UND MATHEMATICS TRACK MEET Individual Test 1

University of North Dakota Grades 7/8
January 12, 2026
School Team Name
Calculators are allowed. Solutions Student Name

• 1.

  Simplify $\left(8-5\right)\times \left[\left(7+4\right)-\left(6÷3\right)\right]$ . Your answer should be an integer or a fraction where the numerator and denominator have no common factors.

    (2 pts) 1. $27$

  Solution: $\left(8-5\right)\times \left[\left(7+4\right)-\left(6÷3\right)\right]=3\times \left[11-2\right]=3\times 9=27$

• 2.

  Each student in a class has a dog, a cat, or both a dog and a cat. Sixteen students have a dog (with or without a cat), and 10 have a cat (with or without a dog). If there are 21 students in all, how many have both a dog and a cat?

    (3 pts) 2. $5$

  Solution: Sixteen students have a dog, so $21-16=5$ must have a cat with no dog. Since 10 have a cat, there must be $10-5=5$ with both. Or use set notation with $A=$ the set of students with dogs and $B=$ the set of students with cats. $\left|A\cup B\right|=\left|A\right|+\left|B\right|-\left|A\cap B\right|\Rightarrow 21=16+10-\left|A\cap B\right|\Rightarrow \left|A\cap B\right|=16+10-21=5$

• 3.

  The 21 students in a morning math class have an average score of 86 on a test. The 18 students in the afternoon class have an average score of 73. What is the average score of all 39 students together?

    (3 pts) 3. $80$

  Solution: The total of the 39 scores is $(21\ast 86+18\ast 73)=3120$, so the average is $3120/39=80$.

• 4.

  A rectangular prism is 8 cm long, 5 cm wide, and 4 cm high. What is the total surface area of all faces of the prism?

    (3 pts) 4. $184$ cm²

  Solution: There are two faces consisting of rectangles with each possible pair of edges, so the total surface area is $2\times 8\times 5+2\times 8\times 4+2\times 5\times 4=184$ cm².

• 5.

  A line passes through three points (1, 2), (7, 4), and (16, $a$). What is the value of $a$?

    (3 pts) 5. $7$

  Solution: The slope of the line is $(4-2)/(7-1)=1/3$ and the $y$-intercept is $2-(1/3)\ast 1=5/3$. Therefore, $a=(1/3)\ast 16+5/3=21/3=7$.

• 6.

  A box contains 3 red balls and 3 blue balls. Alice randomly draws and keeps one of the balls from the box, and then Bill randomly draws a different ball from those left in the box. What is the probability that Alice and Bill both draw red balls? Express your answer as a fraction where the numerator and denominator have no common factors.

    (3 pts) 6. ${\displaystyle \frac{1}{5}}$

  Solution: The probability that Alice draws a red ball is $\frac{3}{6}$, and the probability that Bill draws a red ball after Alice has already removed a red ball is $\frac{2}{5}$. The probability that both happen is $\left(\frac{3}{6}\right)\times \left(\frac{2}{5}\right)=\frac{1}{5}$.

• 7.

  A square has sides of length 5 inches. A circle has a diameter of 6 inches. How much longer (in inches) is the perimeter of the square than the circumference of the circle? Use 3.14 for pi, and write your answer to the hundredth place.

    (3 pts) 7. $1.16$ in

  Solution: The perimeter of the square is $4\times 5=20$ in. The circumference of the circle is $6\pi =6\times 3.14=18.84$ in. The difference is $(20-18.84)=1.16$ in.