Thanks for replying to my previous letter.
'previous' is not needed - 'reply' means that you must have previously sent a letter, and this is the letter in response.
I'd really appreciate it.
I'd = I would. The tense of this verb is the future conditional. It would be correct if you had written: I'd really appreciate it if you would respond to my correspondence a lot quicker in future!!! (lol
So, you would write:
I really appreciate it.
Well, I finished my IGCSE-O'level exams last year when I was in Year 10.
I attended/went till half-year in Year 11, then I moved to this Monash foundation course which I will be finishing this October. I only take 4 subjects: English, Computer Science, Globalisation and Economics - but not Maths. I think it's too late for me to take Maths in the course.
Is the maths is same with in Year 11?
I don't know what you mean here
Is there any chance that I could still join the Business Faculty by getting very good marks in the Monash foundation exams?
Are you sure you mean faculty? This means you will be on the staff (and Monash to me means "Monash University in Melbourne". Do you mean, enter the Business School or Department? If two departments are combined, then they can be referred to as, for example, Faculty of Arts and Science. If that is the case here, then it might be clearer to write 'enroll in'
I'm wondering whether to take (either-omit) Business Management or Marketing.
Allright. (this is odd. What do you mean here?)
I look forward to your response (this is a bit formal).
I look to hearing from you next time/I look forward to your next letter.
Bye for now