9000028110
Level:
B
Given graphs of linear functions \(f\),
\(g\) and
\(h\), find the solution set
of the inequality \(f(x)\leq g(x) < h(x)\).
\([ 4;7)\)
\((-\infty ;4] \)
\([ 1;7)\)
\([ 7;\infty )\)
B
9000026402
Level:
B
To solve the equation with absolute value using interval method we have to divide
the domain of the equation by the zero point of the subexpression in the absolute
value. Find this point.
\[
1 -|x - 2| = x + 2
\]
\(2\)
\(1\)
\(- 2\)
\(0\)
9000028301
Level:
B
The following equation has a solution
\(x = 1\). Find
the sum of the remaining real solutions.
\[
x^{3} - 7x + 6 = 0
\]
\(- 1\)
\(1\)
\(0\)
\(2\)
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.
\(x^{2} - 6x + 9 = 0\)
\(x^{2} + 9x - 3 = 0\)
\(x^{2} - 9x - 3 = 0\)
\(x^{2} + 6x + 9 = 0\)
9000022805
Level:
B
The solution set of one of the following inequalities is the interval
\([ 3;5] \).
Identify this inequality.
\(x^{2} - 8x + 15\leq 0\)
\(x^{2} + 8x + 15\leq 0\)
\(x^{2} - 8x + 15\geq 0\)
\(x^{2} + 8x + 15\geq 0\)