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1003162802

Level:

Find the solution set of the following inequality.

\log_{\frac{1}{2}} (x) \leq 1

[\frac{1}{2}; \infty)

(- \infty; \frac{1}{2}]

(0; \frac{1}{2}]

[1; \infty)

1003162801

Level:

Find the solution set of the following inequality.

\log_{0.3} (x) \geq \log_{0.3} 3

(0; 3]

(- \infty; 3]

[3; \infty)

[0; 3]

1003034502

Level:

Petr would like to buy a new smartphone. If he starts a temporary job at the electro shop he gets payed

120 CZK

per hour plus he gets

20 %

discount on the smartphone bough in the shop. He calculated that for

24

hours of work he would not earn even half of the phone price. Another employer pays

150 CZK

per hour. If Petr gets a temporary job with the other employer he is not eligible for the discount in the electro shop anymore, however he can buy the smartphone from e-shop for the price by

600 CZK

lower than in the electro shop and for

20

hours of work he earns more than one third of the electro shop smartphone price. Determine as closely as possible the smartphone price in the electronics shop.

greater than

7 200 CZK

and less than

9 600 CZK

greater than

7 200 CZK

and less than

10 800 CZK

greater than

4 800 CZK

and less than

9 600 CZK

greater than

4 800 CZK

and less than

10 800 CZK

1003034501

Level:

Two different aquarium fish shops have special price on Congo Tetra. The price is

42 CZK

for one fish. Further, the discount of

50 CZK

from a purchase over

300 CZK

is offered in shop A. In shop B a customer is given

5 %

discount of the price of any purchase. How many of Congo Tetra must one buy to make the total price in shop A lower than the total price in shop B?

greater than

7

and less than

24

less than

24

greater than

23

less than

7

1003187106

Level:

Consider expressions

| 3 x - 12 |

3 | x | + 12

| 3 x | - | - 12 |

3 | x - 4 |

. Which of the expressions has the greatest value if we substitute any

x

from the interval

(0; + \infty)

3 | x | + 12

| 3 x - 12 |

| 3 x | - | - 12 |

3 | x - 4 |

1003187103

Level:

Find the relation that does not hold for any

x

y \in R

| | x | - | y | | > | x + y |

| x y | = | x | | y |

| \frac{x}{y} | = \frac{| x |}{| y |}, y \neq 0 .

| (x y)^{2} | = | x y |^{2} = (x y)^{2}

1003187102

Level:

For

x

y \in R

consider

| x + y | = | x | + | y |

The equality holds if and only if the sign of

x

and

y

is the same.

The equality does not hold for any

x

and

y

The equality holds if and only if

x

and

y

are all positive.

The equality holds if and only if

x

and

y

are both nonpositive.

1003187101

Level:

Which of the following relations is correct for all

x

y \in R

| x + y | \leq | x | + | y |

| x + y | = | x | + | y |

| x - y | < | x | - | y |

| x - y | = | x | - | y |

1003032404

Level:

Simplifying the rational expression

\frac{x^{6} - y^{6}}{x^{2} - y^{2}}

we get:

(x^{2} - x y + y^{2}) (x^{2} + x y + y^{2})

x^{4} - y^{4}

x^{3} - y^{3}

(x^{2} - 2 x y + y^{2}) (x^{2} + 2 x y + y^{2})

1003032403

Level:

Reducing the rational expression

\frac{4 m^{2} - 4 m n + n^{2}}{8 m^{3} - n^{3}}

we get:

\frac{2 m - n}{4 m^{2} + 2 m n + n^{2}}

\frac{m - 4 m n + 1}{2 m - n}

\frac{2 m - n}{4 m^{2} - 4 m n + n^{2}}

\frac{2 m - n}{4 m^{2} + 4 m n + n^{2}}

C

1003162802

1003162801

1003034502

1003034501

1003187106

1003187103

1003187102

1003187101

1003032404

1003032403

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