B

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 \(x = 0\)

9000142002

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ,1)\), concave down on \((1,\infty )\), inflection at \(x = 1\)
concave up on \((1,\infty )\), concave down on \((-\infty ,1)\), inflection at \(x = 1\)
concave up on \((-\infty ,0)\), concave down on \((0,\infty )\), inflection at \(x = 0\)
concave up on \((-\infty ,1)\), concave down on \((1,\infty )\), inflection at \(x = \frac{2} {3}\)

9000141508

Level: 
B
Assuming \(x\in \mathbb{N}\), find the solution set of the following equation. \[ \left({x\above 0.0pt x}\right) +\left ({x + 1\above 0.0pt x} \right) +\left ({x + 2\above 0.0pt x} \right) +\left ({x + 3\above 0.0pt x} \right) = \frac{x^{3} + 59} {6} \]
\(\{1\}\)
\(\{4\}\)
\(\{10\}\)

9000142003

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ,0)\) and \((1,\infty )\), concave down on \((0,1)\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((-\infty ,0)\cup (1,\infty )\), concave down on \((0,1)\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((0,1)\), concave down on \((-\infty ,0)\) and \((1,\infty )\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((-\infty ,0)\) and \((1,\infty )\), concave down on \((0,1)\), a unique inflection at \(x = 0\)

9000141502

Level: 
B
Let \(A\) be set with \(n\) mutually different elements. The number of \(5\)-permutations with repetition is \(1024\). Find \(n\). (The term „\(k\)-permutation with repetition” stands for an ordered arrangement of \(k\) objects from a set of \(n\) objects, when each object can be chosen more than once.)
\(4\)
\(5\)
\(2\)

9000142004

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

9000142005

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 \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)
concave up on \((-1,0)\cup (1,\infty )\), concave down on \((-\infty ,-1)\cup (0,1)\), inflection at \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)
concave up on \((-\infty ,-1)\) and \((0,1)\), concave down on \((-1,0)\) and \((1,\infty )\), inflection at \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)
concave up on \((-\infty ,-1)\cup (0,1)\), concave down on \((-1,0)\cup (1,\infty )\), inflection at \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)