Math Insight

Gateway exam, version 3718

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Solve the equation $-2\left(x - 4\right) \left(x + 8\right)^{2} \left(x + 10\right) \left(6 x - 1\right) =0$.

    The solutions are $x = $

    If there are more than one solution, separate answers by commas

  2. Write the function $f(x)=24e^{ 2x+5 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  3. Solve the system of equations. \begin{align*} 4 s - z &= -2\\ - s - 4 z &= 3 \end{align*}
    $s = $

    $z = $

  4. Simplify the inequality below: \begin{align*} \left|\frac{3 x}{7} + 5\right|<5 \end{align*}


    $\lt x \lt$

  5. Let the variable $x$ be in the range \begin{align*} 1< x <10. \end{align*} If $y= 6 x + 3$, what is the range of the variable $y$?


    $\lt y \lt$

  6. Compute the value of $f(f(\frac{1}{ 5 }))$ for the function $f(x)=2x(1-x)$.

    $f(f(\frac{1}{ 5 })) =$

  7. Solve the equation $y^{2} + 4 y + 4 =0$ by factoring.

    The solutions are $y = $

    If there are more than one solution, separate answers by commas

  8. Let $w(x) = - 10 e^{- 7 x - 10}$ and $u(x) = 9 x^{2} + x$. What is $w(u(x))$?

    $w(u(x)) = $

    Need help?

  9. Rewrite the expression $$\log{\left (\frac{\sqrt[9]{- x^{4} + x - 4}}{\left(- z^{5} - 3 z - 2\right)^{6}} \left(- x^{4} + x^{3} + 5 x + 3\right)^{2} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\frac{\sqrt[9]{- x^{4} + x - 4}}{\left(- z^{5} - 3 z - 2\right)^{6}} \left(- x^{4} + x^{3} + 5 x + 3\right)^{2} \right )} = A \log \left(- x^{4} + x^{3} + 5 x + 3\right) + B \log \left(- x^{4} + x - 4\right) + C\log\left(- z^{5} - 3 z - 2\right),$$ where

    A =

    B =

    C =

  10. Find the equation for the line through the points $(1,-5)$ and $(-2,-9)$.

    $y = $