江苏省盐城市龙冈中学2016-2017学年高一下学期期中考试数学试题

适用年级:高一
试卷号:573778

试卷类型:期中
试卷考试时间:2017/7/3

1.选择题(共1题)

1.通读全文, 根据短文内容理解, 选择最佳答案填空。  
    After Mom died, I began visiting Dad every morning before I went to work. He was weak. He always put a glass of 1 on the kitchen table for me, with a note reading, "Drink your juice."
    As a kid, I once 2 Mom, "Why doesn't Dad love me?" Mom asked me, "3? Why do you think so?" "Well, he never tells me," I said. "But 4, how hard he works to take care of us. That's how he 5 his love."
    Many years later, after drinking the juice, I hugged(拥抱) my father and said, "I love you, Dad." From then on, I did that every 6. My father never told me how he felt about my hugs.
    Then one day, I didn't hug him and just 7 towards the door. Dad said, "Well?"
    "Well, what?" I asked. "Well……" he said again, holding out his    8. Then I hugged him, and told him, "I'm fifty years old, Dad. You've  9 told me you love me." A minute later, Dad said, "All right! I 10 you." Although he spoke in a very low voice, I heard it clearly.

2.填空题(共13题)

2.
已知α∈,且cos α=-,则tan=__________.
3.
已知cos α=,α∈,那么sin 2α=__________.
4.
若tan θ=-,则cos 2θ=__________.
5.
设a=cos 2°-sin 2°,b=,c=,则a,b,c的大小关系为__________.
6.
在△ABC中,内角A,B,C所对的边分别是a,b,c.若3a=2b,则的值为________.
7.
在△ABC中,若,则△ABC的形状是__________.
8.
等差数列的前n项和为,若____
9.
在等比数列中,,则_________.
10.
设Sn为等差数列{an}的前n项和,已知S5=5,S9=27,则S7=
11.
设Sn是等差数列{an}的前n项和,若a1+a3+a5=3,则S5=__________;
12.
各项均为正偶数的数列中,前三项依次成为公差为的等差数列,后三项依次成为公比为的等比数列,若,则的所有可能的值构成的集合为
13.
设m,n是两条不同的直线,α,β,γ是三个不重合的平面,给出下列四个命题:

① 若β∥γ,α∥γ,则α∥β;② 若α⊥β,m∥α,则m⊥β;

③ 若m⊥α,m∥β,则α⊥β;④ 若m∥n,nα,则m∥α.

其中正确的命题是________.(填序号)

14.
设a,b是不同的直线,α,β是不同的平面,则下列四个命题中正确的是________.(填序号)

① 若a⊥b,a⊥α,则b∥α;② 若a∥α,α⊥β,则a⊥β;

③ 若a⊥β,α⊥β,则a∥α;④ 若a⊥b,a⊥α,b⊥β,则α⊥β.

3.解答题(共6题)

15.
(本小题满分16分)如图,有一直径为8米的半圆形空地,现计划种植甲、乙两种水果,已知单位面积种植甲水果的经济价值是种植乙水果经济价值的5倍,但种植甲水果需要有辅助光照.半圆周上的处恰有一可旋转光源满足甲水果生长的需要,该光源照射范围是,点在直径上,且

(1)若,求的长;
(2)设, 求该空地产生最大经济价值时种植甲种水果的面积.
16.
已知α∈,sin α=.

(1)求sin的值;

(2)求cos的值.

17.
已知数列{an}的前n项和Sn=3n2+8n,{bn}是等差数列,且an=bn+bn1.

(1)求数列{bn}的通项公式;

(2)令cn,Tn是数列{cn}的前n项和,求证:

18.
已知等比数列{an}的公比q>1,且满足a2+a3+a4=28,且a3+2是a2,a4的等差中项.

(1)求数列{an}的通项公式;

    (2)若bn=log,Sn=b1+b2+…+bn,求使成立的正整数n的最大值.
19.

在四棱锥P-ABCD中,BC∥AD,PA⊥PD,AD=2BC,AB=PB, E为PA的中点. 

(1)求证:BE∥平面PCD;
(2)求证:平面PAB⊥平面PCD.
20.
如图,在三棱柱ABCA1B1C1中, CC1⊥平面ABC, AC⊥BC, AB1的中点为D,B1C∩BC1
A.求证:

(1)DE∥平面AA1C1C;
(2)AC⊥平面BCC1B1.
试卷分析
  • 【1】题量占比

    选择题:(1道)

    填空题:(13道)

    解答题:(6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:19