May

To refer to something in the past that was possible but did not actually happen, use might have or could have (NOT may have): ‘If you had worked harder, you might have passed the exam.’

May be = Instead of using may be …will, use may + infinitive: ‘They may decide that our offer is too low, of course.’

May be is used mainly in informal styles: ‘May be you should see a doctor.’

Perhaps is used in all styles: ‘Perhaps he’s gone home already.’ ‘Perhaps there are other factors that need to be considered.’