For letter, here is what I have been taught:
Your name
Your address
Your contact information
----------------------
Date
----------------------
Recipient's name
Recipient's address
(Not sure if a line has to be skipped here, but it only seems logical to do so)
Salutation
Subject
(Body of the Letter)
Formal close (Your's faithfully/sincerely)
Signature
Name.
I'm sure this is the format for the letter. I'm just skeptical about where the lines have to be skipped.
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As for Speech writing, there's no particular 'format'. Just have an interesting opening with a proper introduction (+ Don't forget to mention your name). Use one-liners, interesting words etc. Ask a few rhetorical questions and make sure that you cover all the points in detail instead of mentioning irrelevant things that would otherwise bore the audience/examiner.
I've never been interested in Argumentative Essays, so I can't say much about those except that you can either choose to cover both the pros and cons of the topic given, or just give a one sided argument. Use quotations, if possible. I would avoid this though, since Argumentative Topics require you to have knowledge about them beforehand. If you do have the knowledge, don't attempt it just because the topic seems interesting.
Go for descriptive. That's what I always do. Get a few good adverbs and adjectives, along with knowledge of similes and metaphors. Also use personifications and alliterations to make the essay interesting. I also tend to write about all my five senses when being asked to describe something. It may get slightly boring at times, but with the proper words, you can grab the examiner's interest.
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MrDeadman