9000024404
Level:
A
Identify the value of a real parameter \(b\)
such that the graph of the function
\[
f(x) = |x - 0.25| + b
\]
corresponds to the picture.
\(\ \ 0.5\)
\(\ \ - 0.5\)
\(\ \ 0.75\)
\(\ \ - 0.75\)
\(\ \ 0.25\)
A
9000025602
Level:
A
In the following list identify a set which contains at least one solution of the quadratic
equation \(x^{2} - 121 = 0\).
\(\{ - 11,1,13\}\)
\(\{ - 5,0,5,10\}\)
\(\{3,7,9,19\}\)
\(\{ - 15,-12,-7\}\)
9000024405
Level:
A
Identify the value of a real parameter \(b\)
such that the graph of the function
\[
f(x) = \left |x -\frac{1}
{3}\right | + b
\]
corresponds to the picture.
\(\ \ - 1\)
\(\ \ -\frac{2}
{3}\)
\(\ \ \frac{2}
{3}\)
\(\ \ \frac{1}
{3}\)
\(\ \ 1\)
9000025605
Level:
A
Find the interval which contains all the solutions of the following quadratic
equation.
\[
\text{$5x^{2} - 3x - 2 = 0$}
\]
\((-0.5,2)\)
\([ - 1,0] \)
\([ 0,4)\)
\([ - 3,1)\)
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 \((3x - 1)\)
9000024503
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.
\(1\)
\(3\)
\(- 3\)
\(- 1\)
\(4\)
9000025805
Level:
A
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 1)(x + 2)(x - 3)
\]
\(f(x) < 0 \iff x\in (-\infty ,-2)\cup (-1,3)\)
\(f(x) < 0 \iff x\in \left (-\infty ,-\frac{3}
{2}\right )\cup (1,3)\)
\(f(x) < 0 \iff x\in \left (-\infty ,-\frac{3}
{2}\right )\cup (3,\infty )\)
\(f(x) < 0 \iff x\in \left (-\frac{3}
{2},-1\right )\cup (3,\infty )\)
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 \(\left (\frac{x}
{6} + 1\right )\)
9000024504
Level:
A
Identify the value of a real parameter \(b\)
such that the graph of the function
\[
f(x) = |x - 0.5| + b
\]
corresponds to the picture.
\(1\)
\(- 1\)
\(- 0.5\)
\(0.5\)
\(1.5\)
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.