1. $\log_{ 6} \left(\displaystyle {{1}\over{36}} \right)$ =

    −2

    −6

    6

    $\displaystyle -{{1}\over{2}}$

    2

  2. Which of the following is the domain of $f(x)=\sqrt{x^2 - 36 }$?

    $[ -6 ,\infty)$

    $(-\infty,\infty)$

    $\left\{x \,\left\vert -6 \leq x \leq 6 , \,\mbox{$x$\ is a real number} \right.\right\}$

    $\left\{x \,\left\vert\, \vert x\vert \ge 6 , \,\mbox{$x$\ is a real number} \right.\right\}$

    $(-\infty, 6 ]$

  3. If $\displaystyle t=e^{x+4}$ then $x=$

    −8

    $\displaystyle {{t-2}\over{e}}$

    8

    $\displaystyle \ln t-4$

    $\displaystyle \ln t$

  4. The graphs of the two equations $\displaystyle y=5\,x-{{41}\over{8}}$ and $\displaystyle y=2\,x^2$ intersect in how many distinct points?

    three

    unknown

    two

    one

    none

  5. Of the following, which best represents the graph beside?

    \includegraphics{part3_pick_plot0.jpeg}

    y = 1 − x

    $\displaystyle y=1-x^2$

    $\displaystyle y=\ln x$

    $\displaystyle y=\sqrt{x-1}$

    $\displaystyle y=e^ {- x }$

  6. The polynomial equation $\displaystyle x\,\left(x^2-4\right)\,\left(x^2+2\right)=0$ has how many real roots?

    four only

    only one

    three only

    two only

    five


Department of Mathematics
Last modified: 2026-05-18