Algebra/Rate
Probability/Combinatorics
Geometry
100
Water flows at 10 cubic feet per minute into a cylinder with a radius of 5 feet and height of 12 feet. Providing your answer as a fraction in simplest form in terms of pi, how fast is the water rising in feet per minute when the height is 4 feet?
2/(5pi)
100
One fair die has faces 1, 1, 2, 2, 3, 3, and another has faces 4, 4, 5, 5, 6, 6. The dice are rolled and the numbers on the top faces are added. What is the probability that the sum will be odd?
A) 1/3 B) 4/9 C) 1/2 D) 5/9 E) 2/3
D) 5/9
100
Pablo walks 5 miles north, 6 miles east, 2 miles north, 1 mile east, 4 miles south, 1 mile west, and 3 miles north again. Then, he climbs a directly vertical staircase up 1 mile. How many miles is he from his starting point?
√73
200
Keiko walks once around a track at exactly the same constant speed every day. The sides of the track are straight, and the ends are semicircles. The track has a width of 6 meters, and it takes her 36 seconds longer to walk around the outside edge of the track than around the inside edge. What is Keiko's speed in meters per second? Leave in terms of pi.
pi/3
200
Twelve fair dice are rolled. What is the probability that the product of the numbers on the top faces is prime?
A) (1/12)^(12) B) (1/6)^(12) C) 2(1/6)^(11)
D) (5/2)*(1/6)^(11) E) (1/6)^(10)
E) (1/6)^10
200
Two equilateral triangles are contained in a square whose side length is 2sqrt3. The bases of these triangles are the opposite sides of the square, and their intersection is a rhombus. What is the area of the rhombus?
8sqrt(3) - 12
300
What is the product of all the roots of the equation sqrt(5|x|+8) = sqrt(x²-16).
-64
300
Let @(x) denote the sum of the digits of the positive integer x. For example, @(8)=8 and @(123)= 1+2+3=6. For how many two-digit values of x is @(@(x))=3?
A) 3 B) 4 C) 6 D) 9 E) 10
E) 10
300
A dart board is a regular octagon divided into regions as shown. Suppose that a dart thrown at the board is equally likely to land anywhere on the board. What is the probability that the dart lands within the center square?
A) (sqrt2-1)/2 B) 1/4 C) (2-sqrt2)/2
D) (sqrt2)/4 E) 2-sqrt2
A) (sqrt(2) - 1)/2