9000021809
Level:
B
Solve the following inequality.
\[
\frac{2x + 4}
{x - 1} < 1
\]
\(x\in (-5;1)\)
\(x\in (-\infty ;5)\)
\(x\in (1;\infty )\)
\(x\in (-\infty ;-3)\cup (1;\infty )\)
B
9000020909
Level:
B
The sum of squares of two consecutive integers is
\(1201\).
Identify these integers.
\(24\)
and \(25\)
\(23\)
and \(24\)
\(25\)
and \(26\)
\(26\)
and \(27\)
9000021810
Level:
B
Find all the values of \(x\)
for which the following expression takes on values smaller than or equal to
\(1\).
\[
\frac{x + 1}
{x - 1} - \frac{1}
{x + 1}
\]
\(x\in (-\infty ;-3] \cup (-1;1)\)
\(x\in (-\infty ;-3] \)
\(x\in (-\infty ;-1)\cup (-1;1)\cup (1;\infty )\)
\(x\in [ - 3;-1)\)
9000021808
Level:
B
Find the domain of the following function.
\[
f(x) = \sqrt{\frac{(x - 3)(x + 2)}
{(1 - x)(3 - x)}}
\]
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;3)\cup (3;\infty )\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2)\cup (1;3)\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;\infty )\)
\(\mathop{\mathrm{Dom}}(f) =[ -2;1)\cup (3;\infty )\)
9000020409
Level:
B
One of the solutions of the quadratic equation \( x^{2} + bx - 10 = 0\) is \(x_{1} = 5\). Find the second solution \(x_{2}\) and the value of the coefficient \(b\).
\(x_{2} = -2\) and
\(b = -3\)
\(x_{2} = -3\) and
\(b = -2\)
\(x_{2} = 2\) and
\(b = 3\)
\(x_{2} = 3\) and
\(b = 2\)
9000020410
Level:
B
The quadratic equation
\[
ax^{2} + 4x + c = 0
\]
has solutions \(x_{1} = -3\)
and \(x_{2} = 5\). Find the
coefficients \(a\)
and \(c\).
\(a = -2\),
\(c = 30\)
\(a = -2\),
\(c = -30\)
\(a = 2\),
\(c = -30\)
\(a = 2\),
\(c = 30\)
9000021704
Level:
B
Solve the following inequality.
\[
\frac{x + 1}
{4} -\frac{x + 2}
{3} > \frac{x + 3}
{6} -\frac{3x - 4}
{12}
\]
\(x\in \emptyset \)
\(x\in \mathbb{R}\)
\(x\in (-\infty ;29)\)
\(x\in \{0\}\)
9000020406
Level:
B
The ratio of the sides of a rectangle is
\(3 : 4\). The length of
the diagonal is \(100\, \mathrm{cm}\).
Find the perimeter of the rectangle.
\(280\, \mathrm{cm}\)
\(150\, \mathrm{cm}\)
\(480\, \mathrm{cm}\)
\(300\, \mathrm{cm}\)
9000021705
Level:
B
Solve the following inequality in the set of negative integers.
\[
\frac{3x - 4}
{2} -\frac{2x - 5}
{3} + \frac{3 - 4x}
{5} > 0
\]
\(x\in \{ - 7;-6;-5;-4;-3;-2;-1\}\)
\(x\in \emptyset \)
\(x\in [ - 8;0] \)
\(x\in \{ - 8;-7;-6;-5;-4;-3;-2;-1\}\)
9000021708
Level:
B
In the following list identify a function with a domain
\(\left (-\infty ; \frac{1}
{2}\right )\).
\(f(x)= \sqrt{ \frac{10}
{2-4x}}\)
\(f(x)= \sqrt{\frac{2-4x}
{10}} \)
\(f(x) = \sqrt{2 - 4x}\)
\(f(x) = \sqrt{\frac{2-4x}
{3x}} \)