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Gateway exam practice, version 4759

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Find the equation for the line through the point $(0,6)$ with slope given by $m=\frac{7}{2}$

    $y = $

  2. Solve for $u$. \begin{align*} - 10 X + 6 u + 2 = X + u - 8 \end{align*} $u = $

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

    $f(f(f(4))) =$

  4. Solve the equation $z^{2} - 4 z + 4 =0$ by factoring.

    The solutions are $z = $

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

  5. Write the function $f(x)=21e^{ 4x+9 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  6. Let the variable $x$ be in the range \begin{align*} -2< x <8. \end{align*} If $y= 5 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

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


    $\lt x \lt$

  8. Solve the equation $-2\left(z - 6\right) \left(z - 5\right) \left(z + 1\right) \left(2 z + 8\right) =0$.

    The solutions are $z = $

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

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

    A =

    B =

    C =

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

    $g(u(x)) = $

    Need help?

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Math 1241, Fall 2020