2024年高职单招《数学(中职)》每日一练试题11月22日

<p class="introTit">单选题</p><p>1、不等式<img src="https://img2.meite.com/questions/202409/2166ee76a658b12.png" />的解集为（）  </p><ul><li>A：<img src='https://img2.meite.com/questions/202409/2166ee76ac9bdc1.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/2166ee76b58dc74.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/2166ee76beb6782.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/2166ee76c5102a8.png' /></li></ul><p>答 案：A</p><p>解 析：不等式<img src="https://img2.meite.com/questions/202409/2166ee76a658b12.png" />可化为<img src="https://img2.meite.com/questions/202409/2166ee79a8afbfd.png" />,<img src="https://img2.meite.com/questions/202409/2166ee79b48b9ee.png" />,解得<img src="https://img2.meite.com/questions/202409/2166ee79bc65720.png" />,即不等式<img src="https://img2.meite.com/questions/202409/2166ee76a658b12.png" />的解集为<img src="https://img2.meite.com/questions/202409/2166ee76ac9bdc1.png" />.</p><p>2、当<img src="https://img2.meite.com/questions/202409/1266e259b2a0f60.png" />,且m,n∈R时，下列选项不正确的是（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202409/1266e259bf55321.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/1266e259c4c4b8d.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/1266e259ca7e9c1.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/1266e259cf73acb.png' /></li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202409/1266e259d514c9c.png" /><img src="https://img2.meite.com/questions/202409/1266e259dfd6835.png" /><img src="https://img2.meite.com/questions/202409/1266e259e3adba7.png" /></p><p>3、设点P为直线x+y-4=0上的动点,点A(-2,0),B(2,0),则|PA|+|PB|的最小值为()  </p><ul><li>A：<img src='https://img2.meite.com/questions/202409/1966ebccfa35730.png' /></li><li>B：<img src='https://img2.meite.com/questions/202409/1966ebcd00f17f5.png' /></li><li>C：<img src='https://img2.meite.com/questions/202409/1966ebcd06435e2.png' /></li><li>D：<img src='https://img2.meite.com/questions/202409/1966ebcd0bb34ec.png' /></li></ul><p>答 案：A</p><p>解 析：设点 C(x,y)为点B(2,0)关于直线x+y-4=0的对称点,则<img src="https://img2.meite.com/questions/202409/1966ebd3a1647c6.png" />解得<img src="https://img2.meite.com/questions/202409/1966ebd3aa01bbc.png" />所以C(4,2),所以<img src="https://img2.meite.com/questions/202409/1966ebd3b616f1c.png" /></p><p>4、若直线x-y+1=0与圆(x-a)²+y²=2有公共点，则实数a的取值范围是()  </p><ul><li>A：[-3,-1]</li><li>B：(-3,1)</li><li>C：[-3,1]</li><li>D：(-∞,-3)U(-1,+∞)</li></ul><p>答 案：C</p><p>解 析：由方程(x-a)²+y²=2得圆的圆心坐标为(a,0),半径为<img src="https://img2.meite.com/questions/202409/2166ee37d2bb35f.png" />因为直线x-y+1=0与圆有公共点，所以<img src="https://img2.meite.com/questions/202409/2166ee37df6f6d8.png" />,即|a+1|≤2,解得-3≤a≤1.    </p><p class="introTit">填空题</p><p>1、函数f(x)=3-2cos4x的最大值为（）</p><p>答 案：5</p><p>解 析：<img src="https://img2.meite.com/questions/202409/1466e53d4208fa2.png" /> 所以最大值是5</p><p>2、不等式<img src="https://img2.meite.com/questions/202409/1066dff2a5e9096.png" />的解集是（）</p><p>答 案：(-∞,-1)∪(0,+∞)</p><p>解 析：<img src="https://img2.meite.com/questions/202409/1066dff2ac48d51.png" /> 所以原不等式的解集为(-∞,-1)∪(0,+∞)  </p><p>3、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>4、已知函数<img src="https://img2.meite.com/questions/202409/1266e299ffed136.png" />则f(100)=（）</p><p>答 案：<img src="https://img2.meite.com/questions/202409/1266e29a04da2c3.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202409/1266e29a0d61a25.png" /><img src="https://img2.meite.com/questions/202409/1266e29a12920d1.png" /></p><p class="introTit">简答题</p><p>1、已知△ABC的内角A,B,C的对边分别为a,b,c,且a+b=11,c=7,<img src="https://img2.meite.com/questions/202409/1466e545513c1f7.png" /> (1)求a的值； (2)求sinA和△ABC的面积.</p><p>答 案：<img src="https://img2.meite.com/questions/202409/1466e5455891ca5.png" /><img src="https://img2.meite.com/questions/202409/1466e5456084e89.png" /><img src="https://img2.meite.com/questions/202409/1466e54568b2a0a.png" /> <img src="https://img2.meite.com/questions/202409/1466e54571147fe.png" /> <img src="https://img2.meite.com/questions/202409/1466e545772ba08.png" /></p><p>2、已知函数f(x)=x²+2ax+2,x∈[-5,5]. (1)当a=-1时，求函数f(x)的最大值和最小值； (2)若f(x)在区间[-5,5]上是单调函数，求实数a的取值范围</p><p>答 案：(1)当a=-1时，f(x)=x²-2x+2=(x-1)²+1, 所以在区间[-5,5]上，当x=1时，函数f(x)取得最小值，为f(1)=1, 当x=-5时，函数f(x)取得最大值，为f(-5)=37 (2)f(x)=x²+2ax+2=(x+a)²+2-a². 若f(x)在区间[-5,5]上是单调函数，<img src="https://img2.meite.com/questions/202409/1166e15eb5ad7ee.png" /> 故实数a的取值范围为(-∞,-5]∪[5,+∞).</p>