Math Insight

Gateway exam practice, version 4141

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Let $w(x) = - e^{3 x + 7}$ and $v(x) = 9 x^{2} + x$. What is $w(v(x))$?

    $w(v(x)) = $

    Need help?

  2. Solve for $Y$. \begin{align*} - 8 Y - 8 r - 4 = 10 Y - 2 r \end{align*} $Y = $

  3. Find the equation for the line through the points $(5,4)$ and $(4,-6)$.

    $y = $

  4. Write the function $f(x)=24e^{ 4x+2 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  5. Solve for $x$: \[ x(9-x)=x+2x^2 \]

    $x =$
    (If there is more than one solution, separate solutions by commas.)

  6. Rewrite the expression $$\log{\left (\left(- 2 x^{4} - x + 3\right)^{7} \sqrt{- 2 z^{4} - 4 z + 4} \left(- 2 z^{5} + 2 z^{2} + 2 z + 8\right)^{4} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\left(- 2 x^{4} - x + 3\right)^{7} \sqrt{- 2 z^{4} - 4 z + 4} \left(- 2 z^{5} + 2 z^{2} + 2 z + 8\right)^{4} \right )} = A \log \left(- 2 x^{4} - x + 3\right) + B \log \left(- 2 z^{4} - 4 z + 4\right) + C\log\left(- 2 z^{5} + 2 z^{2} + 2 z + 8\right),$$ where

    A =

    B =

    C =

  7. Solve the equation $4\left(z + 4\right)^{2} \left(z + 7\right) \left(z + 8\right) \left(3 z + 3\right) =0$.

    The solutions are $z = $

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

  8. Let the variable $x$ be in the range \begin{align*} 0< x <9. \end{align*} If $y= 6 x + 5$, what is the range of the variable $y$?


    $\lt y \lt$

  9. Compute the value of $f(f(f(4)))$ for the function $f(x)=3x+5$.

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

  10. Simplify the inequality below: \begin{align*} -3<\frac{5 x}{2} - 2<0 \end{align*}


    $\lt x \lt$

Thread navigation

Math 1241, Fall 2020