Sorry for writing so much in advance! I’m a little stressed…
At my school PreCalculus is actually called Math Analysis and is considered one of the hardest classes offered (some say it’s harder than calculus and some say it’s the same difficulty). I’m a sophomore in Math Analysis H and, although I have one of the highest grades in the class, I only have an 88.8. It’s not that I don’t study or do my homework. I always do my homework and I study starting two days before the test (we have a test every week). The tests are pretty long, we get no calculator, and are overall pretty challenging. I never think afterwards like I could have studied harder. The teacher can pull any concepts she’s taught us or we are expected to just know and combine it with the current chapter. In addition, we have to apply our knowledge for the majority of the problems and not just know how to do the ones we practice in class. The tests are given on a strict time limit. The class is basically made to weed out those who actually aren’t good at math. It’s funny because every single test is adjusted up about 3-5% which is a lot but no one would be able to get an A otherwise.
Anyway my last test I pulled out a 92, which raised my grade from 87.9 to 88.8. I really needed the test I took today to bump me up another percent, but it was excruciatingly difficult. My head hurt so bad afterwards and my teacher had to give everyone an extra 25 minutes and still not everyone finished (I barely got all the problems done–but two of them I made up a lot of the work). Almost every test is like this but this one was extra long and involved long proofs.
Sorry for my ranting, but the problem is that was my last test before the midterm (besides a graphing calculator quiz next week which is known to be hard too). The midterm is also known to be impossible and the majority of people get Cs. Last year the highest grade was a 93 on the midterm and she was insanely smart.
I know I’m doomed, but any tips for taking challenging, time crunched tests??
Will this ruin my chances for getting into a good college? Up until now I have a 4.0 unweighted and 4.55 weighted. I do choir and track. I participate in clubs and tutor kids in math. I’m also going to volunteer at the hospital as soon as new spots open up.
Also I’m signed up to be a full IB diploma candidate because I really like every subject, but particularly math and science.
Speak to your guidance counselor.
Not to vent, but to ask about past college admissions from your school.
I bet you a dollar you’ll find that hundreds of kids in recent years have taken this challenging course, and come out on the other side better prepared for college than you think. And that they’ve gotten into some incredibly wonderful schools.
Then take a deep breath.
OK as far as those tests go: I could answer, but that would apply to the math tests I give. Why not stop by after school one day and speak to your math teacher? Ask her about the best methods for studying for her tests.
Of course, being able to come up with the solution quickly helps, which comes through practice.
That’s what a good test is supposed to do. Additionally, exams in college, while testing the same concepts, can vary drastically from previous semesters’ exams.
I don’t know about your case, but for me, on proof-based tests, I try to write as quickly but also as concisely as possible. For example, do not waste time explaining or proving theorems already discussed in class. For long proofs, break them up into lemmas or cases so that the organization is clear, then combine them into your solution. Here is an example problem that appeared in my number theory HW (but could’ve very well appeared on the exam):
Q: Prove that a^m - a^(m - phi(m)) is a multiple of m for any integer a. (phi(m) is Euler’s phi-function).
An example way to write the proof:
Let m = p1^a1 * p2^a2 * … * pk^ak be the prime factorization of m.
Lemma
a^m - a^(m - phi(m)) is divisible by pi^ai for 1 <= i <= k.
Proof of lemma
Expression factors to (a^(m - phi(m)))(a^phi(m) - 1). We have two cases:
Case 1: pi does not divide a.
Proof of Lemma assuming Case 1
Case 2: pi divides a.
Proof of Lemma assuming Case 2
End of proof, because we covered both cases. //
From the lemma, it follows that a^m - a^(m - phi(m)) is divisible by m. (a more rigorous way to prove this implication is by the Chinese remainder theorem). //
Sorry for the somewhat long post, but I hope the above example was helpful - writing proofs takes practice and good organization of your proof is essential.
Thanks for the responses! My test wasn’t actually a proof based test. It was on trigonometry angles, but the proofs were for the law of cosines and Heron’s formula (cosines was simple but herons took me forever to figure out because of trig identities). I would say the proofs were the easiest part compared to the other 13 problems.
Also next chapter we have is Analyical Trig. I always thought I was good at Trig until this class haha.
I really like my teacher but she doesn’t give additional practice problems and she says to just practice ones in the book we haven’t done. She never ever will hint if a certain test is hard or easy. And by easy I mean a little less hard.
Also my counselor is a super sweet old man. He’s more social than helpful when we meet actually.