2024年成考高起点《数学(文史)》每日一练试题04月19日
聚题库
04/19
<p class="introTit">单选题</p><p>1、<img src="https://img2.meite.com/questions/202303/296423ae3b8e9f8.png" />（）
</p><ul><li>A：8</li><li>B：14</li><li>C：12</li><li>D：10</li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202303/296423af026b95d.png" /><img src="https://img2.meite.com/questions/202303/296423af118d116.png" /></p><p>2、<img src="https://img2.meite.com/questions/202303/296423ea22da2e2.png" />的导数是
</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/296423ea2f6b759.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/296423ea33c9ac3.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/296423ea38d76fe.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/296423ea3eba056.png' /></li></ul><p>答 案：C</p><p>解 析：<img src="https://img2.meite.com/questions/202303/296423ea9fad218.png" /><img src="https://img2.meite.com/questions/202303/296423eaa663cb6.png" /><img src="https://img2.meite.com/questions/202303/296423eaada74c7.png" /></p><p>3、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，则这2个球都为红球的概率为（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/14641029ef82334.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/14641029f638ea8.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/14641029fcde88d.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/1464102a010d677.png' /></li></ul><p>答 案：C</p><p>解 析：两个球都是红球的概率为<img src="https://img2.meite.com/questions/202303/146410317f5ded5.png" /></p><p>4、命题甲:x>y且xy>0,命题乙：<img src="https://img2.meite.com/questions/202303/296423aa88de569.png" />则（）
</p><ul><li>A：甲是乙的充分条件,但不是必要条件</li><li>B：甲是乙的必要条件，但不是充分条件</li><li>C：甲是乙的充分必要条件</li><li>D：甲不是乙的必要条件也不是乙的充分条件</li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202303/296423aabe64820.png" /><img src="https://img2.meite.com/questions/202303/296423aac4c7280.png" /><img src="https://img2.meite.com/questions/202303/296423aacbc46fc.png" /><img src="https://img2.meite.com/questions/202303/296423aacfe951a.png" /></p><p class="introTit">主观题</p><p>1、在△ABC中,已知三边 a、b、c 成等差数列,且最大角∠A是最小角的2倍, a: b :c.
</p><p>答 案：<img src="https://img2.meite.com/questions/202303/296423b0ae0659d.png" /></p><p>2、设函数<img src="https://img2.meite.com/questions/202303/1564111c65679ad.png" /><br />(I）求f'(2)；<br />(II）求f(x）在区间[一1,2]的最大值与最小值．</p><p>答 案：(I）因为<img src="https://img2.meite.com/questions/202303/1564111dd4eb139.png" />，所以f'(2)=3×2<sup>2</sup>-4=8.(II）因为x＜-1，f(-1)=3.<img src="https://img2.meite.com/questions/202303/1564111ea39de57.png" />f(2)=0.<br />所以f(x）在区间[一1,2]的最大值为3，最小值为<img src="https://img2.meite.com/questions/202303/1564111eb99e49a.png" /></p><p>3、设函数f(x)<img src="https://img2.meite.com/questions/202303/296423a66bbdb95.png" />且f'(-1)=-36
(Ⅰ)求m
(Ⅱ)求f(x)的单调区间</p><p>答 案：(Ⅰ)由已知得f'=<img src="https://img2.meite.com/questions/202303/296423a74f41b7f.png" /> 又由f'(-1)=-36得
6-6m-36=-36
故m=1.
(Ⅱ)由(Ⅰ)得f'(x)=<img src="https://img2.meite.com/questions/202303/296423a792d1aff.png" />
令f'(x)=0，解得<img src="https://img2.meite.com/questions/202303/296423a7b14cf3f.png" />
当x<-3时，f'(x)>0;
当-3<x<2时，f'(x)<0;
当x>2时，f'(x)>0;
故f(x)的单调递减区间为(-3,2)，f(x)的单调递增区间为(-∞,-3),(2,+∞)
</p><p>4、已知直线l的斜率为1，l过抛物线C：<img src="https://img2.meite.com/questions/202303/1564111c54b8a1f.png" />的焦点，且与C交于A,B两点.<br />(I）求l与C的准线的交点坐标；<br />(II）求|AB|．</p><p>答 案：(I）C的焦点为<img src="https://img2.meite.com/questions/202303/1564111ce1ece45.png" />，准线为<img src="https://img2.meite.com/questions/202303/1564111cf077c15.png" />由题意得l的方程为<img src="https://img2.meite.com/questions/202303/1564111d17b9087.png" />因此l与C的准线的交点坐标为<img src="https://img2.meite.com/questions/202303/1564111d41e334d.png" />(II）由<img src="https://img2.meite.com/questions/202303/1564111d60deac4.png" />得<img src="https://img2.meite.com/questions/202303/1564111d70ccff6.png" />设A（x1,y1）.B（x2,y2），则<img src="https://img2.meite.com/questions/202303/1564111da85efe1.png" />因此<img src="https://img2.meite.com/questions/202303/1564111db86701f.png" /></p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202303/1464102a1d5eac7.png" />（）</p><p>答 案：3</p><p>解 析：<img src="https://img2.meite.com/questions/202303/14641031bbc80a1.png" /></p><p>2、函数y=<img src="https://img2.meite.com/questions/202303/296423a650306d1.png" />的定义域是（）</p><p>答 案：[1,+∞)</p><p>解 析：要是函数y=<img src="https://img2.meite.com/questions/202303/296423a6e097a67.png" />有意义，需使<img src="https://img2.meite.com/questions/202303/296423a6f397863.png" /><img src="https://img2.meite.com/questions/202303/296423a703abb7f.png" /> 所以函数的定义域为{x|x≥1}=[1,+∞)
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