9000088803
Level:
A
Evaluate the following expression at \(x = \frac{1}
{2}\).
\[
1 - \frac{x - 2}
{2x + 1}
\]
\(\frac{7}
{4}\)
\(\frac{1}
{4}\)
\(\frac{5}
{4}\)
\(\frac{3}
{4}\)
A
9000088809
Level:
A
Simplify the following expression.
\[
\left ( \frac{1}
{m - n} - \frac{1}
{m + n}\right )\cdot \left (\frac{m^{2} + 2mn + n^{2}}
{2n} \right )
\]
\(\frac{m+n}
{m-n}\)
\(0\)
\(\frac{m(m+n)}
{n(m-n)} \)
\(2\)
9000085604
Level:
A
Find the sum of the three numbers obtained by rounding the number
\(2\: 013\) to the
nearest tens, hundreds and thousands.
\(6\: 010\)
\(6\: 000\)
\(6\: 020\)
\(6\: 030\)
9000083710
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{(4x + 3)^{2} - (5x - 2)^{2}}
{5 + x}
\]
\(x = 5,\ x = -\frac{1}
{9}\)
\(x = -5\)
\(x = -\frac{5}
{9},\ x = 1\)
\(x = 1,\ x = \frac{5}
{9}\)
9000083602
Level:
A
Evaluate the following expression at \(x = \frac{1}
{2}\).
\[
\frac{x^{2} - 2}
{1 -\frac{1}
{x}}
\]
\(\frac{7}
{4}\)
\(-\frac{7}
{4}\)
\(\frac{7}
{2}\)
\(-\frac{7}
{2}\)
9000081401
Level:
A
Find the inequality which describes the set graphed in the picture.
\(|x| < 1;\ x\in \mathbb{R}\)
\(|x - 1| < 0;\ x\in \mathbb{R}\)
\(|x| > 1;\ x\in \mathbb{R}\)
\(|x + 1| < 1;\ x\in \mathbb{R}\)
\(|x - 1| > 0;\ x\in \mathbb{R}\)
9000083605
Level:
A
Find the common denominator of the fractions.
\[
\text{$ \frac{3x}
{x^{2}+4x+4}$ and $ \frac{x+5}
{x^{2}-4}$}
\]
\((x + 2)^{2}(x - 2),\; x\neq \pm 2\)
\((x + 2)(x - 4),\; x\neq \pm 2\)
\((x + 2)^{2}(x - 4),\; x\neq \pm 2\)
\((x + 2)(x - 4),\; x\neq \pm 2\)
9000081402
Level:
A
Find the inequality which describes the set graphed in the picture.
\(|x - 1| < 2;\ x\in \mathbb{R}\)
\(|x + 1| < 2;\ x\in \mathbb{R}\)
\(|x - 1| > 2;\ x\in \mathbb{R}\)
\(|x + 1| > 2;\ x\in \mathbb{R}\)
\(|x - 2| > 1;\ x\in \mathbb{R}\)
9000083603
Level:
A
Evaluate the following expression at \(x = \frac{1}
{2}\)
and \(y = -\frac{1}
{4}\).
\[
\frac{x -\frac{y}
{x}}
{1 + \frac{x}
{y}}
\]
\(- 1\)
\(3\)
\(4\)
\(1\)
9000081403
Level:
A
Find the inequality which describes the set graphed in the picture.
\(|x + 1| > 2;\ x\in \mathbb{R}\)
\(|x - 1| < 2;\ x\in \mathbb{R}\)
\(|x + 1| < 2;\ x\in \mathbb{R}\)
\(|x - 1| > 2;\ x\in \mathbb{R}\)
\(|x - 2| > 1;\ x\in \mathbb{R}\)