Gateway exam practice - Math Insight

Name:

Section:
Table/group #:

Total points: 10

Time limit: 50 minutes

Let $k(x) = 5 x^{2} + 2$ and $w(x) = \sqrt{ 6 x}$. What is $k(w(x))$?
$k(w(x)) = $
Rewrite the expression $$7 \log{\left (2 y - 1 \right )} - 7 \log{\left (5 z + 3 \right )}$$ as a single logarithm $\log B$. Then,

$B = $

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

Need help?Hide help

Hint
Online, use ^ for an exponent, denoting $a^b$ as a^b.
Hide help
Find the equation for the line through the point $(1,-6)$ with slope given by $m=\frac{7}{10}$
$y = $
Solve the equation $y^{2} + 4 y + 4 =0$ by factoring.
The solutions are $y = $

If there are more than one solution, separate answers by commas
Solve the equation $x^{4} \left(x^{2} - 15 x + 56\right) =0$ by factoring.
The solutions are $x = $

If there are more than one solution, separate answers by commas
Write the function $f(x)=12e^{ 4x+2 }$ in the form $f(x)=Ae^{kx}$. What are the values of the parameters $A$ and $k$?
$A=$
, $k=$

Need help?Hide help

Hint
Use ^ to enter an exponent, e.g., for $a^b$, type a^b.
Hide help
Compute the value of $f(f(\frac{1}{ 5 }))$ for the function $f(x)=3x(1-x)$.
$f(f(\frac{1}{ 5 })) =$
Solve the system of equations. \begin{align*} - 2 t - 4 w &= 2\\ 4 t - 2 w &= -2 \end{align*}
$w = $

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

$\lt y \lt$
Simplify the inequality below: \begin{align*} 1<\frac{7 x}{5} - 1<7 \end{align*}

$\lt x \lt$