Difference between revisions of "2006 AMC 12B Problems"
I like pie (talk | contribs) (Added problem 21; many others still needed) |
I like pie (talk | contribs) (Problem 12 - Fixed typo in LaTeX code) |
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== Problem 12 == | == Problem 12 == | ||
− | The parabola <math>y=ax^2+bx+c</math> has vertex <math>(p,p)</math> and <math>y</math>-intercept <math>(0,-p)</math>, where <math>p\ | + | The parabola <math>y=ax^2+bx+c</math> has vertex <math>(p,p)</math> and <math>y</math>-intercept <math>(0,-p)</math>, where <math>p\ne 0</math>. What is <math>b</math>? |
<math> | <math> |
Revision as of 03:00, 23 April 2008
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
What is ?
Problem 2
For real numbers and
, define
. What is
?
Problem 3
A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score?
Problem 4
Mary is about to pay for five items at the grocery store. The prices of the items are
,
,
,
, and
. Mary will pay with a twenty-dollar bill. Which of the following is closest to the percentage of the
that she will receive in change?
Problem 5
John is walking east at a speed of 3 miles per hour, while Bob is also walking east, but at a speed of 5 miles per hour. If Bob is now 1 mile west of John, how many minutes will it take for Bob to catch up to John?
Problem 6
Francesca uses 100 grams of lemon juice, 100 grams of sugar, and 400 grams of water to make lemonade. There are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar. Water contains no calories. How many calories are in 200 grams of her lemonade.
Problem 7
Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?
Problem 8
The lines and
intersect at the point
. What is
?
Problem 9
How many even three-digit integers have the property that their digits, read left to right, are in strictly increasing order?
Problem 10
Joe and JoAnn each bought 12 ounces of coffee in a 16-ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?
Problem 11
Joe and JoAnn each bought 12 ounces of coffee in a 16-ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?
Problem 12
The parabola has vertex
and
-intercept
, where
. What is
?
Problem 13
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Problem 14
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Problem 15
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Problem 16
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Problem 17
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Problem 18
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Problem 19
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Problem 20
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Problem 21
Rectange has area
. An ellipse with area
passes through
and
and has foci at
and
. What is the perimeter of the rectangle? (The area of an ellipse is
where
and
are the lengths of the axes.)
Problem 22
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Problem 23
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Problem 24
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Problem 25
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