落 fall,drop

The ROCK and roller was so wasted he fell down three times. On the way to the stage .

Each flower petal falls onto the water.

keep your cool. ★★★☆☆
落 (fall,drop) + 着 (wear / arrive) = 落ち着く (keep your cool.)

to keep your cool. Often said as a command： おちつけ!!

corrupt ★★★☆☆
堕 (corrupt) + 落 (fall,drop) = 堕落 (corrupt)

corrupt in one's personal life - not usually political corruption. Drugs, lies, trife behavior.

burakumin ★★☆☆☆ CCWFRABU
部 (section) + 落 (fall,drop) + 民 (folk) = 部落民 (burakumin)

(literally,'the fallen group.') this is - along with Ainu, Korean ex-slaves, the Eta-hin,and the handicapped, one of the main groups discriminated against in Japan. I won't go into the whole story here, but most Japanese will say, 'Don't say 部落民, it's 差別 (さべつ＝ discriminatory)'

What they neglect to tell you is, there is no polite word! Effectively denying someone a voice in the guise of being polite to them is a very. Very. VERY Japanese way of fucking with people.

However, you can say 同和 (どうわ = social integration) instead: speaking of the phenomenon instead of the individuals. For instance, discrimination against people is 同和の問題 ('the social integration problem').

A nice article explaining the importance of using the right language is here and a more general overview of discrimination is here.

fail a test ★★☆☆☆
落 (fall,drop) + 第 (rank or number in series) = 落第 (fail a test)

fail an exam,or get held back a grade.