2008 AMC 12A Problems
- 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
A bakery owner turns on his doughnut machine at . At the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?
What is the reciprocal of ?
Suppose that of bananas are worth as much as oranges. How many oranges are worth as much as of bananas?
Which of the following is equal to the product
Suppose that is an integer. Which of the following statements must be true about ?
Heather compares the price of a new computer at two different stores. Store offers off the sticker price followed by a rebate, and store offers off the same sticker price with no rebate. Heather saves by buying the computer at store instead of store . What is the sticker price of the computer, in dollars?
While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?
Older television screens have an aspect ratio of . That is, the ratio of the width to the height is . The aspect ratio of many movies is not , so they are sometimes shown on a television screen by "letterboxing" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of and is shown on an older television screen with a -inch diagonal. What is the height, in inches, of each darkened strip?
Doug can paint a room in hours. Dave can paint the same room in hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by ?
Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the visible numbers have the greatest possible sum. What is that sum?
Points and lie on a circle centered at , and . A second circle is internally tangent to the first and tangent to both and . What is the ratio of the area of the smaller circle to that of the larger circle?
What is the area of the region defined by the inequality ?
Let . What is the units digit of ?
The numbers , , and are the first three terms of an arithmetic sequence, and the term of the sequence is . What is ?
Let be a sequence determined by the rule if is even and if is odd. For how many positive integers is it true that is less than each of , , and ?
A triangle with sides , , is placed in the three-dimensional plane with one vertex on the positive axis, one on the positive axis, and one on the positive axis. Let be the origin. What is the volume of ?
In the expansion of what is the coefficient of ?
Triangle has , , and . Point is on , and bisects the right angle. The inscribed circles of and have radii and , respectively. What is ?
A permutation of is heavy-tailed if . What is the number of heavy-tailed permutations?
A round table has radius . Six rectangular place mats are placed on the table. Each place mat has width and length as shown. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length . Further, the mats are positioned so that the inner corners each touch an inner corner of an adjacent mat. What is ?
The solutions of the equation are the vertices of a convex polygon in the complex plane. What is the area of the polygon?
Triangle has and . Point is the midpoint of . What is the largest possible value of ?
A sequence , , , of points in the coordinate plane satisfies
Suppose that . What is ?
|2008 AMC 12A (Problems • Answer Key • Resources)|
2007 AMC 12B
2008 AMC 12B
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|All AMC 12 Problems and Solutions|