1. $\displaystyle \frac{1}{ 5 + \sqrt{2}}$ =

    $\displaystyle \frac{ 5 - \sqrt{2}} { 23} $

    $\displaystyle \frac{ 5 + \sqrt{2}} { 23} $

    $-5 + \sqrt{2} $

    $\displaystyle \frac{ 5 + \sqrt{2}} { 27} $

    $\displaystyle \frac{ 5 - \sqrt{2}} { 27} $

  2. The graph of $\displaystyle y=3\,x^2-3\,x+22$ is symmetric with respect to the line

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

    $\displaystyle y={{1}\over{2}}$

    $\displaystyle x={{1}\over{2}}$

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

    x = 1

  3. The graph of the system of equations \begin{displaymath}\begin{cases} 4\,x-8\,y=2 \\ [1ex] 24\,y+12\,x=6 \end{cases}\end{displaymath} consists of

    one line

    two lines intersecting where x = 2

    two distinct parallel lines

    two lines intersecting where $\displaystyle x={{1}\over{2}}$

    two lines intersecting where $\displaystyle y={{1}\over{2}}$

  4. $\displaystyle {{x+2}\over{x^2-9}} \times {{8\,x-24}\over{4\,x+8}} $ = ?

    $\displaystyle {{2}\over{x+3}}$

    $\displaystyle {{2}\over{x-3}}$

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

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

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

  5. An equation of the line passing through ( 4 , 2 ) having slope $\displaystyle {{3}\over{4}}$ is

    3x − 4y = −4

    3x − 4y = −20

    4y + 3x = 4

    4y + 3x = −4

    3x − 4y = 4

  6. The inequality $\displaystyle x^2-9\,x<10$ is equivalent to

    −1 < x < 9

    −9 < x < 1

    −1 < x < 10

    x <  − 1 or x > 10

    −10 < x < 1

  7. If $x>0$ and $y>0$, then $\sqrt{ 216 \sqrt{ 16 x^{ 10} y^{ 4}}}$ =

    $\displaystyle 24\,x^{{{5}\over{2}}}\,y$

    $\displaystyle 4\,6^{{{3}\over{2}}}\,x^{{{5}\over{2}}}\,y$

    $\displaystyle 2\,x^5\,y^2$

    $\displaystyle 24\,x^5\,y^5$

    $\displaystyle 2\,6^{{{3}\over{2}}}\,x^{{{5}\over{2}}}\,y$


Department of Mathematics
Last modified: 2026-04-29