Geometry
Combinatorics & Probability
Algebra
Logic & Trig
Miscellaneous
100
In rectangle ABCD, AB=6 and AD=8. Point M is the midpoint of line segment AD. What is the area of triangle AMC?
12
100
A bag contains only blue balls and green balls. There are 6 blue balls. If the probability of drawing a blue ball at random from this bag is 1/4, what is the number of green balls in the bag?
18
100
What is (20-(2010-201))+(2010-(201-20))?
40
100
Bertha has 6 daughters and no sons. Some of her daughters have 6 daughters, and the rest have none. Bertha has a total of 30 daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and granddaughters have no daughters?
26
100
How many of the twelve pentominoes pictured below have at least one line of symmetry?
6
200
Rectangle DEFA below is a 3x4 rectangle with DC = CB = BA. The area of the "bat wings" is
3
200
A player pays $5 to play a game. A die is rolled. If the number on the die is odd, the game is lost. If the number on the die is even, the die is rolled again. In this case, the player wins if the second number matches the first and loses otherwise. How much should the player win if the game is fair? (In a fair game, the probability of winning times the amount won is what the player pays.)
60 dollars
200
Five positive consecutive integers have an average of b. The smallest of these integers is a. What is the average of 5 consecutive integers of which the smallest is b (in terms of a)?
a+4
200
Evaluate sin of 15 degrees.
(sqrt6 - sqrt2)/4
200
Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains 8 unit squares. The second ring contains 16 unit squares. If we continue this process, what is the number of unit squares in the 100th ring?
800
300
Two congruent circles centered at points A and B each pass through the other circle's center. The line containing both A and B is extended to intersect the circles at points C and D. The circles intersect at two points, one of which is E. What is the degree measure of angle CED?
120
300
When properly sorted, 9 math books on a shelf are arranged in alphabetical order from left to right. An eager student checked out and read all of them. Unfortunately, the student did not realize how the books were sorted, and so after finishing the student put the books back on the shelf in a random order. If all arrangements are equally likely, what is the probability that exactly 6 of the books were returned to their correct (original) position (in simplest terms)?
1/2160
300
A palindrome, such as 83438, is a number that remains the same when its digits are reversed. The numbers x and x+32 are three-digit and four-digit palindromes, respectively. What is x?
969
300
A girl meets a lion and a unicorn in the forest. The lion lies every Monday, Tuesday, and Wednesday, and the other days of the week, he speaks the truth. The unicorn lies on Thursdays, Fridays, and Saturdays, and the other days of the week, he speaks the truth. "Yesterday I was lying," the lion told the girl. "So was I," said the unicorn. What day is it?
Thursday
300
Suppose that n is the product of three consecutive integers and that n is divisible by 7. Which of the following is not necessarily a divisor of n?
28
400
In rectangle ABCD, AD = 1, P is on line segment AB, and DB and DP trisect angle ADC. What is the perimeter of triangle BDP?
2 + (4sqrt3)/3
400
A coin is biased in such a way that on each toss the probability of heads is 2/3 and the probability of tails is 1/3. The outcomes of the tosses are independent. A player has the choice of playing Game A or Game B. In Game A she tosses the coin three times and wins if all three outcomes are the same. In Game B she tosses the coin four times and wins if both the outcomes of the first and second tosses are the same and the outcomes of the third and fourth tosses are the same. In which game is the probability of winning higher, and by how much?
The probability of winning Game A is 2/81 greater than the probability of winning Game B.
400
Suppose that real number x satisfies
sqrt(49-x^2) - sqrt(25-x^2) = 3.
What is sqrt(49-x^2) + sqrt(25-x^2)?
8
400
If 
, what is the value of 
?
3/5
400
How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression?
59
500
One-inch squares are cut from the corners of this 5-inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?
15 in^2
500
Amelia has a coin that lands heads with probability 1/3, and Blaine has a coin that lands on heads with probability 2/5. Amelia and Blaine alternately toss their coins until someone gets a head; the first one to get a head wins. All coin tosses are independent. Amelia goes first. What is the probability that Amelia wins?
5/9
500
Let m = 101^6 + 4^6. What is the sum of the digits of m?
41
500
Evaluate. Final answer must be in simplest form.
(sin(lnx))^6 + 3(sin(lnx)*cos(lnx))^2 + (cos(lnx))^6
1
500
How many perfect cubes lie between (2^8)+1 and (2^18) + 1, inclusive?
58