Mastering Math Contest Questions: Tips, Resources, and Strategies

[bjgawp]

Hi everyone. Getting to the point, the types of questions that math contests have are not really taught, so to speak, in high school. I was just wondering if anyone had any resources or tips for solving these kinds of questions. For example:
Suppose n and D are integers with n positive and 0 ≤ D ≤ 9. Determine n if n / 810 = 0.9D59D59D5 ...
- Questions that involve repeating decimals and such ... I have no clue where to start

Four tiles identical to the one shown, with a > b > 0, are arranged without overlap to form a square with a square hole in the middle.
http://img19.imageshack.us/img19/6818/abcxp8.png
Determine all positive integers N for which there are odd integers a > b > 0 such that the ratio of the area of the inner square to the area of the outer square is 1:N.
- Geometric problems involving ratios are often confusing as well.

I don't expect anyone to answer the questions (I attempted these questions at a math contest already). I just need some tips for future questions that may ressemble these.

 

[Gokul43201]

Most number theory questions, like the first one above, are actually accessible through stuff taught in school. For the problem above, you can use the standard technique that's used for converting a repeating decimal to a rational fraction. Beyond that point, it's just being clever about numbers that are divisible by 11. I've found that for many of these problems you develop a good idea of how to solve them as well as the ability to find solutions quickly, if you learn a little bit of modulo arithmetic. This is learnable by anyone with a high school level math background. You will find a chapter on modulo arithmetic in any introductory text on number theory (e.g., Burton).

 

[tacman]

Thank you for sharing your concerns about mastering math contest questions. It's true that these types of questions may not be explicitly taught in high school, but there are definitely resources and strategies that can help you approach them with confidence.

Firstly, practice is key when it comes to solving math contest questions. The more you expose yourself to different types of problems, the more familiar you will become with the patterns and techniques used to solve them. You can find a variety of math contest questions online or in books specifically designed for these competitions.

When it comes to questions involving repeating decimals, it's important to understand the concept of infinite geometric series. This means that the decimal pattern can be represented as a fraction and solved using algebraic techniques. There are many online resources and tutorials available to help you understand this concept in more detail.

For geometric problems involving ratios, it's important to have a strong understanding of basic geometric principles such as area, perimeter, and similarity. Additionally, using visual aids such as diagrams or graph paper can help you visualize the problem and come up with a solution.

Another helpful tip is to work backwards when solving math contest questions. Start with the answer and try to work your way back to the given information. This can help you identify patterns and understand the logic behind the solution.

Lastly, don't hesitate to ask for help or clarification if you are stuck on a question. Your teacher, peers, or online forums can provide valuable insights and approaches to solving the problem.

Remember to stay calm and focused during a math contest and to use all the resources and strategies at your disposal. With practice and determination, you can master these types of questions and excel in math competitions. Best of luck!