Algebra
Geometry
Number Theory
Combinatorics
Mystery (triple points)
100
Find x: 2πx + 3π = 7πx
2
100
A triangle has side lengths 12, 16, and 20. What is the area?
96
100
How many factors does 2025 have?
15
100
Five people must line up in a row to take a photo. How many ways are there to arrange them?
120
100
A point (4, 3) is reflected across the x-axis, then rotated 90 degrees clockwise around the origin. What is the new point?
(-3, -4)
200
Harold made a plum pie to take on a picnic. He was able to eat only 1/4 of the pie, and he left the rest for his friends. A moose came by and ate 1/3 of what Harold left behind. After that, a porcupine ate 1/3 of what the moose left behind. How much of the original pie still remained after the porcupine left?
1/3
200
Rectangle ABCD and right triangle DCE have the same area. They are joined to form a trapezoid, as shown. What is DE?
13
200
How many integers satisfy |8x| < 25π?
19
200
A class has 7 children. The teacher chooses 3 to help out. How many ways are there to choose the helpers?
35
200
Dave has 3 children. One is a boy. What is the probability that all of Dave's children are boys?
1/7
300
What is the value of 9901 × 101 - 99 × 10101?
2
300
In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of 1 square unit, then what is the area of the shaded region, in square units?
1/2
300
A driver travels for 2 hours at 60 miles per hour, during which her car gets 30 miles per gallon of gasoline. She is paid $0.50 per mile, and her only expense is gasoline at $2.00 per gallon. What is her net rate of pay, in dollars per hour, after this expense?
26
300
How many numbers from 1 to 999, inclusive, are even, and the leftmost digit is odd?
275
300
What is the probability that a randomly chosen divisor of 12! is a perfect square?
1/22
400
Bob eats 1 piece of cheese the first day, 3 pieces the second day, 9 pieces the third day, 27 pieces the fourth day, etc. for a week. How many pieces of cheese in total does he eat?
1093
400
A regular hexagon has side lengths 5. What is the area?
15√3/2
400
How many integers between 2025 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.)
15
400
Alice has 20 pencils. She wants to share them with three other people so that each person has at least three pencils. How many ways can she share the pencils?
165
400
Factor x^4 + x^3 - 2x^2 - 6x - 4.
(x + 1)(x - 2)(x^2 + 2x + 2)
500
The real number x satisfies the equation x + 1/x = √5. What is the value of x^11 - 7x^7 + x^3?
0
500
Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points A and B, as shown in the diagram. The distance AB can be written in the form m/n, where m and n are relatively prime integers. What is m+n?
69
500
For how many (not necessarily positive) integer values of n is the value of 4000 * (2/5)^n an integer?
9
500
Two coins, one fair coin and one unfair coin with 2/3 probability of landing on head are rolled. What is the probability that one lands on heads, and the other on tails?
1/2
500
Find the smallest natural number n that has the following properties:
1. Its decimal representation has 6 as the last digit.
2. If the last digit 6 is erased and placed in front of the remaining digits, the resulting number is four times as large as the original number n.
153846