2010016902
Level:
B
Two dice are rolled. Find the probability that we get the number \(5\) at least once.
\(\frac{11}
{36}\doteq 0.3056\)
\(\frac{25}
{36}\doteq 0.6944\)
\(\frac{12}
{36}\doteq 0.3333\)
\(\frac{10}
{36}\doteq 0.2778\)
B
2010016901
Level:
B
Two different dice (a white die and a black die) are rolled. Find the probability that we get the number
\(4\) on the white die and a number different from \(4\) on the black die.
\(\frac{5}
{36}\doteq 0.1389\)
\(\frac{4}
{36}\doteq 0.1111\)
\(\frac{1}
{6}+\frac56\,=\,1\)
\(\frac{5}
{6}\doteq 0.8333\)
2010016804
Level:
B
How many \( x \)-intercepts has the graph of the function \( f(x)=\sin 2x \) on the interval \( [ -\pi; 2\pi ] \)?
\( 7\)
\( 5\)
\( 8\)
\( 6\)
2010016803
Level:
B
The value of \( \cos\left(-\frac{28\pi}3\right) \) is the same as the value of
\( \cos\frac{4\pi}3 \).
\( \cos\frac{\pi}3 \).
\( \cos\left(-\frac{7\pi}3\right) \).
\( \cos\frac{5\pi}3 \).
2010016802
Level:
B
Choose the true statement:
\( \sin 240^{\circ} < \sin 120^{\circ} \)
\( \cos50^{\circ} < \cos130^{\circ} \)
\( \sin 300^{\circ} < \sin 270^{\circ} \)
\( \cos330^{\circ} < \cos150^{\circ} \)
2010016801
Level:
B
To which quadrant does the angle \( \varphi \) belong if \( \cos\varphi=0.8 \) and \( \sin\varphi < 0 \)?
IV.
I.
II.
III.
2110016704
Level:
B
The triangle \( ABC \) is translated by the vector \( \vec{u} \) (see the picture). Which of the following pictures shows correctly the image \( A'B'C' \) of the triangle \( ABC \) in the given translation?
2110016703
Level:
B
Let a rectangle \( ABCD \) be translated by vector \( \overrightarrow{AS} \), where \( S \) is the center of the rectangle. Which of the following pictures shows correctly the image \( A'B'C'D' \) of the rectangle \( ABCD \) in described translation?
2110016702
Level:
B
An equilateral triangle \( ABC \) rotates \( 90^{\circ} \) clockwise about the point \( O(4;2) \). Which of the pictures shows the triangle \( A'B'C' \) that is the image of the rotated triangle \( ABC \)?
2110016701
Level:
B
Let \(ABCD\) be a rectangle where \(|AB|=2|BC|\) and let \(S\) be a point on the perpendicular bisector of the side \(BC\) such that its distance from \(BC\) is \(\frac12|BC|\) (see the picture). The rectangle \(ABCD\) rotates \(90^{\circ}\) clockwise about \(S\). Which of the pictures shows the rectangle \(A'B'C'D'\) that is the image of rotated rectangle \(ABCD\)?
