Past week x Last week: Qual a diferença

Me deparei com o seguinte exercício: answer: How many times have you done these things in the past week?
What's the difference "in the past week" and "last week"?

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1 resposta
I believe the answer could be:

Present Perfect Tense
>> How many times have you done these things in the past / in the last week?

Past Simple Tense
>> How many times did you do these things last week?

Mixing up last and the last when speaking about time can lead to misunderstandings, so, we, English learners should be careful about how they use them. Let’s look at the difference in meaning between last and the last.

1) Use last before a specific past time reference.

We use last before a past time reference such as Monday, week, month, August, etc. We say:

- last week: the week before this week
- last Monday: Monday of last week
- last year: If we're in 2017 now, last year is 2016.
- last January: This is January of last year. If we're in August 2017 now, then January 2017 is in January, and January 2016 is last January.

>> We don't use past in the same way.
past January
past week

2) Use the last before an unfinished period of time

- The last, the past
We use the last and the past before an unfinished period of time. They both have the same meaning.

in the last / the past week
>> If today is Wednesday, this means the period from Wednesday last week up until now.

in the last / the past year
>> If it'sAugust 2017 now, this means the 365 days from August 2016 until today.

Because the time period is unfinished, we use the present perfect tense with the past and the last:
>> He's had two new cars in the last / in the past three years.
>> It's been too hot the last / the past few days. I hope it cools down soon.