18479.png" /><img src="https://img2.meite.com/questions/202409/1866ea94402c17a.png" /></p>