Take any number. Any number. Believe me. (You might want to use a small one. This one could be a doozy)
Alright, you've got a number. Congratulations! Don't get ahead of yourself, the fun is just beginning!
Here's a tricky part! You need to figure out if the number you picked... was odd or even.
STEP 1:If the number was odd, triple it and add one. (important.... You must realize that the number that was odd... is even now. Continue to step 2.)
STEP 2: If it's even, divide by two. (If your number becomes odd, return to step one.)
Repeat.
....
And repeat....
And repeat....
Eventually, you will find that you're number has become one. That's right! No matter what number you picked, it's become little old 1. Even numbers in the multiples of TRILLIONS will become one. What an amazing trick!
I, for one, am simply aghast.
(Mrs. Armstrong, I hope you understand that my computer is not formatted properly to use all of this sites SUPER COOL features. I can't stick fancy pictures in, I don't even think I can turn on and off bold or italics.)
Welcome to a world where creativity, ingenuity, and mathematics mesh together to create Grade 10 Precalculus math.
posted by Lamael at 4:10 p.m.
SINE LAW - is used when you are solving a non-right triangle.
How would you know when to use Sine law?
You can use Sine Law if:
- You are given Side Angle Side (SAS)
- You are given Side Angle Angle (SAA)
here is the formula:
Example:
Solve for x.
Step 1: Write the informations given. Set the Ratio.
Step 2: Solve by using "cross multiply".
48 ( sin 38 ) = x( sin 101 )
----------- ------------
sin 101 sin 101
30.10 = x
For more practices using sine law, click.
Wednesday, May 23, 2007
posted by MissKyuri at 6:53 p.m.
This time I will explain about area and volume relationship.
[ area ]
when you got the area of a certain region or shape
and know the scale factor,
new area is
(old area) × (scale factor)2
for example,
The area of a triangle is 10cm2.
If each side of the triangle is increased by 4,
the area of the triangle wil be...(4 is a scale factor)
10 × 42
= 10 × 16
= 160 cm2
[ Volume ]
This time I will explain about area and volume relationship.
For volume, you should cube your scale factor to get a volume of the new shape.
New volume is
(old volume) × (scale factor)3
For example, you have two cylinders showing above,
and cylinderA's volume is 785cm3 and it is
decreased by the scale factor 2.
So, to get a cylinderB's volume..
Cylinder B * (scale factor)3 = CylinderA
Cylinder B * 23 = 785
785/8 = Cylinder B
So the volume of CylinderB is 98.125cm3
[ area ]
when you got the area of a certain region or shape
and know the scale factor,
new area is
(old area) × (scale factor)2
for example,
The area of a triangle is 10cm2.
If each side of the triangle is increased by 4,
the area of the triangle wil be...(4 is a scale factor)
10 × 42
= 10 × 16
= 160 cm2
[ Volume ]
This time I will explain about area and volume relationship.
For volume, you should cube your scale factor to get a volume of the new shape.
New volume is
(old volume) × (scale factor)3
For example, you have two cylinders showing above,
and cylinderA's volume is 785cm3 and it is
decreased by the scale factor 2.
So, to get a cylinderB's volume..
Cylinder B * (scale factor)3 = CylinderA
Cylinder B * 23 = 785
785/8 = Cylinder B
So the volume of CylinderB is 98.125cm3
Tuesday, May 22, 2007
posted by MissKyuri at 10:28 p.m.
Here's fun fun number trick for you guys...-_-;
(You need one of your friends, and a calculator for solving it .)
1. Have your friend think of a number between 1 and 100, and to keep it a secret.
2. Now, using your calculator, take your age, multiply by 2, add 5, multiply by 50, and subtract 365.
3. Next, keep that number from the last step on the calculator, hand the calculator to your friend, and tell them to add their secret number, then add 115.
4. The first half of the resulting number is your age, and the other part of the number is your friend's secret number!
For example....
your friend's secret number was 55.
you take your age (14 or 15 or more)
multiply by 2 -> 14 times 2 = 28
ten add 5 -> 28 + 5 = 33
again , multiply the result by 50 -> 33 times 50 = 1650
and lastly subtract 365 from it -> 1650 - 365 = 1185
For next step,
you tell your friend to add his/her secret number to
your result. then add 115. -> 1185 + 55 + 115 = 1455
Neeat,, huh?
(You need one of your friends, and a calculator for solving it .)
1. Have your friend think of a number between 1 and 100, and to keep it a secret.
2. Now, using your calculator, take your age, multiply by 2, add 5, multiply by 50, and subtract 365.
3. Next, keep that number from the last step on the calculator, hand the calculator to your friend, and tell them to add their secret number, then add 115.
4. The first half of the resulting number is your age, and the other part of the number is your friend's secret number!
For example....
your friend's secret number was 55.
you take your age (14 or 15 or more)
multiply by 2 -> 14 times 2 = 28
ten add 5 -> 28 + 5 = 33
again , multiply the result by 50 -> 33 times 50 = 1650
and lastly subtract 365 from it -> 1650 - 365 = 1185
For next step,
you tell your friend to add his/her secret number to
your result. then add 115. -> 1185 + 55 + 115 = 1455
Neeat,, huh?
posted by AngelaG. at 10:03 p.m.
Choose a number from 1 - 9.
multiply it by 9
multiply the answer by 12345679 (notice that there is no 8)
you should get your number, repeated!!
multiply it by 9
multiply the answer by 12345679 (notice that there is no 8)
you should get your number, repeated!!
(c) world book Inc. - mathemagic vol 18
posted by yassir at 8:45 p.m.
| Hi Gummy Bears |
#1 A trick for 2007 only 1. First pick the number of days of the week that you would like to go to the movies with your friends. 2. Multiply this number by 2. 3. Add 5. 4. Multiply it by 50. 5. If you have already had your birthday this year, add 1748. If you have NOT had your birthday, then add 1747. 6. Subtract the four digit year that you were born. 7. You should now have a three digit number (or a two digit number if you picked 0 for the number of times to go to the movies). The first is the number of times you want to go the the movies (it is 0 as previous). The second two are your age!!! Pretty cool huh!!! |
posted by yassir at 8:28 p.m.
Hi Gummy Bears,
This math trick will determine your birthday. Just follow the steps with a calculator and press equal after each step. Go ahead and try the trick without cheating!
This math trick will determine your birthday. Just follow the steps with a calculator and press equal after each step. Go ahead and try the trick without cheating!
- Add 18 to your birth month
- Multiply by 25
- Subtract 333
- Multiply by 8
- Subtract 554
- Divide by 2
- Add your birth date
- Multiply by 5
- Add 692
- Multiply by 20
- Add only the last two digits of your birth year
- Subtract 32940 to get your birthday!
The answer's format is: month/day/year. For example, an answer of 123199 means that you were born on December 31, 1999. If the answer is not right, you followed the directions incorrectly or lied about your birthday.
posted by faven at 7:33 p.m.
HI GUYS, CHECK THIS TRICK OUT!!!
HERE ARE THE DIRECTIONS:
1. Think of your age in years
2. Multiply your age by 2
3. Add 10
4. Multiply by 5
5. Add # of siblings you have
6. Subtract 50
Look at your final answer; the first 2 digits are your age and the last digit is the number of siblings in your family. Have someone else try it! Kind of cool right?
posted by faven at 7:12 p.m.
This trick makes you look like your brain is a mega fast calculator!
Ask a friend to write down ANY three digit number such as 231 or 884. Ask them to multiply the number by
x 7x 11x 13 ...but even if your friend has used a calculator, you will have written down the answer ages ago! It's fiendish!
THE SECRET: all you do is write out the starting number twice! (i know, it's so easy and yet someone may think you have a calculator in your head)So 231 will become 231231 and 884 will become 884884. You don't believe it? Try it yourself ! It's really fun!
Ask a friend to write down ANY three digit number such as 231 or 884. Ask them to multiply the number by
x 7x 11x 13 ...but even if your friend has used a calculator, you will have written down the answer ages ago! It's fiendish!
THE SECRET: all you do is write out the starting number twice! (i know, it's so easy and yet someone may think you have a calculator in your head)So 231 will become 231231 and 884 will become 884884. You don't believe it? Try it yourself ! It's really fun!
posted by Albert at 6:30 p.m.
Number Trick
Do the following:
Write down a 3 digit number so that the first and third digits differ by more than one.
Now reverse the digits to form a second number.
Subtract the smaller number from the larger one.
Now reverse the digits in the answer you got in step 3 and add it to that number.
Multiply by one million.
Subtract 733,361,573.
Then, under each of the digits in your answer, write the letter which corresponds to it using the following table:
0 --> Y
1 --> M
2 --> P
3 --> L
4 --> R
5 --> O
6 --> F
7 --> A
8 --> I
9 --> B
Now read your message backward.
Do the following:
Write down a 3 digit number so that the first and third digits differ by more than one.
Now reverse the digits to form a second number.
Subtract the smaller number from the larger one.
Now reverse the digits in the answer you got in step 3 and add it to that number.
Multiply by one million.
Subtract 733,361,573.
Then, under each of the digits in your answer, write the letter which corresponds to it using the following table:
0 --> Y
1 --> M
2 --> P
3 --> L
4 --> R
5 --> O
6 --> F
7 --> A
8 --> I
9 --> B
Now read your message backward.
I took the # 694
rearranged to 496
subtracted 496 from 694
got a total of 198
reversed it to 891 and add it to 198
the sum was 1089
then i mutiplied by one million
to get a sum of 1089000000
then i subtracted 733,361,573
to get a total of 355638427
this is april fool spelt backwards
it's really tricky, i haven't found the solution to it but i tried with different numbers and you will always get 1089 b4 multiplying by one million. 1089000000 take away 733,361,573 will always be 355638427 the tricky part is getting the two number you reversed to add up to 1089 thats the only part i didn't figure out.
see if you could figure it out
posted by Anonymous at 4:33 p.m.
hi classmates! our assignment for today is to look for a math trick on the internet. and i found a variety of fun and tricky math tricks and i've decided to chose this one, (drumrolls please)...
THE BIRTHDAY TRICK:
THE BIRTHDAY TRICK:
This math trick will determine your birthday. Just follow the steps using a calculator and remember to press equal after each step. remember, follow the directions carefully and DO NOT CHEAT. :>
1. Add 18 to your birth month
2. Multiply by 25
3. Subtract 333
4. Multiply by 8
5. Subtract 554
6. Divide by 2
7. Add your birth date
8. Multiply by 5
9. Add 692
10. Multiply by 20
11. Add only the last 2 digits of your birth year
12. Subtract 32940 to get your birthday!
The answer format is : MONTH / DAY / YEAR . For example, an answer of 123199 means that you were born on December 31, 1999. Or an answer of 20592 means that you were born on February 5, 1992. If the answer is not right, that means you've not followed the directions or you lied about your birthday. :)
feel free to try it. see if it really works. well for me, i've tried it and it really works. yeheyyy. :)
by the way, i got this math trick from amazing math tricks.
-janelle <: see yah guys tomorrow!
Labels: janelle, math trick, scribe
posted by Jenny at 4:28 p.m.
1. Choose a number.
2. Double it.
3. Add 9.
4. Subtract 3.
5. Divide by 2.
6. Subtract your original number from the new number.
(The answer will remain the same regardless of the number chosen in the beginning).
2. Double it.
3. Add 9.
4. Subtract 3.
5. Divide by 2.
6. Subtract your original number from the new number.
(The answer will remain the same regardless of the number chosen in the beginning).
Labels: Jenny, math trick, scibe
posted by Maria at 3:43 p.m.
Trick #1Here's a sneaky way to find out someone's age who won't tell you:
- Ask the person to multiply the first number of his or her age by 5
- Tell them to add 3
- Now tell them to double this figure
- Have the person add the second number of his or her age to the figure and have them tell you their answer
- Deduct 6 and you will have their age!
Trick #2
- multiply your age by 7
- now multiply that product by 1443
What do you get? Your age repeats 3 times.
Watch this: 28 (age) x 7 = 196.
196 x 1443 = 282828!
Actually, what you're doing is multiplying your age by 10101. Your age will repeat 4 times if you multiply it by 1010101. Notice the number of ones? Yep, four, hence four age repetitions.
What if you're age 9 and younger? Does this still work? Well....sort of. You get 90909, or really, 090909. To really enjoy this, though, it helps to be 10 and older.
click the picture for a short trick!!!!posted by Ms. Armstrong at 8:18 a.m.
Hi Gummy Bears,
Your homework tonight it to find and post a neat 'math trick'. It could be a black hole, or your age worked out by following some steps. Here's one for you to try.
Have fun!!
Ms. Armstrong
YOUR AGE BY EATING OUT
Don't tell me your age;
Work this out as you read ...Be sure you don't read the bottom until you've worked it out!This is not one of those waste of time things, it's fun.
1. First of all, pick the number of times a week that you would like to goout to eat.(more than once but less than 10)
2. Multiply this number by 2 (just to be bold)
3. Add 5
4. Multiply it by 50
5. If you have already had your birthday this year add 1757 .If you haven't, add 1756.
6. Now subtract the four digit year that you were born.
You should have a three digit number.
The first digit of this was your original number(i.e., how many times you want to go out to restaurants in a week.)
The next two numbers areYOUR AGE! (Oh YES, it is!!!!!)
THIS IS THE ONLY YEAR (2007) IT WILL EVER WORK, SO SPREAD IT AROUND WHILE IT LASTS.
Your homework tonight it to find and post a neat 'math trick'. It could be a black hole, or your age worked out by following some steps. Here's one for you to try.
Have fun!!
Ms. Armstrong
YOUR AGE BY EATING OUT
Don't tell me your age;
Work this out as you read ...Be sure you don't read the bottom until you've worked it out!This is not one of those waste of time things, it's fun.
1. First of all, pick the number of times a week that you would like to goout to eat.(more than once but less than 10)
2. Multiply this number by 2 (just to be bold)
3. Add 5
4. Multiply it by 50
5. If you have already had your birthday this year add 1757 .If you haven't, add 1756.
6. Now subtract the four digit year that you were born.
You should have a three digit number.
The first digit of this was your original number(i.e., how many times you want to go out to restaurants in a week.)
The next two numbers areYOUR AGE! (Oh YES, it is!!!!!)
THIS IS THE ONLY YEAR (2007) IT WILL EVER WORK, SO SPREAD IT AROUND WHILE IT LASTS.
Monday, May 21, 2007
posted by faven at 7:47 p.m.
THE COSINE LAW:
IS THE RELATIONSHIP BETWEEN SIDES AND ANGLES IN ANY GIVEN TRIANGLE
THE FORMULA IS:
a 2 = b 2 + c 2 - 2 b c cos(A)
let's say we have a triangle with the side lengths a=10cm b=7cm c=5cm now let's find the largest angle A.
*first step is to set up the formula
a 2 = b 2 + c 2 - 2 b c cos(A)
*then substitute the numbers in, and solve for the largest angle A.
cos (A) = [ 7 2 + 5 2 - 10 2 ] / (2*7*5)
= -13/35
(your calculator will be a big help now)
your answer should be 111.80
so angle A=111.8(rounded to one decimal place)
THINGS TO REMEMBER:
*a,b,c are the side lengths of a triangle .
* A,B,C are the angles.
*the cosine law is often useful when dealing with triangles which are not right angle.
* label your sides and angles so that you don't get confused.
THAT'S WHAT I'VE GOT ON COSINE LAW
SEE YOU GUYS TOMORROW :)
POSTED BY FAVEN.
IS THE RELATIONSHIP BETWEEN SIDES AND ANGLES IN ANY GIVEN TRIANGLE
THE FORMULA IS:
a 2 = b 2 + c 2 - 2 b c cos(A)
let's say we have a triangle with the side lengths a=10cm b=7cm c=5cm now let's find the largest angle A.
*first step is to set up the formula
a 2 = b 2 + c 2 - 2 b c cos(A)
*then substitute the numbers in, and solve for the largest angle A.
cos (A) = [ 7 2 + 5 2 - 10 2 ] / (2*7*5)
= -13/35
(your calculator will be a big help now)
your answer should be 111.80
so angle A=111.8(rounded to one decimal place)
THINGS TO REMEMBER:
*a,b,c are the side lengths of a triangle .
* A,B,C are the angles.
*the cosine law is often useful when dealing with triangles which are not right angle.
* label your sides and angles so that you don't get confused.
THAT'S WHAT I'VE GOT ON COSINE LAW
SEE YOU GUYS TOMORROW :)
POSTED BY FAVEN.
Labels: cosine law
Thursday, May 17, 2007
posted by Xochitl at 12:07 p.m.
Hello everybody! :D
This scribes about the properties of;
Parallelograms, rectangles, phombusesessss, and, squares! (yay)
I have a hard time remebering radom facts sometimes so the key thing to keep in mind is to always keep it simple. For example, if instead of remembering each shape seperatly, try remembering them togeather.
Like this;
All 4 shapes have...
*opposite equal sides,
*supplementary consecutive angles,
*and bisecting diagonals
but incase you don't like this way or just lost your sheet (tisk tisk :P);
(the names of the shapes I put beside the property mean they have that property.)
Properties
opposite sides are equal (all)
all sides are equal (rhombus and square)
opposite angles are right angles (rectangle and square)
consecutive angles are supplementary (all)
diagonals are congruent (rectangle and square)
diagonals bisect each other (all)
diagonals bisect opposite angles (square)
diagonals are perpendicular to each other (rhombus and square)
By; Xochitl/ queen of the universe (of chocolate :P) :)
This scribes about the properties of;
Parallelograms, rectangles, phombusesessss, and, squares! (yay)
I have a hard time remebering radom facts sometimes so the key thing to keep in mind is to always keep it simple. For example, if instead of remembering each shape seperatly, try remembering them togeather.
Like this;
All 4 shapes have...
*opposite equal sides,
*supplementary consecutive angles,
*and bisecting diagonals
but incase you don't like this way or just lost your sheet (tisk tisk :P);
(the names of the shapes I put beside the property mean they have that property.)
Properties
opposite sides are equal (all)
all sides are equal (rhombus and square)
opposite angles are right angles (rectangle and square)
consecutive angles are supplementary (all)
diagonals are congruent (rectangle and square)
diagonals bisect each other (all)
diagonals bisect opposite angles (square)
diagonals are perpendicular to each other (rhombus and square)
By; Xochitl/ queen of the universe (of chocolate :P) :)
Labels: scibe
Tuesday, May 15, 2007
posted by Jenny at 9:00 p.m.
GENERAL FORM:
a2 = b2 + c2 - 2bc CosA
** Use this formula when you do not have a complete set of ratios ( a length of a side with its corresponding angle ).
Only use this formula (it's confusing & long) ONCE, and then use the sine law or any other formula to help you complete the trig question you have.
Use the cosine formula given above to substitue in the values:
a2 = b2 ="b + c2 - 2bc CosA
a2 = (7.8)2 + (9.0)2 - 2(7.8)(9.0)Cos112
a2 = 60.84 + 81 - (-52.5947)
a2 = 194.44
a2 = √194.44
a = 13.9
These sites are helpful for extra practice at using cosine law (step-by-step lessons & answers):
http://www.analyzemath.com/Geometry/cosine_law_problems.html
http://www.themathpage.com/aTrig/law-of-cosines.htm
http://dougsimmsonline.googlepages.com/cosinelaw <-- has a vid too!
Labels: cosine law, Jenny, sribe
posted by yassin at 7:28 p.m.
Hi classmates this is yassin so today i'm going to show you guys some examples of Sine Law.
So when we use the law of sines we don't use all three fractions. We use whichever two fractions include the variable we are solving for and allow us to use the given information. Let's work on the following example using the law of sines. It's a lot easier to understand once you've tried a few problems.
Example:
Given triangle ABC, A=50 degrees, B=30 degrees, and b=10, and they told us to find a.
Remember we're looking for a, so we have to use the fraction a over Sin A. We know angle B and side b, so the other fraction to use, let's substitute the values for b, A, and
B into a over Sin A = b over Sin B.
Then we have to do
a over Sin 50 degrees = 10 over sin 30 degrees.
Then we have to divide both sides by sin 30 degrees.
and we get 10 Sin 50 degrees over Sin 30 degrees Then we have to calculate with scientific calculator and the answer is 15.3209.
If you want to try some examples of these. Now it is time for you to try onewww.coolschool.ca
I hope so you guys will find more information there.
By: Yassin .S.
So when we use the law of sines we don't use all three fractions. We use whichever two fractions include the variable we are solving for and allow us to use the given information. Let's work on the following example using the law of sines. It's a lot easier to understand once you've tried a few problems.
Example:
Given triangle ABC, A=50 degrees, B=30 degrees, and b=10, and they told us to find a.
Remember we're looking for a, so we have to use the fraction a over Sin A. We know angle B and side b, so the other fraction to use, let's substitute the values for b, A, and
B into a over Sin A = b over Sin B.
Then we have to do
a over Sin 50 degrees = 10 over sin 30 degrees.
Then we have to divide both sides by sin 30 degrees.
and we get 10 Sin 50 degrees over Sin 30 degrees Then we have to calculate with scientific calculator and the answer is 15.3209.
If you want to try some examples of these. Now it is time for you to try onewww.coolschool.ca
I hope so you guys will find more information there.
By: Yassin .S.
posted by Anonymous at 6:16 p.m.
hi classmates! i just want to remind you of the different vocabulary words we have to know to survive this unit. :)
I think these words are really important because we use them most of the time when solving for parallelograms, squares, rhombus, rectangles and many more.
2. DIAGONALS are lines connecting opposite angles.
congruent segments
I'm hoping that I've enlightened you with some of the words we use in this unit. =)
I think these words are really important because we use them most of the time when solving for parallelograms, squares, rhombus, rectangles and many more.
SO HERE IT GOES:
1. CONSECUTIVE means two lines next to each other and going in the same direction.
2. DIAGONALS are lines connecting opposite angles.
3. BISECT means cutting into 2 equation pieces.
4. SUPPLEMENTARY angles are 2 angles that add up to 180 degrees.
5. CONGRUENT sides or segments have the same exact length. Also, congruent angles have the exact same measure.
congruent segments
All four sides of this rhombus
are marked to show they are
congruent to each other.
6. PERPENDICULAR lines create a 90 degree angle.
7. PARALLEL lines are lines that do not intersect and coplanar. coplanar refers to lines that are lying or occuring in the same plane.
These are just some words we have to know for this unit. It is very important to know the definitions of these words. If you want to know more about these words, you can take a look at these sites : MATHWORDS , MATH DICTIONARY , INTERACTIVATE
I'm hoping that I've enlightened you with some of the words we use in this unit. =)
your classmate, janelle ;)
Labels: janelle, scribe, trigonomety/geometry
posted by Maria at 4:53 p.m.
So far we've only been able to work with right-angle triangles when using trigonometric functions. Although these are really useful triagles, there are lots of other types of trinangles besides right angles. We need a way to deal with those.
If we're working with a non-right angle triangle, that means there's no hypotenuse, so we can't use Pythagorean theorem. Instead, we have 2 tools called the Sine Law and the Cosine Law. Let's take a look at the Sine Law first
If we have this triangle:
.
The Sine Law says that its sides and angles are related in this way:
a b c
------- = ------- = -------
sin A sin B sin C
Main points to notice:
-
the triangle needs to be labelled the way it is in the picture above: side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C (note - c is NOT the hypotenuse)
Thank you!!!!
