Math Insight

Gateway exam practice, version 5238

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Compute the value of $f(f(\frac{1}{ 2 }))$ for the function $f(x)=3x(1-x)$.

    $f(f(\frac{1}{ 2 })) =$

  2. Find the equation for the line through the points $(-3,4)$ and $(1,-7)$.

    $y = $

  3. Let $g(x) = - 2 e^{- x + 9}$ and $v(x) = - 7 x^{2} + x$. What is $g(v(x))$?

    $g(v(x)) = $

    Need help?

  4. Solve the system of equations. \begin{align*} - 4 q - u &= -1\\ 4 q - 4 u &= -2 \end{align*}
    $q = $

    $u = $

  5. Let the variable $x$ be in the range \begin{align*} -1< x <8. \end{align*} If $y= 7 x + 5$, what is the range of the variable $y$?


    $\lt y \lt$

  6. Rewrite the exponential function \[ S(t) = 27 \cdot 2^{t}4^{t - 1 } \] in the form $S(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

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

    The solutions are $z = $

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

  8. Factor the quadratic $z^{2} - 13 z + 30$.

    Answer =

  9. Simplify the inequality below: \begin{align*} \left|\frac{5 x}{2} - 3\right|<3 \end{align*}


    $\lt x \lt$

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

    A =

    B =

    C =

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Math 1241, Fall 2020