Math Insight

Gateway exam practice, version 2258

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Let $v(x) = 8 e^{3 x + 8}$ and $h(x) = 8 x^{2} + x$. What is $v(h(x))$?

    $v(h(x)) = $

    Need help?

  2. Solve the equation $-4\left(z + 2\right)^{2} \left(z + 4\right)^{2} \left(z + 5\right) \left(9 z - 2\right) =0$.

    The solutions are $z = $

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

  3. The difference between two positive numbers is 5 and the sum of their squares is 73.

    The numbers are

    Separate answers by a comma.

  4. Rewrite the expression $$\log{\left (\frac{\sqrt[6]{4 z - 4}}{\left(4 z + 1\right)^{\frac{8}{5}}} \left(- 2 z^{2} + 3 z - 2\right)^{3} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\frac{\sqrt[6]{4 z - 4}}{\left(4 z + 1\right)^{\frac{8}{5}}} \left(- 2 z^{2} + 3 z - 2\right)^{3} \right )} = A \log \left(- 2 z^{2} + 3 z - 2\right) + B \log \left(4 z - 4\right) + C\log\left(4 z + 1\right),$$ where

    A =

    B =

    C =

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

    $m = $

  6. Simplify the inequality below: \begin{align*} \left|\frac{3 x}{4} + 8\right|<9 \end{align*}


    $\lt x \lt$

  7. Write the function $f(x)=27e^{ 2x+1 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  8. Let the variable $x$ be in the range \begin{align*} -1< x <9. \end{align*} If $y= 5 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

  9. Find the equation for the line through the points $(10,-7)$ and $(1,8)$.

    $y = $

  10. Compute the value of $f(f(\frac{1}{ 2 }))$ for the function $f(x)=4x(1-x)$.

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

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Math 1241, Fall 2020