Probability
Geometry
Algebra
Random
Math Facts
100
Each square in a 
grid is randomly filled with one of the 
gray and white tiles shown below on the right.
What is the probability that the tiling will contain a large gray diamond in one of the smaller 
grids? Below is an example of such tiling.
C) 1/64
100
The figure below is a parallelogram with two angles given in terms of x. Determine the value of x.
- 9
- 10
- 20
- 22
- 24
22
100
Positive real numbers 
36
100
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?
D
100
How many colors are needed on a map to make sure that no border will share a color?
4
200
The arrows on the two spinners shown below are spun. Let the number 
equal 
times the number on Spinner 
, added to the number on Spinner 
. What is the probability that is a perfect square number?
B) 1/8
200
A three-quarter sector of a circle of radius inches together with its interior can be rolled up to form the lateral surface area of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches?
C
200
What is the value of
D) 3159
200
Suppose that 
of bananas are worth as much as 
oranges. How many oranges are worth as much as 
of 
bananas?
C) 3
200
What letter does every odd number have in it?
E
300
Janet rolls a standard 
-sided die times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal 
?
B) 49/216
300
As shown in the figure below, six semicircles lie in the interior of a regular hexagon with side length 2 so that the diameters of the semicircles coincide with the sides of the hexagon. What is the area of the shaded region ---- inside the hexagon but outside all of the semicircles?
D
300
Let 
E) 2
300
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?
C) 164
300
There is a 50% chance that two people have the same birthdays in a room of how many people?
23
400
Each square in a 
grid of squares is colored red, white, blue, or green so that every 
square contains one square of each color. One such coloring is shown on the right below. How many different colorings are possible?
D) 72
400
Seven cookies of radius 
inch are cut from a circle of cookie dough, as shown. Neighboring cookies are tangent, and all except the center cookie are tangent to the edge of the dough. The leftover scrap is reshaped to form another cookie of the same thickness. What is the radius in inches of the scrap cookie?
A
400
Let 
4
400
In the expansion of
what is the coefficient of 
?
C) 224
500
Flora the frog starts at 0 on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance 
with probability 
.
What is the probability that Flora will eventually land at 10?
E) 1/2
500
A closed box with a square base is to be wrapped with a square sheet of wrapping paper. The box is centered on the wrapping paper with the vertices of the base lying on the midlines of the square sheet of paper, as shown in the figure on the left. The four corners of the wrapping paper are to be folded up over the sides and brought together to meet at the center of the top of the box, point 
in the figure on the right. The box has base length 
and height 
. What is the area of the sheet of wrapping paper?
A
500
Suppose that 
What is 
3
500
A permutation 
of 
is 
if 
. What is the number of heavy-tailed permutations?
D) 48