Off by heart

Usually used in UK.
If you know something by heart, you can remember all the words in it without any help.
Learned in such a way that you can repeat it from memory.

We learned long passages of poetry off by heart.

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to know anything off by heart

To learn something and keep it in mind for a longer time.

Synonyms:
To memorize
To learn by heart

Andy knows that it isn't easy for him to know anything off by heart.

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