Math Insight

Gateway exam practice, version 9498

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. The difference between two positive numbers is 4 and the sum of their squares is 136.

    The numbers are

    Separate answers by a comma.

  2. Simplify the inequality below: \begin{align*} \left|\frac{7 x}{2} - 3\right|<7 \end{align*}


    $\lt x \lt$

  3. Solve the equation $- 6 x \left(x^{2} - 6 x - 27\right) =0$ by factoring.

    The solutions are $x = $

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

  4. Let the variable $x$ be in the range \begin{align*} 3< x <7. \end{align*} If $y= 5 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

  5. Write the function $f(x)=33e^{ 2x+8 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  6. Rewrite the expression $$\log{\left (\frac{\left(- 4 y - 4\right)^{4} \sqrt[3]{3 z + 6}}{\left(- 5 y + 4\right)^{\frac{7}{9}}} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\frac{\left(- 4 y - 4\right)^{4} \sqrt[3]{3 z + 6}}{\left(- 5 y + 4\right)^{\frac{7}{9}}} \right )} = A \log \left(- 4 y - 4\right) + B \log \left(3 z + 6\right) + C\log\left(- 5 y + 4\right),$$ where

    A =

    B =

    C =

  7. Find the equation for the line through the point $(-1,-7)$ with slope given by $m=\frac{15}{8}$

    $y = $

  8. Compute the value of $f(f(\frac{1}{ 5 }))$ for the function $f(x)=3x(1-x)$.

    $f(f(\frac{1}{ 5 })) =$

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

    $y = $

  10. Let $z(x) = - 4 x^{2} + 4$ and $w(x) = \sqrt{ 7 x}$. What is $z(w(x))$?

    $z(w(x)) = $

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Math 1241, Fall 2020