Math Insight

Gateway exam practice, version 5258

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. The difference between two positive numbers is 5 and the sum of their squares is 73.

    The numbers are

    Separate answers by a comma.

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


    $\lt y \lt$

  3. Compute the value of $f(f(\frac{1}{ 3 }))$ for the function $f(x)=3x(1-x)$.

    $f(f(\frac{1}{ 3 })) =$

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

    $f(k(x)) = $

    Need help?

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

  6. Find the equation for the line through the points $(7,10)$ and $(6,0)$.

    $y = $

  7. Solve the equation $6\left(y - 8\right) \left(y + 3\right)^{2} \left(y + 6\right)^{2} \left(8 y + 9\right) =0$.

    The solutions are $y = $

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

  8. Rewrite the expression $$7 \log{\left (- 2 x + 3 \right )} - 2 \log{\left (- 4 z - 2 \right )}$$ as a single logarithm $\log D$. Then,

    $D = $

    (Note: “log” is not part of your answer.)

    Need help?

  9. Simplify the inequality below: \begin{align*} 1<\frac{3 x}{5} + 5<6 \end{align*}


    $\lt x \lt$

  10. Rewrite the exponential function \[ h(t) = \frac{ 56 }{ 3^{t}5^{ t - 1 } } \] in the form $h(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

Thread navigation

Math 1241, Fall 2020