UND MATHEMATICS TRACK MEET Individual Test 2

University of North Dakota Grades 9/10
January 12, 2026
School Team Name
Calculators are NOT allowed. Solutions Student Name

• 1.

  What is the sum of the roots of the equation $-3x+1=2x^2+5x+7$?

    (2 pts) 1. $-4$

  Solution: $2x^2+8x+6=0⟹x^2+4x+3=0$. The sum is $-4$.

• 2.

  If and , then . What is $a+b$?

    (3 pts) 2. $-3$

  Solution: . So, $a+b=-3$.

• 3.

  Solve ${\displaystyle \frac{2}{|x-1|}}>{\displaystyle \frac{1}{3}}$

    (3 pts) 3.

  Solution: .

• 4.

  Find an equation for the set of all points $(x,y)$ that are equidistant from $(0,0)$ and $(3,1)$.

    (3 pts) 4. $$\begin{array}{c}6x+2y=10\hfill \\ \hfill \text{or}\mathrm{\hspace{0.17em}\hspace{0.17em}3}x+y=5\end{array}$$

  Solution: $x^2+y^2={(x-3)}^2+{(y-1)}^2⟹x^2+y^2=x^2-6x+9+y^2-2y+1⟹6x+2y=10$.

• 5.

  For which value of $k$ is $x^3+2x^2+3kx+1$ divisible by $x-1$?

    (3 pts) 5. $-4/3$

  Solution: $x^3+2x^2+3kx+1=(x-1)(x^2+3x+3k+3)+3k+4$.

• 6.

  If , then $\left|3-|x+1|\right|$ is
  (a) $x+1$  (b) $x+4$  (c) $-x-1$  (d) $-x-4$  (e) None of the above
  

    (3 pts) 6. (d)

  Solution: $\left|3-|x+1|\right|=|3+(x+1)|=|x+4|=-(x+4)$.

• 7.

  A sequence is defined by $a_1=1,a_2=\sqrt{3},a_3=\sqrt{3\sqrt{3}},\mathrm{\cdots },a_n=\sqrt{3a_{n-1}}$. This sequence converges to $L$. What is $L$?

    (3 pts) 7. $3$

  Solution: $L=\sqrt{3L}⟹L^2=3L⟹L(L-3)=0$. Since $L\ne 0$, $L=3$.