New answers tagged politeness
〜くない (casual) 〜くありません (formal) It's basically that simple. So saying 寒くありません is more formal than saying 寒くない. However, I feel that saying 寒くありません is a bit stiff even if you are trying to be polite. Instead, saying 寒くないです sounds more natural and is also more polite than leaving off the です.
Does not really matter how is written the exam, you do not need to answer in ます形.
わかりましたか would be like "did you get it" so avoid it and just ask it in a way where they judge you and not the reverse as you did in English. Something like 説明に不明点はなかったでしょうか。
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