B

9000108807

Level: 
B
Find the angle between the median \(t_{c}\) and side \(c\) in the triangle \(ABC\) for \(A = [1,2]\), \(B = [7,-2]\) and \(C = [6,1]\). Round to the nearest degree. Hint: In geometry, the median \(t_{c}\) of the triangle \(ABC\) is the line segment joining the vertex \(C\) to the midpoint of the opposing side.
\(60^{\circ }\)
\(50^{\circ }\)
\(43^{\circ }\)
\(71^{\circ }\)

9000115602

Level: 
B
Complete the following statement: „The number is divisible by three if and only if ...”
the sum of its digits is divisible by three.
the number constituted from the last two digits is divisible by three.
the sum of its digits is odd.
the last digit of this number is \(3,\ 6\) or \(9\).

9000108808

Level: 
B
Find the angle between the altitude \(v_{c}\) and side \(b\) in the triangle \(ABC\) for \(A = [1,2]\), \(B = [7,-2]\) and \(C = [6,1]\). Round to the nearest degree. Hint: In geometry, the altitude \(v_{c}\) of the triangle \(ABC\) is the line segment through the vertex \(C\) and perpendicular to the line containing the opposite side of the triangle.
\(68^{\circ }\)
\(75^{\circ }\)
\(44^{\circ }\)
\(61^{\circ }\)

9000115603

Level: 
B
Complete the following statement: „The number is divisible by four if and only if ...”
the number constituted from the last two digits is divisible by four.
the sum of its digits is divisible by four.
the last digit of this number is \(4\).
the last digit of this number is even.

9000107505

Level: 
B
Find \(\cos \varphi \) where \(\varphi \) is the angle between the lines \(p\) and \(q\). \[ \begin{aligned}[t] p\colon x& = 1 + 4t, & \\y & = 3 - 3t,\ t\in \mathbb{R}, \\ \end{aligned} \quad q\colon x + y - 3 = 0 \]
\(\frac{7\sqrt{2}} {10} \)
\(- \frac{7} {5\sqrt{2}}\)
\(\frac{\sqrt{2}} {5} \)
\(\frac{\sqrt{2}} {10} \)

9000108701

Level: 
B
Find all vectors which are perpendicular to the vector \(\vec{u} = (3,4)\) and have the length equal to \(1\).
\(\left (\frac{4} {5},-\frac{3} {5}\right )\), \(\left (-\frac{4} {5}, \frac{3} {5}\right )\)
\(\left (\frac{4} {7},-\frac{3} {7}\right )\), \(\left (-\frac{4} {7}, \frac{3} {7}\right )\)
\(\left ( \frac{1} {\sqrt{10}},- \frac{3} {\sqrt{10}}\right )\), \(\left (- \frac{1} {\sqrt{10}}, \frac{3} {\sqrt{10}}\right )\)
\(\left (\frac{4} {5}, \frac{3} {5}\right )\), \(\left (-\frac{4} {5},-\frac{3} {5}\right )\)