9000020010
Level:
A
Choose the equation which is obtained by squaring both
sides of the following equation.
\[
\sqrt{x^{2 } - x + 5} = 2x - 5
\]
\(3x^{2} - 19x + 20 = 0\)
\(x^{2} + 3x + 20 = 0\)
\(3x^{2} + x - 30 = 0\)
\(3x^{2} + x + 20 = 0\)
A
9000020003
Level:
A
Find the domain of the following equation.
\[
\sqrt{3x + 6} + \sqrt{8 - 2x} = 11
\]
\([ - 2,4] \)
\((-\infty ,-2] \)
\([ - 2,\infty )\)
\([ 4,\infty )\)
9000020401
Level:
A
Solve the following quadratic equation.
\[
-x^{2} + 12x - 20 = 0
\]
\(x_{1} = 2\),
\(x_{2} = 10\)
\(x_{1} = -2\),
\(x_{2} = 10\)
\(x_{1} = -2\),
\(x_{2} = -10\)
\(x_{1} = 2\),
\(x_{2} = -10\)
9000020004
Level:
A
Find the domain of the following equation.
\[
\sqrt{x - 7} + \sqrt{3x + 12} = 5
\]
\([ 7,\infty )\)
\([ - 4,7] \)
\([ - 4,\infty )\)
\((-4,7)\)
9000020402
Level:
A
Identify an equation which does not have real solution.
\(x^{2} - 2x + 5 = 0\)
\(x^{2} - 5 = 0\)
\(x^{2} + 0.8x = 0\)
\(- x^{2} + 2x + 35 = 0\)
9000021706
Level:
A
Find all the values of the parameter \(k\) so that the solution of the following equation is bigger than \(10\).
\[
3x - 18 = \frac{10x - 4k}
{2}
\]
\(k\in (19,\infty )\)
\(k\in \{9\}\)
\(k\in (-\infty ,1)\)
\(k\in (9,\infty )\)
9000020407
Level:
A
In the following list identify an equation with real solution.
\(- 0.5x^{2} + 2x + 3 = 0\)
\(- x^{2} + 4x - 5 = 0\)
\(2x^{2} - 3x + 3 = 0\)
\(x^{2} - x + 1 = 0\)
9000021707
Level:
A
Find all the values of the parameter \(k\) so that the solution of the following equation is positive.
\[
2kx + k = 4x + 3
\]
\(k\in (2,3)\)
\(k > 0\)
\(k\in (3,\infty )\)
\(k\in (-\infty ,3)\)
9000014802
Level:
A
Let \(f(x) = -x^{2} + 11x - 2\).
Which of the following statements is true?
\(f(-2) = -28\)
\(f(0) = 2\)
\(f(3.5) = 12.25\)
\(f\left (\frac{1}
{2}\right ) = \frac{15}
{4} \)
9000019903
Level:
A
Identify a true statement related to the following matrix
\(A\).
\[
A = \left (\array{
-2& 3 & 10& 5 & -5\cr
6 & 11 & -7 & 2 & -3
\cr
-7& 15& -6& 2 & 4\cr
-8 & 1 & 13 & -5 & 0
} \right )
\]
\(A\) is
a \(4\times 5\) matrix
and \(a_{(3,\, 2)} = 15\).
\(A\) is
a \(4\times 5\) matrix
and \(a_{(2,\, 3)} = 15\).
\(A\) is
a \(5\times 4\) matrix
and \(a_{(3,\, 2)} = -7\).
\(A\) is
a \(5\times 4\) matrix
and \(a_{(3,\, 2)} = 15\).