Most private schools want to see a sample of your writing ability. To make sure that it is really your work and not somebody else's, the admissions staff will actually seat you at a desk in a room by yourself. All you have to do is write a short essay - short being 150-250 words. You will be told what to write about.
The essay or writing sample is an important part of the school's admissions process. It adds to the picture which the admissions staff already has of you as an applicant to the school. It sheds light on your personality and character, your values and your beliefs. That's really what the admissions people are trying to discover. Whether your point of view is liberal or conservative doesn't matter. Just be honest and be yourself.
It Doesn't Have to be Perfect
Unless you have never written an essay, don't fuss. Express yourself as clearly and as convincingly as possible. Be yourself. Your ideas and the way in which you express them are more important. Show them that you are an original, that you are unique and that you have imagination and creativity. They can teach you how to punctuate. It's much harder to teach you how to think.
Practice Makes Perfect
While it is true that some people are better writers than others, the bottom line is that writing improves dramatically with regular practice. The more you write, the better you write. Write daily if you can. A journal works. So does a serious email exchange with a mentor or family member. Once you are comfortable with putting words on the page, then begin to edit what you have written. Editing is nothing more than reworking your original words and phrases to make them flow better and get your point across better.
Read as much as you can and you will write better.There's nothing wrong with copying a writing style you like. Reading good prose will give you other styles to imitate when you run out of ideas. Read the punchy, direct, snappy prose you can find in People or Sports Illustrated. Observe how those professional writers get their point across with as few words as possible. Try writing like that yourself. Then read something like Harry Potter so you can begin to appreciate devices like irony, foreshadowing and so on. Now write an action scene. Everything you read will add some great idea to your writing bag of tricks.
Don't wait until the last minute to ask for help. A tutor will provide plenty of guidance. You can benefit from skilled professional help and the extra practice.