UND MATHEMATICS TRACK MEET Team Test 1

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

• 1.

  What is the side length of a square with the same area as a triangle with base $10$ and height $6$? Enter your answer as a decimal rounded to three decimal places.

    (20 pts) 1. 5.477

• 2.

  What is the area of a circle with circumference $7\pi$? Enter your answer as a decimal rounded to three places.

    (20 pts) 2. $38.485$

• 3.

  Find positive numbers $r$ and $s$ with $rs=31$ and $r+s=12$. Enter your answers as decimals rounded to three places.

    (20 pts) 3. $\{r,s\}\approx \{3.764,8.236\}$

• 4.

  In a class your grade is determined by the average of five exam scores. If the average of your first three exams is 73%, what must your average on the last two exams be to get at least an 80% in the class?

    (20 pts) 4. $90.5\%$

• 5.

  The value of a new car decreases by $10\%$ each year. If a new car costs $35,000, what will its value be after 5 years?

    (20 pts) 5. $20667.15

• 6.

  What is the greatest common divisor of $175$ and $280$?

    (20 pts) 6. 35

• 7.

  Find the positive solution to $3^{x^2+1}=9^{2x+1}$. Enter your answer as a decimal rounded to three places.

    (20 pts) 7. 4.236

• 8.

  Suppose the price of an item is increased by $20$% and then later the new price is decreased by $30$%. Compared to the original price, what percentage decrease does the final price represent?

    (20 pts) 8. 16%

• 9.

  Solve the system of equations

    (20 pts) 9. $(x,y)=(1138,-2401)$

• 10.

  Suppose $a$ and $b$ are the roots of $x^2+10x-3=0$. What is $a^{2}b+a{b}^2$ ?

    (20 pts) 10. 30