2015-2016年天津市六校联考高三(上)期末数学试卷和答案(理科)

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一、选择题（本大题共8小题，每小题5分，满分40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．（5分）设全集U={1，2，3，4，5，6，7}，M={2，3，4，6}，N={1，4，5}，则{1，5}等于（）

A．M∪N B．M∩N C．（?U M）∩N D．M∩?U N

2．（5分）若{b n}满足约束条件，则z=x+2y的最小值为（）

A．3 B．4 C．7 D．2

3．（5分）执行如图的程序框图，那么输出S的值是（）

A．2 B．C．1 D．﹣1

4．（5分）如图，点A，B，C是圆O上的点，且AB=2，BC=，∠CAB=120°，则∠AOB对应的劣弧长为（）

A．πB．C．D．

5．（5分）在△ABC中，a、b、c分别为角A、B、C所对的边，cosA=，b=2，面积S=3，则a为（）

A．B． C． D．

6．（5分）给出下列命题：

①若a，b，m都是正数，且，则a＜b；

②若f'（x）是f（x）的导函数，若?x∈R，f'（x）≥0，则f（1）＜f（2）一定成立；

③命题“?x∈R，x2﹣2x+1＜0”的否定是真命题；

④“|x|≤1，且|y|≤1”是“|x+y|≤2”的充分不必要条件．

其中正确命题的序号是（）

A．①②③B．①②④C．②③④D．①③④

7．（5分）已知双曲线与抛物线y2=2px（p＞0）的交点

为：A、B，A、B连线经过抛物线的焦点F，且线段AB的长等于双曲线的虚轴长，则双曲线的离心率为（）

A．+1 B．3 C．D．2

8．（5分）已知定义在R上的函数，当x∈[0，2]时，f（x）=8（1﹣|x﹣1|），且对任意的实数x∈[2n﹣2，2n+1﹣2]（n∈N*，且n≥2），都有f（x）=，若方程f（x）=|log a x|有且仅有四个实数解，则实数a的取值范围为（）A．B．C．（2，10）D．[2，10]

二、填空题（本大题共6小题，每小题5分，共30分.把答案填在答题卡中的相应横线上）

9．（5分）若复数的实部和虚部互为相反数，则b=．

10．（5分）如果（3x﹣）n的展开式中各项系数之和为128，则展开式中

的系数是．

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