I'm writing a chapter where my character is having an educational competition and I feel that my writing is very poor. I can't find events to write about aside from asking and answering questions of the competition. Should I just drop this chapter?
You have four primary options:
Edit and rewrite the chapter
This is what you should do first before doing any other options. Start by editing your current chapter. If you substantially improve your writing with edits on grammar and flow you may decide to keep the chapter. If not, try at least one time to completely rewrite the chapter and make it different than your previous try. Who knows? Maybe you'll write a rewrite that you love and decide to keep. You can also make smaller, more technical edits to polish off your chapter for satisfaction levels. If you have done this and it didn't work, you can pick another option.
Revise the event
This would mean changing your event to make it more engaging to your reader. This could be adding an interruption to the school contest or mixing up the event's plot. This could break up the dull parts of the chapter, thus making it worth keeping.
Delete the chapter and summarize the event in a later chapter
This works if the actual event is important to your storyline, but getting a play-by-play for it is not. You can summarize the event through dialogue or narration in the following chapter. For example, Jane could tell Emily about how she won second place in the contest in the next chapter, meaning that you don't have to narrate the actual contest.
Delete the chapter and the event
This is the riskiest option. I assume that the event is important to your storyline, but if it isn't - you can consider this option. It would mean removing the chapter and the event altogether from your story. Avoid doing this unless it is absolutely necessary.
Before doing any of the options I would recommend getting a friend's opinion on your writing. This way they would tell you what they think and what option would work best for your story and be most convenient for you.
If there are no events, it's very likely that this chapter is not moving the story forward.
What is the conflict of the story? How will this contribute to sharpening it? How will it raise the stakes? What effect does it have?
If you conclude that it does not have enough effect to justify its existence, you may certainly be right to excise it. If you keep its having occurred, you may have to allude to how it was a dull affair of many questions, but an allusion may be all you need. And possibly you may excise even the occurrence.
Don't try to judge your chapters on your first time through them. If you only have a few thoughts for it right now, just move onto the next chapter. If you suddenly get inspired, come back to this chapter and add onto it.
Once you have a pretty complete first draft, go back, look at your overall structure, and decide which chapters need to be in the final book, which ones are just going to be backstory that isn't in the book (or were just things you needed to write in order to get to where you wanted to be) and which chapters you haven't written yet, but need.
If it turns out this chapter is crucial, put the work in then to make it good, or figure out something better that will replace it.
You can have other people, such as beta readers, help you if you need it. Sometimes I'll forget a word or need to know how a scene would sound better (with one certain word, or a different one in its place), and so I ask someone to help.
For example, I was writing a scene for one of my dragon books once, and my character was flying through the air. I was stuck on two words, slid or rubbed, and I asked my brother to help me. I asked him which of these two scenarios (put below) that he liked better.
I slid through the air,
I rubbed through the air,
My brother picked the second one.
Now, I think they were slightly different in the actual book, but you get the point. Ask other people for help - whether they think it looks better one way or they think that you should write it differently.