Math Insight

Gateway exam practice, version 2228

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Solve the equation $-42 x \left(x + 7\right)^{2} \left(x + 8\right) \left(x + 10\right) =0$.

    The solutions are $x = $

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

  2. The difference between two positive numbers is 2 and the sum of their squares is 100.

    The numbers are

    Separate answers by a comma.

  3. Let $v(x) = - e^{- x - 1}$ and $k(x) = 2 x^{2} + x$. What is $v(k(x))$?

    $v(k(x)) = $

    Need help?

  4. Find the equation for the line through the points $(5,0)$ and $(-4,-4)$.

    $y = $

  5. Let the variable $x$ be in the range \begin{align*} -2< x <7. \end{align*} If $y= 7 x + 5$, what is the range of the variable $y$?


    $\lt y \lt$

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

    $f(f(f(6))) =$

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

    A =

    B =

    C =

  8. Rewrite the exponential function \[ R(t) = 97 \cdot 6^{t - 1 } \] in the form $R(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  9. Simplify the inequality below: \begin{align*} \left|\frac{5 x}{4} - 4\right|<9 \end{align*}


    $\lt x \lt$

  10. Solve for $z$. \begin{align*} - 5 X + 4 z + 9 = - 5 X + 6 z - 1 \end{align*} $z = $

Thread navigation

Math 1241, Fall 2020