Canadian Mathematics Competition
Thursday, February 25, 2010
"Obvious is the most dangerous word in mathematics." -- E.T. Bell
Ahhh! The math contest killed me. When I first began, it was like, I was so focused and so ready to answer all the questions, but as the end of the 60min period was approaching, it just made me all the more anxious. The 60 minutes passed by too quickly.. I remember looking back and forth at the clock. But although that was a bit of a distracting factor, it helped me to concentrate.
I answered as much as I could, and when Part B questions got too difficult for my brain to analyze, I skipped to Part C, but that wasn't any better. I spent a lot of time trying to figure out Part C questions, so I guess that's why I was so stressed!
But anyways, after it was all finished, I was just glad to get it over with, and a little worried about my answers when we went over them in class. But it was an interesting experience.. something that helped me realize how to deal with the anxiety and time pressure of exams, and helped me prepare for the provincial! =)
Soo this is one question from the Cayley contest that I picked to explain.
#10. There are 400 students at Pascal H.S., where the ratio of boys to girls is 3 : 2. There are 600 students at Fermat C.I., where the ratio of boys to girls is 2 : 3. When considering all the students from both schools, what is the ratio of boys to girls?
This was a bit tricky at first, and I think I had to do it twice because the first time I got an answer, I didn't have to think at all. Soo.. that was kind of weird, because it's a math contest. Just by looking at the ratio's 3:2 and 2:3, I quickly just added them together to get 5:5 and got answer (C) which is 1:1. That completely confused my brain, but I knew it couldn't be right.
Anyways, given the number of students for each school, I divided the ratio's to get how many girls and boys for each school.
(Pascal H.S. = 400 students; boys to girls = 3 : 2)
So I took the 400 total and divided it by 5 (3:2 ratio equals 5 parts when added together) and got 80. So that means there would be 80 students for every 1 part ratio. Since there are "3" boys, it would be 80x3 = 240. And same for the girls. 80x2 = 160. Just to be sure, 240 + 160 = 400, so I was sure that was correct.
And again using the same method for the second school.
Fermat C.I. = 600 students
boys to girls = 2 : 3
600/5 = 120 (120 students for every 1 part ratio)
120x2 = 240; 120x3 = 360
Double check: 240 + 360 = 600
That's the first part of the question, but by using the same method, I figured out the ratio for both schools put together.
Total boys from both schools: 240+240 = 480
Total girls: 160+360 = 520
So with 1000 students, the ratio of 480:520 when simplified (each divided by GCM:40) equals to 12:13.
Answers:
(A) 2 : 3
(B) 12 : 13
(C) 1 : 1
(D) 6 : 5
(E) 3: 2
My Answer: (B) 12 : 13
Monday, March 29, 2010
Friday, March 26, 2010
To be good in math...
These 3 qualities are a few of the most important in order to be good in math
1. Patience/ Perseverance
2. Don't be afraid to ask a lot of questions
3. Willingness to learn
I believe that if anyone has these three traits, they can become good in math; whether they are good at it to start with in the first place or not.
Patience is something that may be easy to obtain, but not easy to keep for long as math will always test your patience. Math isn't always easy, especially when learning new concepts or problem solving. With patience and perseverance you can keep on going, keep on solving these problems no matter how frustrating it gets or no matter how difficult it may become. Having the willingness to learn is also key.
Sometimes math will just make you so angry because you can't get it, or will make you just want to give up, so that's why you need to persevere and be willing to learn. Everyone's bound to make mistakes, but you just need to keep on trying! Keep on asking questions if you don't get something! Questions will always help you to grow in your knowledge and understanding, they will always benefit you!
These traits won't exactly make you smarter right away, or make you genius in that sense.. these characteristics will help you develop good math habits and therefore will help you in the long run to become good in math!
1. Patience/ Perseverance
2. Don't be afraid to ask a lot of questions
3. Willingness to learn
I believe that if anyone has these three traits, they can become good in math; whether they are good at it to start with in the first place or not.
Patience is something that may be easy to obtain, but not easy to keep for long as math will always test your patience. Math isn't always easy, especially when learning new concepts or problem solving. With patience and perseverance you can keep on going, keep on solving these problems no matter how frustrating it gets or no matter how difficult it may become. Having the willingness to learn is also key.
Sometimes math will just make you so angry because you can't get it, or will make you just want to give up, so that's why you need to persevere and be willing to learn. Everyone's bound to make mistakes, but you just need to keep on trying! Keep on asking questions if you don't get something! Questions will always help you to grow in your knowledge and understanding, they will always benefit you!
These traits won't exactly make you smarter right away, or make you genius in that sense.. these characteristics will help you develop good math habits and therefore will help you in the long run to become good in math!
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