2004 AMC 12A 真题与答案及免费中文视频详解(翰林独家)
2004 AMC 12A Problems & Solutions
2004 AMC 12A 真题与答案及中文视频详解(翰林独家)
Problem 1
Alicia earns 
dollars per hour, of which 
is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes?
Problem 2
On the AMC 12, each correct answer is worth 
points, each incorrect answer is worth 
points, and each problem left unanswered is worth 
points. If Charlyn leaves 
of the 
problems unanswered, how many of the remaining problems must she answer correctly in order to score at least 
?
Problem 3
For how many ordered pairs of positive integers 
is 
?
Problem 4
Bertha has daughters and no sons. Some of her daughters have daughters, and the rest have none. Bertha has a total of 
daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no children?
Problem 5
The graph of the line 
is shown. Which of the following is true?
Problem 6
Let 
, 
, 
, 
, 
and 
. Which of the following is the largest?
Problem 7
A game is played with tokens according to the following rules. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard pile. The game ends when some player runs out of tokens. Players 
, 
and 
start with 
, 
and 
tokens, respectively. How many rounds will there be in the game?
Problem 8
In the overlapping triangles 
and 
sharing common side 
, 
and 
are right angles, 
, 
, 
, and 
and 
intersect at 
. What is the difference between the areas of 
and 
?
Problem 9
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars would increase sales. If the diameter of the jars is increased by 
without altering the volume, by what percent must the height be decreased?
Problem 10
The sum of 
consecutive integers is 
. What is their median?
Problem 11
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is cents. If she had one more quarter, the average value would be 
cents. How many dimes does she have in her purse?
Problem 12
Let 
and 
. Points 
and 
are on the line 
, and 
and 
intersect at 
. What is the length of 
?
Problem 13
Let 
be the set of points 
in the coordinate plane, where each of 
and 
may be 
, , or 
. How many distinct lines pass through at least two members of ?
Problem 14
A sequence of three real numbers forms an arithmetic progression with a first term of 
. If 
is added to the second term and is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term in the geometric progression?
Problem 15
Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run meters. They next meet after Sally has run 
meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
Problem 16
The set of all real numbers 
for which
is defined is 
. What is the value of 
?
Problem 17
Let 
be a function with the following properties:
, and
, for any positive integer 
.
What is the value of 
?
Problem 18
Square 
has side length . A semicircle with diameter 
is constructed inside the square, and the tangent to the semicircle from intersects side 
at 
. What is the length of 
?
Problem 19
Circles 
and are externally tangent to each other, and internally tangent to circle . Circles and are congruent. Circle has radius and passes through the center of . What is the radius of circle ?
Problem 20
Select numbers and between and independently and at random, and let be their sum. Let and be the results when 
and , respectively, are rounded to the nearest integer. What is the probability that 
?
Problem 21
If 
, what is the value of 
?
Problem 22
Three mutually tangent spheres of radius rest on a horizontal plane. A sphere of radius rests on them. What is the distance from the plane to the top of the larger sphere?
Problem 23
A polynomial
has real coefficients with 
and 
distinct complex zeroes 
, 
with 
and 
real, 
, and
Which of the following quantities can be a nonzero number?
Problem 24
A plane contains points and with 
. Let be the union of all disks of radius in the plane that cover . What is the area of ?
Problem 25
For each integer 
, let 
denote the base- number 
. The product 
can be expressed as 
, where 
and are positive integers and is as small as possible. What is the value of ?
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