2006 Cayley Contest

Grade 10 Mathematics Contest

Part A
Question #2

I find that this type of question can be very challenging. It's simple, but very tricky.

the value of (√100 - √36 )^2 is
a) 16 b) 6 c) 8 d) 1024 e) 4096

Because there are roots within the brackets, you must figure that out first before a number is squared. So the root of 100 is 10, and the root of 36 is 6. Therefore ten minus six equals to 4. 4 squared equals to 16.

Every time I try this on the calculator or in different ways, I get different answers. You are able to get almost all of them actually.. So if you don't know how to solve it, it is very difficult and can mess up the rest of your equation even just by this simple mistake.

Making a mistake like this has happened many times, especially in homework or in tests. It becomes very frustrating because it is just a simple mistake.

Cayley Contest~~

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

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!

monster questions T_T

-----Solving Radical Expression-----

MATH: Problem Set #2

Math 10 Wings
Problem Solving
02.16.2010

Four points are on a line segment, as shown. If AB : BC = 1 : 2

and BC : CD = 8 : 5, then AB : BD equals:

(A) 4 : 13 (B) 1 : 13 (C) 1 : 7

(D) 3 : 13 (E) 4 : 17

_

Explanation:

Since the ratio of AB:BC is equal to 1:2, then the difference

between them is half. Since BC:CD is compared to each other

by 8:5, then as BC is 8, AB can be 4. The sum of BC - CD

is 8+5 = 13; so therefore, AB : BD would equal (A) 4 : 13.

_

Answer:

(A) 4 : 13

_

Response:

After reading this problem the first time, my initial aswer

was (C) 1 : 7. It was tricky because the two different ratio's

weren't even. But after reading it a coulple more times,

I eventually figured it out. It was one of those questions that

you think you get right the first time and are so sure about it

but after reading it again, your first aswer doesn't seem to

fit anymore. So it made me look back and realize I actually

got the answer wrong!

Problem Solving Set 1

Math 10 Wings
Problem Solving Question
02.10.2010.

#12. The graph shows the number of students who selected each of five possible choices in responding to a question. The correct response was the one most frequently chosen. The percentage of students who selected the correct response was:
(A) 14 (B) 56 (C) 50
(D) 11 (E) 44

_

Response:

I picked this question because i enjoyed this one. I had to read it about 2-3 times to actually understand the question because it seems so overwhelming with all the numbers and the graph.. but actually, it was pretty easy.

_

Explanation:

The correct response was the one most frequently chosen. So what it's asking is for the percentage of those that got the right answer. So first you should figure out how many students there are in total. So you add all of them up.

-

300 + 1100 + 100 + 600 + 400 = 2500 students in total

-

Finding that the most frequently chosen answer was the one with 1100 students, I divided 1100 by 2500 (total students) in order to find out the percentage.
1100/2500 = 0.44
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= 0.44

-

0.44 x 100 = 44 %

_

Answer = (E) 44

Tower of Hanoi

My Strategy:

This was the most frustrating game ever to begin with. I couldn't get it at all, until playing for a while, and figuring out some patterns. Once I figured out how to move 3 discs in 7 moves, and then 4 discs in 15 moves, I realized that you have to move one set at a time. For example, you have to move 3 discs into an empty pole, and then aim for getting 4 discs into an empty one and so on before you can move 5 discs.

I started off by getting the top three pieces (first set) to move all the way to the right.

Secondly, the top four pieces (second set) was moved to the empty middle pole.

And thirdly, back to the far right, all five discs were moved to the empty pole.

To solve: I alternated small pieces with bigger pieces to get the bigger disc on the bottom. The smallest piece always moves to the right if the starting number of pieces is even; and to the left if it is odd.

FORMULA:

______________________________________________

I tried the last level on this specific site as well which was aiming

for moving 12 discs. But after half an hour, multiple mistakes,

and resetting twice, I gave up after moving only 10. (with mistakes)

So many times when I played, I blanked out, repeated steps,

and had no idea what I was doing, or what I was going to do, so

I would end up going in circles. But after so many tries, I figured

out a pattern! And I figured out some basic rules. It was so

confusing at first, but after a while, you get the hang of it.