2024年成考高起点《数学(理)》每日一练试题04月12日
聚题库
04/12
<p class="introTit">单选题</p><p>1、将一颗骰子抛掷1次,到的点数为偶数的概率为
</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/28642253b027cee.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/28642253b3b5865.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/28642253beb605d.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/28642253b9ec882.png' /></li></ul><p>答 案：D</p><p>解 析：一颗骰子的点数分别为1,2,3,4,5,6,其中偶数与奇数各占一半,故抛掷1次,得到的点数为偶数的概率为<img src="https://img2.meite.com/questions/202303/286422545e57429.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、过点（-2，2）与直线x+3y-5=0平行的直线是（）</p><ul><li>A：x+3y-4=0</li><li>B：3x+y+4=0</li><li>C：x+3y+8=0</li><li>D：3x-y+8=0</li></ul><p>答 案：A</p><p>解 析：所求直线与x+3y-5=0平行，可设所求直线为x+3y+c=0，将点（一2,2)带入直线方程，故-2+3×2+c=0，解得c=-4，因此所求直线为线为x+3y-4=0.</p><p>4、方程<img src="https://img2.meite.com/questions/202303/286422844e41cfc.png" />的图像是下图中的（）
</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/286422845f870bc.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/2864228467a7899.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/286422847066eef.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/286422847761b5b.png' /></li></ul><p>答 案：D</p><p>解 析：本题属于读图题型，在寻求答案时,要着重讨论方程的表达式 <img src="https://img2.meite.com/questions/202303/28642284efc983b.png" />
<img src="https://img2.meite.com/questions/202303/286422851faebf4.png" />
<img src="https://img2.meite.com/questions/202303/2864228526ccc03.png" />
</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、已知数列<img src="https://img2.meite.com/questions/202303/286422511c19556.png" />的前n项和<img src="https://img2.meite.com/questions/202303/2864225128dc6e0.png" />
求证：<img src="https://img2.meite.com/questions/202303/286422513318bbb.png" />是等差数列，并求公差和首项。
</p><p>答 案：<img src="https://img2.meite.com/questions/202303/286422514f41b7b.png" /> <img src="https://img2.meite.com/questions/202303/28642251563e39b.png" />
</p><p>3、为了测河的宽,在岸边选定两点A和B,望对岸标记物C,测得<img src="https://img2.meite.com/questions/202303/2864228db8c0e49.png" />AB=120m,求河的宽
<img src="https://img2.meite.com/questions/202303/2864228dd64bdcb.png" /></p><p>答 案：如图， <img src="https://img2.meite.com/questions/202303/2864228df3f06d3.png" />
∵∠C=180°-30°-75°=75°
∴△ABC为等腰三角形，则AC=AB=120m
过C做CD⊥AB,则由Rt△ACD可求得CD=<img src="https://img2.meite.com/questions/202303/2864228e8a387f3.png" />=60m，
即河宽为60m
</p><p>4、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 class="introTit">填空题</p><p>1、函数<img src="https://img2.meite.com/questions/202303/28642285dd68e2c.png" />的定义域是（）</p><p>答 案：<img src="https://img2.meite.com/questions/202303/28642285f367786.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/28642285fcec513.png" /><img src="https://img2.meite.com/questions/202303/2864228601aa2da.png" />所以函数<img src="https://img2.meite.com/questions/202303/286422860d8135c.png" />的定义域是<img src="https://img2.meite.com/questions/202303/286422861644b62.png" /></p><p>2、长方体的长、宽、高分别为2,3,6，则该长方体的对角线长为（）</p><p>答 案：7</p><p>解 析：由题可知长方体的底面的对角线长为<img src="https://img2.meite.com/questions/202303/1564116b1132166.png" />，则在由高、底面对角线、长方体的对角线组成的三角形中，长方体的对角线长为<img src="https://img2.meite.com/questions/202303/1564116b3811959.png" /></p>
