9000025606
Level:
A
In the following list identify a quadratic equation which has a unique solution.
\(x^{2} + 2x + 1 = 0\)
\(x^{2} - 3x - 1 = 0\)
\(x^{2} + 2x - 1 = 0\)
\(x^{2} - 3x + 1 = 0\)
A
9000024803
Level:
A
Removing radical in an equation by squaring both sides may enrich the set of
solutions of this equation and checking the solutions of the new equation in the
original equation may be necessary. Identify a correct conclusion in the particular
case of the following equation.
\[
-\sqrt{x^{2 } - 2x + 1} = x
\]
If we look for the solution in the set
\(\mathbb{R}^{-}\), then
squaring both sides of the equation gives an equivalent equation. The checking of the
solution is not necessary.
If we look for the solution in the set
\(\mathbb{R}^{+}\), then
squaring both sides of the equation gives an equivalent equation. The checking of the
solution is not necessary.
If we look for the solution in the set
\(\mathbb{R}\), then
squaring both sides of the equation gives an equivalent equation. The checking of the
solution is not necessary.
None of the above.
9000024101
Level:
A
Identify the optimal first step to solve the following equation. The operation is
intended to be used on both sides of the equation.
\[
3x + 2 = -5x + 1
\]
add \((5x - 2)\)
multiply by \(\frac{1}
{3}\)
multiply by \(-\frac{1}
{5}\)
add \((-3x + 2)\)
add \((5x + 1)\)
add \((3x - 1)\)
9000025607
Level:
A
In the following list identify a quadratic equation which cannot be factorized in
\(\mathbb{R}\).
\(- 7x^{2} + 3x - 1 = 0\)
\(5x^{2} + 2x - 3 = 0\)
\(- 3x^{2} + 2x + 3 = 0\)
\(6x^{2} + 3x - 1 = 0\)
9000024407
Level:
A
Identify the value of a real parameter \(a\)
such that the graph of the function
\[
f(x) = |x + a|- 2
\]
corresponds to the picture.
\(\ \ - 1\)
\(\ \ 1\)
\(\ \ - 2\)
\(\ \ 2\)
\(\ \ 3\)
9000024102
Level:
A
Identify the optimal first step to solve the following equation. The operation is
intended to be used on both sides of the equation.
\[
x + \frac{x}
{6} = \frac{x}
{15} + 1
\]
multiply by \(30\)
multiply by \(6\)
multiply by \(15\)
subtract \((1 + x)\)
subtract \(\left (\frac{x}
{6} + \frac{x}
{15}\right )\)
subtract \(\left (\frac{x}
{6} + 1\right )\)
9000025609
Level:
A
In the following list identify an equation such that one of the solutions equals
\(- 1\).
\(5x^{2} + 2x - 3 = 0\)
\(5x^{2} - 2x - 3 = 0\)
\(5x^{2} + 2x + 3 = 0\)
\(5x^{2} - 2x + 3 = 0\)
9000025605
Level:
A
Find the interval which contains all the solutions of the following quadratic
equation.
\[
\text{$5x^{2} - 3x - 2 = 0$}
\]
\((-0.5;2)\)
\([ - 1;0] \)
\([ 0;4)\)
\([ - 3;1)\)
9000024103
Level:
A
Identify the optimal first step to solve the following equation. The operation is
intended to be used on both sides of the equation.
\[
\frac{x + 5}
{9} -\frac{x}
{6} = \frac{x - 2}
{9} + \frac{x - 3}
{9}
\]
multiply by \(18\)
multiply by \(6\)
multiply by \(9\)
multiply by \(54\)
multiply by \(\frac{1}
{9}\)
multiply by \(\frac{1}
{18}\)
9000023908
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x - y & = -1, & &
\\4x - y & = 1. & &
\end{aligned}\]
In the following list identify a true statement.
\(y\) is
a prime number.
\(x\) is
a prime number.
\(x + y\) is
a prime number.
\(x - y\) is
a prime number.