University of North Dakota Grades 11/12
January 12, 2026
School Team Name
Calculators are allowed. Student Name
Find the value(s) of such that the equation has exactly one solution. Give an exact answer.
(2 pts) 1.
An investment account is setup with an initial investment and, after 25 years, contains one million dollars. If the amount in the account doubled every 7 years while increasing continuously, find the initial amount invested. Give your answer in dollars and cents.
(3 pts) 2.
A bag contains 3 blue, 2 green, and 5 red marbles. What’s the probability that there are still green marbles in the bag after 4 marbles have been removed? Give the exact answer.
(3 pts) 3.
A group of people is randomly selected to come to a soccer field. Find the minimum number of people required to ensure that it’s possible to form two teams of 11 people such that any two teammates have the same birthday (though are not necessarily the same age). Remember, February 29th is a valid birthday for those born on leap years!
(3 pts) 4.
Find the units place of the sum
(3 pts) 5.
A square is contained in an equilateral triangle with side length 2 such that the bottom edge of the square lies along the base of the triangle and the two top vertices of the square lie on the other two edges of the triangle as shown in the figure below. Find the side length of the square. You may round your answer to two decimal places.
(3 pts) 6.
A spiral staircase climbs the outer wall of a 20 story circular tower with radius 10 meters. Given that the staircase completes one rotation every 3 stories and each story is 3 meters tall, find the (straight line) distance, in meters, between the bottom and top of the staircase. You may round your answer to two decimal places.
(3 pts) 7.
TOTAL POINTS