Problem Solving #5

My favourite question is number 10. I like this question because you basically figure it out by trial and error. To solve it I tried a couple such as 10- 14 etc and kept going higher until I arrived at 13+14+15+16+17= 75.
And 13+ 17= 30.

Problem Solving 2

My favourite question on the problem solving sheet was question 3. I like this question because I haven't done one like this in a while and I liked how despite this, I still remembered how to do it properly. To solve this question and find out how many votes Sue received, you have to find out what how many votes Jim and Jane got. To do this you have to change the percents to actual numbers by reversing the way you would find percents.

To find Jim's number of votes you do 20% x 1000/100 = 200.

To find Jane's number of votes you do 45% x 1000/100= 450.

Then do 450 + 200 = 650.

Then do 1000-650= 350, so the number of votes Sue got was 350

To check, do 450+ 200+350= 1000

If you want to find out the percentage 350 you do 350/1000 x 100 = 35%

Solving Radical Expressions

To solve the first question:

1. Get rid of the first square root by adding brackets around the whole equation and putting a 1/2 outside.

2. Then get rid of the next square root by adding another bracket around the whole equation and putting another 1/2 outside of that bracket.

3. Since 15 and 27 are both factors of 3 you can divide each number by 3

4. Next you deal with the two powers multiplying them together. Now there should only be one set of brackets around the reduced equation

5. Then you multiply the numbers inside the brackets by the 1/4

6. The answer will then be in radical form. The 4 will be the square root of each number. And you just multiply the power of the x by 1/4

7. Then using a calculator find out the answer of the radicals.

To solve the second question:

1. First flip the x and the y so that the x (along with its power) is in the y's place and vise versa

2. Then first multiply each number and variable by the outside power

3. The numbers will be in the radical form and each of them will have five as a power

4. Use the calculator to solve the rest of the equation

Cayley Math Contest

The math contest that we did a few weeks ago wasn't a very good experience for me. Although it was a good learning opportunity to learn new problem solving skills, I did not enjoy it. I don't particularly like doing these math contests because you can't study for them and so it is often difficult for me. Despite this, there were some questions that I liked because I was able to use the knowledge I had to solve them. One question in particular was q.6. To solve this question first you write an equation 3x+6x+x = 180

, 10x= 180

x/10=180/10

x= 18

now that we know x= 18 you have to use times it by 3 and 6 to

find the other angles

so angle P= 3x= 3 x 18= 54

angle Q= 6x= 6 x 18= 108

then check, 54+108+18= 180

Qualities for Doing Good in Math

Today in class we came up with a list of qualities that are important to do good in math. Out of the long list I chose the top 3 qualities for doing well. They are diligence, optimism and patience.

Diligence is the constant and earnest effort to accomplish what is undertaken. Diligence is important because sometimes in math it takes alot of hardwork to fully understand concepts. Without constantly working hard you will never go far in math. Sometimes it takes several hours of doing different equations to understand concepts. With alot of hardwork it's almost impossible not to be succesful in math.

Optimism is just as important because sometimes math can be very frustrating and sometimes you just want to give up. If you are optimistic and believe that you will understand an equation, then eventually you will. Keeping optimistic will give you the drive to continue trying in math and not give up.

Most of the time doing math requires alot of patience. It often takes a long time to figure out complicated equations and without patience you will end up frustrated and want to give up. You need to exercise patience to really grasp concepts because often it takes a long time.

I think these three qualities that every student needs to be succesful in math.

Pascal Contest

My favourite question was number 2. I enjoyed this quesition because we have been learning about square roots, so I was able to figure out the question quickly and mentally. To solve this equation all you have to do is square root each of the numbers and then plus or add them.

Problem Solving

My favourite question on the problem solving sheet was question 7. I like this question because I enjoy solving problems with angles and degrees because you have to figure out the value of different angles and use angle rules to find x.

To solve this puzzle first it's important to know that the triangle is an is Isosceles triangle. Therefore AB = AC and ABC=ACB.

First you do 180-40= 140/2 = 70, so both of the two angles are = 70.

Due to the supplementary angle rule ACB+x+x = 180.

So you do 180- 70= 110 and because there are two x's that are the same value, you divide 110 by 2.

Therefore x= 55.

Tower of Hanoi

In math we did this puzzle called tower of hanoi. The legend behind the tower of hanoi is that in an ancient Indian city, monks in a temple were asked to move a pile of 64 sacred gold disks from one location to another. The disks were fragile and so only one could be moved at a time and larger disks could not be placed on top of a smaller one. The monks began carrying the disks back and forth, between the original pile, the pile at the new location, and the intermediate location, always keeping the piles in order (largest on the bottom, smallest on the top). Legend has it that when the monks make the final move to complete the new pile in the new location, the temple will turn to dust and the whole world will end! In class we calculated that to move 64 disks you use the formula (2 to the power of n) -1. We found that if the monks move each disk per second it would take 590 billion years before they finish.

My strategy for Tower of Hanoi is that for even numbers of discs I put the littlest disc on the middle pole. For odd numbers of disks I put the littlest disc on the right pole. I also try and visualise my next move before I put a disc on a different pole. If I am totally stuck I just watch the solution and then try the puzzle once again. Another method for solving these puzzles is to move the disks in the same direction, (middle if there is an even number of disks and right if there is a odd number). If there is no tower in the direction it should be moved then move it to the opposite end but still continue to move in the proper direction (right or middle).