2024年成考高起点《数学(理)》每日一练试题01月26日

<p class="introTit">单选题</p><p>1、若<img src="https://img2.meite.com/questions/202303/286422574eab213.png" />则<img src="https://img2.meite.com/questions/202303/28642257543afd6.png" />（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/286422575a7b0ce.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/286422575f5d2ea.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/28642257640e720.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/28642257690a458.png' /></li></ul><p>答 案：B</p><p>解 析：首先做出单位圆,然后根据问题的约束条件,利用三角函数线找出满足条件的a角取值范围 <img src="https://img2.meite.com/questions/202303/28642257c3e01c3.png" /> <img src="https://img2.meite.com/questions/202303/28642257d4935f9.png" />  </p><p>2、<img border="0" style="width: 58px; height: 37px;" src="https://img2.meite.com/zzpuce/2023-04/643679c8eed3a35616.jpeg">（ ）</p><ul><li>A：-2</li><li>B：<img border="0" style="width: 24px; height: 37px;" src="https://img2.meite.com/zzpuce/2023-04/643679c9008af39045.jpeg"></li><li>C：<img border="0" style="width: 14px; height: 37px;" src="https://img2.meite.com/zzpuce/2023-04/643679c90917e56279.jpeg"></li><li>D：2</li></ul><p>答 案：C</p><p>3、设函数<img src="https://img2.meite.com/questions/202303/15641163f4b1b54.png" />，则f(x+1)=（）</p><ul><li>A：x²+2x+1</li><li>B：x²+2x</li><li>C：x²+1</li><li>D：x²</li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202303/15641167631a1eb.png" /></p><p>4、<img src="https://img2.meite.com/questions/202303/1564116591bffc0.png" />的展开式中，x²的系数为（）</p><ul><li>A：20</li><li>B：10</li><li>C：5</li><li>D：1</li></ul><p>答 案：C</p><p>解 析：二项展开式的第二项为<img src="https://img2.meite.com/questions/202303/1564116a225f0b5.png" />，故展开式中的x²的系数为5.</p><p class="introTit">主观题</p><p>1、建筑一个容积为8000<img src="https://img2.meite.com/questions/202303/2864224b406cbf6.png" />,深为6m的长方体蓄水池，池壁每<img src="https://img2.meite.com/questions/202303/2864224b5cac16d.png" />的造价为15元，池底每<img src="https://img2.meite.com/questions/202303/2864224b60ac28e.png" />的造价为30元。（I）把总造价y(元)表示为长x(m)的函数；（Ⅱ）求函数的定义域  </p><p>答 案：<img src="https://img2.meite.com/questions/202303/2864224be4311f4.png" /><img src="https://img2.meite.com/questions/202303/2864224bee67713.png" /></p><p>2、在正四棱柱ABCD-A'B'C'D'中，<img src="https://img2.meite.com/questions/202303/28642255fa50503.png" /> （Ⅰ）写出向量<img src="https://img2.meite.com/questions/202303/286422561b1d145.png" />关于基底{a,b,c}的分解式 （Ⅱ）求证：<img src="https://img2.meite.com/questions/202303/286422563d58cde.png" /> （Ⅲ）求证：<img src="https://img2.meite.com/questions/202303/28642256478aacd.png" />  </p><p>答 案：(Ⅰ)由题意知(如图所示) <img src="https://img2.meite.com/questions/202303/286422566983935.png" /> <img src="https://img2.meite.com/questions/202303/28642256740213a.png" /><img src="https://img2.meite.com/questions/202303/286422567c06c5d.png" /> (Ⅱ)<img src="https://img2.meite.com/questions/202303/2864225695c5fbd.png" /><img src="https://img2.meite.com/questions/202303/286422569cdc533.png" /> (Ⅲ)<img src="https://img2.meite.com/questions/202303/28642256a537b6d.png" /> 由已知，a,c是正四棱柱的棱，a,b,c两两垂直 <img src="https://img2.meite.com/questions/202303/28642256d1c4379.png" />  </p><p>3、在△ABC中，B=120°,BC=4,△ABC的面积为<img src="https://img2.meite.com/questions/202303/15641165ec55404.png" />，求AC.</p><p>答 案：由△ABC的面积为<img src="https://img2.meite.com/questions/202303/15641165ec55404.png" />得<img src="https://img2.meite.com/questions/202303/1564116bba3c98d.png" />所以AB =4.因此<img src="https://img2.meite.com/questions/202303/1564116be4bebd5.png" />所以<img src="https://img2.meite.com/questions/202303/1564116be967e8f.png" /></p><p>4、在正四棱柱ABCD-A'B'C'D'中，<img src="https://img2.meite.com/questions/202303/2864229a3bc3098.png" /> （Ⅰ）写出向量<img src="https://img2.meite.com/questions/202303/2864229a57ba174.png" />和<img src="https://img2.meite.com/questions/202303/2864229a5e46ac8.png" />关于基底{a,b,c}的分解式; （Ⅱ）求证：<img src="https://img2.meite.com/questions/202303/2864229a76ba56d.png" /> （Ⅲ）求证：<img src="https://img2.meite.com/questions/202303/2864229a7fdd541.png" />  </p><p>答 案：（Ⅰ）由题意知(如图所示) <img src="https://img2.meite.com/questions/202303/2864229af6b1567.png" /> <img src="https://img2.meite.com/questions/202303/2864229afe90f50.png" /> <img src="https://img2.meite.com/questions/202303/2864229b08314c5.png" />  </p><p class="introTit">填空题</p><p>1、若平面向量a=(x,1),b=(1,-2),且a//b,则x=（）  </p><p>答 案：<img src="https://img2.meite.com/questions/202303/286422508f0554f.png" /></p><p>解 析：由于a//b，故<img src="https://img2.meite.com/questions/202303/286422509cd5c14.png" /></p><p>2、lg(tan43°tan45°tan47°)=（）  </p><p>答 案：0</p><p>解 析：lg(tan43°tan45°tan47°)=lg(tan43°tan45°cot43°)=lgtan45°=lg1=0</p>