The English portion of the written exam is very similar to standardized tests in terms of testing grammar and sentence/paragraph structuring. If you were going to study for the written exam, I'd suggest doing it for this section. An SAT or GRE study book would probably suffice. Grammar rules are pretty straight forward and there's a finite amount of them which you could memorize (as opposed to trying to memorize the essentially infinite amount of information covered in the other section).
If you have trouble spotting errors, mouth the words of the sentence so you can hear the words in your mind. If something sounds funny or off, then you're probably good to eliminate the answer.
On the parts of the test that require you to rearrange parts of a sentence or delete/insert some, remember that you want sentences that are logical and clear to follow. Try to pick the answer that makes the most "sense."
We walk home. He walks home.
We = Plural; Walk = Plural
He = Singular; Walk = Singular
Where did the girls buy their dresses?
Girls = plural; Their = plural
Remember that everybody, anybody, anyone, each, neither, nobody, someone, a person, etc. are singular.
If a student is late to class, he or she will get detention.
If a student is late to class, they will get detention.
Student = singular; They = plural
If grammar is not your strong point, then I suggest you get a book and brush up! Remember, you might not be able to cram in everything about geography/economics/history/management/etc. issues into your head---but you can definitely do it with English rules!
Welcome, Mr. Secretary
6 months ago