Math Insight

Gateway exam practice, version 7241

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Let the variable $x$ be in the range \begin{align*} 0< x <5. \end{align*} If $y= 2 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

  2. Let $f(x) = - 4 e^{2 x + 5}$ and $z(x) = 4 x^{2} + x$. What is $f(z(x))$?

    $f(z(x)) = $

    Need help?

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

    $z = $

  4. Rewrite the expression $$\log{\left (- \frac{\sqrt[7]{4 y^{2} - y - 4}}{1953125 y^{9} \left(- 3 z - 4\right)^{4}} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (- \frac{\sqrt[7]{4 y^{2} - y - 4}}{1953125 y^{9} \left(- 3 z - 4\right)^{4}} \right )} = A \log \left(- 3 z - 4\right) + B \log \left(4 y^{2} - y - 4\right) + C\log\left(- 5 y\right),$$ where

    A =

    B =

    C =

  5. Solve the equation $- 4 z^{3} \left(z^{2} - 7 z + 6\right) =0$ by factoring.

    The solutions are $z = $

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

  6. Write the function $f(x)=6e^{ 2x+4 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  7. Simplify the inequality below: \begin{align*} \left|\frac{4 x}{3} + 3\right|<6 \end{align*}


    $\lt x \lt$

  8. Find the equation for the line through the points $(2,9)$ and $(-4,0)$.

    $y = $

  9. Compute the value of $f(f(f(7)))$ for the function $f(x)=2x+2$.

    $f(f(f(7))) =$

  10. The difference between two positive numbers is 3 and the sum of their squares is 89.

    The numbers are

    Separate answers by a comma.

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Math 1241, Fall 2020