USING OF MUST

Hi everyone

I’m got into trouble with the word “would”.

I just think “would” is the past form of “will” so I can’t understand why people use “would” in some cases like these below:

_ Would you like to have a cup of coffee?
_Yes, I’d love to.
_ I think I’d go for physical education

*** Sometimes people start expressing their opinions or answering a question like these: “ I’d have to say….” Or “ I’d to say…”( That’s just what I think ) for example:

** Tom and Martin discuss what subjects all students should take in school (Note: “would you class…”; “I would say perhaps…”; “That would actually….”)

_ Tom: Well, I'm just wondering, in high school would you class science as one, or would you class it as three subjects: physics, biology, and chemistry. How much space do you think science should have?
Martin: I would say perhaps, three sounds almost too much but at the same time all three are very important. Physics and math can almost go together. Perhaps chemistry and biology can go together.
_Tom: So perhaps we could take those 4 subjects and call them 2.
Martin: 2 or 3 subjects out of that. What do you think? Does that sound all right?
_Tom: That would actually be quite a lot like what happened at my high school. So how many have we got left?
...

So all above are my problems. I think there’re a lot of meanings of “would” not just what I learnt at school: “would” is the past form of “will”. So please help me by showing more things that I don’t know about the word “would”. And please help me by showing any mistakes I've got in this text.
THANK YOU VERY MUCH!!!

Sorry I've got mistaken in the title of the topic. It must be: "USING OF WOULD". Sorry very much!

I think I know why you are confused. Look at the examples below:
(1) If I find my keys, I will go to work.
But: (2) If I found my keys, I would go to work.
and (3) If I had found my keys, I would have gone to work.

These three sentences are all conditional, but only the last one is in the past tense. Sentence (1) is in what is called the present "real" conditional, which is used when the conditional clause ("if...") is probable. When you use this conditional form, you're signifying that there's a good chance you'll find your keys. However, sentence (2) is in the present "unreal" conditional (not the past!), which is used when the conditional clause is improbable or impossible. You can use this form to signify that you don't think you have a snowball's chance in Hell of finding your keys. Sentence (2) may seem to be in the past (because of "found"), but only sentence (3) is in the past tense. Sentence (3) is also in the "unreal" conditional, because the time for finding the keys has already passed (it's too late to find the keys), so the conditional clause is impossible. Thus "would" is not the past tense of "will" - it is a special word that signifies the "unreal" - the imaginary, impossible, or hypothetical.

However that still doesn't explain why "would" is used in the examples you have given. "Would" is a word people throw into sentences to sound polite. For example, "Do you want a cup of coffee?" is not as polite as "Would you like a cup of coffee?" In a way this does have something to do with the conditional, but the the conditional clause is omitted:

"(If there was some coffee around,) would you like to have a cup (of it)?"
"I would love to (have some coffee if there happened to be any)."
Here the person receiving the cup of coffee is trying to sound unimposing. If he/she responded: "Yes, I want some coffee," then the host would feel obligated to provide some. (Of course, this is ridiculous because if someone offers you coffee, then they probably don't mind making it for you, but the English language is funny like that.)

Tom: "(If I asked you to class science into subjects,) would you class it as one or three subjects?"
Martin: "(If you asked me,) I would say..."
In general, if someone asks you a question using "would," you should respond using "would" as well, as Martin has done here.

And in the case of the teacher: "(If I asked you nicely) would you please open your textbooks to page ...?"

All of the examples given are in the present "unreal" conditional, which I'm sure you realize is counterintuitive. If your teacher asks you, "Would you please...?" then the conditional clause is clearly not improbable or impossible - in fact it just occurred!. But that's just the way things work in polite conversation.

Thank u!