AMC 10A 2019
Ahh, AMC season. What a great time to be alive (not). This year's AMCs were... interesting.
So I take the AMC from 12 - 1:15, and on that day, I of course had to have two quizzes before the AMC. Fun. But they were pretty easy, and I mostly just focused on AMC stuff and rest.
Leading up to this AMC 10A, my main goal was to qualify for USAJMO. So optimally, I wanted a > 124 or even 130 to give myself a good shot. So that's around 20-22 questions. So I take the test, and let's get into it.
Problems are here: https://artofproblemsolving.com/wiki/index.php/2019_AMC_10A_Problems
Problem 1: This was a major L. Remember how I said I needed 20-22 correct? Well yeah... I kinda blew it. I got this one wrong X_X I put 2^0 + 1 = 1 on my paper and literally wrote the answer as B) 1. And there goes 6 points ughhhhhhhhhhhhhhh.
Problem 2: This one was surprisingly thought provoking, unlike normal #2s. Quick thing is to just factor out 15! and notice it's divisible by 1000, so the answer is 0. But a lot of people in my school messed this up.
Problem 3: This one was scary for me because I almost solved for the wrong variable, and then I was super nervous I got it wrong for a really long time. Anyway, I managed to get it right. It was just some algebra.
Problem 4: This one was just Pigeonhole Principle, or just a bit of thinking.
Problem 5: And here's another mess up. I decided to consider even and odd number of terms separately for some reason, because I was using a general method to find the solution when the difference between the integers is not necessarily 1. Anyway, I hard messed it up and got 45 as my answer instead of 90 :( There goes another 6 points
Problem 6: This one was weird. I only knew how to do it because I knew the perpendicular bisectors had to intersect at a single point for this to be true. A lot of people in my school missed the iscosceles trapezoid :(
Problem 7: This one was just coordinate bashing and Shoelace Theorem for me. There's probably a better method, but mine worked.
Problem 8: Why did MAA put these on? This one was easy if you just considered the orientations of the flags to do process of elimination and then just slide the paper around for getting the first two.
Problem 9: This one was just factoring and then considering factorial function, but it was a bit bashy with answer choices for me.
Problem 10: Oh no, this one. So my school provides everyone with graph paper for the exam as a tool, so nearly everyone in my school just graphed it. Here's the problem: our graph paper wasn't square! So it was really hard to draw it accurately, especially if you had a thick pencil. I actually used this solution at first and got the correct answer, but I eventually realized you could just count line crossings and get the same answer.
Problem 11: This one was pretty easy if you know how prime factorizations work and how the formula for number of factors works. Also uses some PIE, but overall not hard.
Problem 12: This one killed me. I have no clue how to do statistics, so yeah, this one wasn't great. Essentially, you can think about it as having a full dataset of 1-31 and then cutting the ends, which will decrease mean and not median. However, I thought of it as having a full dataset of 1-28 and then adding a bit extra, which increases mean and not median. However, it didn't quite work out as adding actually increases the median a sizeable amount. So yeah, I got this wrong. 3 wrong so far :(
Problem 13: This was just angle chasing in a bunch of shapes/cyclic quadrilaterals. I literally drew a diagram and magically saw it somehow, so oh well. I'm getting better at geo :D
Problem 14: This one also hurt a lot of people in my grade as they didn't consider all cases, but I luckily managed to and drew a TON of pictures.
Problem 15: This one was pretty easily solveable via induction (except I just assumed it, and didn't prove it). But yeah, you can just find a general formula and plug in.
Problem 16: This one was just drawing radii and equilateral triangles and finding the radius of the big circle pretty easily.
Problem 17: Why is this a #17. Really easy to solve using caseworks and permutations of indistinguishable objects.
Problem 18: This one was also easy IF you knew how bases worked. I didn't really, but I guessed from just knowing how in base 10, to get repeating, you did some number of 99...99. So I just guessed 23 / (k^2 - 1) to get 0.23232323... and it worked :D
Problem 19: This one was just bleh. I just found out through experimentation (x+1)(x+2)(x+3)(x+4) couldn't possibly be less than -1, so I got 2018. There's a more clever solution, but mine's works too I guess :D
Problem 20: This one was just casework bashing and figuring out how many arrangements were possible. It took a lot of paper, but honestly wasn't that hard if you were being precise.
Problem 21: This was 3D geo, bleh. Honestly though, not that hard with a good diagram and visualization. At first though, I totally derped and forgot that they gave you the radius so I started doing some magic to find it (it didn't work). Anyway, I eventually got it :D
Problem 22: This one was just a page of casework. Probably an easier method somewhere, but it wasn't that bad.
So I answered 22, and got 3 wrong because of sillies :( So yeah, a 118.5 with freaking #1 wrong :( That kinda kills my chances at USAJMO, but with the AIME floor being 103.5, I easily qualified for that. So I take AIME this Wednesday, and hopefully I can get like a 11 or 12 to qualify :D I don't have high hopes, but who knows? But I have so much work (robotics, school, applications), and I can't study that much. I'll have another shot next year. I'll post about AMC 12B later, but I kinda choked on it and have pretty much 0 shot of qualifying for USAMO :(
So I take the AMC from 12 - 1:15, and on that day, I of course had to have two quizzes before the AMC. Fun. But they were pretty easy, and I mostly just focused on AMC stuff and rest.
Leading up to this AMC 10A, my main goal was to qualify for USAJMO. So optimally, I wanted a > 124 or even 130 to give myself a good shot. So that's around 20-22 questions. So I take the test, and let's get into it.
Problems are here: https://artofproblemsolving.com/wiki/index.php/2019_AMC_10A_Problems
Problem 1: This was a major L. Remember how I said I needed 20-22 correct? Well yeah... I kinda blew it. I got this one wrong X_X I put 2^0 + 1 = 1 on my paper and literally wrote the answer as B) 1. And there goes 6 points ughhhhhhhhhhhhhhh.
Problem 2: This one was surprisingly thought provoking, unlike normal #2s. Quick thing is to just factor out 15! and notice it's divisible by 1000, so the answer is 0. But a lot of people in my school messed this up.
Problem 3: This one was scary for me because I almost solved for the wrong variable, and then I was super nervous I got it wrong for a really long time. Anyway, I managed to get it right. It was just some algebra.
Problem 4: This one was just Pigeonhole Principle, or just a bit of thinking.
Problem 5: And here's another mess up. I decided to consider even and odd number of terms separately for some reason, because I was using a general method to find the solution when the difference between the integers is not necessarily 1. Anyway, I hard messed it up and got 45 as my answer instead of 90 :( There goes another 6 points
Problem 6: This one was weird. I only knew how to do it because I knew the perpendicular bisectors had to intersect at a single point for this to be true. A lot of people in my school missed the iscosceles trapezoid :(
Problem 7: This one was just coordinate bashing and Shoelace Theorem for me. There's probably a better method, but mine worked.
Problem 8: Why did MAA put these on? This one was easy if you just considered the orientations of the flags to do process of elimination and then just slide the paper around for getting the first two.
Problem 9: This one was just factoring and then considering factorial function, but it was a bit bashy with answer choices for me.
Problem 10: Oh no, this one. So my school provides everyone with graph paper for the exam as a tool, so nearly everyone in my school just graphed it. Here's the problem: our graph paper wasn't square! So it was really hard to draw it accurately, especially if you had a thick pencil. I actually used this solution at first and got the correct answer, but I eventually realized you could just count line crossings and get the same answer.
Problem 11: This one was pretty easy if you know how prime factorizations work and how the formula for number of factors works. Also uses some PIE, but overall not hard.
Problem 12: This one killed me. I have no clue how to do statistics, so yeah, this one wasn't great. Essentially, you can think about it as having a full dataset of 1-31 and then cutting the ends, which will decrease mean and not median. However, I thought of it as having a full dataset of 1-28 and then adding a bit extra, which increases mean and not median. However, it didn't quite work out as adding actually increases the median a sizeable amount. So yeah, I got this wrong. 3 wrong so far :(
Problem 13: This was just angle chasing in a bunch of shapes/cyclic quadrilaterals. I literally drew a diagram and magically saw it somehow, so oh well. I'm getting better at geo :D
Problem 14: This one also hurt a lot of people in my grade as they didn't consider all cases, but I luckily managed to and drew a TON of pictures.
Problem 15: This one was pretty easily solveable via induction (except I just assumed it, and didn't prove it). But yeah, you can just find a general formula and plug in.
Problem 16: This one was just drawing radii and equilateral triangles and finding the radius of the big circle pretty easily.
Problem 17: Why is this a #17. Really easy to solve using caseworks and permutations of indistinguishable objects.
Problem 18: This one was also easy IF you knew how bases worked. I didn't really, but I guessed from just knowing how in base 10, to get repeating, you did some number of 99...99. So I just guessed 23 / (k^2 - 1) to get 0.23232323... and it worked :D
Problem 19: This one was just bleh. I just found out through experimentation (x+1)(x+2)(x+3)(x+4) couldn't possibly be less than -1, so I got 2018. There's a more clever solution, but mine's works too I guess :D
Problem 20: This one was just casework bashing and figuring out how many arrangements were possible. It took a lot of paper, but honestly wasn't that hard if you were being precise.
Problem 21: This was 3D geo, bleh. Honestly though, not that hard with a good diagram and visualization. At first though, I totally derped and forgot that they gave you the radius so I started doing some magic to find it (it didn't work). Anyway, I eventually got it :D
Problem 22: This one was just a page of casework. Probably an easier method somewhere, but it wasn't that bad.
So I answered 22, and got 3 wrong because of sillies :( So yeah, a 118.5 with freaking #1 wrong :( That kinda kills my chances at USAJMO, but with the AIME floor being 103.5, I easily qualified for that. So I take AIME this Wednesday, and hopefully I can get like a 11 or 12 to qualify :D I don't have high hopes, but who knows? But I have so much work (robotics, school, applications), and I can't study that much. I'll have another shot next year. I'll post about AMC 12B later, but I kinda choked on it and have pretty much 0 shot of qualifying for USAMO :(
Comments
Post a Comment