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Measurement & Geometry
Number Sense
Probability/Statistics
Algebra
100
Simplify: (6a4 bc2)(7a4 b3 c)
42 a8 b4 c3
100
Find the degree measure of an angle whose complement is 25% of its supplement.
60
100
How could you rewrite (45)3?
415
100
For each real number 
with 
, let numbers 
and 
be chosen independently at random from the intervals 
and 
, respectively, and let 
be the probability that
What is the maximum value of P()?
2-√2
100
Compute the sum of all the roots of 
7/2
200
Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB, 12 of the files take up 0.7 MB, and the rest take up 0.4 MB. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files?
13
200
A sphere is inscribed in a truncated right circular cone as shown. The volume of the truncated cone is twice that of the sphere. What is the ratio of the radius of the bottom base of the truncated cone to the radius of the top base of the truncated cone?
200
For how many integers is the number 
negative?
200
An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color?
1/5
200
For how many positive integers 
does there exist at least one positive integer n such that 
?
infinitely many
300
The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is
14
300
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 
?
300
Randy drove the first third of his trip on a gravel road, the next 
miles on pavement, and the remaining one-fifth on a dirt road. In miles how long was Randy's trip?
300/7
300
What is the probability of randomly pulling a J, Q or K from a deck of cards?
3/13
300
The largest divisor of 
is itself. What is its fifth-largest divisor?
251,750,000
400
The graph of the function 
is shown below. How many solutions does the equation 
have?
400
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?
3+(√69/3)
400
Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
400
The numbers 
are to be arranged in a circle. An arrangement is 
if it is not true that for every 
from to 
one can find a subset of the numbers that appear consecutively on the circle that sum to . Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?
400
For certain real numbers , 
, and 
, the polynomial
has three distinct roots, and each root of 
is also a root of the polynomial
What is 
?
500
Find the number of ordered pairs of real numbers 
such that 
.
500
A 
arc of circle A is equal in length to a 
arc of circle B. What is the ratio of circle A's area and circle B's area?
500
Let be a function with the following properties:
,
and
,
for any positive integer. What is the value of 
?
500
A set of three points is randomly chosen from the grid shown. Each three point set has the same probability of being chosen. What is the probability that the points lie on the same straight line?
500
Driving at a constant speed, Sharon usually takes 
minutes to drive from her house to her mother's house.
One day Sharon begins the drive at her usual speed, but after driving 
of the way, she hits a bad snowstorm and reduces her speed by miles per hour. This time the trip takes her a total of 
minutes. How many miles is the drive from Sharon's house to her mother's house?