B | math4u.vsb.cz

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.

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

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

$(a \wedge b) \vee c$

$a \iff (b \vee c)$

9000085606

Level:

Find the product of all divisors of $12$ and round to nearest hundreds.

$1\: 700$

$1\: 200$

$600$

$100$

Suppose we are given the following equality of two fractions with nonzero denominators. From the given expressions, choose the one that by substituting to the starred position makes the equality true. \[ \frac{3 - 2x} {x - 2} = \frac{3(4x^{2} - 12x + 9)} {*} \]

$(3x - 6)(3 - 2x)$

$(x - 2)(2x - 3)$

$(x - 2)(9 - 4x)$

$(3x - 6)(2x - 3)$

9000086601

Level:

Determine the truth values of propositions $a$ and $b$ if you know that the compound proposition \[ \neg (a \vee b) \] is true.

Both statements are false.

Both statements are true.

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

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

B

9000088802

9000088806

9000088808

9000085308

9000086606

9000085605

9000086609

9000085606

9000088807

9000086601

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