9000024801
Level:
B
In the following list identify an inequality which does not have a solution.
\(\sqrt{2x - 3} < -6\)
\(\sqrt{x^{2 } - 3x} > 5\)
\(\sqrt{1 + x^{2}} > -10\)
\(\sqrt{2x^{2}} < 4\)
B
9000024804
Level:
B
How many solutions does the inequality
\[
\sqrt{x + 17} > x - 3
\]
have in the set \(\mathbb{N}\)?
Seven solutions in \(\mathbb{N}\).
No solution in \(\mathbb{N}\).
Five solutions in \(\mathbb{N}\).
More than seven solutions in \(\mathbb{N}\).
9000025610
Level:
B
Identify a quadratic equation which is solved by a graphical method in the
picture.
\(x^{2} - 6x + 9 = 0\)
\(x^{2} + 9x - 3 = 0\)
\(x^{2} - 9x - 3 = 0\)
\(x^{2} + 6x + 9 = 0\)
9000024806
Level:
B
In the following list identify the interval which is a subset of the solution set of
the following inequality.
\[
\sqrt{x^{2 } + 2x - 3} > x + 2
\]
\((-\infty ,-3] \)
\(\left (-\frac{7}
{2},+\infty \right )\)
\((1,+\infty )\)
\((-\infty ,-2)\)
9000024809
Level:
B
Find the solution set of the following inequality.
\[
\sqrt{x + 3} > x - 3
\]
\([ -3,6)\)
\( (1,6)\)
\([ -3,3] \)
\( (-\infty ,1)\cup (6,+\infty )\)
9000025804
Level:
B
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 1)(x + 2)(x - 3)
\]
The function \(f\)
is positive on \(I_{1} = (-2,-1)\)
and \(I_{2} = (3,\infty )\).
The function \(f\)
is an increasing function (in its whole domain).
The function is decreasing only on
\(I = (-1,3)\).
The function is decreasing on \(I_{1} = (-\infty ,-2)\)
and \(I_{2} = (3,\infty )\).
9000022807
Level:
B
Complete the following statement: Quadratic inequality
\[
2x^{2} - 3x + 4 > x^{2} + 2x - 2
\]
is satisfied if and only if
\(x\in (-\infty ,2)\cup (3,\infty )\).
\(x\in (2,3)\).
\(x\in (-\infty ,-2)\cup (-3,\infty )\).
\(x\in (-2,-3)\).
9000022810
Level:
B
Find the solution set of the following quadratic inequality.
\[
-x^{2} + 2x + 3 > 0
\]
\((-1,3)\)
\((-\infty ,-1)\)
\((-\infty ,-1)\cup (3,\infty )\)
\((3,\infty )\)
9000022804
Level:
B
Establish the values of the real parameter
\(t\) which
ensure that the following expression is nonpositive.
\[
\frac{2}
{2t^{2} + t - 1}
\]
\(\left (-1, \frac{1}
{2}\right )\)
\(\left [ -\frac{1}
{2},1\right ] \)
\(\left [ -1, \frac{1}
{2}\right ] \)
\(\left (-\frac{1}
{2},1\right )\)
9000022306
Level:
B
Using the graph of the function \(f(x)= -x^{2} - 2x + 8\)
solve the following inequality.
\[
-x^{2} - 2x + 8\leq 5
\]
\(\left (-\infty ,-3\right ] \cup \left [ 1,\infty \right )\)
\(\left (-\infty ,-4\right ] \cup \left [ 2,\infty \right )\)
\(\left [ -3,1\right ] \)
\(\left [ -4,2\right ] \)