B | math4u.vsb.cz

9000085310

Level:

The pad in the form of (not necessarily regular) octagon is manufactured from a square. The side of the square is $4\, \mathrm{cm}$. An isosceles right triangle of the hypotenuse $1\, \mathrm{cm}$ is removed from each corner of the square which results in the desired octagon. How much of the material of the initial square goes to the waste?

$12.5\, \%$

$10\, \%$

$15\, \%$

$20\, \%$

9000086608

Level:

Determine the truth values of statements $a$ and $b$ if you know that the compound statement \[ \neg a \iff (a \wedge b) \] is true.

The statement $a$ is true, $b$ is false.

Both statements are true.

The statement $a$ is false, $b$ is true.

Both statements are false.

9000086610

Level:

Let statements $a$ and $b$ be false while $c$ is a true statement. Find the false statement.

$a \iff (b \vee c)$

$(\neg a \vee b) \vee c$

$(a \wedge b) \vee c$

$(a \vee b)\implies \neg c$

9000088801

Level:

Find the domain of the following expression. \[ \frac{2x + 1} {6x^{2} + 3x} \]

$\mathbb{R}\setminus\left\{0,-\frac{1}{2}\right\}$

$\mathbb{R}\setminus\{0,- 2\}$

$\mathbb{R}\setminus\{0\}$

$\mathbb{R}\setminus\left\{0,\frac{1}{2}\right\}$

9000088802

Level:

Find the domain of the following expression. \[ \frac{a} {a^{2} + 9}\cdot \frac{a^{2} - 9} {a^{2} + 3a} \]

$\mathbb{R}\setminus\{0,- 3\}$

$\mathbb{R}\setminus\{3,- 3\}$

$\mathbb{R}\setminus\{0,3\}$

$\mathbb{R}\setminus\{- 3\}$

9000088806

Level:

Identify a correct expression which should be placed to the starred position in the following expression to obtain a valid statement. \[ \frac{mn} {m^{2} + 2mn + n^{2}} = \frac{*} {2m(m + n)^{3}} \]

$2m^{2}n(m + n)$

$2mn(m + n)$

$2m(m + n)$

$2m(m + n)^{2}$

9000085307

Level:

A machine fills $2\: 000$ bottles per hour. As a consequence of technical problems, the efficiency of the machine decreased by $10\, \%$. How many bottles can be filled by the machine with the mentioned technical problems during a time period of $8$ hours?

$14\: 400$

$13\: 800$

$14\: 500$

$15\: 200$

9000083601

Level:

Find the conditions on $x$ under which the expression \[ \frac{\frac{x-y} {x+y} -\frac{x+y} {x-y}} { \frac{xy} {x^{2}-y^{2}} } \] is well-defined.

$x\neq 0,\, y\neq 0,\, x\neq \pm y$

$x\neq - y$

$x\neq \pm y$

$x\neq 0,\, y\neq 0$

9000085301

Level:

A bike was introduced to the market with the initial price $\$10\: 000$ in April. As a consequence of bad sales values, the price has been decreased by $20\, \%$ in June and by another $20\, \%$ in September. Find the price in September.

$\$6\: 400$

$\$6\: 000$

$\$6\: 125$

$\$6\: 500$

9000085305

Level:

The price for the first issue of the book was $\$100$, the price for the second issue $\$125$. Find the rate of sale of the second issue if the target price for the second issue is the same as for the first issue.

$20\, \%$

$22.5\, \%$

$17.5\, \%$

$25\, \%$

B

9000085310

9000086608

9000086610

9000088801

9000088802

9000088806

9000085307

9000083601

9000085301

9000085305

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