Algebra
Number Theory
Geometry
Combinatorics
Trivia
100
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes. How many minutes was this?
665 (2016 AMC8 #1)
100
Positive integers a and b are each less than 6. What is the smallest possible value for 2a - ab?
-15 (2013 AMC10B #5)
100
Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?
150 (2019 AMC8 #2)
100
In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 1/3 of all the ninth graders are paired with 2/5 of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?
4/11 (2015 AMC8 #16)
100
What place did Team Canada rank at the 2023 IMO in Japan? (Hint: there were 112 participating countries)
5th (Fun fact, this is tied for the highest ever ranking for Team Canada)
200
How many digits are in the product 4^5 * 5^10?
11 (2011 AMC8 #15)
200
For how many (not necessarily positive) integer values of n is the value of 4000 * (2/5)^n an integer?
9 (2018 AMC10A #7)
200
Let angle ABC = 24 degrees and angle ABD = 20 degrees. What is the smallest possible degree measure for angle CBD?
4 (2012 AMC10A #4)
200
At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?
245 (2017 AMC10A #8)
200
What is the full name of the Repechage?
Canadian Mathematical Olympiad Qualifying Repechage
300
Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number?
8 (2015 AMC12B #3)
300
The 25 integers from -10 to 14, inclusive, can be arranged to form a 5-by-5 square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum?
10 (2020 AMC10A #7)
300
A solid cube of side length 1 is removed from each corner of a solid cube of side length 3. How many edges does the remaining solid have?
84 (2013 AMC10A #14)
300
Two different numbers are selected at random from {1,2,3,4,5} and multiplied together. What is the probability that the product is even?
7/10 (2016 AMC10B #12)
300
What is the maximum number of contests a contestant can qualify for through COMC alone?
4 (EGMO TST, Repechage, CMO, APMO)
400
One day the Beverage Barn sold 252 cans of soda to 100 customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?
7/2 (2014 AMC8 #24)
400
Which of the following expressions is never a prime number when p is a prime number?
A) p^2 + 16
B) p^2 + 24
C) p^2 + 26
D) p^2 + 46
E) p^2 + 96
C (2018 AMC10B #11)
400
A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?
120/17 (2016 AMC8 #25)
400
Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?
7/72 （2014 AMC10B #16)
400
What is the mascot of the Canadian national math teams?
Moose (Fun fact: the name is Canmoo and is usually a stuffed animal moose wearing a Canadian sweater)
500
Let a, b, and c be real numbers such that a+b+c=2, a^2+b^2+c^2=12 What is the difference between the maximum and minimum possible values of c?
16/3 (2013 AMC12B #17)
500
A positive integer x has a remainder of 14 when divided by 19, a remainder of 6 when divided by 11 and a remainder of 18 when divided by 23. What is the least possible value of x?
4802 (Original)
500
The y-intercepts, P and Q, of two perpendicular lines intersecting at the point A(6,8) have a sum of zero. What is the area of triangle APQ?
60 (2014 AMC10 #14)
500
Johann has 64 fair coins. He flips all the coins. Any coin that lands on tails is tossed again. Coins that land on tails on the second toss are tossed a third time. What is the expected number of coins that are now heads?
56 (2015 AMC10B #18)
500
What is the largest number of gold medals a single contestant has ever won at the IMO?
5 (Fun fact: As of the 2023 IMO, Alex Song (CAN) is the only contestant to receive 5 gold medals. He has ranked first in the IMO hall of fame since the 2015 IMO in Thailand with 5 golds (1 perfect), 1 bronze.)