1. $\displaystyle {{x-1}\over{x^2-9}} \times {{16\,x-48}\over{4\,x-4}} $ = ?

    $\displaystyle {{8}\over{x-3}}$

    $\displaystyle {{4}\over{x-3}}$

    $\displaystyle {{4}\over{x^2-9}}$

    $\displaystyle {{4}\over{x+3}}$

    $\displaystyle {{16}\over{x+3}}$

  2. $\displaystyle \frac{1}{ -3 + \sqrt{7}}$ =

    $\displaystyle \frac{ -3 + \sqrt{7}} { 16} $

    $\displaystyle \frac{ -3 - \sqrt{7}} { 16} $

    $\displaystyle \frac{ -3 + \sqrt{7}} { 2} $

    $\displaystyle \frac{ -3 - \sqrt{7}} { 2} $

    $3 + \sqrt{7} $

  3. If $x>0$ and $y>0$, then $\sqrt{ 27 \sqrt{ 256 x^{ 6} y^{ 8}}}$ =

    $\displaystyle 48\,x^{{{3}\over{2}}}\,y^2$

    $\displaystyle 4\,x^3\,y^4$

    $\displaystyle 16\,3^{{{3}\over{2}}}\,x^{{{3}\over{2}}}\,y^2$

    $\displaystyle 4\,3^{{{3}\over{2}}}\,x^{{{3}\over{2}}}\,y^2$

    $\displaystyle 48\,x^3\,y^3$

  4. The graph of the system of equations \begin{displaymath}\begin{cases} 8\,y-4\,x=4 \\ [1ex] -24\,y-12\,x=12 \end{cases}\end{displaymath} consists of

    two lines intersecting where x = −1

    two lines intersecting where x = 4

    two distinct parallel lines

    one line

    two lines intersecting where y = −1

  5. The inequality $\displaystyle x^2-8\,x<9$ is equivalent to

    −1 < x < 8

    −9 < x < 1

    −1 < x < 9

    x <  − 1 or x > 9

    −8 < x < 1

  6. An equation of the line passing through ( 1 , −2 ) having slope $\displaystyle -{{1}\over{4}}$ is

    −4y − x = −7

    −4y − x = 9

    −4y − x = 7

    4y − x = −7

    4y − x = 7

  7. The graph of $\displaystyle y=x^2-20\,x+22$ is symmetric with respect to the line

    y = 10

    x = −10

    y = −10

    x = 20

    x = 10


Department of Mathematics
Last modified: 2026-02-08