广东省深圳市宝安区2019-2020学年高二上学期期末数学试题

适用年级:高二
试卷号:592772

试卷类型:期末
试卷考试时间:2020/1/29

1.单选题(共11题)

1.
等差数列的首项为,且从第10项开始为比1大的项,则公差d的取值范围是
A.B.C.D.
2.
已知是首项为32的等比数列,是其前n项和,且,则数列前10项和为
A.58B.56C.50D.45
3.
数列中,,且数列是等差数列,则等于(   )
A.B.C.D.
4.
在等差数列中,,则201是该数列的第项.
A.60B.61C.62D.63
5.

   空间四边形ABCD的四边相等,则它的两对角线ACBD的关系是 (  )

A.垂直且相交B.相交但不一定垂直
C.垂直但不相交D.不垂直也不相交
6.
经过点且在两坐标轴上截距相等的直线是(   )
A.B.C.D.
7.
已知抛物线上的点A到焦点F距离为4,若在y轴上存点使得,则该抛物线的方程为
A.B.C.D.
8.
方程所表示的图形是
A.前后两者都是一条直线和一个圆B.前后两者都是两点
C.前者是一条直线和一个圆,后者是两点D.前者是两点,后者是一条直线和一个圆
9.
直线关于直线对称的直线方程是
A.B.
C.D.
10.
直线的倾斜角的取值范围是
A.B.C.D.
11.

   焦点在y轴上的椭圆mx2y2=1的离心率为,则m的值为(  )

A.1B.2
C.3D.4

2.选择题(共1题)

12.

阅读下面短文,用括号内所给动词的适当形式填空。(必要时可加情态动词或助动词)
   Once there was a baby eagle {#blank#}1{#/blank#} (live) in a nest on a cliff(山崖). The baby eagle loved his nest. It was warm, soft and comfortable. And even better, he had all the food and love that his mother could give. Whenever the baby eagle was hungry, his mother would always come just in time with the delicious food he liked.
   He {#blank#}2{#/blank#}  (grow) happily day after day. But suddenly his world changed. His mother stopped {#blank#}3{#/blank#}  (come) to the nest. He was full of sadness and fear. He thought he{#blank#}4{#/blank#}  (die) soon. He cried, but nobody heard him.
   Two days later his mother appeared with some nice food. The baby eagle was wild with joy. But his mother {#blank#}5{#/blank#}  (put) the food at the top of the mountain and then looked down at her baby. The baby eagle cried out. “Mum, why did you do this to me? I’m hungry. Don’t you know I will die if I have nothing {#blank#}6{#/blank#} (eat)?”
   “Here{#blank#}7{#/blank#} (be) the last meal I give you. Come and get it by yourself, ”his mother said. Then she flew down and pushed the baby eagle out of the nest.
   The baby eagle {#blank#}8{#/blank#} (fall) down, faster and faster. He looked up at his mum, “Why do you abandon me?” He looked down at the earth. The ground was much closer. Then something strange happened. The air caught behind his arms and he began{#blank#}9{#/blank#} (fly)! He wasn’t moving to the ground any more. Instead, his eyes were pointed up at the sun.
   “You{#blank#}10{#/blank#} ( fly)! You can make it!” His mother smiled.

3.填空题(共4题)

13.
《九章算术》“竹九节”问题:现有一根9节的竹子,自上而下各节的容积成等差数列,上面4节的容积共3升,下面3节的容积共4升,则第5节的容积为  升;
14.
设等差数列满足的前n项和的最大值为M,则______.
15.
设函数,利用课本中推导等差数列前项和公式的方法,可求得_______________
16.
分别是椭圆的左、右焦点,若在直线上存在点,使线段的中垂线过点,则椭圆的离心率的取值范围是__________.

4.解答题(共5题)

17.
已知四棱锥的底面为直角梯形,底面,且的中点.

(1)证明:面
(2)求夹角的余弦值;
(3)求面与面所成二面角余弦值的大小.
18.
如图所示,在长方体ABCDA1B1C1D1中,ABAD=1,AA1=2,M是棱CC1的中点.证明:平面ABM⊥平面A1B1M
19.
已知点,点P为平面上的动点,过点P作直线l的垂线,垂足为Q,且
求动点P的轨迹C的方程;
设点P的轨迹Cx轴交于点M,点AB是轨迹C上异于点M的不同的两点,且满足,求的取值范围.
20.
设椭圆的中心是坐标原点,长轴在x轴上,离心率,已知点到椭圆的最远距离是,求椭圆的标准方程.
21.
已知为圆上的动点,为定点,
(1)求线段中点M的轨迹方程;
(2)若,求线段中点N的轨迹方程.
试卷分析
  • 【1】题量占比

    单选题:(11道)

    选择题:(1道)

    填空题:(4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:20