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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. \[ \frac{3 - 2x} {x - 2} = \frac{3(4x^{2} - 12x + 9)} {*} \]

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

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

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

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

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.

$20\, \%$

$22.5\, \%$

$17.5\, \%$

$25\, \%$

9000080907

Level:

Find $B'_{A}$ (the complement to $B$ in $A$) for $A =\mathbb{Z}$ and $B = \{x\in \mathbb{Z};\left |x\right | > 3\}$.

$\{ - 3;-2;-1;0;1;2;3\}$

$\{ - 2;-1;0;1;2\}$

$\{0;1;2;3\}$

$\{1;2;3\}$

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9000088808

9000085308

9000086606

9000085605

9000086609

9000085606

9000088807

9000085301

9000085305

9000080907

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