Math Insight

Gateway exam practice, version 3010

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Simplify the inequality below: \begin{align*} 4<\frac{7 x}{4} + 1<9 \end{align*}


    $\lt x \lt$

  2. Let the variable $x$ be in the range \begin{align*} 3< x <10. \end{align*} If $y= 6 x + 5$, what is the range of the variable $y$?


    $\lt y \lt$

  3. Solve the equation $-4\left(z - 10\right) \left(z - 8\right) \left(z - 3\right)^{2} \left(7 z + 7\right) =0$.

    The solutions are $z = $

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

  4. Factor the quadratic $y^{2} - 10 y + 16$.

    Answer =

  5. Find the equation for the line through the points $(-9,-3)$ and $(9,-4)$.

    $y = $

  6. Solve for r. \begin{align*} - 10 r + 5 = - 5 r + 10 \end{align*} $r = $

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

    A =

    B =

    C =

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

    $h(v(x)) = $

    Need help?

  9. Rewrite the exponential function \[ w(t) = \frac{ 84 }{ 2^{ t - 1 } } \] in the form $w(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  10. Compute the value of $f(f(\frac{1}{ 2 }))$ for the function $f(x)=4x(1-x)$.

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

Thread navigation

Math 1241, Fall 2020