UND MATHEMATICS TRACK MEET Individual Test 3

University of North Dakota Grades 9/10
January 12, 2026
School Team Name
Calculators are allowed. Student Name

• 1.

  Susan has ordered a package and lives $7$ miles east and $24$ miles north of the fulfillment center. The delivery drone flies in a straight line above the buildings at $50$ miles per hour. How long will it take Susan to get her package in minutes?

    (2 pts) 1.

• 2.

  A new public policy goal states that the number of high school graduates pursuing STEM careers in North Dakota must increase by $45$ students per year. If the target cohort size is $2026$ students in the year $2026$, how many students must the policy cohort include in the baseline year $2012$?

    (3 pts) 2.

• 3.

  Let $x$ and $y$ be positive integers such that $x^2+y^2=2026$ and $x^2{y}^2=2025$. What is $|x-y|$?

    (3 pts) 3.

• 4.

  A standard deck of 52 cards has 13 values in each of 4 different suits. I draw two cards from the deck that are both aces and do not replace back in the deck. What is the probability that the next card I draw is an ace? Give your answers as a reduced fraction.

    (3 pts) 4.

• 5.

  Kanesha just had a birthday. Now her daughter is half as old as her and her mother is twice as old as her. The sum of all of their ages is $161$. How old did Kanesha just turn?

    (3 pts) 5.

• 6.

  A composite animal pen is made up of a square and an equilateral triangle that meet at exactly one vertex (see picture below). Let $x$ be the length of the side of the square, and the length of the side of the triangle is $\frac{2}{3}x$. The total perimeter of the pen is $78$ units, what is the perimeter of the triangle alone?
  

    (3 pts) 6.

• 7.

  A new smoothie bar is opening, and the menu offers a fixed list of four premium add-ins: Açaí, Chia Seeds, Protein Powder, and Honey. The manager wants to feature every single combination of add-ins that a customer could order: no add-ins, one add-in all the way to all four add-ins. How many total distinct menu options, representing every possible combination of add-ins, must the manager prepare prices for?

    (3 pts) 7.

TOTAL POINTS