9000025605
Level:
A
Find the interval which contains all the solutions of the following quadratic
equation.
\[
\text{$5x^{2} - 3x - 2 = 0$}
\]
\((-0.5;2)\)
\([ - 1;0] \)
\([ 0;4)\)
\([ - 3;1)\)
A
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.
9000024403
Level:
A
Identify the value of a real parameter \(a\)
such that the graph of the function
\[
f(x) = |x - a|- 3
\]
corresponds to the picture.
\(\ \ 1\)
\(\ \ - 2\)
\(\ \ - 3\)
\(\ \ 4\)
\(\ \ 3\)
9000024104
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.
\[
5x = \frac{2 + x}
{5}
\]
multiply by \(5\)
multiply by \(\frac{1}
{5}\)
multiply by \(\frac{1}
{2}\)
multiply by \(2\)
multiply by \(\frac{1}
{x}\),
assuming \(x\neq 0\)
multiply by \(x\),
assuming \(x\neq 0\)
9000023909
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 3y & = 0, & &
\\3x + 2y & = 5. & &
\end{aligned}\]
In the following list identify a true statement.
\(- 3\leq y\leq - 1\)
\(- 1\leq x\leq 2\)
\(- 2\leq x\leq 2\)
\(2\leq y\leq 4\)
9000024406
Level:
A
Identify the values of real parameters \(a\)
and \(b\)
such that the graph of the function
\[
f(x)= |x + a| + b
\]
corresponds to the picture.
\(\ \ a = 3,\quad \phantom{ -} b = 2\)
\(\ \ a = 2,\quad \phantom{ -} b = 3\)
\(\ \ a = 2,\quad \phantom{ -} b = -3\)
\(\ \ a = -3,\quad b = 2\)
9000023802
Level:
A
Find the product of the solutions of the following equation.
\[
\sqrt{3x - 8} = \frac{x}
{2}
\]
\(32\)
\(4\)
\(8\)
\(16\)
9000023708
Level:
A
Identify a true statement which concerns the following equation.
\[
\sqrt{x + 5} = x - 1
\]
The solution is an even number.
The solution is from the interval \([ - 2;2)\).
The solution is from the set \(A = \left \{x\in \mathbb{R} : -1\leq x < 3\right \}\).
The solution is a divisor of \(6\).
9000023810
Level:
A
Denote by \(x_{1}\)
the solution of the equation
\[
\sqrt{6 - 2x} = -x - 1
\]
and by \(x_{2}\)
the solution of the equation
\[
\sqrt{2x + 6} = 9 - x.
\]
Identify a correct statement about \(x_{1}\)
and \(x_{2}\).
\(|x_{1}| = |x_{2}|\)
\(|x_{1}| < |x_{2}|\)
\(|x_{1}| > |x_{2}|\)
\(5|x_{1}| = |x_{2}|\)