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河南省洛阳市2019届高三年级下学期第一次月考
数学（文）试题
（解析版）
第Ⅰ卷
一、选择题：本大题共12个小题，每小题5分，共60分.在每小题给出的四个选项中，只有一项是符合题目要求的.
1.设集合![](https://wkrtcs.bdimg.com/rtcs/image?w=117&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"117","h":"21","dataType":"png","c":"word/media/image1.png","imgOriW":245,"imgOriH":43})
，，则（ ）
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=36&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"36","h":"16","dataType":"png","c":"word/media/image4.png","imgOriW":76,"imgOriH":34})
B. C. D.
【答案】D
【解析】
【分析】
解一元二次不等式求得集合![](https://wkrtcs.bdimg.com/rtcs/image?w=8&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"8","h":"15","dataType":"png","c":"word/media/image8.png","imgOriW":18,"imgOriH":31})
的范围，然后求的交集，由此得出正确结论.
【详解】对于集合，由，解得，故，故选D.
【点睛】本小题主要考查两个集合的交集，考查一元二次不等式的解法，属于基础题.
2.已知复数![](https://wkrtcs.bdimg.com/rtcs/image?w=57&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"57","h":"35","dataType":"png","c":"word/media/image13.png","imgOriW":119,"imgOriH":73})
，其中，为虚数单位， 且，则
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=31&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"31","h":"15","dataType":"png","c":"word/media/image19.png","imgOriW":64,"imgOriH":31})
B. C. D.
【答案】A
【解析】
【分析】
由商的模等于模的商求解b的值．
【详解】由z![](https://wkrtcs.bdimg.com/rtcs/image?w=51&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"51","h":"35","dataType":"png","c":"word/media/image23.png","imgOriW":106,"imgOriH":73})
，得|z|，
即![](https://wkrtcs.bdimg.com/rtcs/image?w=38&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"38","h":"35","dataType":"png","c":"word/media/image25.png","imgOriW":81,"imgOriH":73})
，得b＝±25．
故选：A．
【点睛】本题考查复数模的求法，是基础题．
3.等差数列![](https://wkrtcs.bdimg.com/rtcs/image?w=23&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"23","h":"18","dataType":"png","c":"word/media/image26.png","imgOriW":49,"imgOriH":38})
中，为其前项和，若，，则（ ）
A. 32 B. 18 C. 14 D. 10
【答案】B
【解析】
【详解】设等差数列![](https://wkrtcs.bdimg.com/rtcs/image?w=26&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"26","h":"20","dataType":"png","c":"word/media/image32.png","imgOriW":55,"imgOriH":41})
的公差为 ,首项为,
因为![](https://wkrtcs.bdimg.com/rtcs/image?w=74&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"74","h":"18","dataType":"png","c":"word/media/image35.png","imgOriW":155,"imgOriH":38})
,
![](https://wkrtcs.bdimg.com/rtcs/image?w=143&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"143","h":"68","dataType":"png","c":"word/media/image36.png","imgOriW":298,"imgOriH":142})
,解得,
![](https://wkrtcs.bdimg.com/rtcs/image?w=261&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"261","h":"35","dataType":"png","c":"word/media/image38.png","imgOriW":545,"imgOriH":73})
,故选B.
【点睛】本题主要考查等差数列的前![](https://wkrtcs.bdimg.com/rtcs/image?w=8&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"8","h":"15","dataType":"png","c":"word/media/image28.png","imgOriW":16,"imgOriH":31})
项和公式,以及方程思想的应用,属于基础题. 等差数列基本量的运算是等差数列的一类基本题型,数列中的五个基本量一般可以“知二求三”,通过列方程组所求问题可以迎刃而解.
4.哈六中数学兴趣小组的同学们为了计算六中数学组二维码中黑色部分的面积,在如图一个边长为![](https://wkrtcs.bdimg.com/rtcs/image?w=7&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"7","h":"15","dataType":"png","c":"word/media/image40.png","imgOriW":16,"imgOriH":31})
的正方形区域内随机投掷个点,其中落入黑色部分的有个点,据此可估计黑色部分的面积为（ ）
![](https://wkrtcs.bdimg.com/rtcs/image?w=120&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"120","h":"131","dataType":"png","c":"word/media/image43.png","imgOriW":240,"imgOriH":261})
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=15&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"15","h":"15","dataType":"png","c":"word/media/image44.png","imgOriW":31,"imgOriH":31})
B. C. D.
【答案】C
【解析】
【分析】
设黑色部分的面积为![](https://wkrtcs.bdimg.com/rtcs/image?w=7&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"7","h":"15","dataType":"png","c":"word/media/image48.png","imgOriW":15,"imgOriH":31})
,利用几何概型概率计算公式列出方程能估计黑色部分的面积.
【详解】设黑色部分的面积为,
![](https://wkrtcs.bdimg.com/rtcs/image?w=14&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"14","h":"15","dataType":"png","c":"word/media/image49.png","imgOriW":29,"imgOriH":31})
正方形二维码边长为4,
在正方形区域内随机投掷400个点,其中落入黑色部分的有225个点,
![](https://wkrtcs.bdimg.com/rtcs/image?w=82&md5sum=c042ed337ff403f329f1962d24f9aba1&sign=7d9a2d4a37&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=199&ipr={"t":"img","w":"82","h":"35","dataType":"png","c":"word/media/image50.png","imgOriW":171,"imgOriH":73})
,解得,
据此可估计黑色部分的面积为9,故选C.
【点睛】本题主要考查几何概型概率公式以及模拟实验的基本应用,属于简单题,求不规则图形的面积的主要方法就是利用模拟实验,列出未知面积与已知面积之间的方程求解.
本文来源：https://www.2haoxitong.net/k/doc/98d9f298df80d4d8d15abe23482fb4daa48d1d72.html
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