人教B版高中数学必修三同步测试:3.3 随机数的含义与应用

适用年级:高二
试卷号:617298

试卷类型:课时练习
试卷考试时间:2018/3/27

1.单选题(共7题)

1.
在面积为S的△ABC的边AB上任取一点P,则△PBC的面积大于的概率是(  )
A.B.C.D.
2.
在区间上随机地取一个数,则事件“”发生的概率为(   )
A.B.C.D.
3.
在区间[-1,1]上任取两数x和y,组成有序实数对(x,y),记事件A为“”,则P(A)为(  )
A.B.C.πD.2π
4.
在长为10 cm的线段AB上任取一点G,以AG为半径作圆,则圆的面积介于36π~64π cm2的概率是(  )
A.B.C.D.
5.
某人睡午觉醒来后,发现表停了,他打开收音机想听电台整点报时,则他等待小于10 min的概率为(  )
A.B.C.D.
6.
一只小蜜蜂在一个棱长为4的正方体内自由飞行,若蜜蜂在飞行过程中始终保持与正方体六个表面的距离均大于1,称其为“安全飞行”,则蜜蜂“安全飞行”的概率为(  )
A.B.C.D.
7.
已知所在平面内一点,,现将一粒红豆随机撒在内,则红豆落在内的概率是()
A.B.C.D.

2.选择题(共2题)

8.

与下段文字衔接自然、连贯、得体的一句是(    )

       财富是什么?商人摆弄着手机说,财富就是赚来的金钱;学者推了推眼镜说,财富就是创造的知识;哲人拍了拍地球仪说,财富就是拥有的智慧;农民望了望金黄的麦浪说,           ……不同的人,不同的经历,得出了不同的答案。

9.阅读理解

    Steven Spielberg never fails to blow us away with his imagination.

    The US director's latest film Ready Player One, which was released in Chinese mainland cinemas on March 30, is a story set in the year 2045, when people escape their hopeless everyday lives by putting on a VR mask and entering a virtual (虚拟的) world named Oasis. This fantasy land is filled with characters and settings right out of classic films and videogames like The Shining and Overwatch. It's a feast both for the eyes and mind. And at the age of 71, Spielberg is still “at the top of his game”, wrote reporter Rafer Guzman on Newsday.

    Indeed, Spielberg has always been a gamer himself or rather a game changer. When his thriller Jaws came out in 1975, it struck a chord (引起共鸣) with audiences all over the world and kept people from going swimming for fear. The film was also the first example of what we now know as summer blockbusters.

    “Jaws invented that form of pleasurable entertainment, wrote Stephen Marche on Esquire. It also turned sharks, in the popular imagination, from fish into monsters.”

    And again, in his 1982 film E. T. the Extra-Terrestrial Spielberg challenged people's beliefs that aliens are something to be feared by telling a story about a loving friendship between a space creature and a little boy. “Spielberg redefined popular sci-fi”, wrote Marc Lee on The Telegraph. “Extra-terrestrials no longer had to be a threat to humanity: the universe, he was saying, is also full of awe and wonder.”

    Now comes Ready Player One. When Wade Watts, the film's teenage protagonist (主角), finally prevents Oasis from falling into the wrong hands, he's given ownership of the virtual world by its late designer James Halliday. But Watts makes a decision that he hopes will make people want to appreciate their real lives, instead of spending all their free time escaping reality in Oasis, which is a real-life message that Spielberg is trying to deliver to the audience.

3.填空题(共4题)

10.
设有1个正方形网格,其中每个最小正方形的边长都为6cm.现用直径为2cm的硬币投掷到此网格上,则硬币落下后与格线有公共点的概率为____
11.
在边长为2的正三角形ABC内任取一点P,则使点P到三个顶点的距离至少有一个小于1的概率是________.
12.
已知正三棱锥S-ABC的底面边长为a,高为h,在正三棱锥内取点M,则点M到底面的距离小于的概率为_____
13.
如图所示,在等腰直角三角形ABC中,在斜边AB上取一点M,则AM的长小于AC的概率为_____

4.解答题(共5题)

14.
设有关于的一元二次方程
(Ⅰ)若是从四个数中任取的一个数,是从三个数中任取的一个数,求上述方程有实根的概率.
(Ⅱ)若是从区间任取的一个数,是从区间任取的一个数,求上述方程有实根的概率.
15.
小明一家订阅的晚报会在下午5:30~6:30之间的任何一个时间随机地被送到,小明一家人在下午6:00~7:00之间的任何一个时间随机地开始晚餐.
(1)你认为晚报在晚餐开始之前被送到和晚餐开始之后被送到哪一种可能性更大?
(2)晚报在晚餐开始之前被送到的概率是多少?
16.
如图,∠AOB=60°,OA=2,OB=5,在线段OB上任取一点C,试求:

(1)△AOC为钝角三角形的概率;
(2)△AOC为锐角三角形的概率.
17.
向图中所示正方形内随机地投掷飞镖,求飞镖落在阴影部分的概率.
18.
在0~1之间随机选择两个数,这两个数对应的点将长度为1的线段分成三条,试求这三条线段能构成三角形的概率.
试卷分析
  • 【1】题量占比

    单选题:(7道)

    选择题:(2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:16