1. How should I get the most out of taking practice tests? (aka AMC 10’s, Mathcounts, etc)
If you want to be really thorough, you can:
(Let’s take AMC 10 as an example)
Time yourself for 75 minutes. Record what you have so far. Then continue working on the problems (maybe in a different color pen) until you cannot make any more progress on any more problems. Check your answers that you got within the 75 minutes, and the ones you got after.
Review the solutions to ones you felt you had a chance of solving but didn’t solve. Reflect on how you could have thought of the solution(s) to those problems yourself. Review the solutions to ones you got right if you feel the need to, to see if there were faster ways to do some problems.
Reflect. (maybe on careless mistakes, and how to avoid them in the future, on time management, etc)
Rinse and repeat.
To be honest, this is going a bit overboard if you do it on all 40 past AMC 10’s.
What I actually recommend if your goal is to maximize your score:
Do the above for a few tests.
Get a sense for how many of the easy/earlier questions you can consistently get right.
Take as many tests as it takes to feel confident on the first 10 or 15 or X questions.
Avoid doing the the first X questions on future tests, and only work on problems slightly above your comfort zone to continuously improve your the range of problems you can solve.
Reflect: Are there any recurring themes between certain types of questions? Can I categorize many commonly occurring types or themes of easier or hard questions?
Continue.
Go forward in life with confidence.
1b. Should I review the questions I got right? The ones I got wrong? The ones I left blank?
Definitely retry the ones you got wrong. See if you can find your mistake on your own. This is one of the most important parts of the learning process.
If you feel the need to review some ones you got right (i.e. they felt hard but doable, you suspect there was an easier way than the way your did it, etc.) then review them.
For the ones you left blank, you should try them more on your own, and if you get stuck, peak at the solution for a hint or just read the solution to try to learn something new. Some problems may be too hard for this though, so it may be good to save those for later.
2. Can I make Contest Y from where I am now in X amount of time?
Honestly, I can’t answer this question for you.
What this question is really asking is: how far am I from the level of having a chance to qualify for contest X?
Again, I can’t answer, but I can give a rough idea of the amount of math knowledge and experience needed to have a chance to qualify for contest X.
How fast you work, how hard you work, how efficiently you learn, how well you remember, – those are things that you know better than me.
Who am I to say how much you can grow as a person and as a mathlete in X amount of time?
I can only give guidance on how to learn math better, and help people understand concepts.
3. How do I prepare for AMC 10/12? Are there any prereq’s?
Make sure you have mastered a lot of the concepts tested on Mathcounts States and Natioanals, if you haven’t already done so. I highly recommend this for many reasons:
- Mathcounts teaches you the basic problem solving, Number theory, and counting skills you will need to solve hard AMC 10 problems.
- Mathcounts is good accuracy and speed training.
- The recent AMC 10’s are not as beginner friendly. I would recommend starting at old Mathcounts State and moving to newer ones. I recommend the same for going through past AMC 10’s.
There are two things to prepare for.
- Learn the theory you need.
- Practice with lots of problems. This will extend the range of problems you can do with your current arsenal. This will also give you the confidence and experience you need to more forward confidently through the problems on test day. Nothing beats doing lots and lots of problems for preparation.
4. How can I learn the math I read on the AoPS wiki better (or learn math from the internet more efficiently in general)? I find many new concepts don’t stick to my brain well for a long time.
Honestly, learning math is so personal that everyone does it differently. You will need to try different ways of learning to figure out what works best for you. Ideally you want to rediscover as much of math on your own as possible, and minimize reading how others solve problems – figure out your own way to solve problems and understand deeply, even if you don’t read much of what others write on AoPS wiki. But you also need to learn from past mathematician’s theorems to get you started (like Vieta’s, etc).
Once you have the foundation theorems, you should ideally be problem solving own your own 90%+ of the time and reading other’s solutions < 10% of the time. Of course, doing so requires being able to figure out which problems are good for your “range”. Like maybe your current range is #16-20 on AMC 12’s. A good range of difficulty would be when you can solve about 50% to 80% of the problems in your “range”.
The range of problems you should attempt should be challenging, but not too challenging for you, so that each problem you solve feels like a victory.
I personally leave unsolved problems as future challenges instead of reading solutions, but this is a decision you will need to figure out.
5. How do I deal with nerves while taking the AMC’s, AIME, or Mathcounts?
Short answer: Practice by participating in lots of local and online national contests throughout the year.
Long winded answer:
I was extremely nervous every time taking a mathcounts test, and same for AMC 10/12 in 9th/10th grade, so I know how you feel. Keep in mind that lots of other people also feel nervous on the day of the test, so you’re not alone!
Also, there is life after math competitions. In the end it’s not such a big deal.
A much bigger deal would be something like, being born in a poor country and not having enough to eat, or suffereing from depression, or any other unfortunate thing that might happen in life.
So just be happy, and do your best! Also, realize that many other people get nervous too, so you’re not in the boat alone! There’s always a big subset of people who get very nervous, an a bigger subset who very nervous, and maybe an even bigger subset who don’t get nervous at all.
However, lots of the people in the “don’t get nervous at all” category probably have never prepared for AMC 10/12, or just don’t care about their results very much. So better to care a lot and be a little nervous, then to not care and not be nervous.
6. If my goal is to qualify for the AIME for the first time, should I take the AMC 10 or the AMC 12?
It really depends on you and how hard you find each test relative to their approximate cutoffs. Many students find it easier to qualify for the AIME via the AMC 12. The AIME cutoffs for the AMC 12 are usually 10-20 points lower than the cutoff for the AMC 10. This means you can answer 2-3 fewer questions correctly on the AMC 12 compared to the AMC 10, and still make the AIME cutoff.
Another small factor to consider is whether or not you are familiar with Trig, Logs, Complex Numbers, and Conics to answer those questions on the AMC 12. However, this is largely irrelevant for AIME qualification purposes, and the first 12 questions on the AMC 12 typically don’t require knowledge of those “Precalc” topics to be solved.
In summary, if you think you can answer 12-13 questions correctly on the AMC 12 more easily than 15-16 questions on the AMC 10, then take the 12. If not, take the 10. The first half of both tests are generally just problem solving and don’t require advanced knowledge, for either test, so there isn’t much difference between the types and styles and difficulty of the first 12 questions on the AMC 12 and the first 15 on the AMC 10.
12-13 correct and 12-13 blank on the AMC 12 has been enough to qualify for AIME in recent years. 15-16 correct and 9-10 blank has been enough to qualify for AIME via AMC 10 in recent years.
Don’t take my word for it. You should just take both the AMC 10 and the AMC 12 of a previous year (preferably the same year, but with A/B tests, like 2017 10A and 2017 12B or something) and see how close to the cutoffs you are on each of them. Then decide for yourself. AIME cutoffs of past years are found here:
7. Other Useful Links:
Xinke's Math Academy 