Math Insight

Gateway exam practice, version 8059

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Find the equation for the line through the points $(-9,-4)$ and $(-7,7)$.

    $y = $

  2. Let the variable $x$ be in the range \begin{align*} 1< x <8. \end{align*} If $y= 3 x + 4$, what is the range of the variable $y$?


    $\lt y \lt$

  3. Solve for R. \begin{align*} 10 R + 1 = - 5 R - 1 \end{align*} $R = $

  4. Solve the equation $x^{2} - 4 =0$ by factoring.

    The solutions are $x = $

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

  5. Solve the equation $4 z^{3} \left(z^{2} - 5 z + 6\right) =0$ by factoring.

    The solutions are $z = $

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

  6. Compute the value of $f(f(f(3)))$ for the function $f(x)=5x+4$.

    $f(f(f(3))) =$

  7. Rewrite the exponential function \[ u(t) = \frac{ 57 }{ 4^{ t - 2 } } \] in the form $u(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  8. Simplify the inequality below: \begin{align*} 5<\frac{x}{5} + 3<8 \end{align*}


    $\lt x \lt$

  9. Let $w(x) = 9 e^{- x + 1}$ and $g(x) = 10 x^{2} + x$. What is $w(g(x))$?

    $w(g(x)) = $

    Need help?

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

    A =

    B =

    C =

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Math 1241, Fall 2020