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

    −2

    6

    −6

    2

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

  2. If $\displaystyle t=e^{x-1}$ then $x=$

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

    $\displaystyle \ln t+1$

    2

    −2

    $\displaystyle \ln t$

  3. Which of the following is the domain of $f(x)=\sqrt{x^2 - 25 }$?

    $[ -5 ,\infty)$

    $(-\infty, 5 ]$

    $\left\{x \,\left\vert\, \vert x\vert \ge 5 , \,\mbox{$x$\ is a real number} \right.\right\}$

    $(-\infty,\infty)$

    $\left\{x \,\left\vert -5 \leq x \leq 5 , \,\mbox{$x$\ is a real number} \right.\right\}$

  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?

    two

    three

    unknown

    none

    one

  5. The polynomial equation $\displaystyle x\,\left(x^2-4\right)\,\left(x^2-3\right)=0$ has how many real roots?

    only one

    four only

    two only

    five

    three only

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

    Image part3_pick_plot0

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

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

    $\displaystyle y=\ln x$

    $\displaystyle y=1-x^2$

    y = 1 − x


Department of Mathematics
Last modified: 2026-06-14