9000028104
Level:
B
Given graphs of the linear functions \(f\)
and \(g\), find the solution
set of the inequality \(f(x)\leq g(x)\).
\((-\infty ;2.4] \)
\(\emptyset \)
\((-\infty ;-2.3] \)
\([ 6;\infty )\)
B
9000028106
Level:
B
Given graphs of the linear functions \(f\)
and \(g\), find the solution
set of the inequality \(f(x)\leq g(x)\).
\(\emptyset \)
\((-\infty ;0] \)
\(\mathbb{R}\)
\([ 0;\infty )\)
9000028107
Level:
B
Given graphs of the linear functions \(f\)
and \(g\), find the solution
set of the inequality \(f(x)\leq g(x)\).
\(\mathbb{R}\)
\(\emptyset \)
\((-\infty ;0] \)
\([ 0;\infty )\)
9000024801
Level:
B
In the following list identify an inequality which does not have a solution.
\(\sqrt{2x - 3} < -6\)
\(\sqrt{x^{2 } - 3x} > 5\)
\(\sqrt{1 + x^{2}} > -10\)
\(\sqrt{2x^{2}} < 4\)
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 \(\mathbb{N}\).
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 \(I_{2} = (3;\infty )\).
9000024806
Level:
B
In the following list identify the interval which is a subset of the solution set of
the following inequality.
\[
\sqrt{x^{2 } + 2x - 3} > x + 2
\]
\((-\infty ;-3] \)
\(\left (-\frac{7}
{2};+\infty \right )\)
\((1;+\infty )\)
\((-\infty ;-2)\)
9000025610
Level:
B
Identify a quadratic equation which is solved by a graphical method in the
picture.
\(x^{2} - 6x + 9 = 0\)
\(x^{2} + 9x - 3 = 0\)
\(x^{2} - 9x - 3 = 0\)
\(x^{2} + 6x + 9 = 0\)
9000022308
Level:
B
Using graphs of the functions \(f(x)= -2x^{2} + 3x + 4\)
and \(g(x) = x\)
solve the following quadratic inequality.
\[
-2x^{2} + 3x + 4\geq x
\]
\(\left [ -1;2\right ] \)
\(\{ - 1;2\}\)
\(\left (-1;2\right )\)
\(\left (-\infty ;-1\right )\cup \left (2;\infty \right )\)