B | math4u.vsb.cz

9000068701

Level:

Identify the real number $x$ which converts the numbers $a_{1} = 10^{2}$, $a_{2} = 10^{3}$ and $a_{3} = x$ into three consecutive numbers of a geometric series.

$x = 10\: 000$

$x = 1\: 000$

$x = 1\: 900$

$x = 1\: 990$

$x = 100\: 000$

9000068702

Level:

Identify the real number $x$ which converts the numbers $a_{1} = -12$, $a_{2} = x$ and $a_{3} = -48$ into three consecutive numbers of a geometric series.

$x = -24$

$x = 0$

$x = 6$

$x = 12$

$x = -2$

9000068703

Level:

Identify the real number $x$ which converts the numbers $a_{1} = -x$, $a_{2} = -5$ and $a_{3} = 5$ into three consecutive numbers of a geometric series.

$x = -5$

$x = 0$

$x = 5$

$x = -10$

$x = 10$

9000065904

Level:

Evaluate the following integral on the interval $(0;+\infty)$. \[ \int \frac{x^{3} + 2x} {x^{2}} \, \text{d}x \]

$\frac{1} {2}x^{2} + 2\ln |x| + c,\ c\in \mathbb{R}$

$x +\ln |x| + c,\ c\in \mathbb{R}$

$\frac{1} {4}x^{4} + 4x^{2} +\ln |x^{2}| + c,\ c\in \mathbb{R}$

$2x^{2} + 2 +\ln |x^{2}| + c,\ c\in \mathbb{R}$

9000066002

Level:

Evaluate the following integral on $\mathbb{R}$. \[ \int x\sin x\, \mathrm{d}x \]

$- x\cos x +\sin x + c,\ c\in \mathbb{R}$

$- x\cos x -\sin x + c,\ c\in \mathbb{R}$

$x\cos x +\sin x + c,\ c\in \mathbb{R}$

$x\cos x -\sin x + c,\ c\in \mathbb{R}$

9000066008

Level:

Evaluate the following integral on $\mathbb{R}$. \[ \int x\mathrm{e}^{x}\, \mathrm{d}x \]

$x\mathrm{e}^{x} -\mathrm{e}^{x} + c,\ c\in \mathbb{R}$

$x^{2}\mathrm{e}^{x} - 2x\mathrm{e}^{x} + 2\mathrm{e}^{x} + c,\ c\in \mathbb{R}$

$2x^{3}\mathrm{e}^{x} - x\mathrm{e}^{x} + c,\ c\in \mathbb{R}$

$\frac{1} {2}x^{2}\mathrm{e}^{x} + c,\ c\in \mathbb{R}$

9000065901

Level:

Evaluate the following integral on the interval $(-1;+\infty)$. \[ \int \frac{1} {x + 1}\, \text{d}x \]

$\ln |x + 1| + c,\ c\in \mathbb{R}$

$\ln |x| + c,\ c\in \mathbb{R}$

$\frac{1} {x} + c,\ c\in \mathbb{R}$

$-\frac{1} {2}(x + 1)^{-2} + c,\ c\in \mathbb{R}$

9000068708

Level:

Identify the real number $x$ which converts the numbers $a_{1} = 2^{x-4}$, $a_{2} = 1$ and $a_{3} = 2^{x}$ into three consecutive terms of a geometric series.

$x = 2$

$x = 1$

$x =\log 2$

$x = 10$

$x = 100$

9000065307

Level:

In the arithmetic sequence given by the first term $a_{1} = 4$ and the common difference $d = 2$ find the sum of the first twelve terms of the sequence.

$s_{12} = 180$

$s_{12} = 72$

$s_{12} = 120$

$s_{12} = 168$

9000065308

Level:

For the arithmetic sequence with the first term $a_1=3$ holds $a_n=27$ and the sum of the first $n$ terms is $195$. Find $n$.

$n = 13$

$n = 14$

$n = 15$

$n = 16$

B

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