I Hope You Had an Easy Start for the Year

Hope

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We use 'hope' to talk about things in the present or future that we think have a good chance of happening. On the other hand, we use 'wish' to talk about things that are impossible or unlikely. See more about 'wish' here.

We usually need to use '(that) + clause' after 'hope' or 'to + infinitive'. It's very common to drop 'that'.

I hope that you have a great time.
I hope that she passed the exam.
I hope to pass the exam.
I hope to get there early.

We can also use two short answers: 'I hope so' and 'I hope not'.

Hope for the present
We can use the present simple (mostly for stative verbs) or the present continuous.

I hope (that) it's sunny where you are.
I hope (that) she's having a wonderful time.

Hope for the future
We can use either the present simple (more common) or the future simple (less common). It usually doesn't change the meaning.

I hope that she comes to the party tomorrow.
I hope that she'll come to the party tomorrow.

We often use 'can' with 'hope' for the future.

I hope you can come to the party tomorrow.

We can use 'to + infinitive' with 'hope' for the future. When we use 'to + infinitive', the subject is the same as the subject of 'hope'.

I hope to come to the party tomorrow. (=I hope I can come to the party tomorrow.)
I hope to run a marathon this year.

Hope for the past
We can also use 'hope' to talk about the past when we think it was possible for the thing to really happen.

1: We can use 'hope' for the past when something happened and is finished, but we don't know what the result was. For example, if you have taken an exam, but I don't know if you passed or not. We still use 'hope' in the present tense, because it's something that we hope now, but the thing that we're thinking about is in the past. We can use the past tenses and the present perfect in the normal way (if something has an effect on the present, we use the present perfect and so on).

I hope she passed the exam.
I hope John hasn't got lost.
I hope Amanda found her keys.

2: We can use 'hope' for the past when we do know the result or outcome. For example, if you have taken an exam and failed and I know you failed. In this case, we use 'hope' in a past tense, because we no longer hope for the event or thing; we know it didn't happen. We use it to tell someone about how we felt in the past.

I hoped you would pass the exam. (But you didn't pass).
I hoped I'd see Lucy at the meeting. (But I didn't see her.)

It's common to use 'hope' in the past continuous (which doesn't really change the meaning from the past simple) and in the past perfect (which makes the idea that the hoping is finished stronger) in these kinds of sentences.

I was hoping you would pass the exam.
I had hoped you would pass the exam.

This use is very compatible with the third conditional.

I was hoping to pass the exam, and I would have passed it if I hadn't got sick.

Hope for 'future in the past'
Advanced point: Sometimes we use 'hope' for 'future in the past'. So, in the following example, the mother thought, in the past, 'I hope my son will go to university', and when we talk about this from the present, we use 'would'. We don't know if the son in fact went to university or not from this sentence.

She always hoped that her son would go to university.

Another example:

I got lost in the middle of London and I hoped that I would be able to find my way back to my hotel. (We don't know if the person found the hotel or not.)

Hope for negative wishes
It's also possible to use 'hope' in a very negative way. In this case, the thing doesn't need to be possible.