C

9000104809

Level: 
C
Among the following lines (which all pass through the point \([-1;3]\)) identify a line which is tangent to the following hyperbola. \[ (x + 2)\cdot (y - 2) = 1 \]
\(k\colon \ y = -x + 2\)
\(p\colon \ y = 3\)
\(q\colon \ x = -1\)
\(r\colon \ y = x + 4\)
None of the given answers is correct.

9000101708

Level: 
C
Factor the following polynomial. \[ 8x^{3} - 27 \]
\(\left (2x - 3\right )\left (4x^{2} + 6x + 9\right )\)
\(\left (2x - 3\right )\left (4x^{2} - 6x + 9\right )\)
\(\left (2x + 9\right )\left (4x^{2} - 6x + 9\right )\)
\(\left (2x - 3\right )\left (4x^{2} + 6x - 9\right )\)

9000101709

Level: 
C
Factor the following polynomial. \[ 27x^{6}z - 8y^{3}z \]
\(z\left (3x^{2} - 2y\right )\left (9x^{4} + 6x^{2}y + 4y^{2}\right )\)
\(z\left (3x^{2} + 2y\right )\left (9x^{4} + 6x^{2}y - 4y^{2}\right )\)
\(z\left (3x^{2} + 2y\right )\left (9x^{4} - 6x^{2}y + 4y^{2}\right )\)
\(z\left (3x^{2} - 2y\right )\left (9x^{4} + 6x^{2}y^{2} + 4y\right )\)

9000101707

Level: 
C
Factor the following polynomial. \[ x^{6} - 1 \]
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + x + 1\right )\left (x^{2} - x + 1\right )\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + x + 1\right )\left (x^{2} - x - 1\right )\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + 2x + 1\right )\left (x^{2} - 2x + 1\right )\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + x - 1\right )\left (x^{2} - x + 1\right )\)

9000089007

Level: 
C
A class in the school has \(35\) students. On the last holiday the students visited Slovakia, Croatia and Bulgaria. From the total amount of \(35\), \(7\) students have been in Slovakia, \(7\) students have been in Croatia, \(5\) students have been in Bulgaria, \(21\) students have not been abroad, one student was in every of these countries, two students have been in both Bulgaria and Croatia but not in Slovakia, one student has been in both Bulgaria and Slovakia but not in Croatia. How many students visited either Slovakia or Croatia?
\(11\)
\(7\)
\(3\)

9000089003

Level: 
C
Students from a class bought a snack in the school lunch-room. There were \(31\) students in the class in total. Altogether \(8\) students had snack from their home and they did not buy anything. Altogether \(12\) students bought hamburger and \(15\) students bought hot-dog. How many students bought both hamburger and hot-dog?
\(4\)
\(19\)
\(8\)

9000090906

Level: 
C
Given lines \(p\) and \(q\), find \(m\in \mathbb{R}\) such that the lines \(p\) and \(q\) are parallel. \[ \begin{aligned}p\colon x& = 1 + t, & \\y & = -3t;\ t\in \mathbb{R}, \\ \end{aligned}\qquad \begin{aligned}q\colon x& = 3 - 2u, & \\y & = 1 + mu;\ u\in \mathbb{R} \\ \end{aligned} \]
\(m = 6\)
\(m = \frac{3} {2}\)
\(m = -\frac{2} {3}\)
does not exist