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Gateway exam practice, version 9846

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Solve the equation $- 9 z^{4} \left(z^{2} + 5 z - 6\right) =0$ by factoring.

    The solutions are $z = $

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

  2. Write the function $f(x)=33e^{ 4x+7 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

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

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

  4. Solve the system of equations. \begin{align*} r + 2 s &= -1\\ 3 r - 3 s &= 0 \end{align*}
    $r = $

    $s = $

  5. Let $u(x) = 8 e^{- 7 x + 7}$ and $h(x) = 6 x^{2} + x$. What is $u(h(x))$?

    $u(h(x)) = $

    Need help?

  6. Factor the quadratic $y^{2} - 16$.

    Answer =

  7. Find the equation for the line through the points $(10,1)$ and $(-3,-1)$.

    $y = $

  8. Let the variable $x$ be in the range \begin{align*} 1< x <9. \end{align*} If $y= 7 x + 4$, what is the range of the variable $y$?


    $\lt y \lt$

  9. Rewrite the expression $$\log{\left (\frac{\sqrt[3]{- 4 z + 4}}{\left(2 z - 6\right)^{\frac{6}{5}}} \left(- z^{2} - 4 z - 3\right)^{4} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\frac{\sqrt[3]{- 4 z + 4}}{\left(2 z - 6\right)^{\frac{6}{5}}} \left(- z^{2} - 4 z - 3\right)^{4} \right )} = A \log \left(- z^{2} - 4 z - 3\right) + B \log \left(- 4 z + 4\right) + C\log\left(2 z - 6\right),$$ where

    A =

    B =

    C =

  10. Simplify the inequality below: \begin{align*} \left|\frac{x}{2} - 6\right|<4 \end{align*}


    $\lt x \lt$

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Math 1241, Fall 2020