1003023309
Level:
B
What angle sweeps the hour hand of a clock in \( 3 \) hours?
\( -90^{\circ} \)
\( 45^{\circ} \)
\( -45^{\circ} \)
\( 90^{\circ} \)
Angles, arcs and sectors
1003055101
Level:
B
How many different values of \( \theta \) meet both conditions:
\[\theta\in\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{3\pi}4+2k\pi\right\}\text{, }\ \theta\in[-2\pi;4\pi ] \]
\( 3 \)
\( 4 \)
\( 5 \)
\( 2 \)
1003055102
Level:
B
The measure of the angle \( \theta \) meets the following conditions:
\[\theta\in\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac23\pi+k\frac{\pi}3\right\},\ \theta\in\left[-\frac{\pi}2;2\pi\right].\]
Choose the smallest value of $\theta$.
\( -\frac{\pi}3 \)
\( -\frac{\pi}2 \)
\( \frac23\pi \)
\( \frac{\pi}3 \)
1003055103
Level:
B
Find out for which \( k\in\mathbb{Z} \) is true:
\[ -\frac{11}4\pi = \frac74\pi+k\frac{\pi}2 \]
\( -9 \)
\( 9 \)
\( -18 \)
\( 18 \)
1003055104
Level:
B
The measures of given angles belong to the set \( M \):
\[ M = \left\{ 120^{\circ} + k\,360^{\circ}\right\},\ k\in\{-1;0;1\}.\]
Determine their arithmetic mean.
\( 120^{\circ} \)
\( 420^{\circ} \)
\( -120^{\circ} \)
\( -420^{\circ} \)
1003055105
Level:
B
The measurements of angles \( \theta \) form the set \( M \):
\[ M=\left\{\pi+k\frac23\pi\right\},\ k\in\{-2;-1;1;2\}.\]
Calculate their sum.
\( 4\pi \)
\( 0 \)
\( \frac23 \pi \)
\( -\frac23 \pi \)
1003055106
Level:
B
Given two angles \( \alpha= \frac{66}{15}\pi \) and \( \beta=\frac{*}{5}\pi \), which of the following numbers is to be substituted for \( * \) so that both angles take the same position on the unit circle?
\( 2 \)
\( 1 \)
\( 0 \)
\( 3 \)
1003055109
Level:
B
What is the maximum error that can be obtained by adding four angles, if the size of each of them is rounded to the nearest degree before the addition?
\( 2^{\circ} \)
\( 0^{\circ} \)
\( 3^{\circ} \)
\( 4^{\circ} \)
1003055110
Level:
B
How many times in \( 12 \) hours (from \( 0\!:\!00 \) to \( 11\!:\!59\!:\!59 \)) will the minute hand and the hour hand make an angle of \( 1 \) degree?
\( 22 \)
\( 11 \)
\( 12 \)
\( 24 \)
1003055201
Level:
B
In \( 12 \) hours (from \( 0\!:\!00 \) am to \( 11\!:\!59\!:\!59 \) am), how many times do the minute and the hour hand make an angle of \( 0 \) rad ?
\( 11 \)
\( 22 \)
\( 12 \)
\( 24 \)