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
9000024110
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.
\[
11x - 2 = 2 - 4x
\]
add \((4x + 2)\)
multiply by \(\frac{1}
{11}\)
multiply by \(\left (-\frac{1}
{4}\right )\)
add \((-11x + 4x)\)
subtract \((4x + 2)\)
add \((4x + 2)\)
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.
\(\ \ - 1\)
\(\ \ -\frac{2}
{3}\)
\(\ \ \frac{2}
{3}\)
\(\ \ \frac{1}
{3}\)
\(\ \ 1\)
9000025801
Level:
A
Find all intersections of the graph of the following function with
\(x\)-axis.
\[
f(x) = x^{3} - x^{2} - 2x
\]
\(X_{1} = [0;0]\),
\(X_{2} = [-1;0]\),
\(X_{3} = [2;0]\)
\(X = [0;0]\)
\(X_{1} = [0;0]\),
\(X_{2} = [-1;0]\)
\(X_{1} = [0;0]\),
\(X_{2} = [1;0]\),
\(X_{3} = [-2;0]\)
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.
\(1\)
\(3\)
\(- 3\)
\(- 1\)
\(4\)
9000025603
Level:
A
In the following list identify an equation equivalent to the following quadratic
equation.
\[
2(x - 8)\left (x + \frac{1}
{2}\right ) = 0
\]
\(2x^{2} - 15x - 8 = 0\)
\(2x^{2} - 8x + \frac{1}
{2} = 0\)
\(8x^{2} - 15x + \frac{1}
{2} = 0\)
\(8x^{2} - 8x - 1 = 0\)
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.
\(1\)
\(- 1\)
\(- 0.5\)
\(0.5\)
\(1.5\)
9000025601
Level:
A
Which of the quadratic equations from the following list has all solutions in the interval
\([ - 5;3] \)?
\(x^{2} - 2x - 3 = 0\)
\(x^{2} - 3x - 10 = 0\)
\(x^{2} - 2x - 15 = 0\)
\(x^{2} - 3x - 18 = 0\)
9000024505
Level:
A
Identify the value of a real parameter \(b\)
such that the graph of the function
\[
f(x) = \left |x + \frac{1}
{2}\right | + b
\]
corresponds to the picture.
\(- 1\)
\(-\frac{3}
{2}\)
\(-\frac{1}
{2}\)
\(\frac{1}
{2}\)
\(1\)
9000025602
Level:
A
In the following list identify a set which contains at least one solution of the quadratic
equation \(x^{2} - 121 = 0\).
\(\{ - 11;1;13\}\)
\(\{ - 5;0;5;10\}\)
\(\{3;7;9;19\}\)
\(\{ - 15;-12;-7\}\)