fandomhigh | 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.]

Flat | Top-Level Comments Only

Talk, discuss, and turn 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?"

Pippi looked up at Broots with a relieved smile.

"Would I ever!"

"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?"

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."

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

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

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."

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."

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

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

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

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

"Scouts honor."

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.

Oh, okay! Now Victor got it!

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

Mathematics: All Classes: Friday 3.31.06 Period 1

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