Gateway exam practice - Math Insight

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Total points: 10

Time limit: 50 minutes

Compute the value of $f(f(f(10)))$ for the function $f(x)=5x+2$.
$f(f(f(10))) =$
Rewrite the expression $$7 \log{\left (y - 1 \right )} - 2 \log{\left (5 z + 3 \right )}$$ as a single logarithm $\log D$. Then,

$D = $

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

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Hint
Online, use ^ for an exponent, denoting $a^b$ as a^b.
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Let $v(x) = - 3 x^{2} + 7$ and $z(x) = \sqrt{ 9 x}$. What is $v(z(x))$?
$v(z(x)) = $
Solve the system of equations. \begin{align*} 2 m + z &= -1\\ 3 m + 2 z &= -3 \end{align*}
$z = $

$m = $
Let the variable $x$ be in the range \begin{align*} 3< x <10. \end{align*} If $y= 4 x + 4$, what is the range of the variable $y$?

$\lt y \lt$
The difference between two positive numbers is 5 and the sum of their squares is 97.
The numbers are

Separate answers by a comma.
Write the function $f(x)=27e^{ 2x+8 }$ in the form $f(x)=Ae^{kx}$. What are the values of the parameters $A$ and $k$?
$A=$
, $k=$

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Hint
Use ^ to enter an exponent, e.g., for $a^b$, type a^b.
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Find the equation for the line through the points $(0,-5)$ and $(5,2)$.
$y = $
Solve the equation $-4\left(x - 5\right)^{2} \left(x - 4\right)^{2} \left(x + 9\right) \left(9 x - 10\right) =0$.
The solutions are $x = $

If there are more than one solution, separate answers by commas
Simplify the inequality below: \begin{align*} -3<\frac{3 x}{4} - 5<-1 \end{align*}

$\lt x \lt$