9000035701
Level:
A
What is the algebraic form of the complex number \( A \) graphed in the complex
plane (as shown in the picture)?
\( -3 + 2\mathrm{i}\)
\( 2 - 3\mathrm{i}\)
\( 2 + 3\mathrm{i}\)
\( -3 - 2\mathrm{i}\)
A
9000036105
Level:
A
The side \(b\) in
the triangle \(ABC\)
is \(17\, \mathrm{cm}\) and
the angle \(\beta \)
is \(58^{\circ }\).
Find the radius of the circle circumscribed to this triangle and round your answer to
the nearest centimeters.
\(10\, \mathrm{cm}\)
\(8\, \mathrm{cm}\)
\(9\, \mathrm{cm}\)
\(11\, \mathrm{cm}\)
9000033901
Level:
A
Associate the angle \(\frac{7}
{6}\pi \)
to the corresponding quadrant.
III.
I.
II.
IV.
9000034804
Level:
A
Find the absolute value of the complex number
\(z = 3 -\mathrm{i}\).
\(\sqrt{10}\)
\(2\)
\(2\sqrt{2}\)
\(\sqrt{2}\)
9000034709
Level:
A
Consider equation
\[
p(2 - p)x = 4p
\]
with a real parameter \(p\).
Solve the equation for \(p = 2\).
\(\emptyset \)
\(\mathbb{R}\)
\(\left \{ \frac{4}
{2-p}\right \}\)
\(\mathbb{R}\setminus \left \{0\right \}\)
9000034801
Level:
A
Given complex numbers \(z_{1} = 4 -\mathrm{i}\)
and \(z_{2} = 1 - 2\mathrm{i}\),
find \(z_{1} - z_{2}\).
\(3 + \mathrm{i}\)
\(3 - 3\mathrm{i}\)
\(5 - 3\mathrm{i}\)
\(3 -\mathrm{i}\)
9000033910
Level:
A
Convert the angle \(292.5^{\circ }\)
to radians.
\(\frac{13}
{8} \pi \)
\(\frac{11}
{4} \pi \)
\(\frac{15}
{8} \pi \)
\(\frac{13}
{4} \pi \)
9000034901
Level:
A
Find the domain of the following expression.
\[
\sqrt{\left (2x - 3 \right ) \left (3x + 1 \right )}
\]
\(\left (-\infty ,-\frac{1}
{3}\right ] \cup \left [ \frac{3}
{2},\infty \right )\)
\(\left [ -\frac{1}
{3}, \frac{3}
{2}\right ] \)
\(\left (-\frac{1}
{3}, \frac{3}
{2}\right )\)
\(\left (-\infty ,-\frac{1}
{3}\right )\cup \left (\frac{3}
{2},\infty \right )\)
9000034708
Level:
A
Consider the equation
\[
2x^{2} + 5px + 2 = 0
\]
with the real parameter \(p\).
Solve the equation for \(p = -\frac{4}
{5}\).
\(\left \{1\right \}\)
\(\left \{-1\right \}\)
\(\left \{0\right \}\)
\(\emptyset \)
9000034903
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\sqrt{\left (3x + 4 \right ) \left (\frac{1}
{5} - x\right )}
\]
\(\left (-\infty ,-\frac{4}
{3}\right )\cup \left (\frac{1}
{5},\infty \right )\)
\(\left [ -\frac{4}
{3}, \frac{1}
{5}\right ] \)
\(\left (-\infty ,-\frac{4}
{3}\right ] \cup \left [ \frac{1}
{5},\infty \right )\)
\(\left (-\frac{4}
{3}, \frac{1}
{5}\right )\)