UND MATHEMATICS TRACK MEET Team Test 1

University of North Dakota Grades 11/12
January 12, 2026
School Team Name
Calculators are allowed. Key

• 1.

  A rectangular piece of plywood is 3.7 feet wide and 7.6 feet long. Find the area of the piece of plywood. Round your answer to one decimal place. Express your answer in square feet.

    (20 pts) 1. $28.1$ ft²

• 2.

  The tires of a truck are exactly 4 feet in diameter. As the truck travels, the wheels of the truck rotate at the rate of 5 revolutions per second. How fast is the truck traveling? Express your answer in feet per second, and round your answer to one decimal place.

    (20 pts) 2. $62.8$ ft/s

• 3.

  A scientist predicts that $t$ hours from now, a petri dish will contain $39\cdot 2^{3t}$ bacteria ($39$ times $2^{3t}$ bacteria). After how many hours will there be $497$ bacteria in the petri dish? Round your answer to one decimal place.

    (20 pts) 3. $1.2$ hrs

• 4.

  Amanda is 6 inches taller than Tom. The sum of the heights of Amanda and Tom is 112 inches. Find Tom’s height, in inches.

    (20 pts) 4. $53$ in

• 5.

  A large jar contains 4 yellow balls, 7 blue balls, and 6 red balls. Mrs. Smith randomly selects one ball from the jar. Then, without putting this ball back into the jar, she randomly selects a second ball from the jar. What is the probability that the two selected balls are both yellow? Express your answer as a percentage, and round it to one decimal place.

    (20 pts) 5. $4.4$%

• 6.

  Consider the polynomial $x^3-4x^2-11x+30$. Factor this polynomial completely.

  Hint: Let $f(x)=x^3-4x^2-11x+30$. Let $c$ be any real number. Then $x-c$ is a factor of $x^3-4x^2-11x+30$ if and only if $f(c)=0$. You may wish to experiment with some obvious choices of $c$. Try to find a real number $c$ such that $f(c)=0$. If you find such a $c$, this may help you find a correct solution to this problem.

    (20 pts) 6. $$\begin{array}{c}(x-2)(x-5)\hfill \\ \hfill (x+3)\end{array}$$

• 7.

  The front row of a movie theater consists of five seats. These seats are permanently attached to the floor and cannot be rearranged. A group of five students arrives at the theater, and these students would like to sit together in the front row of the theater. Three of the students are boys, and two are girls. The students all agree that the two girls must not sit in adjacent seats. In how many different ways can the five students be arranged in the five seats of the front row?

    (20 pts) 7. $72$ ways

• 8.

  In this problem, we consider the rightmost two digits of various positive integers. For example, the rightmost two digits of 539 are 39. The rightmost two digits of 255201 are 01.

  What are the rightmost two digits of $7^{998795}$?

    (20 pts) 8. $43$

• 9.

  Consider a group of five towns, no three of which lie along a single straight line. We wish to construct a railway network connecting these five towns. The network must consist of four straight tracks. Each track must start at one town and end at another town. It must be possible for a train to travel from any of the five towns to any of the other four towns by using the tracks of the network. Two tracks may cross at a point $P$, where $P$ does not lie in any town; if this happens, however, a train may not move from one track to the other at $P$. But if any two tracks go to the same town, a train may move from one of these tracks to the other at that town. How many different railway networks are possible?

    (20 pts) 9. $125$ networks

• 10.

  Consider $n$ lines in the plane, where $n>0$. Suppose that no two of these lines are parallel and no two of them are the same line. Suppose that no single point in the plane lies on more than two different lines. (So you never have more than two lines intersecting at the same point.) The $n$ lines divide the plane into different regions. The number of such regions depends on $n$. Into how many regions do the $n$ lines divide the plane?

    (20 pts) 10. $$\begin{array}{c}\frac{n^2+n+2}{2}\hfill \\ \hfill \text{or }2+(2+3+4+\mathrm{\cdots }+n)\\ \hfill \text{or }1+(1+2+3+\mathrm{\cdots }+n)\\ \hfill \text{or }1+\frac{n(n+1)}{2}\end{array}$$