2014届北京市朝阳二模理科数学试卷

适用年级:高三
试卷号:532515

试卷类型:高考模拟
试卷考试时间:2017/7/19

1.单选题(共5题)

1.
已知集合,集合,则( )
A.
B.
C.
D.
2.
已知命题:复数在复平面内所对应的点位于第四象限;命题,则下列命题中为真命题的是( )
A.B.C.D.
3.
已知函数)的部分图象如图所示,则()

A.B.C.D.
4.
若双曲线的一条渐近线与圆至多有一个交点,则双曲线离心率的取值范围是()
A.B.C.D.
5.
执行如图所示的程序框图,若输出的结果为2,则输入的正整数的可能取值的集合是
A.B.
C.D.

2.选择题(共12题)

6.Ice—cream tastes _____, but it isn't good _____ our health.
7.完型填空

先通读下面短文,掌握大意,然后在所给的四个选项中选出一个最佳答案。

    About 70,000,000 Americans are trying to lose weight(减肥). That is almost 1 out of every 3 people in the United States. Some people eat 1 food and they hardly have any fats or sweets. Others do running, exercise with machines (机器), take medicines, or even have operations (手术).2 you can see losing weight is 3 work, and it will also cost a lot of money. But 4 do so many people in the United States want to lose weight?

    Many people in the United States worry about their look of the body. For many people, looking nice also means to be 5. Other people worry about their health as many doctors 6 overweight is not good.

    Most people want to find an 7 way to take off fat, and books of this kind are very popular. These books tell people how to lose weight. Each year a lot of new books like these are 8. Each one says it can easily help people take fat away.

    Losing weight can be 9. Some overweight people go to health centres, like La Costa in California. Men and women 10 some hundred dollars a day at these health centres. People live there for one week or two,11 exercise, eating different foods. Meals there may be just a little. All these work for losing weight.12 4 days on it, one woman , Mrs. Warren lost 5 pounds (2.27kg). At $ 400 a day, she spent $ 320 to lose each pound. But she said she was still 13 to do so.

    Health centres, books, medicines, operations, running and exercise machines all 14 a lot of money. So in the United States, losing weight may mean losing15 too.

8.Sally _____ a very interesting country. She often gets up _____ night.
9.Sally _____ a very interesting country. She often gets up _____ night.
10.My sister doesn't like rice _____ dumplings, _____ she likes beef _____ tomato noodles.
11.Go straight and _____ left. The hospital is next to the post office.
12.阅读理解

    Miss White is in Beijing on vacation. Here is her hotel card. Have a look at it and answer the questions.

Welcome to Garden Hotel

Garden Hotel


Happy   Street


Phone

Number:83645792

Email:www.gardenhotel.com

Buses to: Bus No. 103

        Bus No. 395

        Bus No. 39


Park

Bank

13.My brother doesn't wear a coat. He often _____ a white T—shirt.
14.My brother doesn't wear a coat. He often _____ a white T—shirt.
15.My brother doesn't wear a coat. He often _____ a white T—shirt.
16.Please find out the different pronunciation ____?
17.Please find out the different pronunciation ____?

3.填空题(共2题)

18.
由两个四棱锥组合而成的空间几何体的三视图如图所示,则其体积是   ;表面积是  
19.
的展开式中项的系数为___.(用数字表示)

4.解答题(共5题)

20.
已知函数
(Ⅰ)若曲线在点处的切线与直线垂直,求的值;
(Ⅱ)求函数的单调区间;
(Ⅲ)设,当时,都有成立,求实数的取值范围.
21.
如图,在四棱锥中,底面是正方形,侧面底面分别为中点,

(Ⅰ)求证:∥平面
(Ⅱ)求二面角的余弦值;
(Ⅲ)在棱上是否存在一点,使平面?若存在,指出点的位置;若不存在,说明理由.
22.
已知椭圆的中心在原点,焦点在轴上,离心率为,右焦点到右顶点的距离为
(Ⅰ)求椭圆的标准方程;
(Ⅱ)是否存在与椭圆交于两点的直线,使得成立?若存在,求出实数的取值范围,若不存在,请说明理由.
23.
某市教育部门规定,高中学生三年在校期间必须参加不少于80小时的社区服务.教育部门在全市随机抽取200位学生参加社区服务的数据,按时间段,,,,(单位:小时)进行统计,其频率分布直方图如图所示.

(1)求抽取的200位学生中,参加社区服务时间不少于90小时的学生人数,并估计从全市高中学生中任意选取一人,其参加社区服务时间不少于90小时的概率;
(2)从全市高中学生(人数很多)中任意选取3位学生,记为3位学生中参加社区服务时间不少于90小时的人数.试求随机变量的分布列和数学期望
24.
已知是函数的两个零点,其中常数,设
(Ⅰ)用表示
(Ⅱ)求证:
(Ⅲ)求证:对任意的
试卷分析
  • 【1】题量占比

    单选题:(5道)

    选择题:(12道)

    填空题:(2道)

    解答题:(5道)

  • 【2】:难度分析

    1星难题:0

    2星难题:0

    3星难题:0

    4星难题:0

    5星难题:0

    6星难题:0

    7星难题:0

    8星难题:0

    9星难题:12