ability in the past

• could + base form; could + subject + base form?
• couldn't (could not) + base form = wasn't / weren't + able to + base form
• was / were + able to + base form; was / were + subject + able to + base form?
• managed to + base form; didn't manage to + base form; did + subject + manage to + base form?
• succeeded in + -ing form; didn't succeed in + -ing form; did + subject + succeed in + -ing form?

use 

• general abilities in the past - example: she could swim when she was five.
• in their negative forms, could and was / were able to can be used interchangeably
• a specific ability or an action that has been successfully concluded - example: i was able to fix the car yesterday.
• a specific achievement that was difficult, unexpected or uncertain - example: she succeeded in climbing the mountain.

modal verbs of deduction (past)

use to make logical deductions about past events and situations

100% certainty → we are certain about something in the past 

• subject + must + have + past participle - example: he must have forgotten about the meeting.

50% uncertainty and possibility → we are unsure or open to various outcomes in the present or future

• subject + may / might / could + have + past participle - example: they are still at the platform. they may have missed the 6.30 train.
• subject + may / might + … have + past participle - example: she might have left her keys at home.

we do not use could not or couldn't.

0% impossibility → we consider something to be impossible based on existing knowledge or conditions

• subject + can't / couldn't + have + past participle - example: tom can't have been at school yesterday. he was ill.