2025年高职单招《数学(中职)》每日一练试题03月01日

<p class="introTit">单选题</p><p>1、若点A在直线a上,直线a在平面α内,点B在α内,则下列表述正确的是()  </p><ul><li>A：<img src='https://img2.meite.com/questions/202409/1366e3e48b77dd0.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/1366e3e497eb6e0.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/1366e3e49f37946.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/1366e3e4a67fc0a.png' /></li></ul><p>答 案：B</p><p>解 析：由题意得<img src="https://img2.meite.com/questions/202409/1366e3ee2f097d3.png" /></p><p>2、直线2x-y+2=0与圆x²+y²+4x-6y-7=0交于M,N两点,则|MN|=（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202409/1966eb927f37443.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/1966eb9285d6682.png' /></li><li>C： <img src='https://img2.meite.com/questions/202409/1966eb928c51e5c.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/1966eb929410861.png' /></li></ul><p>答 案：D</p><p>解 析：由x²+y²+4x-6y-7=0得(x+ 2)²+(y-3)²= 20,所以圆心为(-2,3),半径为<img src="https://img2.meite.com/questions/202409/1966eba088c0a0f.png" />.又圆心(-2,3)到直线2x-y+2=0的距离<img src="https://img2.meite.com/questions/202409/1966eba09e3c9d2.png" />,所以<img src="https://img2.meite.com/questions/202409/1966eba0a87f7dd.png" /></p><p>3、已知双曲线<img src="https://img2.meite.com/questions/202409/2166ee2a60a9061.png" />的一条渐近线与直线2x+y+3=0垂直，则该双曲线的离心率为()  </p><ul><li>A：<img src='https://img2.meite.com/questions/202409/2166ee2a675eb25.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/2166ee2a6ed3340.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/2166ee2a760502f.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/2166ee2a7c12b73.png' /></li></ul><p>答 案：A</p><p>解 析：易知双曲线<img src="https://img2.meite.com/questions/202409/2166ee2d4e048fc.png" />的渐近线方程为<img src="https://img2.meite.com/questions/202409/2166ee2d571c733.png" />,直线2x+y+3=0,即y=-2x-3的斜率为-2.由题意知直线<img src="https://img2.meite.com/questions/202409/2166ee2d6d217e6.png" />与直线y=-2x-3垂直，所以<img src="https://img2.meite.com/questions/202409/2166ee2d785aa34.png" />,所以双曲线的离心率<img src="https://img2.meite.com/questions/202409/2166ee2d7f9b1e5.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<img src="https://img2.meite.com/questions/202409/1266e2a058ada6c.png" />的展开式中,x³的系数为8,则实数k的值为()  </p><p>答 案：2</p><p>解 析：易知<img src="https://img2.meite.com/questions/202409/1266e2a058ada6c.png" />的展开式的通项<img src="https://img2.meite.com/questions/202409/1266e2a79585233.png" />令6-r=3,解得r=3,所以x³的系数是<img src="https://img2.meite.com/questions/202409/1266e2a7b63f873.png" />,解得k=2.</p><p>2、已知{a_n}为等差数列，且a₄+a₈+a₁₀=50,则a₂+2a₁₀=（）</p><p>答 案：50</p><p>解 析：由数列{an}为等差数列得a₄+a₈+a₁₀=a₂+a₈+a₁₂=a₂+2a₁₀=50</p><p>3、若函数<img src="https://img2.meite.com/questions/202501/06677b77ec9c2a3.png" />则<img src="https://img2.meite.com/questions/202501/06677b77f150cd6.png" />= _______</p><p>答 案：1</p><p>解 析：解法一： 由<img src="https://img2.meite.com/questions/202501/06677b77f774d1e.png" />得<img src="https://img2.meite.com/questions/202501/06677b77fb171be.png" /> ∴<img src="https://img2.meite.com/questions/202501/06677b77ff42d12.png" /> 解法二： 由<img src="https://img2.meite.com/questions/202501/06677b780471001.png" />得x=1 ∴<img src="https://img2.meite.com/questions/202501/06677b78085f5ac.png" /></p><p class="introTit">简答题</p><p>1、已知数列{an}是等差数列，a1=1,a3=3. (1)求数列{an}的通项公式； (2)设b_n=(-1)ⁿa_n,数列{b_n}的前n项和为T_n,求T₁₀₀</p><p>答 案：<img src="https://img2.meite.com/questions/202409/1866ea3b778423a.png" /> <img src="https://img2.meite.com/questions/202409/1866ea3b80b8bb9.png" /></p>