Math Insight

Gateway exam practice, version 8342

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 $f(x)=2x(1-x)$.

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

  2. Let $w(x) = 6 x^{2} + 10$ and $h(x) = \sqrt{ 5 x}$. What is $w(h(x))$?

    $w(h(x)) = $

  3. Rewrite the exponential function \[ w(t) = 12 \cdot 3^{t - 2 } \] 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 = $

  4. Rewrite the expression $$\log{\left (\frac{\left(x + 1\right) \sqrt[3]{2 x + 2}}{\left(- 4 x^{2} - 3 x + 6\right)^{\frac{2}{9}}} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\frac{\left(x + 1\right) \sqrt[3]{2 x + 2}}{\left(- 4 x^{2} - 3 x + 6\right)^{\frac{2}{9}}} \right )} = A \log \left(x + 1\right) + B \log \left(2 x + 2\right) + C\log\left(- 4 x^{2} - 3 x + 6\right),$$ where

    A =

    B =

    C =

  5. Factor the quadratic $x^{2} - 25$.

    Answer =

  6. Solve the equation $2\left(y - 6\right) \left(y + 2\right)^{2} \left(y + 8\right) \left(8 y + 5\right) =0$.

    The solutions are $y = $

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

  7. Let the variable $x$ be in the range \begin{align*} 0< x <6. \end{align*} If $y= 2 x + 3$, what is the range of the variable $y$?


    $\lt y \lt$

  8. Solve the system of equations. \begin{align*} - 3 u - 3 z &= -1\\ - 2 u + 3 z &= -2 \end{align*}
    $z = $

    $u = $

  9. Simplify the inequality below: \begin{align*} 5<\frac{7 x}{8} - 1<12 \end{align*}


    $\lt x \lt$

  10. Find the equation for the line through the points $(-6,4)$ and $(2,7)$.

    $y = $

Thread navigation

Math 1241, Fall 2020