fandomhigh | Mathematics: All Classes: Friday 3.31.06 Period 1

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mathematics

Mathematics: All Classes: Friday 3.31.06 Period 1

"Okay, um, people who own me work because they were sick? Turn it and present please. Both classes will be working on some problems today.

Begginers:
1. What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers?
2. What is the probability that a randomly drawn positive factor of 60 is less than 7?
3. What is the maximum number for the possible points of intersection of a cirlce and a triangle?

Intermediate:
1. A solid box is 15cm by 10cm by 8cm. A new solid is formed by removing a cube 3cm on a side from each corner of this box. What percent of the original volume is removed?
2. It takes Mary 30 minutes to walk uphill 1km from her home to school, but it takes her only 10 minutes to walk from school to home along the same route. What is her average speed, in km/hr, for the round trip?
3. The sum of two numbers is S. Suppose 3 is added to each number and then each of the resulting numbers is double. What is the sum of the final two numbers?

If you have any questions or problems, wave me down. Have at it!"

[OOC: Answers will go up in the OOC thread as soon as I solve the problems. Someone stole my answer booklet. All problems are from either AMC10 - 2003 or 2001.]

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Coffee, milk, orange juice, apple juice, and cereal.

Talk, discuss, and turn in.

Broots has stopped talking to his computer, but now it's singing at him.

Give me a sec here while I decipher my notes and try to figure out what x and y have to do with circles.

Begin:
1. 2003
2. 1/2
3. 6
Inter:
1. 18%
2. 3km/hr
3. 2S+12

That's what I get for choosing problems that I lost the answers to. If you want the explanations, ping here.

Molly signed in and took some of everything except the coffee.

Pippi signs in

Pippi knew right away the answer to #3 was 6.

But she sits at her desk and bites her lip at the other two questions.

Broots sat down by Pippi. "Want a nudge to get you going in the right direction?"

Molly's answers:

1. I have no clue.

2. 50%?

3. 6. Definitely 6.

"Yup and yup. Hm, for number one? Try thinking about the problem if you only wanted to know the difference between the first three even and three odd. See if anything interesting happens."

Molly thought for a moment. "Okay, so two plus four plus six equals twelve. And one plus three plus five equals nine. So the difference is three. Which is the number of... numbers I was adding."

She thought for a moment longer. "Sooooo, the answer would be 2003?" She gave Broots a perplexed look. It couldn't be that easy.

Broots gave her a thumbs-up. "That's the trick. See, you get such an easy answer and you figure, hey this is too easy! So you try to find something more confusing. But in math the most obvious and simple answer is almost always the right one."

Walter signs in and only skips the apple juice.

Pippi looked up at Broots with a relieved smile.

"Would I ever!"

Molly nodded, but narrowed her eyes a little. "That's a really mean trick," she said. "I'm glad I didn't try to work it out first."

"Okay, problem one? Try it as if there are only three even and three odd numbers. See what happens. Then try four. You should definetly see a pattern then.

For two, list out all the factors of 60. Um, do you know what factors are?"

Broots's eyes grew wide. "Molly? I'm evil, but I wouldn't make you add up 4006 numbers."

Pippi scribbled on the paper as Broots suggested for problem one.

"Oh!" she said, "The differences is the number of... Numbers! Neat!"

At his question about #2, she bit her lip.

"... I forget."

Broots defined factors for Pippi. "Does that help a little?"

"Oh!" she said.

After a few moments of making factor trees, Pippi came up with the answer.

"Look at that, it's a 50/50 chance."

John signs in and steals a hearty breakfast.

Molly raised an eyebrow at him. "I don't know you very well. You might."

Broots gave her a high-five. "You got it!"

Broots pouted. "Arithmetic is evil. I would never burden someone with large amounts of it."

1.
15x2+10x2+8x2
30+20+36=86
86-(6x(3x3x3)
86-6 x 18
~~ahfuckit~~

2. 3km ~~cuz the mun is a cheater~~

3.
S=a+b
S=6+a+b
2s=6+a+b
s=3+.5a+.5b
that can't be right
S=a+b
S=6+a+b
S=12+2a+2b...?

"Thanks!" she grinned and returned it on the downlow.

"Okay then," Molly said with a nod and a grin. "I'll hold you to that for the rest of the semester."

Broots glanced over at John's work. "Okay, number one? You need to start by looking at total volume of the original shape. Volume is equal to lenght times width times height. For number three, your second try is good, but see if you can simplify it a little."

"Scouts honor."

1.
Original volume is 1200 cm³
Removed volume is 27 cm³
2.25% of the original volume is removed per corner with 8 corners = 18%

2.
40 minutes for 2 km, 1 km/20 minutes = 3km/hr

3.
a + b = S
a + 3 = 2a
b + 3 = 2b
a = 6
b = 6
a + b = 12

Walter finishes up and turns in his work. At least this one wasn't too hard.

Victor signs in ~~because his mun is finally back online~~.

"Good job on the problems. You owe me a presentation for the missed class though."

"I don't have anything prepared right away. What sort of presentation do you want?"

Broots frowned. "Remember the book you were supposed to read and come up with a math based question and answer from? Yeah, that presentation."

"Oh that one. I thought you meant separate make up work for having missed class last week. Not the other presentation."

"Yup. You ready to present?"

Victor didn't really know what to make of the first question, so he tried writing the numbers out for a little bit. After a while he noticed a pattern. On his sheet he wrote.

1)2003

He skipped the second one for now because he didn't remember what a factor was, and moved on to the next. After a moment of sketching, he wrote down:

3)6

But what about the second question?

Broots defined factors for Victor and made a note to go over them for them in class next week.

"Definitely." Walter is ready to give a ~~handwavily~~ well-prepared presentation. He had extra time and all.

Rulers might figure in to a lot of his reasons for not doing a halfway job.

Oh, okay! Now Victor got it!

After some more writing, he came to the conclusion that the answer was 50%.

Victor approached Broots after class to turn in his makeup work.

1) 9(2+8)+6+4+(1+3+5+7)(0) = 100
2) (3+7)(6+4)+(0/(1+2+5+8+9)) = 100
3) (9+8+7+6+5-2)3+1-4(0) = 100

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