Math Insight

Gateway exam, version 8225

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Simplify the inequality below: \begin{align*} -4<\frac{5 x}{2} - 5<0 \end{align*}


    $\lt x \lt$

  2. Write the function $f(x)=3e^{ 3x+9 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  3. Rewrite the expression $$\log{\left (\left(- 2 y^{2} + 2 y + 4\right)^{5} \sqrt[6]{- z^{2} - z - 6} \left(2 z^{2} + 3 z + 7\right)^{\frac{5}{4}} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\left(- 2 y^{2} + 2 y + 4\right)^{5} \sqrt[6]{- z^{2} - z - 6} \left(2 z^{2} + 3 z + 7\right)^{\frac{5}{4}} \right )} = A \log \left(- 2 y^{2} + 2 y + 4\right) + B \log \left(- z^{2} - z - 6\right) + C\log\left(2 z^{2} + 3 z + 7\right),$$ where

    A =

    B =

    C =

  4. Solve the equation $z^{2} - 4 z + 4 =0$ by factoring.

    The solutions are $z = $

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

  5. Find the equation for the line through the points $(-5,3)$ and $(6,6)$.

    $y = $

  6. Solve the system of equations. \begin{align*} - 3 s - y &= 1\\ - 3 s + 3 y &= 3 \end{align*}
    $s = $

    $y = $

  7. Let $k(x) = - 5 e^{7 x - 9}$ and $g(x) = - 3 x^{2} + x$. What is $k(g(x))$?

    $k(g(x)) = $

    Need help?

  8. Compute the value of $f(f(\frac{1}{ 4 }))$ for the function $f(x)=3x(1-x)$.

    $f(f(\frac{1}{ 4 })) =$

  9. Let the variable $x$ be in the range \begin{align*} -1< x <7. \end{align*} If $y= 5 x + 5$, what is the range of the variable $y$?


    $\lt y \lt$

  10. Solve the equation $10 z^{2} \left(z^{2} - 13 z + 42\right) =0$ by factoring.

    The solutions are $z = $

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