9000029309
Level:
B
Find the solution set of the following inequality.
\[
(x - 1)(x - 2)(x - 3) < (x - 1)(x - 2)
\]
\((-\infty ;1)\cup (2;4)\)
\(\emptyset \)
\((0;3)\)
\((-\infty ;-3)\cup (3;\infty )\)
\((-3;3)\)
B
9000031101
Level:
B
Solve the following system of equations and identify a correct statement.
\[\begin{aligned}
(x - 3)^{2} + (y - 1)^{2} = 1 & &
\\2x^{2} + 2y^{2} - 12x - 4y + 18 = 0 & &
\end{aligned}\]
The system has more than two solutions.
The system does not have any solution.
The system has a unique solution.
The system has two solutions.
9000029310
Level:
B
Find the solution set of the following inequality.
\[
(x + 2)(x^{2} + 4x + 3) > x^{2} + 5x + 6
\]
\((-3;-2)\cup (0;\infty )\)
\((-\infty ;-3)\cup (3;\infty )\)
\((-\infty ;-1)\cup (1;\infty )\)
\((-1;1)\)
\(\mathbb{R}\)
9000031103
Level:
B
Solve the following system of equations in \( \mathbb{R} \times \mathbb{R}\) and identify the correct statement.\[\begin{aligned}
x - 2y + 5 = 0 & &
\\x^{2} + y^{2} = 9 & &
\end{aligned}\]
The system has two solutions.
The system does not have any solution.
The system has a unique solution.
The system has more than two solutions.
9000031001
Level:
B
Find the sum of all real roots of the following equation.
\[
(3x - 1)(2x + 1)(4x^{2} + 3x - 1) = 0
\]
\(-\frac{11}
{12}\)
\(- \frac{1}
{12}\)
\(-\frac{1}
{6}\)
\(\frac{1}
{6}\)
9000031102
Level:
B
Solve the following system of equations and identify a correct statement.
\[\begin{aligned}
(x - 1)^{2} + y^{2} = 1 & &
\\(x - 4)^{2} + y^{2} = 4 & &
\end{aligned}\]
The system has a unique solution \(\left [x,y\right ]\),
where \(y = 0\).
The system does not have any solution.
The system has a unique solution \(\left [x,y\right ]\),
where \(y > 0\).
The system has two solutions \(\left [x_{1},y_{1}\right ]\),
\(\left [x_{2},y_{2}\right ]\), where
\(y_{1} = -y_{2}\).
9000031004
Level:
B
Assuming \(y\in \mathbb{R}\),
find the number of the solutions of the following algebraic equation.
\[
y^{4} + 5y^{2} + 6 = 0
\]
\(0\)
\(4\)
\(3\)
\(2\)
9000031005
Level:
B
Assuming \(x\in \mathbb{R}\),
solve the following algebraic equation.
\[
(x + 1)^{4} - 5(x + 1)^{2} + 4 = 0
\]
\( \{ - 3;-2;0;1\}\)
\( \{1;4\}\)
\( \{ - 2;-1;1;2\}\)
\( \{ - 1;3\}\)
9000031008
Level:
B
Assuming \(x\in \mathbb{R}\),
solve the following equation.
\[
4x^{3} - 3x^{2} - x = 0
\]
\( \left \{-\frac{1}
{4};0;1\right \}\)
\(\{0;1;4\}\)
\( \{1;4\}\)
\( \{0\}\)
9000031010
Level:
B
Identify a true statement on the following equation.
\[
x^{5} - x^{3} - 6x = 0
\]
The equation has three solutions in \(\mathbb{R}\).
The equation does not have solution in
\(\mathbb{R}\).
The equation has five solutions in \(\mathbb{R}\).
The equation has one solution in \(\mathbb{R}\).