I made an exercise in livemocha 2 days ago and here are the corrections I got. My friend Caate gave me some lectures with different words in English that also confuses even native english speakers.
My sentence: My mom talked with my dad couple of hours ago.
Correct: My mom talked with my dad a couple of hours ago.
My question: " couple of hours ago is not considered plural? "
Explanation: Hours ago is plural but "a couple" is a singular set. It's sort of like saying, "I bought a bag of peaches" where you have many peaches but only one bag. Couple indicates that there is a set of around two of something. You can either say "a couple" or "couples" but not simply "couple." A couple was kissing in the park. Many couples were kissing in the park.
My sentence: I am solving math problems this moment.
Correct: I am solving math problems at this moment.
My question: " I am not aware that we must use at with this. How will we know if "at" will be use? "
While you can lose the "at" in slang, it's proper to have it there and it makes more sense. You do things at a certain time. I will go shopping at noon. I ate the pear at night. He was king at the turn of the century. If you are specifying a small chunk of time, you generally use at. Or a very specific chunk of time.
If you are specifying a day, you use "on": I ate turkey on Thanksgiving. My final is on Tuesday.
If you're specifying a time in the future, you use "in": I will be gainfully employed in a year. I will be dead in a century. I'll get it done in a day or two.
My sentence: I solved math problems a while ago.
Correct: I solved math problems awhile ago.
My question: "What is the difference between awhile and a while? I always use a while but I am not familiar with awhile."
"Awhile" functions as an adverb while "while" functions as a noun, conjunction, or verb. You do something awhile ago. It has been awhile. I whiled (verb) away the hours while (conjunction) all the while (noun/idiom) it was hardly worth my while (noun/idiom).
It's also something most native speakers don't really pay much attention to alongside words like every day (each day...functions as a noun) and everyday (adjective). On a formal paper it's a pet peeve for teachers but in conversational English, not a big deal.