B | math4u.vsb.cz

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. \[ \frac{mn} {m^{2} + 2mn + n^{2}} = \frac{*} {2m(m + n)^{3}} \]

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

$2mn(m + n)$

$2m(m + n)$

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

9000088808

Level:

Find the common denominator of the following three fractions. \[ \text{$ \frac{a} {a^{2}-ab}\ ,\qquad \frac{-b} {a^{2}-b^{2}} \ ,\qquad \frac{2b} {ab+b^{2}} $} \]

$ab(a^{2} - b^{2})$

$ab(a - b)$

$ab(a + b)$

$ab(a + b)^{2}$

9000085308

Level:

The number $\frac{1} {2} + \frac{1} {3}$ is bigger than $\frac{1} {2} -\frac{1} {3}$. Express the difference between these numbers in percents of the smaller quantity.

$400\, \%$

$500\, \%$

$300\, \%$

$600\, \%$

9000086606

Level:

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

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

Both statements are true.

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

Both statements are false.

9000085605

Level:

Find the product of all one-digit primes and round to nearest hundreds.

$200$

$100$

$300$

$400$

9000086609

Level:

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

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

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

$(a \wedge b) \vee c$

$a \iff (b \vee c)$

B

9000086608

9000086610

9000088801

9000088802

9000088806

9000088808

9000085308

9000086606

9000085605

9000086609

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