B | math4u.vsb.cz

9000083610

Level:

Assuming $x\neq \pm y$ and $y\neq 2x$, simplify the expression: \[ \left ( \frac{2x} {x + y} + \frac{y} {x - y} - \frac{y^{2}} {x^{2} - y^{2}}\right ) : \left ( \frac{1} {x + y} + \frac{x} {x^{2} - y^{2}}\right ) \]

$x$

$2x - y$

$\frac{x} {2x-y}$

$1$

9000085302

Level:

There are $32$ students in the class ($20$ boys and $12$ girls). One quarter of the boys and one quarter of the girls are excellent students. Suppose that one boy and one girl, both excellent students, move to another school. Find the difference in the ratio of excellent students in the class before and after the change in the class.

$5\, \%$

$6.25\, \%$

$7.5\, \%$

$8.25\, \%$

9000080910

Level:

Find the set difference $A\setminus B$ for $A = \{x\in \mathbb{Z};\left |x\right | < 3\}$ and $B = \{x\in \mathbb{N};x < 5\}$.

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

$\emptyset $

$\{- 2;-1\}$

$\{3;4\}$

9000085303

Level:

The shop received $30$ pieces of TV from the manufacturer NoName. Five TVs in this delivery were defect. The shop also received TVs from the manufacturer GoodName. All these TVs were perfect. The final inspection revealed that $10\, \%$ of TVs were defect in total. Use these information to find out how many TVs have been supplied from the producer GoodName.

$20$

$25$

$18$

$16$

9000078905

Level:

A new laptop has been introduced to the marked with the original price $\$1\: 090$. Soon after the introduction the price has been increased temporarily by $20\, \%$ and after several months decreased by $30\, \%$. Find the final price for the laptop. Round your result to the nearest integer.

$\$916$

$\$981$

$\$952$

$\$930$

9000078508

Level:

Assuming $x\in (1;\infty )$, simplify the following expression. \[ 3x -|2x + 1| + |x - 1| \]

$2x - 2$

$4x - 2$

$2x + 2$

$2x$

9000078906

Level:

The price of a ship decreased in autumn by $16\, \%$ and in spring increased by $4\, \%$. This final price was $\$367\: 000$. Find the original price of the ship. (Round to the nearest thousand.)

$\$420\: 000$

$\$417\: 000$

$\$409\: 000$

$\$415\: 000$

9000079207

Level:

Assuming $x\not \in \{0;1;3\}$, simplify the following expression. \[ \frac{x^{2} - 9} {x^{2} - x}\cdot \left (\frac{x^{2} - 3x} {x - 1} \right )^{-1} \]

$\frac{x+3} {x^{2}} $

$\frac{x-3} {x^{2}} $

$\frac{x+3} {2x} $

$\frac{x+3} {x} $

9000078907

Level:

The unknown number $x$ has been increased by $20\, \%$ and then decreased by $5\, \%$. The final value was $513$. Find $x$. (Round to the closest integer.)

$450$

$446$

$430$

$436$

9000078901

Level:

If we increase an unknown number $x$ by $5\, \%$, we get $378$. Find $x$.

$360$

$359.1$

$396.9$

$350$

B

9000083610

9000085302

9000080910

9000085303

9000078905

9000078508

9000078906

9000079207

9000078907

9000078901

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