Can/ Shall (Requests, offers and suggestions)

Shall I help you with the exercises?
I can bring you your books tonight

Do you mind/ would you mind/ would you like (Requests, offers and suggestions)

Would you like to have another piece of cake?
Do you mind changing the mobile phone?
Would you mind reading this book?

Can/ Could (Requests, offers and suggestions)

Can you tell me the answers?
Could you bring me the books?

Must/ Can't (Speculation, deduction and probability)

She must be happy, she is going to go on holidays tomorrow
He can't be here becuse he is driving now
I can't open the door because I have lost my keys
They must be at home, it is holiday

May not/ Might not or mightn't/ could not or couldn't (Speculation, deduction and probability)

Reaching pluto couldn't be possible
I am studying, but I may not pass the exam
She mightn't catch the train because she has got up late

May/ Might/ Could (Speculation, deduction and probability)

Father christmas may visit our house
He might have broken the computer
My bag could be in your house
I may do another degree course

Can/ Could/ May (Permission)

Can I turn on the TV?
May I tell you something?
Could you pass me the sugar, please?
Can I play football in your team?

Can/ Could/ Be able to (Ability and Knowledge)

I can sing very well
He was able to run for one hour
Yesterday, we couldn't remember his name
I am not able to do these exercises
The dress is too tight, you couldn’t wear it

Should/ Ought to/ had better (Advice)

It is dark, we had better go home now
You ought to study more to pass the exam
They should be more tolerant
You ought to eat vegetables and drink water

Mustn't (Prohibition)

You mustn't go out because it is raining
They mustn't be here
She mustn't play with fire
We mustn't exceed the speed limit

Need to

I need to buy a new computer
We need to take a holydays because we are tired
Do you need to take something else?
Did you need to go to the hospital?

Don't have to/ don't need to/ needn't (No obligation)

I don't have to go if is not necessary
You didn't need to get up early because yesterday you didn't have to go to school
Oh! I'm sorry! You needn't have got up early today! you don't have to go to school!
We needn't come together, I prefer take a taxi later
They don't have to work because their boss has married

Must and have to (Obligation)

You must take this train if you don't want be late
You have to get up early because the train leaves at 7.00 am
You must help my brother
My niece had to do her homework yesterday because today she has no time
I have to go to the hospital to visit my neighbor
You must turn off your mobile phone in the hospital
I have to do my composition for next week