Math Insight

Gateway exam, version 2346

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Simplify the inequality below: \begin{align*} -5<\frac{x}{8} + 2<4 \end{align*}


    $\lt x \lt$

  2. Find the equation for the line through the points $(3,10)$ and $(-5,8)$.

    $y = $

  3. Let $w(x) = - 2 e^{- x + 1}$ and $y(x) = 10 x^{2} + x$. What is $w(y(x))$?

    $w(y(x)) = $

    Need help?

  4. Solve the equation $- 8 x^{2} \left(x^{2} + 15 x + 56\right) =0$ by factoring.

    The solutions are $x = $

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

  5. Let the variable $x$ be in the range \begin{align*} 0< x <10. \end{align*} If $y= 5 x + 4$, what is the range of the variable $y$?


    $\lt y \lt$

  6. Solve for $x$: \[ x(5-x)=x+6x^2 \]

    $x =$
    (If there is more than one solution, separate solutions by commas.)

  7. Compute the value of $f(f(f(10)))$ for the function $f(x)=4x+2$.

    $f(f(f(10))) =$

  8. Consider the function $f(t)=18(0.55)^t. \;\;$ Find the half-life, i.e. find $t$ such that $f(t)=\frac{1}{2}f(0).$

    Half-life =

    (If you round your answer, include at least 4 significant digits.)

  9. Write the function $f(x)=21e^{ 4x+7 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  10. Solve for $U$. \begin{align*} 6 P + 2 U + 1 = - 10 P - 5 U - 8 \end{align*} $U = $