9000078504
Level:
A
Write the following set in an interval notation.
\[
\{x\in \mathbb{R};|x + 10| > 7\}
\]
\((-\infty ;-17)\cup (-3;\infty )\)
\((-\infty ;3)\cup (17;\infty )\)
\((-3;\infty )\)
\((17;\infty )\)
A
9000079205
Level:
A
Assuming \(x\neq 0\)
and \(x\neq 2\),
simplify the following expression.
\[
\frac{x^{3} - x^{2}}
{x - 2} \cdot \frac{2 - x}
{x^{2}}
\]
\(1 - x\)
\(x - 1\)
\(x + 1\)
\(x^{2} - 1\)
9000079201
Level:
A
Evaluate
\[
\frac{-x^{2}}
{x - y} -\frac{y - x}
{x + y}
\]
at \(x = -1\),
\(y = 2\).
\(-\frac{8}
{3}\)
\(-\frac{10}
{3} \)
\(-\frac{2}
{3}\)
\(-\frac{4}
{3}\)
9000079210
Level:
A
Consider the expression
\[
V (x) = \frac{x}
{x - 1} - \frac{1}
{1 - x}.
\]
Find the correct ordering of the values
\(V (-2)\),
\(V (0)\) and
\(V (2)\).
\(V (0) < V (-2) < V (2)\)
\(V (-2) < V (0) < V (2)\)
\(V (0) < V (2) < V (-2)\)
\(V (2) < V (0) < V (-2)\)
9000079206
Level:
A
Assuming \(x\neq 0\),
\(y\neq 0\),
\(x\neq y\),
simplify the following expression.
\[ {
\frac{1}
{x^{2}} - \frac{1}
{y^{2}}
\over -\frac{1}
{y} + \frac{1}
{x}}
\]
\(\frac{x+y}
{xy} \)
\(-\frac{x+y}
{xy} \)
\(\frac{1}
{y} -\frac{1}
{x}\)
\(\frac{1}
{x} -\frac{1}
{y}\)
9000078509
Level:
A
Evaluate the following expression.
\[
|3 - 7|-|2(-4)| + |(-5)(-2)|
\]
\(6\)
\(14\)
\(22\)
\(- 2\)
9000079101
Level:
A
Find the intervals of monotonicity for the following function.
\[
f(x)= \frac{3x + 1}
{2x - 5}
\]
Decreasing on \(\left (-\infty ; \frac{5}
{2}\right )\)
and \(\left (\frac{5}
{2};\infty \right )\).
Decreasing on \(\left (-\infty ; \frac{5}
{2}\right )\cup \left (\frac{5}
{2};\infty \right )\).
Decreasing on \(\left (-\infty ; \frac{5}
{2}\right )\),
increasing on \(\left (\frac{5}
{2};\infty \right )\).
Increasing on \(\left (-\infty ; \frac{5}
{2}\right )\),
decreasing on \(\left (\frac{5}
{2};\infty \right )\).
9000079102
Level:
A
Find the intervals where the following function is a decreasing function.
\[
f(x) = \frac{x^{2} + 1}
{x}
\]
\([ - 1;0)\) and
\((0;1] \)
\([ - 1;1] \)
\((-\infty ;-1] \) and
\([1;\infty) \)
\([1;\infty) \)
9000079103
Level:
A
Find the $x$ at which has the function $f$ a local maximum.
\[
f(x) = x^{3} - 3x^{2} - 9x + 2
\]
\(x=- 1\)
\(x=- 3\)
\(x=1\)
\(x=3\)
9000073404
Level:
A
Find the sum of the following infinite series.
\[
\sqrt{2} - 2 + \sqrt{8} - 4 + \sqrt{32} - 8+\cdots
\]
The sum does not exist.
\(\frac{\sqrt{2}}
{1+\sqrt{2}}\)
\(\frac{\sqrt{2}}
{1-\sqrt{2}}\)
\(\sqrt{2} - 2\)