Math Insight

Gateway exam practice, version 9360

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Solve the equation $4\left(x - 9\right) \left(x - 6\right) \left(x + 10\right) \left(4 x + 1\right) =0$.

    The solutions are $x = $

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

  2. Simplify the inequality below: \begin{align*} -5<\frac{3 x}{8} - 4<1 \end{align*}


    $\lt x \lt$

  3. Find the equation for the line through the point $(-8,-6)$ with slope given by $m=\frac{19}{4}$

    $y = $

  4. Compute the value of $f(f(f(6)))$ for the function $f(x)=3x+2$.

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

  5. Solve for $x$: \[ x(5-x)=x+8x^2 \]

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

  6. Consider the function $f(t)=15(0.3)^t. \;\;$ 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.)

  7. Let the variable $x$ be in the range \begin{align*} -2< x <9. \end{align*} If $y= 4 x + 3$, what is the range of the variable $y$?


    $\lt y \lt$

  8. Solve the system of equations. \begin{align*} - 3 t - 4 z &= 0\\ 3 t + 2 z &= 4 \end{align*}
    $t = $

    $z = $

  9. Rewrite the exponential function \[ R(t) = \frac{ 75 }{ 4^{ t - 3 } } \] in the form $R(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  10. Let $z(x) = 5 e^{- 6 x - 10}$ and $g(x) = - 9 x^{2} + x$. What is $z(g(x))$?

    $z(g(x)) = $

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Math 1241, Fall 2020