Okay, i was finally able to log onto this math blog, and can now write about my trip to the UBC math contest field trip.Well... it was fun. While I understood hardly anything in the actual contest, the experience of walking around UBC and doing the small math workshop were great. I liked working with Joon, and occasionally Margaret and Kimberly. Anyways, 10 things I learned about math are:

1. The ! symbol means like... continuing of all the numbers after the number... I think. For example, if there is (1-x)! , that means (1-x)(2-x)(3-x)(4-x)... etc...

2. It is much easier to do math problems if i don't actually calculate pi when doing them, and instead just substitute the n symbol thing. Like, instead of actually typing in my calculator 3.14 multiplied by 4, its easier to just write on my paper 4pi.

3. Hmm... I am already running out of things to write about... I liked the Chinese speaker man... I got to shake his hand... and he taught me about how to make one formula into other formulas and stuff... something that I recently did in Physics 11 class.

4. That reminds me, I learned that there are 7 or so math problems that if you solve, you get 1 million dollars! That's quite exciting.

5. Umm... I learned that I have quite messy writing when writing on chalk boards. But that doesn't have to do much with math. I hope this counts.

6. I thought that UBC was all Asian people, but, to my surprise, there was a fair amount of white people and other races. Again, I hope this comment is passable for something I learned about math.

7. I recently learned that I actually have to write a blog about this field trip. That is what I am doing now... even though I don't even have math this semester...hmm...

8. I actually already knew this, but I didn't ever really use it in anything ever or anything so...um... when two circles are tangent, they are touching and the angles on either side are equal... I think

9. I really can't think of anything else I learned about math... um... I guess I can say there are different ways to explain the Pythagorean Theorem...

10. Oh yea, some math problems have no answer... I think... there was one thing like a^2 + b^3 + c ^4 = d^5 .... or something like that... and it had no answer.

There, those are 10 things that I "learned about math". Thank you

- Jeffrey Boschman

edit*

Okay, so I actually also have to talk about what I learned through the talk. I learned that math talks don't always have to boring, and that some mathematicians have senses of humour. Anything else I may have learned through the talk I mentioned above.

Also, um... how can the workshop help me in future math endeavors or something like that? ... well... everything I did in that workshop was for grades 8-10, and so I had already learned all of it, and could do most of them. However, I guess I could say that I learned that there can be more than one way to solve math problems, I should have written that in my 10 things i learned about math initially.... oh well.

Now I am done, hopefully. Sorry this post is quite late Mr. Cheng

qualities of a mathemagician

Helloooo, today in math class, we did a test. It wasnt too hard, but I kept messing up in my formula for the last question, and so I eventually just counted spaces on a graph to solve it. Anyways, that has nothing to do with this blog entry. I only included it because right after we were done the test, Mr Cheng wrote about good qualities that make someone good at math. The top 3 qualities that I think make a good mathemagician (not a magician plus a smart math guy, just a smart math guy) are:

- knowing the fundamentals of math
- thinking outside of the box
- being patient and diligent

I think that having basic math skills are very important because without them, you would not be able to do any questions at all. eg. You need to know how to do subtraction and addition to do algebra.

Also, being able to think outside the box is really useful in solving math problems. Sometimes in math, questions are worded strangely or are just plain hard, but if you think outside the box and try unorthadox methods, then you can usually figure them out.

Lastly, you gotta be patient. Math takes a really long time sometimes, and it might get really annoying. Even though you might be frustrated, you have to be patient and work through the questions in order to succeed.

These are the three major things I think that you need in order to be good at math.

solving radical expressions

Okay so a couple of weeks ago, we learned about radical expressions, which I think these are examples of. They are pretty hard, but after a while they get easier. These 3 examples we solved on Microsoft Word, and just figuring that out is harder than the actual math. On the other hand, I haven't done one of these in a few weeks, so I might not remember how to do them right. But anyways, these are radical expressions (I think).


The steps to solve this one are (stolen off Mr. Cheng):
1. resolve the negative exponent x^-2 by flipping it to the top
2. distribute the exponent 3/2 to all components
3. 3/2 means cube and then square root, so 16^(3/2) = 64, 25^(3/2) = 125
4. for the x term, power on power, so you multiply 3 with 3/2 to get 9/2
5. write x as a radical and simplify
Done! Yay!



To solve this second one, you:
1. resolve the negative exponents 81x^-2 and 49y^-4 by flipping them to the bottom and top accordingly
2. ditribute the exponent 5/2 to all components
3. 5/2 means find square root and then do to the power of 5, so 81^(5/2) = 59049, 49^(5/2) = 16807
4. for the x and y terms, power on power so you multiply 4 with 5/2 to get 20/2 and you multiply 2 by 5/2 to get 10/2
5. write x and y as radicals
6. simplify x and y
Yea! Done this one too!

cayley canadian math contest

Okay so a couple of weeks ago (Thursday, February 25, 2010 to be exact) our math class participated in an across Canada (I think) math contest. It wasn't the hardest thing I've ever done, but it was still pretty stressful. Most of questions were do-able, and I know I could I have gotten some of the harder ones if I had enough time. For one of the questions (number 16), I almost figured it out, but ran out of time at the last second. There was also one more question (number 14) that I thought I got right, but after we went over the contest in class, I learned the answer I put was wrong. :( In the end, I tried to leave exactly 5 questions that I did not know the answer to blank in order to get the max 10 free marks from unanswered questions, which was pretty good because there was in total 6 questions that I didn't know the answer to.

During the contest, I was quite focused. I think that the pressure helped me concentrate better, but from this contest I learned that being calm was the key to figuring out the answer. I also think that because near the end of the contest, I was running out of time and I was forced to work harder and faster - the pressure helped me do better.

My favourite question from this contest was number 23, but it would take way to long for me to explain what I did (and I don't quite remember everything I did anyways), and so I'm going to choose a different question. Another question that I liked was number 21, but it involves a drawing, and I don't really want to make it on paint, and so I'll choose an easier question. A fun and easy question was number 7. and so I'll do that one. I like it because it is fun and easy and simple. =D

The mean (average) of 5 consecutive integers is 9. What is the smallest of these 5 integers?

a) 4
b) 5
c) 6
d) 7
e) 8

If the Average of 5 consecutive integers is 9, then 9 must be the middle number. If there are 5 numbers, then the middle number must be 3. The number 3 is two less than 5. The number 7 is two less than 9. The answer is d) 7.

problem solving 3. question 19

Okay so yesterday in math class, we got the grade 10 Canadian Mathematics Contest from 2006. I came in late so I had to rush through all the questions, but there was one that stood out to me as both challenging and fun. I liked it because it was a little bit confusing and I almost got it wrong the first time because I read it wrong. From this I learned that I always have to read the questions very carefully and make sure I understand what they are asking. The question was number 19.

19. In a bin at the Cayley Convenience Store, there are 200 candies. Of these candies, 90 % are black and the rest are gold. After Yehudi eats some of the black candies, 80 % of the remaining candies in the bin are black. How many black candies did Yehudi eat?

a) 2
b) 20
c) 40
d) 100
e) 160

At first when I looked at this question, I automatically assumed that the answer was 20. Then I saw that in the question, it stated that 80% of the REMAINING candies were black. I then looked at the multiple choice answers given to you. I knew the answer wasn't a) 2, because the number is way too small. I also knew that b) 20 was wrong now, and so I tried out c) 40, to see if it worked out.

If 90 % of the 200 were black at the beginning, then that means that 180 of them were black.

200 x 0.9 = 180

If I take away c) 40, then I am left with 140 black candies and 20 gold candies,

200 - 180 = 20

and this is obviously not 80%.

140/160 = 0.875 = 87.5%

All of a sudden, the answer was really obvious. I didn't even have to look at the next multiple choice answer to know that the answer was d) 100. If I take away 100 from 180, then I am left with 80 black candies, and 20 gold candies, which works out to be the answer.

180 - 100 = 80

80/100 = 0.8 = 80%

The answer is d) 100

solving radical expressions

This is a really hard radical expression thing done on word...

problem solving 2. question 15

So this is my second problem solving set blog thing. I personally liked this problem solving set better than the last one, but I'm not sure why. I guess i just found the questions more challenging or something. I also learned that for some questions, you just have to concentrate. If you focus and think about the questions more, then you can figure them out easier. That is why I liked question 15. - at first I had no idea what to do, but then I stopped to think about it a bit, and I started understood how to do it. It was challenging, but not too challenging and forced me to really understand what the question was asking. But anyways, the question that I liked from this set was question number 15.

15. Four points are on a line segment, as shown.
If AB:BC = 1:2 and BC:CD = 8:5, then AB:BD equals?

•-----•----------•-----•
A. . . . B. . . . . . . .C. . . . D

a) 4:13
b) 1:13
c) 1:7
d) 3:13
e) 4:17

To solve this question, I first compared the second bit of information, where it says that BC:CD = 8:5, to the first part, where it says that AB:BC = 1:2. From this I figured out that if BC is equal to 8, then AB is equal 4.

1:2 = ?:8
1:2 = 4:8

I also know that CD is equal to 5. Then, in order to get BD, I added up BC and CD (8 and 5).

8 + 5 = 13

This gave me my final answer of AB:BD = 4:13 and showed that the answer is a) AB:BD = 4:13

problem solving 1. question 6

This blog is about a problem solving page we got. I really like problem solving, especially math questions, and I'm not just trying to be a nerd or a suck-up. I actually think they are really fun, especially when you do them with your friends. Problem solving is always easier and more fun with other people, that's what i learned from this problem solving set. Anyways, there was a particular question in this math set that I thought was both more fun and easier than the others. This is the question:

6. If x = -2, the value of (x)(x^2)(1/x) is...?

a) 4
b) -8 1/2
c) -4
d) -8
e) 16


To solve this question, I first replaced all the x's in the equation by -2.

(-2)(-2^2)(1/(-2))

Then, I simplified this equation.

(-2)(4)(-1/2)

After that, I changed the (-1/2) to a decimal so that it was -0.5.

(-2)(4)(-o.5)

Finally, I solved the equation by multiplying all the different numbers.

(-2)(4)(0.5) = 4

The answer is a) 4

Tower of Hanoi

Today in Math 10 Wings class, Mr Cheng showed us a game on the internet and let us play it. The game was called Tower of Hanoi, and we were supposed to figure out how to beat the game in the least amount of moves. At first I just did Trial and Error to figure it out, and then i started to get the game - it really wasn't thaat hard. Overall, i thought Tower of Hanoi was an okay game - it is not the most fun game ever, but it makes you think a bit and it kinda addicting. I'm probably not ever going to play it again after math class though.



Describe the Strategy and the formula for the puzzle Tower of Hanoi.

For 3 Rings - You start by putting the smallest ring on the far right, so that you can put the second smallest on the second post, and then put the smallest on top of the second one also. This frees up the far right pole to put the biggest ring there. Then you proceed to put the smallest ring on the far left pole, so that you can put the second ring on top of the biggest ring, and then finish the game.

For 4 Rings - You start by putting the smallest ring on the second post (When there is an even number of rings, you start with the second post, while when you have an odd number of rings , you start on the far right post). Then you put the second smallest on the far right, and then put the smallest ring on top of that. The third ring goes on the second pole, and then you use the same steps to put the second ring on top of the third ring, and then put the smallest ring on that (Move the smallest ring to the post that the third ring is not, which in this case is the far left post). Now the far right post is freed up for the biggest ring, and so you move that there. After that, you move the smallest ring on top of the biggest ring, then put the second ring on the empty pole so that you can move the smallest piece onto it. Then move the third ring on the biggest ring, and move the smallest two rings on top of that in the previous way (move the smallest ring off, then put the second ring on the third ring, and then put the smallest one on the second one). Essentially, you have just all the steps for the 3 Rings game, a move to put the largest ring on the far right pole, and all the moves for the 3 Rings game again (taking into account that you start with all the rings on the second pole compared to having them start in the first pole, and that you want them on the third pole instead of the second pole).

For 5 Rings - The Tower of Hanoi game follows a pattern. To do the 5 Ring version, you follow all the moves in the 3 Ring game, and then moves from the 4 Ring game to free up the largest ring so that you can put it on the far right pole. After that, you just do all the same moves again (taking into account that you are starting with all the rings on the second pole instead of the first pole, and you want them on the third pole instead of the second pole).

Formula For The Miniumum Amount of Moves -

Minimum amount of moves for n amount of rings = 2^n - 1