Math Insight

Gateway exam practice, version 1110

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Solve for $W$. \begin{align*} - 6 W - 6 Z = 6 W + Z - 9 \end{align*} $W = $

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

    The solutions are $x = $

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

  3. Let $y(x) = - 2 x^{2} - 7$ and $w(x) = \sqrt{ 9 x}$. What is $y(w(x))$?

    $y(w(x)) = $

  4. Solve the equation $-10\left(y + 2\right) \left(y + 6\right)^{2} \left(y + 10\right)^{2} \left(4 y + 5\right) =0$.

    The solutions are $y = $

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

  5. Simplify the inequality below: \begin{align*} \left|3 x - 1\right|<8 \end{align*}


    $\lt x \lt$

  6. Find the equation for the line through the point $(-5,0)$ with slope given by $m=- \frac{1}{2}$

    $y = $

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

    $A=$
    , $k=$

    Need help?

  8. Rewrite the expression $$\log{\left (\left(- 5 z + 2\right)^{7} \sqrt[9]{z - 6} \left(4 z - 1\right)^{9} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\left(- 5 z + 2\right)^{7} \sqrt[9]{z - 6} \left(4 z - 1\right)^{9} \right )} = A \log \left(- 5 z + 2\right) + B \log \left(z - 6\right) + C\log\left(4 z - 1\right),$$ where

    A =

    B =

    C =

  9. Compute the value of $f(f(f(9)))$ for the function $f(x)=5x+3$.

    $f(f(f(9))) =$

  10. Let the variable $x$ be in the range \begin{align*} 2< x <4. \end{align*} If $y= 4 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

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Math 1241, Fall 2020