Algebra Practice Questions - Part 3

Q1) $\sqrt[3]{81}+\sqrt[3]{24}=$

A. $5$

B. $\sqrt[3]{125}$

C. $6\sqrt[3]{3}$

D. $5\sqrt[3]{3}$

E. $35$

Q2) What is the slope of the line perpendicular to the line with equation $2x+7y=8$?

A. $\dfrac{2}{7}$

B. $-\dfrac{2}{7}$

C. $-\dfrac{7}{2}$

D. $\dfrac{7}{2}$

E. $\dfrac{1}{7}$

Q3) What are the real roots of the equation $(x+1)(x−2)=4$?

A. $1$, $2$ and $4$

B. $-1$ and $2$

C. $3$ and $-2$

D. $-3$ and $2$

E. No real roots

Q4) If $\dfrac{4}{\sqrt{|x|+1}}=1$, then $|x|=$?

A. $0$

B. $-15$

C. $-5$

D. $10$

E. $15$

Q5) What is the equation of the line shown below?

A. $y=2x+2$

B. $-x+2y=2$

C. $y=2$

D. $y=\dfrac{1}{2}x+2$

E. $x+2y=4$

Q6) Factor completely $6 x^3 y+10 x^2 y−4 x y$

A. $2 x y(x+2)(3x−1)$

B. $2 x y(3x^2+5 x−2)$

C. $2(3 x^3 y+5 x^2 y−2 x y)$

D. $2 x(3x^2 y+5 x y − 2 y)$

E. $12 x^4 y$

Q7) The volume $V$ of a cylindrical tube with circular base is given by by $V=\pi r^2 \times h$ where $\pi$ is a constant and $r$ is the radius of the base ans $h$ is the height of the tube. Which equation may be used to find the radius $r$ of a cylindrical tube whose height is $4$ cm more than $3$ times its radius and its volume is $4000$ cm$^3$?

A. $12\pi r^2=4000$

B. $r^2(3 r+4)=\dfrac{4000}{\pi}$

C. $3r^3=\dfrac{4000}{\pi}$

D. $3r^3+4=\dfrac{4000}{\pi}$

E. $3\pi r+4=4000$

Q8) What is the distance between point $C$ and the midpoint of segment $AB$?

A. $2\sqrt 5$

B. $2\sqrt {10}$

C. $25$

D. $5$

E. $5\sqrt 2$

Q9) Find the values of the coefficients $b$ and $c$ in the quadratic equation $3 x^2+b x+c$ if the sum and product of the roots of this equation are respectively $2\dfrac{1}{3}$ and $4\dfrac{1}{3}$.

A. $b=−7$ and $c=13$

B. $b=−\dfrac{7}{3}$ and $c=\dfrac{13}{3}$

C. $b=\dfrac{13}{3}$ and $c=−\dfrac{7}{3}$

D. $b=13$ and $c=-7$

E. $b=1$ and $c=-1$

Q10) For all nonzero $x$ and $y$, $(\tfrac{25 x^2 y^{-2}}{5^3 x^{-2} y^{-1}})^{-2}$

A. $\dfrac{x^8}{25 y^2}$

B. $\dfrac{y^8}{25 x^2}$

C. $\dfrac{25 y^2}{x^8}$

D. $\dfrac{x^2}{25 y^8}$

E. $\dfrac{y^2}{x^8}$