2024年高职单招《数学(中职)》每日一练试题11月01日

<p class="introTit">单选题</p><p>1、设A,B 分别为椭圆<img src="https://img2.meite.com/questions/202409/1866ea3c4bcb3ef.png" />的左顶点和上顶点,F为C的右焦点,则F到直线AB的距离为()  </p><ul><li>A：<img src='https://img2.meite.com/questions/202409/1866ea3c5dd9eda.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/1866ea3c65a7f05.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/1866ea3c6bd6037.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/1866ea3c718a797.png' /></li></ul><p>答 案：A</p><p>解 析：由题意可得A(-2,0),B(0,<img src="https://img2.meite.com/questions/202409/1866ea45cda5e51.png" />),F(1,0),所以直线 A8 的方程为<img src="https://img2.meite.com/questions/202409/1866ea45dbab264.png" />,整理得<img src="https://img2.meite.com/questions/202409/1866ea45e3a8bde.png" /><img src="https://img2.meite.com/questions/202409/1866ea45f0a228d.png" />,所以F到直线AB 的距离<img src="https://img2.meite.com/questions/202409/1866ea4613e1d0b.png" /></p><p>2、若a,b,c为实数，且<img src="https://img2.meite.com/questions/202409/1066dfb4b3ba02d.png" />则下列结论错误的是（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202409/1066dfb4bf539b3.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/1066dfb4c4be9bd.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/1066dfb4cb1a55c.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/1066dfb4d0c3f6b.png' /></li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202409/1066dfb503dc744.png" /> 故A不符合题意;当c=0时不等式不成立,故B符合题意;<img src="https://img2.meite.com/questions/202409/1066dfb50ec580a.png" /><img src="https://img2.meite.com/questions/202409/1066dfb514270d4.png" /> 故C不符合题意;<img src="https://img2.meite.com/questions/202409/1066dfb51d3dce6.png" /> D不符合题意.</p><p>3、若集合A={0,1,2,3},B={1,2,4},则AUB=（）  </p><ul><li>A：{0,1,2,3,4}</li><li>B：{1,2,3,4}</li><li>C：{1,2}</li><li>D：{0}</li></ul><p>答 案：A</p><p>解 析：因为集合A={0,1,2,3}与B={1,2,4}的所有元素为0,1,2,3,4,所以AUB={0,1,2,3,4}.</p><p>4、函数f(x)=√3sinx-cosx的值域为（）</p><ul><li>A：[-√3,√3]</li><li>B：[-√3-1,√3+1]</li><li>C：[-1,1]</li><li>D：[-2,2]</li></ul><p>答 案：D</p><p>解 析：易知<img src="https://img2.meite.com/questions/202409/2166ee3ba941fba.png" /><img src="https://img2.meite.com/questions/202409/2166ee3badbb548.png" />。因为<img src="https://img2.meite.com/questions/202409/2166ee3bb8e3771.png" /><img src="https://img2.meite.com/questions/202409/2166ee3bc1b16a0.png" />，所以函数f(x)=√3sinx-cosx的值域为[-2,2].</p><p class="introTit">填空题</p><p>1、如图,在长方体ABCD-A₁B₁C₁D₁中,AB=1,AD=2,AA₁=2,则二面角A-DD₁-B的正切值为() <img src="https://img2.meite.com/questions/202409/1366e3a1e9e4681.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202409/1366e3aabede20b.png" /></p><p>解 析：易得<img src="https://img2.meite.com/questions/202409/1366e3aae9a9b6c.png" />,<img src="https://img2.meite.com/questions/202409/1366e3ab007062c.png" />平面角.在<img src="https://img2.meite.com/questions/202409/1366e3ab1ab51b8.png" />,AB=1AD=2,<img src="https://img2.meite.com/questions/202409/1366e3ab2d83821.png" />,∴二面角A-DD₁-B的正切值为<img src="https://img2.meite.com/questions/202409/1366e3aabede20b.png" />.</p><p>2、<img src="https://img2.meite.com/questions/202409/1266e29a3e0507a.png" />=（）</p><p>答 案：2</p><p>解 析：<img src="https://img2.meite.com/questions/202409/1266e29a4563c46.png" /></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、<img src="https://img2.meite.com/questions/202409/1266e28fe1b5259.png" />展开式中的常数项为（）  </p><p>答 案：<img src="https://img2.meite.com/questions/202409/1266e29459792a1.png" /></p><p>解 析：易知<img src="https://img2.meite.com/questions/202409/1266e28fe1b5259.png" />展开式的通项为<img src="https://img2.meite.com/questions/202409/1266e293f5bb2a2.png" />令12-3k =0,解得k=4,所以<img src="https://img2.meite.com/questions/202409/1266e28fe1b5259.png" />展开式中的常数项为<img src="https://img2.meite.com/questions/202409/1266e2942b3e608.png" /></p><p class="introTit">简答题</p><p>1、已知<img src="https://img2.meite.com/questions/202409/1266e2a116c4f74.png" />,该展开式的二项式系数之和为 32. (1)求n的值;(2)求<img src="https://img2.meite.com/questions/202409/1266e2a1279029b.png" />的值.  </p><p>答 案：(1)因为<img src="https://img2.meite.com/questions/202409/1266e2a9e3ae8f8.png" />的展开式的二项式系数之和为 32, 所以2ⁿ=32,解得n=5. (2)令x=1,得<img src="https://img2.meite.com/questions/202409/1266e2aa147b4a4.png" /> 所以<img src="https://img2.meite.com/questions/202409/1266e2aa1f4438a.png" /></p><p>2、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>