1.bear in mind:You should bear the advice in mind 你应该牢记这个忠告
2.keep in mind:You only have one day to complete the task ,you must keep that in mind.你必须记住你只有一天(的时间)去完成这个任务.
3.learn by heart:The peom is too long for him to learn by heart.这首诗对他来说太长而难以记住.
3.remember well:If I remember well,she is a bubbly little girl.如果我记得对的话,她是一个活泼的小女孩.
这几个是比较常用的表达.