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
Cards numbered 1 through 10 lie on a table. If two cards are picked at random, without replacement, what is the probability, as a fraction in lowest terms, that the two cards will have values within one of each other?
1/5
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
Solve the following equation for x between 0 and pi/2 inclusive: cos(2x)−5cos(x) +3 = 0.
pi/3
200
Two real numbers are selected independently at random from the interval [-20,10]. What is the probability that the product of those numbers is greater than zero?
5/9
200
A right prism has equilateral triangles with side length 6 as bases. If the volume of the prism is 54 square root of 3, what is the lateral surface area?
Note: Lateral surface area excludes the bases.
108
300
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
300
In Timlandia, two-thirds of the population always tell the truth, while the remaining one-third always lie. Emmy asks four inhabitants of Timlandia whether it is snowing currently, and three of them say yes. What is the probability that it is snowing, given that Emmy’s prior is that it is equally likely to snow or not snow in Timlandia?
4/5
300
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
400
What is the product of all the roots of the equation sqrt(5|x|+8) = sqrt(x²-16).
-64
400
Suppose that one of every 500 people in a certain population has a particular disease, which displays no symptoms. A blood test is available for screening for this disease. For a person who has this disease, the test always turns out positive. For a person who does not have the disease, however, there is a 2% false positive rate--in other words, for such people, 98% of the time the test will turn out negative, but 2% of the time the test will turn out positive and will incorrectly indicate that the person has the disease. Let p be the probability that a person who is chosen at random from this population and gets a positive test result actually has the disease. Which of the following is closest to p?
C) 1/11
400
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) (sqrt(2) - 1)/2