Since it is that time of the year with all the high school math competitions around the corner, I am sharing the tips and what worked for me.
How to prepare?
The best way to prepare is to practice, practice, practice. There are no real shortcuts to prepare for any math competitions that involve problem solving. If you are lucky and you can find a group (or even one more problem solver) that helps a lot as you always learn from others on different ways to solve a problem or parts of a problem. Solving problems from older tests is always helpful and solving problems from Art of Problem Solving books can assist greatly as well. Most old contests can be found on the web or can be ordered from MAA websites for AMC competitions. Most of the AMC contests including solutions can be found on Art of Problem Solving (AoPS) website. AoPS website has AMC 8, AMC 10, AMC 12, AIME and many other competition problems. Practicing problems will help reinforces concepts and help you with creative and beautiful solutions.. I also found that making mistakes and learning from them has helped me understand the higher level concepts much better. I highly recommend taking systematic approach and gradually building up skills in problem solving. I always ordered books from MAA and AoPS. Besides going gradually through Introduction and Intermediate Series of AoPS books, my favorites were Competition Math for Middle School, AoPS Volume 1: The Basics, and AoPS Volume 2: and Beyond.
Here are some basic tips:
- Don’t be discouraged if you cannot solve all the problems. As you practice more, over time, you will become better for sure. You have to start somewhere. I was able to solve only a few problems (below 10) initially for both AMC 8 and AMC 10/12. I would practice with past tests every weekend (one test per week) during the school year and a few weeks in the summer.
- You can try challenging yourself by trying to solve AMC 12 while you prepare for AMC 10.
- There are almost always multiple ways to solve problems. You will learn the beauty of math and learn how to apply concepts better as you practice consistently.
- It is totally okay to get stuck. It happens to everyone. Come back the next day or next week, and try solving that problem again.
- There are many online courses, summer camps, classes during school years that can help you with new or advanced concepts. I found (and many of my friends) AwesomeMath summer camps very helpful.
- Most previous competitions have solutions online. Try to understand the solution when you cannot solve a problem. Even if you have solved a problem, see the solution as they may have solved it using different methods.
- There is no shortage of problems or competitions that happen throughout the year. Start participating in one and slowly start participating in more as you get more confidence. Not all competitions are created equally. Do not get discouraged when you do not perform well in a particular one. I did horrible in AMC 10 in 8th grade but did a lot better in 9th grade and 10th grade.
- Check if your school has math club, math teams, or other organizations that meet regularly and participate in individual or team competitions. If not, attempt the problems and ask your math department if they can help especially if you get stuck on a concept.
- AoPS has a very active and mostly supportive community. You can always become a member and members usually respond when you have a questions.
- Practice-Be persistent-Don’t be discouraged-Practice again.