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Gateway exam practice, version 7023

Math 1241, Fall 2020
Name:
Section:
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Total points: 10
Time limit: 50 minutes
  1. Solve the equation $y^{2} + 4 y + 4 =0$ by factoring.

    The solutions are $y = $

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

  2. Solve for R. \begin{align*} 9 R + 9 = 5 R - 1 \end{align*} $R = $

  3. Let $k(x) = - 8 e^{- x - 3}$ and $u(x) = - 4 x^{2} + x$. What is $k(u(x))$?

    $k(u(x)) = $

    Need help?

  4. Rewrite the exponential function \[ V(t) = 43 \cdot 5^{t - 1 } \] in the form $V(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

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

    A =

    B =

    C =

  6. Simplify the inequality below: \begin{align*} 1<2 x - 4<6 \end{align*}


    $\lt x \lt$

  7. Solve the equation $-7\left(y - 7\right) \left(y - 6\right) \left(y + 9\right) \left(3 y - 6\right) =0$.

    The solutions are $y = $

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

  8. Compute the value of $f(f(\frac{1}{ 5 }))$ for the function $f(x)=4x(1-x)$.

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

  9. Let the variable $x$ be in the range \begin{align*} 2< x <8. \end{align*} If $y= 6 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

  10. Find the equation for the line through the point $(0,-5)$ with slope given by $m=- \frac{3}{8}$

    $y = $

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Math 1241, Fall 2020