2017-2018学年广东省广州八十九中高二（上）期末数学试卷（文科）
一、填空题（每小题5分，共60分）
1．（5分）已知集合A={x|x2﹣2x≤0}，B={x|﹣1＜x＜1}，则A∩B=（ ）
A．{x|0≤x＜1} B．{x|﹣1＜x≤0} C．{x|﹣1＜x＜1} D．{x|﹣1＜x≤2}
2．（5分）设命题p：∃n∈N，n2＞2n，则￢p为（ ）
A．∀n∈N，n2＞2n B．∃n∈N，n2≤2n C．∀n∈N，n2≤2n D．∃n∈N，n2=2n
3．（5分）设a，b是实数，则“a+b＞0”是“ab＞0”的（ ）
A．充分不必要条件 B．必要不充分条件
C．充分必要条件 D．既不充分也不必要条件
4．（5分）已知向量![](https://wkrtcs.bdimg.com/rtcs/image?w=76&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"76","h":"22","dataType":"png","c":"word/media/image1.png","imgOriW":76,"imgOriH":22})
，，且∥，则的值为（ ）
A．13 B．14 C．![](https://wkrtcs.bdimg.com/rtcs/image?w=28&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"28","h":"18","dataType":"png","c":"word/media/image6.png","imgOriW":28,"imgOriH":18})
D．
5．（5分）已知{an}为等比数列，a4+a7=2，a5a6=﹣8，则a1+a10=（ ）
A．7 B．5 C．﹣5 D．﹣7
6．（5分）如图，一个简单空间几何体的三视图其主视图与侧视图都是边长为2的正三角形，俯视图轮廓为正方形，则此几何体的表面积是（ ）
![](https://wkrtcs.bdimg.com/rtcs/image?w=149&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"149","h":"154","dataType":"png","c":"word/media/image8.png","imgOriW":149,"imgOriH":154})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=46&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"46","h":"18","dataType":"png","c":"word/media/image9.png","imgOriW":46,"imgOriH":18})
B．12 C． D．8
7．（5分）如表是某厂1﹣4月份用水量（单位：百吨）的一组数据：
月份x | 1 | 2 | 3 | 4 |
用水量 | 4.5 | 4 | 3 | 2.5 |
由散点可知，用水量y与月份x之间有较好的线性相关关系，其线性回归方程是![](https://wkrtcs.bdimg.com/rtcs/image?w=10&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"10","h":"32","dataType":"png","c":"word/media/image11.png","imgOriW":10,"imgOriH":32})
=﹣0.7x+a，则a等于（ ）
A．5.1 B．5.25 C．5.3 D．5.4
8．（5分）函数![](https://wkrtcs.bdimg.com/rtcs/image?w=85&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"85","h":"35","dataType":"png","c":"word/media/image12.png","imgOriW":85,"imgOriH":35})
的零点所在的区间为（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=57&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"57","h":"35","dataType":"png","c":"word/media/image13.png","imgOriW":57,"imgOriH":35})
B． C． D．
9．（5分）已知双曲线C：![](https://wkrtcs.bdimg.com/rtcs/image?w=22&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"22","h":"46","dataType":"png","c":"word/media/image17.png","imgOriW":22,"imgOriH":46})
﹣=1（a＞0，b＞0）的离心率为，则C的渐近线方程为（ ）
A．y=±![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"13","h":"35","dataType":"png","c":"word/media/image20.png","imgOriW":13,"imgOriH":35})
x B．y=±x C．y=±x D．y=x
10．（5分）已知log2a＞log2b，则下列不等式一定成立的是（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=44&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"44","h":"35","dataType":"png","c":"word/media/image23.png","imgOriW":44,"imgOriH":35})
B．log2（a﹣b）＞0 C． D．2a﹣b＜1
11．（5分）已知F1，F2分别是双曲线C：![](https://wkrtcs.bdimg.com/rtcs/image?w=22&md5sum=cacd6641f3a9076739d3bc86fb5e295e&sign=97d9f179cc&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=113&ipr={"t":"img","w":"22","h":"46","dataType":"png","c":"word/media/image25.png","imgOriW":22,"imgOriH":46})
﹣=1（a，b＞0）的左、右焦点，点P在C上，若PF1⊥F1F2，且PF1=F1F2，则C的离心率是（ ）
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