B

9000146208

Level: 
B
Factor the following expression. \[ \left (2x - 1\right )^{2} -\left (x + 3\right )^{2} \]
\(\left (x - 4\right )\left (3x + 2\right )\)
\(\left (x - 4\right )\left (3x - 2\right )\)
\(\left (x + 4\right )\left (3x + 2\right )\)
\(\left (x + 4\right )\left (3x - 2\right )\)

9000146202

Level: 
B
Expand the following expression. \[ \left (a^{2} + \sqrt{3}b\right )^{3} \]
\(a^{6} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{6} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)

9000141501

Level: 
B
Let \(A\) be set with \(n\) mutually different elements. If \(n\) is increased by \(2\), then number of \(3\)-permutations is increased by \(384\). Find \(n\). (The term „\(k\)-permutation” stands for an ordered arrangement of \(k\) objects from a set of \(n\) objects.)
\(8\)
\(64\)
\(32\)

9000142001

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-1;0)\) and \((1;\infty )\), concave down on \((-\infty ;-1)\) and \((0;1)\), inflection at \(x = 0\)
concave up on \((-\infty ;-1)\) and \((0;1)\), concave down on \((-1;0)\) and \((1;\infty )\), inflection at \(x = 0\)
concave up on \((-1;0)\) and \((1;\infty )\), concave down on \((-\infty ;-1)\) and \((0;1)\), no inflection
concave up on \((-1;0)\cup (1;\infty )\), concave down on \((-\infty ;-1)\cup (0;1)\), inflection at \(x = 0\)

9000138309

Level: 
B
Two dices are rolled. Find the probability that we get either the same number on both dices or the sum of the numbers on both dices is \(6\).
\(\frac{10} {36}\doteq 0{.}2778\)
\(\frac{11} {36}\doteq 0{.}3056\)
\(\frac{6} {36}\doteq 0{.}1667\)
\(\frac{5} {36}\doteq 0{.}1389\)