Qualities of a GooooD Mathematician

Mr. Cheng wrote a blog post about good qualities of a mathematician. He asked us to write about the three characteristics that I find most important. The qualities that I think are most important are: never giving up (perseverance), willing to learn, and teamwork.
I think it is important to have perseverance because sometimes, even the best mathematician makes mistakes and gets questions wrong. If he/she has perseverance, they will keep trying the question and uses different techniques.
Another quality that goes well with perseverance is being willing to learn. If you don't get the question, you should be willing to learn how to solve it. People who are willing to learn more are the people who strive to do well in school.
The final quality that I find essential is teamwork. You should have good communication skills and be able to work well with others. In math, and the jobs that require math, you have to work with the people around you. If you do that well, you will succeed at what you do.

Pascal Contest

Recently, I completed the 2006 Pascal (grade 9) Contest for fun. This was a question that looked really hard when I first read it, but I figured it out really quickly. Let me show you!

19. The sum of ten consecutive integers is S. Ten times the smallest of these integers is T. What is the value of S-T?

A.) 45 B.) 55 C.) 10 D.) 9 E.) 66

To solve this question, I made an equation of it. First, let the smallest integer be x. This will be what the first equation looks like: x+(x+1)+(x+2)+..........(x+9) = S In total, that would be: 10x+9=S. T would be 10 times the smallest integer, and T would be 10x. To figure this out, you just take away (10x+9) - 10x. Simply the answer would be D.) 9. My reflection on this contest and the problem solving was that it was quite easy, partly because I am in grade 10 and this is a grade 9 contest, but also because I have improved a lot since the last time. I have done a lot more different problems and figured out more different ways to solve them. I feel that now I can solve almost any problem.

Math Contest!

Last Monday, we took part in a Canadian Math Competition. At the beginning, it was quite nervous and people were chatting anxiously. When we received our answer sheets and booklets, I felt more relaxed as I started to do the math. The first few questions were quite simple, but as I worked on, they got harder and harder. I managed to complete most of the questions with some confidence. I thought I did really good at the beginning, but not so good at the end. I tried not to guess any questions, but some of them I wasn't sure about. I felt that I did really good and it was easier than I thought, but when we went over a question I was confident about, I discovered that I got it wrong. I will show you one question that was on the contest that I liked and how I solved it:
12. The price for each item at the Gauss Gadget Store has been reduced by 20% from its original price. An MP3 player has a sale price of $112. What would the same MP3 player sell for if it was on sale for 30% off its original price?

A.) $78.40 B.) $100.80 C.) $89.60 D.) $168.00 E.) $98.00

First, to solve this problem, you have to figure out how much the MP3 player cost at full price. Because I forgot how I solved this problem two months ago, I will use the tried and true guess-and-check method. You just multiply a number by 0.8 until you get 112. First, I plugged in 150 and got 120. Then, I tried 145 and got 116. Eventually, I got 140. From here, solving this problem is easy. You just multiply 140 by 0.7 and you will get your answer, which is E.) $98.00.
I did pretty good this time around and hope to do better next year!