Which famous mathematician discovered the formula for the sum of the first n positive integers as a kid?
Gauss
100
What is x if x^4 + 3x^2 + 2x = 0?
0, -1, -2
100
What is the remainder when 1234567890 is divided by 13
10
100
What is AB if right triangle ABC (right angle at C) has side lengths BC = 12 and AC = 13?
square root of 313
100
How many ways are there to rearrange the letters in MATTHEW?
2520
200
Which branch of mathematics was developed by Muhammad ibn Musa al-Khwarizmi?
Algebra
200
Suppose hops, skips, and jumps are specific units of length. We know that b hops equal c skips, d jumps equal e hops, and f jumps equal g meters. How many skips are equal to one meter?
cef/(bdg)
200
The number 25^64 * 64^25 is the square of a positive integer N. What is the sum of the decimal digits of N?
14
200
The sides of a triangle have lengths of 15, 20, 25. What is the length of the shortest altitude?
12
200
A restaurant offers three desserts, and exactly twice as many appetizers as main courses. A dinner consists of an appetizer, a main course, and a dessert. What is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night for a year?
8
300
Name at least six instructors teaching math at A-Star this summer.
Answers will probably vary.
300
Let f(x) = ax^7 + bx^3 + cx - 5, where a, b, and c are constants. Suppose that f(-7) = 7. What is f(7)?
-17
300
For how many values of n will an n-sided regular polygon have interior angles with integer degree measures?
22
300
The convex polygon ABCDE has angle A = angle B = 120 degrees, EA = AB = BC = 2, and CD = DE = 4. What is the area of ABCDE?
7*square root of 3
300
Ali wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?
15
400
Computers use the binary system. We ordinarily use the decimal system. But the Babylonians used the sexagesimal system that had what number as its base?
60
400
Let *(n) denote the sum of the digits of the positive integer n. For example, *(8) = 8 and *(123) = 1 + 2 + 3 = 6. For how many two-digit values of n is *(*(n)) = 3?
10
400
Suppose that the base-8 representation of a perfect square is ab3c, where a is not 0. What is c?
1
400
In triangle ABC we have AB = 5, BC = 7, and AC = 9. Also, D is on AC with BD = 5. What is AD/DC?
19/8
400
Using the letters A, M, O, S, and U, we can form 5! = 120 five-letter words. If these words are arranged in alphabetical order, then what position does the word USAMO occupy?
115
500
Who collaborated with Alfred North Whitehead in writing "Principia Mathematica" and later won the 1950 Nobel prize for literature?
(Bertrand) Russell
500
Suppose that P(x/3) = x^2 + x + 1. What is the sum of all values of x for which P(3x) = 7?
-1/9
500
How many positive integers less than 50 have an odd number of positive integer divisors?
7
500
A parallelogram ABCD has angle ABC = 120 degrees, AB = 16, and BC = 10. Extend CD through D to E so that DE = 4, and label as F the intersection of AD and BE. What is the value of DF?
2
500
Define [a, b, c] = (a + b) / c. What is the value of [[60, 30, 90], [2, 1, 3], [10, 5, 15]]?