We did it! Let's reflect on your experience. How do you feel? Did the pressure help you focused or make you anxious? How is your performance throughout the 60 minutes period (at the beginning, in the middle, near the end)? Do you guess any questions? How do you feel after you are done? When we went over the question? I hope you enjoy the challenge.
After you reflected on your experience, pick 1 question and talk about it.
Here are the answers for the contests (official):
Grade 10 Cayley
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1D 2C 3A 4E 5B 6E 7D 8B 9C 10B
11A 12E 13D 14C 15C 16B 17D 18E 19A 20C
21A 22C 23B 24A 25D
Grade 9 Pascal
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1D 2C 3C 4A 5C 6E 7B 8E 9B 10E
11E 12C 13B 14B 15D 16B 17A 18C 19A 20B
21D 22D 23A 24C 25E
Thursday 25 February 2010
Solving Radical Expression
For this posting, I want you to explain how to solve rational expression with negative or fractional exponent. If you don't have Word 2007 Equation Editor, just explain how to do it. I did the first one for you as an example. You can pick either the second or third.
1) I 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 I multiply 3 with 3/2 to get 9/2
5) write x as a radical and simplify
Done!
1) I 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 I multiply 3 with 3/2 to get 9/2
5) write x as a radical and simplify
Done!
Thursday 18 February 2010
Problem Set #2
Just like last time. Choose 1 of your favorite questions and write something about it.
Ideas:
Explain how you solve it.
Why do you like this question?
What have you learned about the process of problem solving.
Have fun.
My Pick: What is the largest x value that will satisfy the following inequality?
This question seems impossible at first because 3^500 is too big for the calculator to handle. To solve for x, first take 200th root for both sides! No one will ever take 200th root of a number in real life, but the principles of math work for both small and large numbers. Take 200th root is same as raise it to the power of 1/200 (this is what we just learned!!). And exponent law says power on power is to multiple the power. 3^(500/200) or simplier 3^(5/2) is something the calculator will accept. The largest x is 15.
I learned that big numbers are not scary because math principles work the same no matter how big or small the numbers are.
Ideas:
Explain how you solve it.
Why do you like this question?
What have you learned about the process of problem solving.
Have fun.
My Pick: What is the largest x value that will satisfy the following inequality?
This question seems impossible at first because 3^500 is too big for the calculator to handle. To solve for x, first take 200th root for both sides! No one will ever take 200th root of a number in real life, but the principles of math work for both small and large numbers. Take 200th root is same as raise it to the power of 1/200 (this is what we just learned!!). And exponent law says power on power is to multiple the power. 3^(500/200) or simplier 3^(5/2) is something the calculator will accept. The largest x is 15.
I learned that big numbers are not scary because math principles work the same no matter how big or small the numbers are.
Wednesday 10 February 2010
Problem Set #1
Choose 1 of your favorite questions and write something about it.
Ideas:
Explain how you solve it.
Why do you like this question?
What have you learned about the process of problem solving.
Have fun.
This one is my favorite. Find c.
I first tried to solve this system of equations by working backward, substitute each answer into the system to see which answer works. I found the answer but it takes a while. This question can be easily solved by adding the second and third equations together:
The interesting discovery is that we can substitute (a+b) by 3 without knowing what a and b are. System of equations is a topic in Math 11, but it doesn't mean we need to wait til grade 11 to understand it.
Ideas:
Explain how you solve it.
Why do you like this question?
What have you learned about the process of problem solving.
Have fun.
This one is my favorite. Find c.
I first tried to solve this system of equations by working backward, substitute each answer into the system to see which answer works. I found the answer but it takes a while. This question can be easily solved by adding the second and third equations together:
The interesting discovery is that we can substitute (a+b) by 3 without knowing what a and b are. System of equations is a topic in Math 11, but it doesn't mean we need to wait til grade 11 to understand it.
Thursday 4 February 2010
Tower of Hanoi
Describe the strategy and the formula for the puzzle Tower of Hanoi.
Embed a screen shot of the completed puzzle with 5 dics.
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