2024年成考高起点《数学(理)》每日一练试题05月08日

聚题库

05/08

单选题1、设集合M={x||x-2|＜1}，N={x|x＞2}，则M∩N=（）<ul><li>A：{x|1＜x＜3}</li><li>B：{x|x＞2}</li><li>C：{x|2＜x＜3}</li><li>D：{x|1＜x＜2}</li></ul>答案：C解析：M={x||x-2|＜1}解得{x|-1＜x-2＜1}={x|1＜x＜3}，故M∩N={x|2＜x＜3}2、袋中有6个球，其中4个红球，2个白球，从中随机取出2个球，则其中恰有1个红球的概率为（）<ul><li>A：<img src='https://img2.meite.com/questions/202303/15641165c5e79d0.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/15641165cb7ed67.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/15641165d0b1aa2.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/15641165d3de24c.png' /></li></ul>答案：A解析：<img src="https://img2.meite.com/questions/202303/1564116ab1b1548.png" />3、<img src="https://img2.meite.com/questions/202303/2864225b891ad2c.png" />展开式中,末3项的系数(a,x 均未知) 之和为() <ul><li>A：22</li><li>B：12</li><li>C：10</li><li>D：-10</li></ul>答案：C解析：<img src="https://img2.meite.com/questions/202303/2864225bbb4b976.png" /><img src="https://img2.meite.com/questions/202303/2864225bc299c02.png" /><img src="https://img2.meite.com/questions/202303/2864225bcaa8096.png" />末三项数之和为<img src="https://img2.meite.com/questions/202303/2864225bdfc7788.png" /><img src="https://img2.meite.com/questions/202303/2864225beaa0cc1.png" />4、已知α∩β=a，b⊥β，b在α内的射影是b’，那么b'和α的关系是（）<ul><li>A：b'//α</li><li>B：b'⊥α</li><li>C：b'与α是异面直线</li><li>D：b'与α相交成锐角</li></ul>答案：B解析：<img src="https://img2.meite.com/questions/202303/28642296837771f.png" /> ∴由三垂线定理的逆定理知,b在α内的射影b'⊥α，故选B 主观题1、已知函数f(x)=(x-4)(x2-a) （I）求f"(x)； (Ⅱ)若f"(-1)=8，求f(x)在区间[0，4]的最大值与最小值答案：<img src="https://img2.meite.com/questions/202404/1966222f3f733cc.png" /><img src="https://img2.meite.com/questions/202404/1966222f47c8e62.png" />2、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 答案：<img src="https://img2.meite.com/questions/202303/2864224be4311f4.png" /><img src="https://img2.meite.com/questions/202303/2864224bee67713.png" />3、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" /> 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" /> 4、已知a,b,c成等差数列，a,b,c+1成等比数列．若b=6，求a和c．答案：由已知得<img src="https://img2.meite.com/questions/202303/1564116c009cc19.png" />解得<img src="https://img2.meite.com/questions/202303/1564116c0e039c1.png" />填空题1、函数y=-x2+ax图像的对称轴为x=2，则a=______。 答案：4解析：本题主要考查的知识点为二次函数的性质由题意，该函数图像的对称轴为<img src="https://img2.meite.com/questions/202404/1966222eb326e16.png" />2、过点（2，0）作圆x2+y2=1的切线，切点的横坐标为（）。答案：<img src="https://img2.meite.com/questions/202404/20662380f056b37.png" />解析：本题主要考查的知识点为圆的切线. 设切点(x0,y0)则有<img src="https://img2.meite.com/questions/202404/20662380f985f55.png" /> 即<img src="https://img2.meite.com/questions/202404/20662381033a418.png" /><img src="https://img2.meite.com/questions/202404/206623810c425f9.png" />所以<img src="https://img2.meite.com/questions/202404/2066238119981c7.png" />故切点横坐标为<img src="https://img2.meite.com/questions/202404/206623812263a88.png" />