9000025602
Level:
A
In the following list identify a set which contains at least one solution of the quadratic
equation \(x^{2} - 121 = 0\).
\(\{ - 11;1;13\}\)
\(\{ - 5;0;5;10\}\)
\(\{3;7;9;19\}\)
\(\{ - 15;-12;-7\}\)
A
9000024506
Level:
A
Identify the value of real parameters \(a\)
and \(b\)
such that the graph of the function
\[
f(x)= \left |x + a\right | + b
\]
corresponds to the picture.
\(a = 2,\ b = -3\)
\(a = 2,\ b = 3\)
\(a = 3,\ b = 2\)
\(a = -3,\ b = -2\)
9000025604
Level:
A
In the following list identify an equation which does not have solution in the set of
real numbers.
\(8x^{2} - x + 1 = 0\)
\(8x^{2} + 8x - 1 = 0\)
\(8x^{2} - 8x + 1 = 0\)
\(8x^{2} - x - 1 = 0\)
9000024507
Level:
A
Identify the value of a real parameter \(a\)
such that the graph of the function
\[
f(x) = -|a - x| + 2
\]
corresponds to the picture.
\(3\)
\(2\)
\(1\)
\(- 1\)
\(4\)
9000024105
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.
\[
\frac{4 + x}
{x + 1} = \frac{x - 3}
{x + 2}
\]
multiply by \((x + 2)\cdot (x + 1)\),
assuming \(x\neq - 2\)
and \(x\neq - 1\)
multiply by \((4 + x)\cdot (x - 3)\),
assuming \(x\neq - 4\)
and \(x\neq 3\)
multiply by \((4 + x)\cdot (x + 1)\),
assuming \(x\neq - 4\)
and \(x\neq - 1\)
multiply by \((x - 3)\cdot (x + 2)\),
assuming \(x\neq 3\)
and \(x\neq - 2\)
multiply by \((x - 3)\),
assuming \(x\neq 3\)
multiply by \((4 + x)\),
assuming \(x\neq - 4\)
9000024408
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.
\(\ \ a = 3,\quad \phantom{ -} b = -2\)
\(\ \ a = -3,\quad b = 2\)
\(\ \ a = 2,\quad \phantom{ -} b = -3\)
\(\ \ a = -2,\quad b = 2\)
9000024106
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. Assume
\(x\neq 1\) and
\(x\neq 2\).
\[
\frac{1}
{x - 1} = \frac{2}
{x - 2}
\]
multiply by \((x - 1)\cdot (x - 2)\)
multiply by \((x - 1)\)
multiply by \((x - 2)\)
multiply by \((x + 1)\)
multiply by \((x + 2)\)
multiply by \((x - 1)\cdot (x + 2)\)
9000024508
Level:
A
Identify the value of real parameters \(a\)
and \(b\)
such that the graph of the function
\[
f(x) = \left |x - a\right | + b
\]
corresponds to the picture.
\(a = 2,\ b = -2\)
\(a = -2,\ b = 2\)
\(a = 2,\ b = 2\)
\(a = -2,\ b = -2\)
9000024109
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.
\[
\frac{2x + 1}
{x - 1} + \frac{x + 1}
{x - 1} = \frac{11}
{2}
\]
multiply by \(2(x - 1)\),
assuming \(x\neq 1\)
multiply by \((2x + 1)\),
assuming \(x\neq -\frac{1}
{2}\)
multiply by \((x + 1)\),
assuming \(x\neq - 1\)
multiply by \(\frac{1}
{2x+1}\),
assuming \(x\neq -\frac{1}
{2}\)
multiply by \(\frac{1}
{x+1}\),
assuming \(x\neq - 1\)
multiply by \(2(2x + 1)(x + 1)\),
assuming \(x\neq -\frac{1}
{2}\)
and \(x\neq - 1\)
9000024802
Level:
A
Consider the equation
\[
\sqrt{x^{2 } - 2x + 1} = x + 2
\]
and the equation which arises from this equation by squaring both sides of the
equation, i.e. the equation
\[
\left (\sqrt{x^{2 } - 2x + 1}\right )^{2} = (x + 2)^{2}.
\]
Identify a true statement.
Both equations are equivalent only if
\(x\geq - 2\).
Both equations are equivalent.
Both equations are equivalent only if
\(x\leq - 2\).
None of the above.