第3部分考前热身训练(六)

第3部分考前热身训练(六)
第3部分考前热身训练(六)

考前热身训练(六)

概率、统计、复数、算法、推理与证明[学生用书P148(独立成册)]

1.某中学有高中生3 500人,初中生1 500人.为了解学生的学习情况,用分层抽样的方法从该校学生中抽取一个容量为n 的样本,已知从高中生中抽取70人,则n 为( )

A .100

B .150

C .200

D .250

A [解析] 法一:由题意可得70n -70=3 500

1 500,解得n =100,故选A.

法二:由题意,抽样比为703 500=150,总体容量为3 500+1 500=5 000,故n =5 000×1

50

=100.

2.已知复数z 满足(z -3)(2-i)=5(i 为虚数单位),则z 的共轭复数z -

为( ) A .2+i B .2-i C .5-i

D .5+i

C [解析] 依题意得,z -3=52-i =5(2+i )(2-i )(2+i )

=2+i ,z =5+i ,z -=5-i ,选C.

3.在长为3 m 的线段AB 上任取一点P ,则点P 与线段AB 两端点的距离都大于1 m 的概率等于( )

A.12

B.14

C.23

D.13

D [解析] 将线段AB 平均分成3段,设中间的两点分别为C ,D ,所以当点P 在线段CD 上时,符合题意,线段CD 的长度为1,所以所求概率P =13

.

4.在中秋节前,小雨的妈妈买来5种水果,4种肉类做月饼.要求每种馅只能用2种食材,且水果和肉类不能混合在一起做馅,则小雨妈妈做出水果馅月饼的概率是( )

A.13

B.58

C.23

D.79 B [解析] 设5种水果分别为A 1,A 2,A 3,A 4,A 5,4种肉类分别为B 1,B 2,B 3,B 4,用2种食材,且水果和肉类不能混合在一起做馅的所有可能结果为(A 1,A 2),(A 1,A 3),(A 1,A 4),(A 1,A 5),(A 2,A 3),(A 2,A 4),(A 2,A 5),(A 3,A 4),(A 3,A 5),(A 4,A 5),(B 1,B 2),(B 1,

B 3),(B 1,B 4),(B 2,B 3),(B 2,B 4),(B 3,B 4),共16种,用水果做馅的共10种,所以做出水果馅月饼的概率是5

8

.

5.某公司为确定明年投入某产品的广告费,对近5年的年广告费x (单位:千元)与年销售量y (单位:吨)进行了初步统计,得到下列表格中的数据:

经测算,年广告费x 与年销售量y 满足线性回归方程y ^

=0.76x -71,则n 的值为( ) A .4 B .4.5 C .5

D .6

C [解析] 由表格中的数据可得,x -=100,y -=2+3+n +7+8

5=4+n 5,因为回归直

线y ^=0.76x -71必经过样本点的中心(x -,y -

),所以4+n 5=0.76×100-71,解得n =5,故选

C.

6.一次数学考试后,某老师从自己所带的两个班级中各抽取5人,记

录他们的考试成绩,得到如图所示的茎叶图.已知甲班5名同学成绩的平均数为81,乙班5名同学成绩的中位数为73,则x -y 的值为( )

A .2

B .-2

C .3

D .-3

D [解析] 由题意得,72+77+80+x +86+90

5=81 x =0,易知y =3,所以x -y =

-3,故选D.

7.从某小学随机抽取100名同学,现已将他们的身高(单位:厘米)数据绘制成频率分布直方图(如图).若要从身高在[120,130),[130,140),[140,150]三组内的学生中,用分层抽样的方法选取18人参加一项活动,则从身高在[140,150]内的学生中选取的人数应为( )

A .2

B .3

C .4

D .5

B [解析] 依题意可得10×(0.005+0.010+0.020+a +0.035)=1,解得a =0.030,故身高在[120,130),[130,140),[140,150]三组内的学生比例为3∶2∶1,所以从身高在[140,150]内的学生中选取的人数应为3.

8.执行如图所示的程序框图,如果输入的a =-1,b =-2,则输出的a 的值为( )

A .16

B .8

C .4

D .2

B [解析] 当a =-1,b =-2时,a =(-1)×(-2)=2<6;当a =2,b =-2时,a =2×(-2)=-4<6;当a =-4,b =-2时,a =(-4)×(-2)=8>6,此时输出的a =8,故选B.

9.若运行如图所示程序框图,则输出结果S 的值为( )

A .94

B .86

C .73

D .56

A [解析] 由程序框图可得i =1,S =1;i =2,S =4;i =3,S =10;i =4,S =22;i =5,S =46;i =6,S =94,结束循环.输出的S =94.

10.某学校为了了解该校学生对某项运动的爱好是否与性别有关,通过随机抽查110名学生,得到如下2×2列联表:

由公式K 2

=n (ad -bc )(a +b )(c +d )(a +c )(b +d ),算得K 2=

110×(40×30-20×20)2

60×50×60×50

≈7.8.

附表(临界值表):

参照附表,以下结论正确的是( )

A .在犯错误的概率不超过0.1%的前提下,认为“爱好该项运动与性别有关”

B .只有不超过1%的把握认为“爱好该项运动与性别有关”

C .有99%以上的把握认为“爱好该项运动与性别有关”

D .有99%以上的把握认为“爱好该项运动与性别无关”

C [解析] 因为7.8>6.635,所以有99%以上的把握认为“爱好该项运动与性别有关”.

11.如图所示,以边长为1的正方形ABCD 的一边AB 为直径在其内部作一半圆.若在正方形中任取一点P ,则点P 恰好取自半圆部分的概率为( )

A.π

2 B.12 C.π4

D.π8 D [解析] 所求概率P =12×π×????1221×1

=π

8.故选D.

12.阅读如图的程序框图,运行相应的程序,若输出S 的值为1,则判断框内为( )

A .i >6?

B .i >5?

C .i ≥3?

D .i ≥4?

D [解析] 依题意,执行程序框图,进行第一次循环时,S =1×(3-1)+1=3,i =1+1=2;进行第二次循环时,S =3×(3-2)+1=4,i =2+1=

3

;进行第三次循环时,S =4×(3-3)+1=1,i =4,因此当输出的S 的值为1时,判断框内为“i ≥4?”,选D.

13.某中学采用系统抽样方法,从该校高一年级全体800名学生中抽50名学生做牙齿健康检查,现将800名学生从1到800进行编号.已知从[497,513)内的16个编号中取得的学生编号是503,则在第1小组中随机抽到的学生编号是________.

[解析] 由题意可得,把800人平均分为50组,每组16人,设第1小组中随机抽到的学生编号为x ,则第k 组应取的编号为16(k -1)+x ,由503=16×(32-1)+x ,得x =7,故第1小组中随机抽到的学生编号为7.

[答案] 7

14.已知不等式1+14<32,1+14+19<53,1+14+19+116<7

4,照此规律总结出第n 个不等式为

________.

[解析] 由已知,三个不等式可以写成1+122<2×2-12,1+122+132<2×3-13,1+122+1

32+

142<2×4-14,所以照此规律可得到第n 个不等式为1+122+132+…+1n 2+1

(n +1)2<2(n +1)-1n +1=2n +1

n +1

.

[答案] 1+122+132+…+1n 2+1(n +1)2<2n +1n +1

15.在某次数学考试中,甲、乙、丙三名同学中只有一个人得了优秀.当他们被问到谁得到了优秀时,丙说:“甲没有得优秀”;乙说:“我得了优秀”;甲说:“丙说的是真话”.事实证明:在这三名同学中,只有一人说的是假话,那么得优秀的同学是________.

[解析] 分析题意只有一人说假话可知,甲与丙必定说的都是真话,故说假话的只有乙,即乙没有得优秀,甲也没有得优秀,得优秀的是丙.

[答案] 丙

16.在以点O 为圆心,1为半径的半圆弧上任取一点B ,如图所示,则△AOB 的面积大于1

4

的概率为________.

[解析] 如图甲所示,过点B 作直线OA 的垂线,垂足为D ,则△AOB 的面积大于1

4等价

于12×1×|BD |>14,即|BD |>1

2.如图乙所示,作CO ⊥OA ,取P 为CO 的中点,过P 作MN ⊥OC ,连接OM ,ON ,则当点B 在MCN ︵上运动(不包括点M ,N )时,|BD |>1

2,故所求概率P =2π

3π=

2

3

.

2 [答案]

3

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中考考前热身练习 (热量计算 )

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所做的功是多少? (3)货车在这一过程中消耗燃油4kg,其热机的效率是多少? 3.一台电热水器,其铭牌数据如下表所示.现将水箱中装满水,通电后正常工作40min, =4.2×103J/(kg·℃),请完成下列计算: 水温从25℃上升到45℃,水的比热容c 水 型号FED-H50额定电压220V 最大装水量50㎏额定功率2000W (1)水吸收的热量是多少? (2)电热水器的效率是多少? 4.某校为师生饮水方便,安装了电热水器。为测定热水器消耗的电能,关闭其它用电器,只用电热水器给水加热,一段时间后,可把20kg初温为25℃的水加热至100℃,电能表的示数由图甲示数变为图乙示数。求: (1)该电热水器在这段时间内消耗的电能; (2)这段时间内水吸收的热量;(水的比热容c=4.2×103J/(kg?℃)) (3)电热水器的热效率(结果保留一位小数)。 5.天然气热水器已经普遍使用,小明在家中尝试估测家中热水器的热效率,他把家里自动洗衣机的“水量”设置为50L,用热水器输出的热水注入洗衣机,当注入水的体积达到50L 时洗衣机便会自动停止注水.已知当时的自来水的温度是15℃,设定热水器输出热水的温 =4.2×103J/(kg?℃),q天然气= 度为35℃,注水前后天然气表的示数变化了0.15m3.(c 水

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拓展训练破冰游戏

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高考英语考前热身训练面表达

高考英语考前热身训练面表达

Passage 1 (2010·河南调研) 假定你是李华。你的英国笔友Pauline写信告诉你她想在七月份到河南旅游,并请你帮助安排有关事宜。请你给她写一封邮件,告诉她以下内容: 1.已经联系好郑州的国际旅行社,安排好了一切; 2.旅行安排是:她将参加一个20人的旅游团队,时间为7月10日至22日,有一名说英语的导游陪同,有车接送; 3.如对就餐、旅馆、费用等有疑问,请来信; 4.请她提前告知航班信息,以便接机。 注意:1.信的开头和结尾已给出; 2.词数100左右(不含开头和结尾部分)。 参考词汇:旅行社Travel Agency;旅馆住宿accommodation; 长途客车coach Dear Pauline, I'm very happy to receive your e-mail and to know you are coming to visit___________________________________

_______________________ Yours Li Hua 范文: Dear Pauline, I'm very happy to receive your e-mail and to know you are coming to visit Henan, which is a beautiful place with a long history. I have contacted the International Travel Agency in Zhengzhou, which has arranged everything for you as follows:You are to travel by coach together with a group of 20 people from July 10th to 22nd, and you will have a guide who speaks Standard English. If you have any questions on your accommodation, meals as well as how much you have to pay, you are welcome to write to me again. What's more, remember to inform me of the information about your flight ahead of time so that I can meet you at the airport. Looking forward to meeting you soon. Yours, Li Hua Passage 2 (2010·海淀期末)

六级级冲刺试题一及答案解析

冲刺试题一 Part I Writing (30 minutes) Directions: For this part, you are allowed 30 minutes to write a short essay entitled The Safety of Food. You should write at least 150 words following the outline given below in Chinese: 1. 目前食品安全问题屡见不鲜 2. 分析产生这些现象可能的原因 3. 提出自己解决问题的意见 The Safety of Food ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ Part II Reading Comprehension (Skimming and Scanning) (15 minutes) Directions:In this part, you will have 15 minutes to go over the passage quickly and answer the questions on Answer Sheet 1. For questions 1-7, choose the best answer from the four choices marked [A] , [B], [C] and [D]. For questions 8-10, complete the sentences with the information given in the passage. How to Create a Home Library “I cannot live without books,” declared U.S. President Thomas Jefferson to his friend John Adams. Indeed, Jefferson was an obsessive book collector from a young age, amassing (收集) three separate home libraries in his lifetime. The first collection was destroyed when his family home burned down in 1770. When the Library of Congress was destroyed in the War of 1812, Jefferson sold his second collection of about 6,000 books to the federal library. Jefferson’s librar y was considered the finest in the country, and his collection doubled the holdings of the Library of Congress. Still, Jefferson didn’t let the shelves at Monticello sit empty. By the time he died 11 years later, he had more than 2, 000 volumes in his library. Jefferson’s library might fit your conception of an old-fashioned home library with leather-bound books, wood paneling and uncomfortable furniture. But home libraries can be a dynamic expression of the owner’s pers onality. Creating a home library is a fun way to display your interests while establishing a special space for reading. Home Library Organization When you started using the public library, you probably learned about Melvil Dewey and his system for ordering libraries. The Dewey Decimal Classification System has ten broad categories for organizing books, including philosophy, religion and the arts. Each category is assigned a number, so for example, when you want a book on modern art, you head to the 700 block. Larger libraries, such as those at universities, tend to use the Library of Congress Classification System because it offers a more specific array of subjects for categorization, adding subjects such as medicine and law for a total of 21 categories. Your home library may or may not be as large as your local public library, but a good system of organization will still help you find the book you want quickly. You could take a page from Dewey and the Library of Congress and sort books by subject matter. Sections for subjects such as history, technology or fiction might make their retrieval easier. This system also would allow you to highlight a particular passion, such as an extensive collection of World War II history.

六级阅读考前冲刺1

A lot of animals are afraid during an eclipse1 of the sun. Birds stop singing. Sometimes people too are afraid. Astronomers2 know the dates of eclipses and they are not afraid. The old astronomers of Babylon and Egypt had no telescopes3; but the sky in those countries is usually clear,and so they could watch the stars easily. They studied everything in the sky and they also noticed both total and partial eclipses. Because they knew the dates of eclipses,they had great power. People believed that the sky was important. They believed that an eclipse could kill a man. About 2500 years ago there was a very long war. One battle followed another, and the end never came. During one of the battles, there was a partial eclipse of the sun. The day got very dark,and the soldiers on both sides were filled with fear. They believed that the gods were angry. So they stopped fighting,and ended their long war. The sun is a star. It appears to be bigger than any other star. That is because it is near us; but the other stars are far away. The sun shines because it is very hot,but the moon shines because it reflects the sun's light. It is like a big mirror. If we visited the moon,we should see the earth. It is also like a mirror and it reflects the light of the sun. Does the sun ever get dark during the day? It does so when the moon hides it. Sometimes the moon goes in front of the sun. We can watch its edge when it slowly crosses the sun's disc5. Everything gets darker and darker; then,at last,we cannot see any part of the sun's disc. The moon is hiding it completely. That is a total eclipse of the sun; sometimes only part of the sun's disc is hidden; that is not a total eclipse. It is a partial eclipse of the sun.

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