Math Insight

Gateway exam practice, version 8042

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Rewrite the expression $$\log{\left (\left(- 4 z + 2\right) \sqrt[6]{4 z + 2} \left(2 z^{3} + 5 z - 5\right)^{\frac{2}{9}} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\left(- 4 z + 2\right) \sqrt[6]{4 z + 2} \left(2 z^{3} + 5 z - 5\right)^{\frac{2}{9}} \right )} = A \log \left(- 4 z + 2\right) + B \log \left(4 z + 2\right) + C\log\left(2 z^{3} + 5 z - 5\right),$$ where

    A =

    B =

    C =

  2. Let $z(x) = - 4 e^{- 3 x + 2}$ and $h(x) = - 4 x^{2} + x$. What is $z(h(x))$?

    $z(h(x)) = $

    Need help?

  3. Simplify the inequality below: \begin{align*} \left|\frac{6 x}{7} - 2\right|<4 \end{align*}


    $\lt x \lt$

  4. Compute the value of $f(f(f(2)))$ for the function $f(x)=4x+6$.

    $f(f(f(2))) =$

  5. Solve the equation $8y^{2} \left(y - 4\right) \left(y - 2\right) \left(9 y + 6\right) =0$.

    The solutions are $y = $

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

  6. Let the variable $x$ be in the range \begin{align*} -1< x <6. \end{align*} If $y= 4 x + 3$, what is the range of the variable $y$?


    $\lt y \lt$

  7. The difference between two positive numbers is 2 and the sum of their squares is 74.

    The numbers are

    Separate answers by a comma.

  8. Find the equation for the line through the points $(-1,-2)$ and $(-2,-1)$.

    $y = $

  9. Rewrite the exponential function \[ f(t) = \frac{ 66 }{ 3^{t}7^{ t - 2 } } \] in the form $f(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  10. Solve the system of equations. \begin{align*} - 3 p + 2 x &= 0\\ - p - x &= 0 \end{align*}
    $x = $

    $p = $

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Math 1241, Fall 2020