9000019802
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
2x^{3} - 3x^{2} = 0
\]
\(\emptyset \)
\(\left \{0\right \}\)
\(\left \{2\right \}\)
\(\left \{0, \frac{3}
{2}\right \}\)
A
9000019807
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
\left (3x + 2\right )\left (x\sqrt{2} + 1\right )\left (x^{2} + 1\right ) = 0
\]
\(\left \{-\frac{\sqrt{2}}
{2} ,-\frac{2}
{3}\right \}\)
\(\left \{-\frac{2}
{3}, \frac{1}
{\sqrt{2}}\right \}\)
\(\left \{\frac{2}
{3}, \frac{1}
{\sqrt{2}}\right \}\)
\(\left \{-1,-\frac{\sqrt{2}}
{2} ,-\frac{2}
{3}\right \}\)
9000014801
Level:
A
Identify a point which is on the graph of the function
\(f(x) = 3x^{2} + 3x - 2\).
\(B = [2,16]\)
\(A = [0,3]\)
\(C = [-1,0]\)
\(D = [5,-8]\)
9000014807
Level:
A
Find the \(x\)-intercepts
of the function \(f(x)= 3x^{2} + 6x - 9\).
\([-3,0]\) and
\([1,0]\)
\([0,9]\) and
\([1,0]\)
\([-3,2]\) and
\([-3,-2]\)
The function \(f\) does
not have \(x\)-intercepts.
9000014808
Level:
A
Find the intervals of monotonicity of the quadratic function
\(f(x) = 2x^{2} + 3\).
The function is increasing on \(\left [ 0,\infty \right )\)
and decreasing on \(\left (-\infty ,0\right ] \).
The function is increasing on \(\left (3,\infty \right )\)
and decreasing on \(\left (-\infty ,3\right )\).
The function is increasing on \(\left [ -\frac{3}
{2},\infty \right )\)
and decreasing on \(\left (-\infty ,-\frac{3}
{2}\right ] \).
The function is increasing on its domain.
9000014809
Level:
A
Find the \(y\)-intercept
of the following function: \[f(x) = 10x^{2} - 18x - 6.3\]
\([0,-6.3]\)
\([10,0]\)
\([0.3,0]\)
There is no \(y\)-intercept.
9000014810
Level:
A
Find the domain and range of the quadratic function
\(f\)
graphed in the picture.
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left (-\infty ,2\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2,\infty \right )
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left [ 0,\infty \right )&
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2,4\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left (-\infty ,0\right ] &
\\&\mathop{\mathrm{Ran}}(f) =\mathbb{R}
\\ \end{aligned}\)
9000014802
Level:
A
Let \(f(x) = -x^{2} + 11x - 2\).
Which of the following statements is true?
\(f(-2) = -28\)
\(f(0) = 2\)
\(f(3.5) = 12.25\)
\(f\left (\frac{1}
{2}\right ) = \frac{15}
{4} \)
9000010501
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}
\]
\(x\root{3}\of{x^{2}}\)
\(x^{2}\root{3}\of{x^{2}}\)
\(x^{3}\root{3}\of{x^{2}}\)
\(x^{2}\root{5}\of{x^{3}}\)
9000010502
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}\cdot \root{3}\of{x^{4}}
\]
\(x^{3}\)
\(\root{3}\of{x^{12}}\)
\(\root{3}\of{x}\)
\(x\root{3}\of{x^{4}}\)