The Bakajo Kimatsu tests are special episodes of a Japanese variety show called Mechaike. Mechaike is an ensemble comedy show where they occasionally do sketches, but generally spend most of their time doing jokes, playing games, and making fun of each other and other famous people who are on the shows.
(There is a thing you need to know about Japanese entertainers to make this all make more sense. Japanese entertainers work for agencies, which control their booking, etc. Unless you are a enormous star, or just strange enough that you don't care how your career goes, you do what the agency tells you. So if you are a famous movie actor, you still go on comedy shows if asked. Are you the most famous singer in Japan? You still go on the weekly music shows like a beginner star would. It's very different from the US where an A list star would almost never be on TV.)
During the episodes, the lead comedian Okamura (a fantastic talent) is the teacher of a fictional school, Bakajo (like Stupid person school) and he gives a standardized test to a bunch of people, sometimes actors, sometimes other comedians, members of his show, and in my favorite, to Morning Musume, a young group of idol singers who are the time these shows were done were huge stars, but apparently not the brightest bulbs in the room. Okamura gives their tests, then goes over their answers, highlighting the wrong ones.
Part 6 of the Test. All 11 parts are here WITH subtitles.
It's really hard to explain just how funny these shows are. The answers are hysterical, and watching the girls squirm to avoid the title of Baka Queen (the dumbest girl) is great. The answers range from not knowing even and odd (calling them indivisable and divisable), thinking the capital of China is Cham Po Chan, translating into english wrong (instead of telephone - Telepudding) and some extremely bizarre rememberances of Japanese history and geography.
Again, it's hard to explain - just watch it. You'll be glad you did.
http://en.wikipedia.org/wiki/Mechaike - Mechaike Wikipedia Page
http://en.wikipedia.org/wiki/Morning_musume - Morning Musume Wikipedia Page