问题 填空题

正方体ABCD-A1B1C1D1中二面角A1-BD-C1的余弦值为______.

答案

如图所示,取BD的中点O,连接A1O,C1O,则A1O⊥BD,C1O⊥BD,

∴∠A1OC1为二面角A1-BD-C1的平面角

设正方体的棱长为1,则A1C1=

2
,A1O=C1O=
6
2

∴cos∠A1OC1=

6
4
+
6
4
-2
2•
6
2
6
2
=-
1
3

故答案为:-

1
3

填空题
阅读理解

What might the future be like? Here are some predictions(预言).

Returning home during the Spring Festival is difficult for many Chinese people. More than 2 billion people travel at the same time, making buying travel tickets and the journey difficult. But 28 years later, Spring Festival travel may not be a problem at all. China plans to build more railways and a fast transportation network that will serve 90% of the population by 2020. And because most of China will be cities, people will not have to go to other places to find a job, so it will no longer be a problem.

Oil is running out faster than expected. But scientists have found something else for oil as fuel(燃料). Coal, natural gas, sun power, nuclear power(核能) and even water can take the place of oil as energy.

Schools will go electronic. Computers will be important and popular among the students. Everything will be in the computer and students will not need to bring books to school. They will find information on the Internet. A computer will be the students’ library, schoolbag and connection to the outside world. There will be robot teachers, they will check homework on computers and communicate with the students’ parents through e-mail. And school buses will be like spaceships, comfortable and safe.

小题1:More than 2 billion people have a hard time returning home during          according to the passage.

A.Christmas Day

B.National Day

C.the Spring Festival

D.the Mid-autumn Festival小题2:In 2020, China will build a fast transportation network that will serve          of the population.

A.60%

B.70%

C.80%

D.90%小题3:        is not mentioned in the passage as energy.

A.Coal

B.Wind

C.Nuclear power

D.Water小题4:From the passage we can know          in the future.

A.the Spring Festival travel may still be a problem in China

B.90% of the population will live in the city

C.robot teachers will check students’ homework

D.readers can discuss topics with each other face to face小题5:What’s the main idea of the last paragraph?

A.Schools will go electronic.

B.Computers will be important.

C.There will be robot teachers.

D.School buses will be like spaceships.