University of North Dakota Grades 7/8
January 12, 2026
School Team Name
Calculators are allowed. Student Name
Two fair 6-sided dice are rolled and their product is recorded. Find the probability that their product is a multiple of 3. Round your answer to two decimal places.
(2 pts) 1.
An isosceles right triangle is inscribed in a circle as shown below. Given that the area of the circle is , find the area of the shaded region. Round your answer to two decimal places.
(3 pts) 2.
Suppose that the population of a bacterial colony is currently 1248. If the population shrinks to half of its size every hour, how many hours will it be until the population reaches 156?
(3 pts) 3.
Quinn invested $500 in a fund which is growing at a rate of 3.5% per month and $1000 in a fund which is shrinking at a rate of 2% per month. By how much did Quinn’s investment change after one month?
(3 pts) 4.
Find the set of all for which .
(3 pts) 5.
Suppose the date of the third Friday of October is two times the date of the second Tuesday of October. What day of the week is October 5th?
(3 pts) 6.
Starting with the number 5/7, we will begin repeating the following process. If the number is bigger than 1, subtract 1. Otherwise we multiply it by 2. Then repeat this again with the new number. How many repetitions do we make before we arrive back at 5/7?
(3 pts) 7.
TOTAL POINTS