qualities of a good mathmatician

TOP 3 :

- hard working / diligent
- intelligent / smart
- focused

its important to work hard and be diligent because
its the basics ..
if youre lazy , the work wont be finished on time
and thats not a good work habit

its important to be intelligent / smart because
it is neccessary to be able to comprehend the question
and be able to answer it properly
showing work proves that you know how to do the question

its important to be focused and concentrated
because if there is a distraction , the work may not be finished
or may have mistakes because they didnt pay attention to their work

favourite math question number.three

17) If w is a positive integer and w^3 = 9w , then w^5 is equal to ..

for this question , i just guessed 3 randomly
and ..

3^3 = 27
9 x 3 = 27

so then ,

3^5 is 243

to solve this question i just used
guess and check
and somehow , my first guess was correct
YAY :)

math contest question

soo , there was a math contest
and i epically failed under the time limit and
got like 60 points :(
i think i couldve done waaaaay better
if there had been more time ..
i couldnt even check my answers or pick of a logical answer to guess ..
i did terrible and was mad ..
i felt so stressed during one question
that i felt like yelling and screaming in the middle of the contest LOL

anyways , one of the questions i can do
without using any diagrams is number ten

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 students from both schools , what is the ratio of boys to girls ?

so heres the work ::

pascal -
400 / 5 = 80
80 x 3 = 240 boys
80 x 2 = 160 girls

fermat -
600 / 5 = 120
120 x 2 = 240 boys
120 x 3 = 360 girls

the total number of boys and girls
480 : 520
if this ratio is reduced ,
it becomes 12 : 13
hence , the answer is B) 12 : 13

yay ! what an easy question ..
i epically failed this question
because , in the rush ,
i misread the numbers and made a miscalculation ..
becuase , my stupid brain wasnt reading properly
so i didnt get this answer
although i figured something was wrong -
because none of the amounts matched
i couldnt find the problem
anyways , yah ..
hopefully ill do better next time :)

coolio equation

so , mister cheng taught us how to use microsoft word to make
MATH EQUATIONS ! how cool :D



to solve this equation ::
first , i flipped the negative exponent (x^-2) to the top
then , the exponent is distributed 3/2 to all components
basically 3/2 means cubing a number then taking the square root of it
also goes for the x term .. so 9/2 becomes the square root of x to the power of 9
lastly , x can be changed into a mixed radical
TAADAA !



to solve this equation ::
first , flip the negative exponents ( y^-4 and x^-2 ) to the opposite side
then , distribute 5/2 to all the components
5/2 means taking the 5th power of a number then taking the square root of it
after multiplying the powers , the same goes for the x and y terms ..
20/2 becomes the square root of x to the power of 20
and 10/2 becomes the square root of y to the power of 10
finally , x and y are radicals and they can be simplified
.. they become x^10 and y^5

THE END !

favourite math question number.two

23) The numbers 123 456 789 and 999 999 999 are multiplied. How many of the digits in the final result are 9's ?
123456789
x999999999
_____________
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
__________________
123456788876543211

[ its difficult to show the places exactly and they dont line up , but i hope this shows what i mean ]

first , i multiplied 123 456 789 x 9 = 1 111 111 101
then added them 9 times ; each time moving it forward one decimal space

the final answer was 123456788876543211
which concluded that there were no 9s

i chose this question because it looked really interesting
and it seemed challenging
( 123456789 x 999999999 )
i liked the question becuase it had a pattern
( 12345678887654321 )
and the question was fun to figure out

my favourite math problem :)

my favourite math problem was number seventeen ..

17) The digits 1 , 2 , 3 , 4 can be arranged to form 24 different 4-digit numbers. If these numbers are then listed from smallest to largest , what postition is 3142 ?

The numbers from smallest to largest are ::
1234 , 1243 , 1324 , 1342 , 1423 , 1432
2134 , 2143 , 2314 , 2341 , 2413 , 2431
3124 , 3142 , 3214 , 3241 , 3412 , 3421

3124 is the 14th number.

i solved this by writing out all the possible combinations of the four digits
as i listed them , i also put them in order from smallest to largest ..
therefore concluding that 3124 is in the 14th position

i liked this question because you have to make combinations of numbers
and thats fun :P
it wasnt hard to figure out
but i chose this question because of the different numbers
and it requires a bit of thinking and organization

tower of hanoi

describe the strategy and the formula for the tower of hanoi puzzle ::

basically ,
the objective of the puzzle was to move all the pieces from the left pole
to the right in the least possible amount of steps ..
as you can see , i have completed it in 36
while the minimum number of steps is actually 31 ..
anyhow , basically i just used trial and error and in the end ,
somehow , got all the pieces onto the right side ..
the most important thing is moving the top pieces
but not blocking or preventing the movemnet of the last piece ..

my strategy was moving the first piece to the middle pole
( in order to not block the other pieces from moving there )
then going back and forth and stacking the pieces in the middle
so that i could move the last piece to the third pole