Esmv Mathematics Diagnostic test

Which expression is equivalent to

 $\frac{3x^{-2\ }y^3}{9x^3y^{-5\ }}$  

•  $\frac{y^8}{3x^5}$  

•  $\frac{3x^{-5\ }}{y^8}$  

•  $\frac{xy^2}{3}$  

•  $3xy^2$  

Evaluate

 $\frac{-5x^3y^5}{15x^{-7\ }y^5z^{-2}}\ for\ \ x=-1,\ y=5,\ and\ z=3$  

•  $3$  

•  $9$  

•  $-3$  

•  $-1$  

Find the equation of the line that passes through (-2, 7), and is perpendicular to the line

 $2x\ -\ 5y\ =\ 3$  

•  $y=\ \frac{2}{5}x\ +2$  

•  $5x+2y\ =4$  

•  $2x\ +\ 5y=4$  

•  $y=\ \frac{5}{2}x\ +\ 2$  

Which of the following expressions ouwld give the area of the triangle shown in the figure?

• 
  

  $60x^2y^2$
  

• $90x^3y^3$

• $180x^2y^2$

• $180x^3y^3$

Simplify

 $4\sqrt{75}\ +\ \sqrt{27}$  

•  $12\sqrt{3}$  

•  $23\sqrt{3}$  

•  $4\sqrt{102}$  

•  $5\sqrt{102}$  

Simplify

 $\left(3\sqrt{5}\ -\ \sqrt{2}\right)\left(\sqrt{5}+5\sqrt{2}\right)$  

•  $5+14\sqrt{10}$  

•  $19\sqrt{10}$  

•  $14\sqrt{10}$  

•  $20$  

Which of the following are solution(s) of

 $\sqrt{2x+1}=\ \sqrt{3x-5}$  

•  $-1$  

•  $6$  

•  $\frac{4}{5},\ 6$  

•  $no\ \ solution$  

If   $\tan\ \theta=\frac{5}{12}$   , then  $\cos\ \theta\ =\$  

•  $\frac{12}{13}$  

•  $\pm\frac{12}{13}$  

•  $\frac{5}{13}$  

•  $\pm\frac{5}{13}$  

•  $\frac{12}{11}$  

 $\log_4\left(2x+1\right)-\log_4\left(x-3\right)=1$  

Solve

•  $x=-2\ only$  

•  $x=\ -4\ only$  

•  $x=4\ or\ x=\ \frac{7}{2}$  

•  $x=\frac{13}{2}only$  

•  $x=\ \frac{11}{2\ }only$  

What is the solution for the following system of equations?

• $\left(3,\ 1\right)$

• $\left(1,\ 3\right)$

• $\left(-1,\ 4\right)$

• $\left(4,\ -1\right)$