山西省实验中学2017-2018学年高二上学期10月月考数学(理)试卷

适用年级:高二
试卷号:599958

试卷类型:月考
试卷考试时间:2017/10/27

1.选择题(共6题)

1.亚硝酸钠又称为“工业盐”,在新闻报道中常出现因误食工业盐而导致中毒的事件,下列关于亚硝酸钠的叙述不正确的是(   )
2.亚硝酸钠又称为“工业盐”,在新闻报道中常出现因误食工业盐而导致中毒的事件,下列关于亚硝酸钠的叙述不正确的是(   )
3.解方程:
4.

根据短文内容,选择正确答案。

D

    More and more people like bicycling and it is no surprise. It is fun, healthy and good for the environment. Maybe that's why there are 1.4 billion bicycles and only 400 million ears on roads worldwide today. Bikes can take you almost anywhere, and there is no oil cost!

    Get on a bicycle and ride around your neighbourhood. You may discover something new all around you. Stopping and getting off a bike is easier than stopping and getting out of your car. You can bike to work and benefit(受益) from the enjoyable exercise without polluting the environment. You don't even have to ride all the way.

    Folding(折叠) bikes work well for people who ride the train. Just fold the bike and take it with you. You can do the same on an airplane. A folding bike can be packed in a suitcase. You can also take a common bike with you when you fly. But be sure to look for information by getting on airline websites. Not all airlines are bicycle-friendly to travelers.

    Health Benefits of Bicycling:

    It helps to prevent heart diseases.

    Bicycling helps to control your weight.

    A 15-minute bike ride to and from work three times a week burns off five kilos of fat in a year.

    Bicycling can improve your mood(心情).

    Exercise like bicycling has been shown to make people feel better, more relaxed and self-confident.

    Bicycling is healthier than driving.

5.

根据短文内容,选择正确答案。

D

    More and more people like bicycling and it is no surprise. It is fun, healthy and good for the environment. Maybe that's why there are 1.4 billion bicycles and only 400 million ears on roads worldwide today. Bikes can take you almost anywhere, and there is no oil cost!

    Get on a bicycle and ride around your neighbourhood. You may discover something new all around you. Stopping and getting off a bike is easier than stopping and getting out of your car. You can bike to work and benefit(受益) from the enjoyable exercise without polluting the environment. You don't even have to ride all the way.

    Folding(折叠) bikes work well for people who ride the train. Just fold the bike and take it with you. You can do the same on an airplane. A folding bike can be packed in a suitcase. You can also take a common bike with you when you fly. But be sure to look for information by getting on airline websites. Not all airlines are bicycle-friendly to travelers.

    Health Benefits of Bicycling:

    It helps to prevent heart diseases.

    Bicycling helps to control your weight.

    A 15-minute bike ride to and from work three times a week burns off five kilos of fat in a year.

    Bicycling can improve your mood(心情).

    Exercise like bicycling has been shown to make people feel better, more relaxed and self-confident.

    Bicycling is healthier than driving.

6.

研究历史讲究“论从史出”。下面是影响人类历史发展进程的一些重大事件,其中结论和史实不相符的是(   )

2.单选题(共6题)

7.
下列说法正确的是(   )
A.有一个面是多边形,其余各面都是三角形,由这些面围成的几何体是棱锥
B.有两个面平行且相似,其余各面都是梯形的多面体是棱台
C.如果一个棱锥的各个侧面都是等边三角形,那么这个棱锥可能为六棱锥
D.有两个相邻侧面是矩形的棱柱是直棱柱
8.
一个空间几何体的三视图如图所示,则该几何体的体积为( )
A.B.C.40D.80
9.
如图,已知四边形的直观图是一个边长为 1 的正方形,则原图形的周长为(   )
A.B.6C.8D.
10.
下列命题中错误的是(   )
A.如果平面不垂直于平面,那么平面内一定不存在直线垂直于平面
B.如果平面平面,平面平面,那么平面
C.不存在四个角都是直角的空间四边形
D.空间图形经过中心投影后,直线还是直线,但平行直线可能变成相交的直线
11.
直四棱柱内接于半径为的半球,四边形为正方形,则该四棱柱的体积最大时,的长是(   )
A.1B.C.D.2
12.
如图,在直三棱柱中,,过的中点作平面的垂线,交平面,则与平面所成角的正切值为()
A.B.C.D.

3.填空题(共7题)

13.
如图,在棱长为的正方体中,点分别是棱的中点,是侧面内一点,若平行于平面,则线段长度的取值范围是_________.
14.
如图,正方体的棱长为1,PBC的中点,Q为线段上的动点,过点A,P,Q的平面截该正方体所得的截面记为S.则下列命题正确的是_________(写出所有正确命题的编号). ①当时,S为四边形;②当时,S为等腰梯形;③当时,S的交点R满足;④当时,S为六边形;⑤当时,S的面积为.
15.
如图,在三棱锥中,,且平面,过作截面分别交,且二面角的大小为,则截面面积的最小值为 .
16.
,的中点,将沿折叠,使之间的距离为1,则三棱锥外接球的体积为__________.
17.
若一条直线与一个正四棱柱各个面所成的角都为,则=_____.
18.
在棱长为1的正方体中,的中点,的中点,为平面的中心,过作一直线与交于,与交于,则的长为__________.
19.
如图,在正方体中,分别是的中点,则异面直线所成角的大小是____________.

4.解答题(共3题)

20.
(本小题共12分)
如图,在直三棱柱中,,点的中点,

(1)求证:平面
(2)求证:平面
21.
如图,在四棱锥中,平面,,为线段上的点,
 
(1)证明:平面
(2)若的中点,求与平面所成的角的正切值;
(3)若满足,求的值.
22.
已知四棱锥的底面为直角梯形,底面,且的中点.

(1)证明:平面平面
(2)求二面角的余弦值.
试卷分析
  • 【1】题量占比

    选择题:(6道)

    单选题:(6道)

    填空题:(7道)

    解答题:(3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:16