大家好，这是我第二天在iTalki。在这儿我写了有汉字，它们的意思差不多一样。 你们可不可以纠正我的错误？ 如果你帮助我，我就很高兴^^。。

锻炼 is more formal. When you spare a certain time to exercise, like yoga and running, you can say that 我在做锻炼/ 我在锻炼

活动 is usually used in oral speaking, it usually refers to some less strenuous activities like walking. I think it is a verb in this group. I could be a noun whose meaning includes an event or an activity, e.g. 聚会（party），促销(promotion)

终于。。。。。。In the end
到底。。。。。。In the end
When use what?

价格。。。。。。more formal
价钱。。。。。。oral
When to use which?

They are almost the same. 

以为。。。。。。expressing your personal oppinions. Usually the thing that you believed is proved wrong.
认为。。。。。。more formal, the thing you are talking about is usually based on some facts or other reliable source


输。。。。。。。To lose or be beaten
失败。。。。。。
When use which? same meaning?

They are almost the same, but the former one is usually used in games and matches

教育。。。。。。Education
教学。。。。。。teaching


下降。。。。。。To decline
减少。。。。。。reduce（amount,number）
降低。。。。。。reduce， cut sth down (more intangible ) e.g risk, efficiency


担心。。。。。。to worry about sth    我很担心他的健康
着急。。。。。。There is no time to do sth. 我很着急，因为明天就是截止日期了（deadline）
烦恼。。。。。。trouble    他们意见不合，这让我很烦恼。