Start with the right mindset

Before we even get into all the math, I’m going to give you a few tips that will save you a lot of trouble. Basically, a bunch of things I’ve learned over the last twenty years (yep, really) as I’ve helped people a lot like you to do really well.

Who you’re really competing against

I’ve said before that the people you’re competing against here are really, really good. But now I’m going to focus us on your most important competitor, and that’s the person you were last week. Also known as your past self.

In the time since you were that person, you’ve learned some stuff, you’ve practiced some stuff, and you’ve thought about some stuff. You’ve gotten better. You’ve gotten smarter. So you’re a slightly different person now. A different person who can do things you couldn’t do before.

From now on, no one else matters.

Your real goal

Your goal through this work is to become better. Nothing more or less.

When you do better than your past self, you are proving that you’ve changed. That you’ve improved. That your work made a difference for yourself.

So focus only on improvement.

Do not aim to get a particular score.

Do not aim to match a particular person.

Do not aim to break a record.

Aim only to do better than you did last week. Do this week after week after week.

How to practice

The best way to improve your AMC 12 ability is to use a technique called deliberate practice. Since it’s the best way, that’s what you’re going to do.

There are three phases to deliberate practice:

Take a practice test.
Based on your performance, figure out exactly where you could improve most easily.
Do whatever it takes to improve in that area.

You repeat these three phases over and over, getting better each time.

Please note: most people completely skip phases 2 and 3 above. As a result, they improve very little, if at all. So don’t make that mistake.

What’s a good score

A good score is any score higher than the score you got last week.

Anyone who tells you otherwise doesn’t know what they’re talking about.

What’s an impressive score

The best answer is: Who cares? We’re not doing this to impress anyone. So quit worrying about it.

But since we’re talking about it, I’ll let you in on a secret: an impressive score on the AMC 12 is much lower than most people realize.

After all, most people who take the AMC 12 are used to scoring all the problems right on most tests, so they expect that you need to get 25 out of 25 in order to have an impressive score. But that’s actually crazy – almost no one does this.

Here’s a fun quiz: out of 100 people who take the AMC 12, how many do you think get 20 out of 25 right? That’s 80% right, which is a B- in many classrooms. So how many?

Well, in 2019, 95% of the people taking the 12A test did not get that many right; they got 19 or fewer.

Surprised? Just wait: the most common score was 7 out of 25. If you got 9, you were in the top half. And remember, this is not just the top half of students in general. This is the top half of students who took the AMC 12. They all thought they were going to do great!

…and in fact, many of them did do great, but they didn’t realize it. Which is a little sad, right?

There are three things I’m trying to get you to see here:

These questions can be hard. You have to be patient when you’re working on them.
These questions can be tricky. You have to be careful when you’re working on them.
Your score can be very misleading. You have to set aside all your normal expectations, except that you want the number to go up over time.

Oh, also this: if you do all these things, you will earn an impressive score. You just won’t realize how impressive it is while you’re in the middle of it, because you are not used to a test whose score works like this. So like I said at the beginning, quit worrying about it.

Pacing

You have 75 minutes for the 25 questions. So you have about three minutes for each question, right?

No! Definitely wrong. Sure, the arithmetic checks out, but it’s the wrong arithmetic.

There are two reasons why:

First, if you go that fast, you’re going to make avoidable (careless) mistakes. What good is it to get to problem #25 right if you answered #1 wrong? That’s silly.

Second, you’re going to stress yourself out if you try to go at that pace. It’s just too fast.

Third, you’re going be paying attention to the clock instead of the problem in front of you. You need your full attention on your work.

Fourth, these problems are arranged more or less in order from easiest to hardest. So why give yourself the same time budget for each question? Your solve rate will go down as you get to harder questions, and that’s fine. Just take as long as it takes to get to a good answer, then move on.

Fifth, since they’re arranged from easiest to hardest, but they are all worth the same point value, why not spend your time making sure to get the first ones right? It will take extra time to do it that way, but you’ll get a higher overall score for sure.

Sixth, pretty much no one gets the last problems right. So why plan to waste time on those, when you could be spending the same time nailing the easier ones?

Wait, did I say two reasons? Whoops, nope, there are a lot more reasons than that. So don’t rush and don’t worry about your pace.

You’re not supposed to get to the end. (Surprise!)

How to use paper

In short, you need to use paper as though it matters.

Yeah, of course they won’t collect your scratchwork, so in that sense you don’t need to do it. And yeah, of course, you can do work in your head faster than you can on paper.

But here’s the thing. When you do work in your head, you make little mistakes. Not many, maybe, but they add up. And here’s the other thing. Writing things down doesn’t take as long as you think it does. Plus, writing things down lets you check your work and think things through more clearly.

It all adds up to one thing: if you do your work on paper, you’ll get a higher score overall.

Don’t believe me? That’s fine. So put it to the test:

Try doing one timed test where you do everything in your head, and a second one where you write all your thoughts and calculations on paper. Here’s what I bet will happen: the test you did in your head will feel better, will feel faster, will seem so obviously better that you will swear that the test you did in your head will be the one with the higher score.

And then you’ll check your scores and discover that you were wrong about that.

And then you’ll re-check your scores because you won’t believe it.

And then you’ll look back at the test you did in your head and notice the mistakes you made.

And then you’ll wonder how you did that.

And then you’ll be tempted not to count those as wrong answers. Because you knew what you were doing; you just messed up on something small.

So pay really close attention here: small mistakes are the main reason people underperform on the AMC 12.

So, don’t make that mistake. Instead, use your scratch paper as though it matters. Because it does matter.