B | math4u.vsb.cz

9000142004

Level:

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

9000141503

Level:

Let $A$ be a set with $n$ mutually different elements. If two elements are removed from $A$, the number of all permutations of set $A$ decreases $20$-times. Find $n$.

$5$

$4$

$5$ or $- 4$

9000142005

Level:

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 $x_{3} = 1$

9000141504

Level:

Let $A$ be a set with $n$ mutually different elements. If we add one element to the set $A$, the number of $3$-combinations of a set $A$ is increased by $21$. Find $n$.

$7$

$6$

$43$

9000142006

Level:

Identify a correct statement related to the function $f$ shown in the picture.

concave up on $(-\infty ,0)$ and $(1,\infty )$, concave down on $(0,1)$, a unique inflection at $x = 0$

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 $(0,1)$, a unique inflection at $x = 0$

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

9000146207

Level:

Factor the following expression. \[ 4a^{2} -\left (a - 1\right )^{2} \]

$\left (a + 1\right )\left (3a - 1\right )$

$\left (a - 1\right )\left (3a - 1\right )$

$\left (a + 1\right )\left (3a + 1\right )$

$\left (a - 1\right )\left (3a + 1\right )$

9000140506

Level:

Simplify $\frac{2!} {1!} + \frac{3!} {2!} + \frac{4!} {3!}$.

$9$

$\frac{29} {6} $

$\frac{9} {6}$

$\frac{12!+9!+8!} {6!} $

9000140507

Level:

Simplify for $n\in \mathbb{N}$. \[ \frac{(n + 2)!} {n! + (n + 1)!} \]

$n + 1$

$\frac{n!+2} {2n!+1}$

$\frac{n+2} {2n+1}$

$\frac{n!+2!} {2n!+1!}$

9000140508

Level:

Simplify for $n\in \mathbb{N}$. \[ \frac{(n + 1)!} {n! - (n + 1)!} \]

$- 1 - \frac{1} {n}$

$n + 1$

$n! + 1$

$- \frac{n+1} {(n-1)!}$

9000140502

Level:

Simplify for $n\in \mathbb{N}$. \[ \frac{(n + 1)!} {(n - 1)!} \]

$n^{2} + n$

$(n + 1)^{2}$

$\frac{n+1} {n-1}$

$- 1$

B

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