如图.在四棱锥P-ABCD中.PA⊥底面ABCD.底面为直角梯形..且PA=AB=BC=1.AD=2．(Ⅰ)设M为PD的中点.求证:平面PAB,(Ⅱ)求侧面PAB与侧面PCD所成二面角的平面角的正切值——青夏教育精英家教网——

如图，在四棱锥P—ABCD中，PA⊥底面ABCD，底面为直角梯形，

，且PA=AB=BC=1，AD=2．

（Ⅰ）设M为PD的中点，求证：

平面PAB；
（Ⅱ）求侧面PAB与侧面PCD所成二面角的平面角的正切值．

（本题满分14分）如图，α⊥β，α∩β=l， A∈α， B∈β，点A在直线l上的射影为A₁，点B在l的射影为B₁，已知AB=2，AA₁=1， BB₁=，求:
(Ⅰ) 直线AB分别与平面α，β所成角的大小;
(Ⅱ)二面角A₁－AB－B₁的余弦值．

（本小题满分12分）(注意:在试题卷上作答无效)

是直角梯形，

.
（Ⅰ）求证：

；
（Ⅱ）设

的值，使得二面角

.

（本小题共12分）如图所示，

的中点．
（Ⅰ）求证：

；
（Ⅱ）求证：平面

．
(Ⅲ)求凸多面体

（本小题满分12分）
如图，菱形

折起，得到三棱锥

.
（Ⅰ）求证：

；
（Ⅱ）求证：平面

；
（III）求三棱锥

如图，在四棱锥P－ABCD中，底面ABCD是菱形，∠BAD＝

，AB＝2，PA＝1，PA⊥平面ABCD，E是PC的中点，F是AB的中点．

（1）求证：BE∥平面PDF；
（2）求证：平面PDF⊥平面PAB；
（3）求三棱锥P－DEF的体积．

（本小题满分12分）在直三棱柱

中， AC=4,CB=2,AA₁=2

，E、F分别是

的中点。
（1）证明：平面

；
（2）证明：

平面ABE；
(3)设P是BE的中点，求三棱锥

One day an old man went into a cafeteria (自助餐厅) to eat in America for the first time. He sat down at an empty table and waited for   43  to take his order. Of course nobody did. Finally, a woman with a plate full of food sat down opposite him and told him how a cafeteria   44 .
“Start out at that end,” she said. “Just go along the line and   45  what you want. At the other end they’ll tell you how much you have to pay.”
“I soon learned that’s how everything works in the US,” the old man later told a friend. “ 46  is a cafeteria here. You can get anything you want   47  you are willing(自愿的) to pay the price. You can even get success, but you’ll never get it if you wait for someone to   48  it to you. You have to get up and get it yourself.”
49 , life everywhere is like a cafeteria. Don’t wait for things to happen to you. Success lies in your own   50 .

On the night of May 9, 2011, musician Gao Xiaosong ran his car into three other cars in Beijing.
But it wasn’t just a car accident—he was drunk(喝醉的).
Now, Gao has to go to prison (监狱) for six months and pay a 4,000 yuan fine.
Gao is the first star to be punished under China’s new drunk driving law.
From May 1 on, drunk drivers will pay a fine, and be banned from driving for five years or even forever.
Drunk driving has become a serious social problem in China.
According to the Ministry of Public Security (公安部), police caught more than half a million drunk drivers last year, a 68 % increase from 2009.
The new law sees drunk driving as a crime.
In the West, drunk driving is also a crime.
In the US, for example, if the police catch a drunk driver, the driver will pay a fine, lose his or her license (驾照) and even go to prison. If the driver wants to drive again, he or she must do
public service, and take part in educational programs.
You may think: drunk driving is a crime? Isn’t this law too unkind? But experts say: not at all.
“It is to protect people’s rights to life and health,” Li Gang, lawyer in Chengdu, told China Daily. “Drunk driving is very dangerous. No matter what the results are, it should not be allowed.”
【小题1】 Mr. Gao ran his car into three other cars because _________.
A. he went home too late
B. he drank too much wine
C. the road was too crowded
【小题2】 What does the underlined word “fine” in the third paragraph refer to(指)?
A. Health.    B. Weather.    C. Money.
【小题3】When did the new law come into use?
A. May 1, 2010.      B. May 1, 2011.     C. May 9, 2011.
【小题4】What do experts think of the new law?
A. Drunk driving is a crime.
B. The law is not kind to drunk drivers.
C. Driving has become a serious problem.
【小题5】 Which of the following sentence is TRUE?
A. Li Gang from Chengdu doesn’t like the law.
B. In the US, drunk drivers will only lose their licenses.
C. There were more drunk drivers in 2010 than in 2009.

Alexis Rocha is a 13-year-old boy from California, US. He weighs 147 pounds (67 kg). But six months ago, he weighed more than 202 pounds (91 kg). How did he lose all that weight in only half a year?
“One day, I was surprised to find that I weighed about 200 pounds,” Rocha says. “I thought I had to do something.”
Rocha is from a boxing (拳击) family—his father and two older brothers are professional boxers. So he decided to start boxing. He began with simple exercises, like sit-ups and push-ups (俯卧撑). Then Rocha started jogging(慢跑). “No kid likes running,” he says. “I don’t want to do it, either, but I have no choice but to keep on.”
Months later, Rocha joined a boxing club in his city. He is always the first kid at the club to begin exercising, and the last to leave with sweat (汗水) on his face. Every day he boxes for about three hours.
“Rocha works very hard,” says his coach, Hector Lopez. “It’s surprising to see him lose the pounds so quickly. I’ve never seen anything like this in my 20 years of coaching.”
Rocha is very happy with his weight now. There is a family photo in his room from 18 months ago. “Each time I look at the photo, I laugh at myself. I was so big back then,” Rocha says. “I look 100 times thinner and 1,000 times stronger now.”
【小题1】How much weight did Rocha lose in six months?
A. At least 24 pounds. B. At least 30 pounds.　　 C. At least 55 pounds.
【小题2】 Rocha said he had no choice but to keep on running because_______.
A. he liked running very much
B. he wanted to be thin and strong
C. he wanted to be a professional boxer
【小题3】What makes Coach Hector Lopez surprised?
A. Rocha lost weight so quickly.
B. Rocha was so fat 18 months ago.
C. Rocha comes from a boxing family.
【小题4】What’s the correct order of the following sentences?
a. He did some sit-ups and push-ups.
b. He lost the pounds quickly.
c. He joined a boxing club.
d. He began running.
f. He boxed for about three hours every day.
A. a-d-c-f-b B. d-a-f-c-b C. a-d-f-c-b
【小题5】The writer mainly wants to tell us _______.
A. Rocha is a hardworking boy
B. it is important to get exercise
C. everything is possible if you work hard

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