Algebra (ish)
Probability/Combinatorics
Geometry
100
Each day, Jenny ate 20% of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, 32 remained. How many jellybeans were in the jar originally?
A) 40 B) 50 C) 55 D) 60 E) 75
B) 50
2000 AMC 12
100
There are 1001 red marbles and 1001 black marbles in a box. Let 
be the probability that two marbles drawn at random from the box are the same color, and let 
be the probability that they are different colors. Find 
C) 1/2001
100
Which of the cones listed below can be formed from a 252 degree sector of a circle of radius 10 by aligning the two straight sides?
C) A cone with slant height of 10 and radius 7
2001 AMC 12
200
Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?
A) 22 B) 60 C) 119 D) 194 E) 231
C) 119
2000 AMC 12
200
How many three-digit numbers have at least one 2 and at least one 3?
A) 52
200
The point P = (1,2,3) is reflected in the xy-plane, then its image Q is rotated 180 degrees about the x-axis to produce R, and finally, R is translated 5 units in the positive-y direction to produce S. What are the coordinates of S?
A) (1,7,-3) B) (-1,7,-3) C) (-1,-2,8)
D) (-1,3,3) E) (1,3,3)
E) (1,3,3)
2000 AMC 12
300
How many positive integers not exceeding 2001 are multiples of 3 or 4 but not 5
B) 801
2001 AMC 12
300
A box contains exactly five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are drawn or all the white chips are drawn. What is the probability that the last chip drawn is white?
D) 3/5
2001 AMC 12
300
The parabola with equation y=ax²+bx+c and vertex (h,k) is reflected about the line y=k. This results in the parabola with equation y=dx²+ex+f. Which of the following equals a+b+c+d+e+f?
E) 2k
2001 AMC 12
400
Let A, M and C be nonnegative integers such that A+M+C=12. What is the maximum value of A*M*C + A*M + M*C + A*C?
112
2000 AMC 12
400
Given the nine-sided regular polygon 
, how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set 
?
D) 66
2001 AMC 12
400
A circle centered at O has radius 1 and contains the point A. The segment AB is tangent to the circle at A and angle AOB = x. If point C lies on line OA and line BC bisects angle ABC, then OC =
A) sec²x - tanx B) 1/2 C) cos²x / (1+sinx)
D) 1/(1+sinx) E) sinx/(cos²x)
D) 1/(1+sinx)
2000 AMC 12 Problem 17
500
If x, y, and z are positive numbers satisfying 
and 
then what is the value of xyz?
B) 1
2000 AMC 12
500
Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)
E) 1680
2000 AMC 12
500
If circular arcs AC and BC have centers at B and A, respectively, then there exists a circle tangent to both 
and 
, and to 
. If the length of is 12, then the circumference of the circle is
D) 27
2000 AMC 12