By the time the course ends,we___(learn)a lot about math.

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By the time the course ends,we___(learn)a lot about math.

By the time the course ends,we___(learn)a lot about math.
By the time the course ends,we___(learn)a lot about math.

By the time the course ends,we___(learn)a lot about math.
have learned/learnt 绝对没有错.

have learned

will learn
意思是:到时候结束的时候,我们将学到很多关于数学的知识。
所以现在课程还没有结束,后面用将来时。