Math Insight

Gateway exam, version 0342

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Find the equation for the line through the points $(-4,-1)$ and $(-8,-10)$.

    $y = $

  2. Solve the equation $5 x^{2} \left(x^{2} + 2 x - 8\right) =0$ by factoring.

    The solutions are $x = $

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

  3. Let $w(x) = 2 x^{2} - 7$ and $z(x) = \sqrt{ 7 x}$. What is $w(z(x))$?

    $w(z(x)) = $

  4. Solve for $P$. \begin{align*} - 9 P - 5 z + 8 = - 5 z - 6 \end{align*} $P = $

  5. Consider the function $f(t)=16(1.35)^t. \;\;$ 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.)

  6. Let the variable $x$ be in the range \begin{align*} 0< x <5. \end{align*} If $y= 7 x + 4$, what is the range of the variable $y$?


    $\lt y \lt$

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

    $f(f(\frac{1}{ 3 })) =$

  8. The difference between two positive numbers is 4 and the sum of their squares is 80.

    The numbers are

    Separate answers by a comma.

  9. Rewrite the exponential function \[ g(t) = \frac{ 60 }{ 2^{t}3^{ t - 2 } } \] in the form $g(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  10. Simplify the inequality below: \begin{align*} -2<\frac{3 x}{5} + 3<0 \end{align*}


    $\lt x \lt$