四川省雅安市2018届高三下学期三诊数学(文)试题

适用年级:高三
试卷号:644441

试卷类型:高考模拟
试卷考试时间:2018/4/28

1.单选题(共11题)

1.
已知集合,则(   )
A.B.C.D.
2.
偶函数f(x)在[0,+∞)单调递增,若f(-2)=1,则f(x-2)≤1的x的取值范围是(  )
A.[0,2]B.[-2,2]C.[0,4]D.[-4,4]
3.
表示不大于的最大整数,如,且,定义:.若,则的概率为(  )
A.B.C.D.
4.
若曲线与曲线在它们的公共点处具有公共切线,则实数(  )
A.B.C.D.
5.
将函数图象向左平移个单位,所得函数图象的一条对称轴的方程是(  )
A.B.C.D.
6.
已知向量,且,则(  )
A.B.C.D.
7.
执行如图的程序框图,如果输入,则输出的(  )
A.B.C.D.
8.
已知实数满足条件,若目标函数取得最大值时的最优解有无穷多个,则实数的值为(  )
A.B.C.D.
9.
如图,网格纸上小正方形的边长为,粗线画出的是某几何体的正视图(等腰直角三角形)、侧视图、俯视图.则该几何体的体积为(  )
A.B.C.D.
10.
是双曲线的左、右焦点,在双曲线的右支上存在一点,满足,则双曲线的离心率为( )
A.B.C.D.
11.
若复数满足,则的虚部是(  )
A.B.C.D.

2.选择题(共1题)

12.

    A famous study was done in a school by a professor from a university. At the start of the school year, the teachers were given the names of five children. They were told that these five were the most excellent students in the class. But the fact was that these students were only average, and they were not the best students at all. Well, guess what? At the end of the year, all the five average students scored among the highest in the class.
 What made these average students change so much to become top students? The only difference was the change in their teachers' attitude. Because the teachers believed that these five kids were the top students, they expected more from them. And so these five average students began to believe and expect more from themselves. So they worked harder to do as well as they could.
 Do you know why? If you expect the best from people, they'll usually want to give you their best. A great leader said, “Treat a person just how he appears to be on the outside, and you'll make him even worse. But treat a person like he's already a success, and you'll help make him the best he can be.”
 Like the true story of 7-year-old Johnny, his teacher got so angry with him that one day she said,“Johnny, you're the naughtiest boy in this class. I'm sure you'll never change.” The next year Johnny had a new teacher. And on the first day of class, she met with Johnny after school and said,“Johnny, I've heard a lot about you! But do you know that I don't believe a word of it.” And every day after that, this new teacher treated Johnny as if he was one of the smartest students even when Johnny did naughty things. Later on, Johnny became a school leader. Because that's the power of our belief and attitude toward children.

3.填空题(共4题)

13.
函数的最小值是__________.
14.
在锐角中,内角的对边分别为,且满足,若,则的取值范围是__________.
15.
观察下列式子:,…,根据以上式子可以猜想:_____.
16.
若圆锥与球的体积相等,且圆锥底面半径与球的直径相等,则圆锥侧面积与球面面积之比为    

4.解答题(共4题)

17.
设函数(其中).
(1)当时,求函数的单调区间;
(2)当时,讨论函数的零点个数.
18.
已知公差不为零的等差数列满足成等比数列,;数列满足.
(1)求数列的通项公式;
(2)记,求数列的前项和.
19.
如图,在四棱锥中,底面的中点,底面为直角梯形,,且

(1)求证:平面
(2)若与平面所成角的正弦值为,求四棱锥的体积.
20.
某校初一年级全年级共有名学生,为了拓展学生的知识面,在放寒假时要求学生在假期期间进行广泛的阅读,开学后老师对全年级学生的阅读量进行了问卷调查,得到了如图所示的频率分布直方图(部分已被损毁),统计人员记得根据频率直方图计算出学生的平均阅读量为万字.根据阅读量分组按分层抽样的方法从全年级人中抽出人来作进一步调查.

(1)在阅读量为万到万字的同学中有人的成绩优秀,在阅量为万到万字的同学中有人成绩不优秀,请完成下面的列联表,并判断在“犯错误概率不超过”的前提下,能否认为“学生成绩优秀与阅读量有相关关系”;
 
阅读量为万到万人数
阅读量为万到万人数
合计
成绩优秀的人数
 
 
 
成绩不优秀的人数
 
 
 
合计
 
 
 
 
(2)在抽出的同学中,1)求抽到被污染部分的同学人数;2)从阅读量在万到万字及万到万字的同学中选出人写出阅读的心得体会.求这人中恰有人来自阅读量是万到万的概率.
参考公式:,其中.
参考数据:














 
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:(4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