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, 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:
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?
Go forward in life with confidence.
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. Other Useful Links: