2008 AMC 12A Problems
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
Problem 1
A bakery owner turns on his doughnut machine at 8:30 AM. At 11:10 AM the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?
(Solution)
Problem 2
What is the reciprocal of ?
(Solution)
Problem 3
Suppose that of
bananas are worth as much as
oranges. How many oranges are worth as much is
of
bananas?
(Solution)
Problem 4
Which of the following is equal to the product
?
(Solution)
Problem 5
Suppose that
is an integer. Which of the following statements must be true about ?
(Solution)
Problem 6
Heather compares the price of a new computer at two different stores. Store A offers off the sticker price followed by a <dollar/>
rebate, and store B offers
off the same sticker price with no rebate. Heather saves <dollar/>
by buying the computer at store A instead of store B. What is the sticker price of the computer, in dollars?
(Solution)
Problem 7
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?
(Solution)
Problem 8
What is the volume of a cube whose surface area is twice that of a cube with volume 1?
(Solution)
Problem 9
(Solution)
Problem 10
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
?
$\textbf{(A)}\ \left( \frac{1}{5}+\frac{1}{7}\right)\left( t+1 \right)=1 \qquad \textbf{(B)}\ \left( \frac{1}{5}+\frac{1}{7}\right)t+1=1 \qquad \textbf{(C)}\left( \frac{1}{5}+\frac{1}{7}\right)t=1 \\
\textbf{(D)}\ \left( \frac{1}{5}+\frac{1}{7}\right)\left(t-1\right)=1 \qquad \textbf{(E)}\ \left(5+7\right)t=1$ (Error compiling LaTeX. Unknown error_msg)
(Solution)
Problem 11
(Solution)
Problem 12
A function has domain
and range
. (The notation
denotes
.) What are the domain and range, respectively, of the function
defined by
?
(Solution)
Problem 13
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?
(Solution)
Problem 14
What is the area of the region defined by the inequality ?
(Solution)
Problem 15
Let . What is the units digit of
?
(Solution)
Problem 16
The numbers ,
, and
are the first three terms of an arithmetic sequence, and the
term of the sequence is
. What is
?
(Solution)
Problem 17
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
?
(Solution)
Problem 18
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
?
(Solution)
Problem 19
In the expansion of
,
what is the coefficient of ?
(Solution)
Problem 20
Triangle has
,
, and
. Point
is on
, and
bisects the right angle. The inscribed circles of
and
have radii
and
, respectively. What is
?
(Solution)
Problem 21
Triangle has
,
, and
. Point
is on
, and
bisects the right angle. The inscribed circles of
and
have radii
and
, respectively. What is
?
(Solution)
Problem 22
(Solution)
Problem 23
The solutions of the equation are the vertices of a convex polygon in the complex plane. What is the area of the polygon?
(Solution)
Problem 24
(Solution)
Problem 25
(Solution)
This is an empty template page which needs to be filled. You can help us out by finding the needed content and editing it in. Thanks.