Solving Radical Expressions.

I think the picture basically explains itself. But anyways here we go. T_T
1.Kill the negative by flipping it to the top
2.Put in the 3/2 into the package
3.16^3 and square root, same with 25^3 and square root
4.For the X term, it's X^3 x X^3/2 which is X^9/2
5.Take out X^4 and there you go! T^T



1.Kill the negatives again by flipping them to the opposite side
2.Put in the 5/2 into the package
3.81^5 to square root and etc.
4.For X and Y terms, it's simply power on power so you x4 with 5/2 to get 20/2 and x2with 5/2 to get 10/2
5. Simplify X and Y
6.There you go :D
7. Picture Mistake. You have to flip X and Y. Sorry about that!

I really don't like doing all the clicking and making sure you have the right terms. It's time consuming and I much rather write it out by hand neatly rather than doing it on a computer. I'm not a tech-junkie and so it was confusing when we had to do it at home. Anyways, always good to learn something new!

Good Qualities for Math!

*Sigh* I really don't like giving my opinions on what qualities you need because people judge you based on the opinions. They might observe you and see if you live up to what you say. I've chose 3 qualities nevertheless. Humbleness is necessary and a very good skill to have. If you're not humble than people will be jealous or even hate you for being what I call, "A Jerk." People shouldn't boast about what they got on their test marks or what they have accomplished. It just causes hate and sadness for the people around you. Being humble will resolve many potential problems.

The second quality that is good for math, would be confidence/intelligence. I couldn't decide which one was more important. They were both pretty important to my standards. Being confident will allow you to go beyond your comfort zone. Being intelligent doesn't mean being smart, it basically means making sure you don't make careless mistakes and putting down every necessary detail in the answer and in your work.

The last most important quality would be to work hard. I've heard that success is like an equation. It's 10% intelligence and 90% being a hard worker. Working hard has brought many people success. It can be seen around the world. Laziness is very common with the "people" today. It can cause very bad effects to you and other people. Working hard is the best quality that everyone should have in math.

It was fun thinking about what qualities that would be good in math. Hahahahahaha!

Cayley Contest Experience.

It was quite an experience. I forgot the day it was on but it was the easiest one yet. It was unexpected because Mr. Cheng hadn't warn us about it. Usually we would do the contest at lunch. But this time we did it in the class room. I thought it was the easiest one yet. I'm also pretty sure I got the 3 questions right. But, you can never be too sure......

I think this contest was my last one and I don't have the sheet with me right now.
I could show you guys a question but the Mr. Cheng didn't give us the sheet back yet.
Thank You for reading!

[EDIT]
Mr. Cheng gave the Math Contest sheet back to me. That's a relief! So, I've decided to share one question with you guys :D
Question 10 goes like this.
"A class of 30 students recently wrote a test. If 20 students scored 80, 8 students scored 90, and 2 students scored 100, then the class average on this test was...."

At first when I looked at the question I got confused because I only counted 22 students. And I was like, that isn't 30! But then I realized that I had misread something and that was the remaining 8 students. T.T
So, for this question I first remembered my old French teacher talking about how bad the class average was. Then I thought of a list with all of our names on it with percentages next to them. I found it easier to do that. So, you want to find the total average right? First, you take 20x80, take off the percent for now, and that gives you 1600. Why do this? Average is adding up all the terms and then dividing by the number of terms you have. In this case, you 20 students and a 80% average doesn't give you a term but two terms and you just have to add them together. Do the same with the next two which is 8x90=720 and 2x100=200.

Add the terms now. 1600+720+200= 2620. Now you divide by 3. And you get 84%.
It was a very fun experience when you do it using personal experiences to solve math problems. Sometimes I find some questions on the contest as difficult as the ones for homework.

Math Contest- March 4, 2010

This was really easy. I can't believe how simple the first 20 questions were. Anyways, I chose to show you guys question 3. It goes like this. The value of 43-41+39-37+35-33+31-29 is?

Well, this is hilarious. It doesn't feel like a Grade 10 question. First, take 43-41 and you get 2. Then you look at 39-37 and you get 2. Now you see that every pair gives you 2. So then you will have 4 pairs of 2s. 4x2=....... (DRUM ROLL)

8!

Very good experience. I felt good about myself when I got 5th in class. But that is not important because it's about improving from the first time. I should work harder because I know I can do this. Back then, when I was in Grade 3, I would always have trouble in Math. I'm not good at Math but what keeps me going is working hard and believing that I can do what other people can do. Math is like a game. If you win you will feel happy but if you lose you will feel disappointed. So, that is why I liked this contest. I did well on it and I want to improve!

Problem Set #2- Math Question

Domo!

Last weeks Problem Set was quite hard, wasn't it?
But anyways, I chose question 8.
The question goes like this, "The average (mean) of a list of 10 numbers is 0. if 72 and -12 are added to the list, the new average will be...."

If you look at the question carefully it says a "list of 10 numbers is 0." What else gives you an average of 0? 0 of course!Now if you write down 10 zeros and add 72 on the right side and -12 on the other side, you will have 12 numbers. Now to find an average you add all the numbers and divide by the amount of numbers you have. -12+72= 60. Now, take 60 and divide by the amount of numbers you have. Which is 12! 60/12=5.

The final answer is 5. :D
My reflection on this is that it was easy since I have learned the basics. I think the key to solving these questions is being calm and adding up all the basics you've learned correctly and you will have the answer. Sometimes it may also require some guessing but that rarely occurs if you have your basics. I really like these problem solving Tuesdays. It gives me a break from doing repetitive stuff and gives me a challenge. Each question is different in its own way and it just feels refreshing and fun!

Feb 9, 2010 - Math Question

Domo!

So, for homework we had to do Math Problems. I did pretty well and our teacher told us to pick a favourite question. Okay! So the question I chose goes like this, "The greatest number of Mondays that can occur in the first 45 days of a year is..." So,this was really easy to explain.

First, you draw out a calendar. The question says "45 days" Then, you write out the numbers. From 1-45 because the question says so. So, you would write out "1" on the first Monday because you want the greatest number of Mondays. If you put it somewhere else, it will not work. Then you continue and eventually you will reach an end. After that, you count the number of Mondays that appear. You will get 7. Good Luck and try your best!

Tower of Hanoi

I must say, it was quite difficult!

My strategy was to watch the first couple seconds of the solution and then figure out the rest!

I've solved 4 disks and currently just solved 5 disks!

It is amusing yet difficult! (\#o_o)/

5 Disks:

The minimum moves for the 5 disks is 31. The first move you should do is move the smallest ring to far right. This is different from the 4 disks where you first move the smallest ring to the middle. I think for 6 disks you would move the smallest ring to the middle. So this suggests that when you have an odd number of rings, you would move the smallest ring to the far right. When you have an even number or rings, you would move the smallest ring to the middle.

Your objective would be to move the last ring to the right. In order to do that, you would have to move the rings above it away. What I found out is, when you move the rings properly they will always end up in the middle! Strange isn't it? Though the first moves are different, all the rings above the last ring will always end up in the middle. X_X

Once you move the last ring to the far right then your next objective would be to isolate the 4th ring. Another interesting thing I found out is when you have four rings in the middle and the last ring on the far right you would move the smallest ring to the empty left space. For the 4 disks, you would move the smallest ring with the last ring. This game is mostly about precision and if you make the right choices or if you make the unnecessary choices.

Formula. Okay. It is quite hard to figure out the formula but here we go.

No. of Disks No. of Moves

1 1

2 3

3 7
4 15
5 31

Observing the table, I've found out that all the minimum number of moves are all odds. This means it doesn't matter if you have an even number of disks because in the end you will have an odd number of moves. Here is a formula that will determine the number of moves. 2^n-1=No. of Moves. n will represent No. of Disks. Eg. 2^3-1=7, 2^4=16-1=15

It is a good formula ne?

Some good points when trying to solve the Tower of Hanoi

- First goal is to move the last ring to the right

-When you have moved the last ring to the right, check if your number of moves is half of the minimum moves required. This means that the next moves you make are heavy important. :D

-Let's say I'm trying to solve the 4 Disks and that I have successfully moved the last ring to the right. Half of the 15 would be 7. What I also found out was if you made the right choices then when you were half-way done it would be an odd number. It it was an even number half-way through or if the number of moves you have made was over half of the minimum moves required then restart. >.<

-Always move the smallest to a space available where it won't interfere with the movement of the other rings below it. This will be quite helpful.

Here is a picture of my personal experience with the dreadful 5 Disks!