UND MATHEMATICS TRACK MEET Individual Test 3

University of North Dakota Grades 9/10
January 12, 2026
School Team Name
Calculators are allowed. Solutions 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. 30

  Solution: The distance the drone travels can be found using the Pythagorean Theorem: $7^2+{24}^2={25}^2$. If the drone travels $50$ miles in one hour, then it will take $30$ minutes to travel $25$ miles.

• 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. $1396$

  Solution: $2026-2012=14$, so there are $14$ years with an increase of $45$ students each year, which is $14\ast 45=630$, so $2026-630=1396$

• 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. $44$

  Solution: $x^2{y}^2=2025\to {(xy)}^2=2025$, so $xy=45$. Checking all of the positive integer factors of $45$, you will find that they must be $1$ and $45$, so the absolute value of the difference is $44$

• 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. $\frac{1}{25}$

  Solution: There are two aces left in the deck and a total of $50$ cards, giving $\frac{2}{50}$, which reduces to $\frac{1}{25}$

• 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. $46$

  Solution: Let $x$ be Kanesha’s age. Then her daughter is $.5x$ and her mother is $2x$. $2x+x+.5x=161$, so $x=46$.

• 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. $26$

  Solution: $3\ast \frac{2}{3}x+4x=78$, so $x=13$. The perimeter of the triangle would be $3\ast \frac{2}{3}\ast 13=26$

• 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. $16$

  Solution: Each add-in is either in the order or not, so there are two options for each of the four add-ins. Thus $2^4=16$. Alternatively, you could just list all $16$ options.