Math Insight

Gateway exam, version 1074

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Let the variable $x$ be in the range \begin{align*} 1< x <7. \end{align*} If $y= 5 x + 3$, what is the range of the variable $y$?


    $\lt y \lt$

  2. Let $h(x) = 4 x^{2} + 7$ and $w(x) = \sqrt{ 8 x}$. What is $h(w(x))$?

    $h(w(x)) = $

  3. Simplify the inequality below: \begin{align*} -1<\frac{x}{2} - 5<6 \end{align*}


    $\lt x \lt$

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

    $v = $

  5. Find the equation for the line through the point $(4,6)$ with slope given by $m=\frac{7}{20}$

    $y = $

  6. Solve the equation $6\left(y - 3\right)^{2} \left(y + 6\right)^{2} \left(y + 9\right) \left(8 y - 2\right) =0$.

    The solutions are $y = $

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

  7. The difference between two positive numbers is 6 and the sum of their squares is 90.

    The numbers are

    Separate answers by a comma.

  8. Write the function $f(x)=6e^{ 4x+9 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

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  9. Compute the value of $f(f(f(6)))$ for the function $f(x)=5x+1$.

    $f(f(f(6))) =$

  10. Consider the function $f(t)=2(1.35)^t. \;\;$ Find the doubling time, i.e. find $t$ such that $f(t)= 2f(0).$

    Doubling time =

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