9000014804
Level:
B
The graph of the function \(f(x) = x^{2} - 4x + 13\) is a parabola. Which of the following points is the vertex of this parabola?
\([2,9]\)
\([-2,13]\)
\([-4,13]\)
\([0,13]\)
B
9000018104
Level:
B
Find the maximal integer which solves the following inequality.
\[
1 - 3x > 3\left (4 - x\right ) + 2x
\]
\(- 6\)
\(- 5\)
\(- 3\)
\(- 2\)
9000018002
Level:
B
Assuming positive integer \(x\),
solve the following inequality.
\[
-5x\geq - 1
\]
\(x\in \emptyset \)
\(x\in \left \{0\right \}\)
\(x\in \left (0, \frac{1}
{5}\right ] \)
\(x\in \left \{\frac{1}
{5}\right \}\)
9000014206
Level:
B
Find the domain \(\mathrm{Dom}(f)\)
and range \(\mathop{\mathrm{Ran}}(f)\) of
the function \(f(x) = \frac{2+x}
{x+4}\).
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ,-4)\cup (-4,\infty ),\\
\mathop{\mathrm{Ran}}(f) &= (-\infty ,1)\cup (1,\infty )
\end{align*}
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ,4)\cup (4,\infty ), \\
\mathop{\mathrm{Ran}}(f) &= (-\infty ,1)\cup (1,\infty )
\end{align*}
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ,2)\cup (2,\infty ),\\
\mathop{\mathrm{Ran}}(f) &= (-\infty ,4)\cup (4,\infty )
\end{align*}
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ,4)\cup (4,\infty ), \\
\mathop{\mathrm{Ran}}(f) &= (-\infty ,2)\cup (2,\infty )
\end{align*}
9000019806
Level:
B
Find the smallest integer solution of the following equation.
\[
x^{4} - 2x^{3} - x^{2} + 2x = 0
\]
\(- 1\)
\(0\)
\(1\)
\(2\)
9000018003
Level:
B
Assuming \(x\in \left (0,3\right ] \),
solve the following inequality.
\[
6 - 2x\leq 3x - 4
\]
\(x\in \left [ 2,3\right ] \)
\(x\in \left (0,3\right ] \)
\(x\in \left (0,2\right ] \)
\(x\in \left (0,\infty \right )\)
9000014209
Level:
B
Consider the function \(f(x) = \frac{3x+1}
{x-2} \).
Find all \(x\)
such that \(f(x) > 0\).
\(x\in \left (-\infty ,-\frac{1}
{3}\right )\cup (2,\infty )\)
\(x\in \left (-\frac{1}
{3},\infty \right )\)
\(x\in (2,3)\)
\(x\in (-\infty ,-3)\cup (2,\infty )\)
9000019809
Level:
B
Find the factorization of the following equation.
\[
x^{3} + 3x^{2} - x - 3 = 0
\]
\(\left (x + 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x - 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x + 1\right ) = 0\)
9000018006
Level:
B
Assuming negative integer \(x\),
solve the following inequality:
\[
x - 2 > 1 - x - 8
\]
\(x\in \left \{-2,-1\right \}\)
\(x\in \left \{-3,-2,-1\right \}\)
\(x\in \left \{-3,-2\right \}\)
\(x\in \left \{-1\right \}\)
9000014210
Level:
B
Consider the function \(f(x) = \frac{2x+1}
{x+3} \).
Find all \(x\)
such that \(f(x) < 0\).
\(x\in \left (-3,-\frac{1}
{2}\right )\)
\(x\in (-\infty ,-3)\cup \left (\frac{1}
{2},\infty \right )\)
\(x\in (-3,\infty )\)
\(x\in \left (-\infty ,-\frac{1}
{2}\right )\)