Math Insight

Gateway exam practice, version 1891

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Solve the equation $-\left(x + 3\right)^{2} \left(x + 6\right)^{2} \left(x + 8\right) \left(4 x - 1\right) =0$.

    The solutions are $x = $

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

  2. Find the equation for the line through the point $(10,4)$ with slope given by $m=- \frac{5}{9}$

    $y = $

  3. Solve the equation $x^{2} - 3 x + 2 =0$ by factoring.

    The solutions are $x = $

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

  4. Solve the system of equations. \begin{align*} - 4 m + 3 n &= 4\\ - m - 4 n &= -1 \end{align*}
    $m = $

    $n = $

  5. Simplify the inequality below: \begin{align*} 0<\frac{x}{7} + 5<4 \end{align*}


    $\lt x \lt$

  6. Let the variable $x$ be in the range \begin{align*} 3< x <5. \end{align*} If $y= 7 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

  7. Rewrite the exponential function \[ u(t) = 59 \cdot 5^{t - 3 } \] in the form $u(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  8. Consider the function $f(t)=5(1.6)^t. \;\;$ 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.)

  9. Let $y(x) = - 10 e^{7 x - 8}$ and $k(x) = 9 x^{2} + x$. What is $y(k(x))$?

    $y(k(x)) = $

    Need help?

  10. Compute the value of $f(f(\frac{1}{ 2 }))$ for the function $f(x)=2x(1-x)$.

    $f(f(\frac{1}{ 2 })) =$

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Math 1241, Fall 2020