Gateway exam practice - Math Insight

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Section:
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Total points: 10

Time limit: 50 minutes

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

$b = $
Let the variable $x$ be in the range \begin{align*} -2< x <10. \end{align*} If $y= 4 x + 1$, what is the range of the variable $y$?

$\lt y \lt$
Consider the function $f(t)=18(1.5)^t. \;\;$ Find the doubling time, i.e. find $t$ such that $f(t)= 2f(0).$
Doubling time =

(If you round your answer, include at least 4 significant digits.)
Find the equation for the line through the points $(-3,10)$ and $(5,1)$.
$y = $
Solve the equation $- 9 x^{2} \left(x^{2} + 7 x + 6\right) =0$ by factoring.
The solutions are $x = $

If there are more than one solution, separate answers by commas
Solve for Z. \begin{align*} - 5 Z + 6 = - 6 Z - 7 \end{align*} $Z = $
The difference between two positive numbers is 2 and the sum of their squares is 74.
The numbers are

Separate answers by a comma.
Let $w(x) = - 3 x^{2} - 10$ and $y(x) = \sqrt{ 2 x}$. What is $w(y(x))$?
$w(y(x)) = $
Simplify the inequality below: \begin{align*} \left|2 x - 1\right|<4 \end{align*}

$\lt x \lt$