Rational functions

1003108601

Level:

Peter drove from Ostrava to Warsaw. He drove at an average speed of

104

kilometres per hour and reached Warsaw in

4

hours. Select the function that describes the dependence of Peter’s driving time

t

on the average speed

v

of the car. (The driving time

t

is given in hours and the average speed

v

is given in kilometres per hour.)

t = \frac{416}{v}, v \in (0; \infty)

t = \frac{26}{v}, v \in (0; \infty)

t = \frac{v}{26}, v \in (0; \infty)

t = \frac{104}{v}, v \in (0; \infty)

1003108603

Level:

The fuel consumption of Skoda Fabia

1.4

MPi/

44 kW

stated by the manufacturer varies between

5.5 l

100 km

(out of a town) to

9.6 l

100 km

(in a town). Suppose the car’s fuel tank of capacity

45 l

is filled completely. Choose the function describing relation between the distance

p

km

that the car can travel without tanking on the fuel consumption

s

f : p = \frac{4 500}{s}; s \in [5.5; 9.6]

h : p = \frac{45}{s}; s \in [5.5; 9.6]

r : p = \frac{s}{0.45}; s \in [5.5; 9.6]

g : p = 45 \cdot s; s \in [5.5; 9.6]

1003109501

Level:

Let

f (x) = - \frac{1}{2 x}

. Find the false statement.

The function

f

is increasing.

The range of

f

(- \infty; 0) \cup (0; \infty)

The function

f

is odd.

The function

f

is not bounded.

1003109502

Level:

Let

f (x) = - \frac{2}{x}, x \in [- 2; 0) \cup (0; \infty)

. Find the true statement.

The function

f

is injective (one-to-one).

The function

f

has minimum at

x = - 2

The range of

f

[0; 1)

The function

f

is odd.

1103108602

Level:

In a simple electric circuit a voltage source and a variable resistor with resistance

R

in the range

[1 Ω; 10 Ω]

are connected. Suppose the source gives fixed voltage of

5 V

. From the graphs given below select the one that describes the dependence of the electric current

I

on the resistance

R

in this circuit. (Note: The relationship between electric currant, voltage and resistance is described by Ohm’s law:

U = R I

1103108604

Level:

The hall’s floor needs a new tiling. All tiles used will be of the same size. The picture shows the graph of the function describing dependence of the number

p

of tiles needed in the hall on the area

S

of one tile. What is the area of the hall’s floor?

10.5 m^{2}

1 050 m^{2}

2 100 m^{2}

42 m^{2}

1103124503

Level:

The picture shows graphs of functions:

\begin{aligned} f (x) & = \frac{2}{x}, x \in [\frac{1}{2}; 4], \\ g (x) & = \frac{- 3}{x}, x \in [\frac{1}{2}; 4], \\ h (x) & = \frac{4}{x}, x \in [\frac{1}{2}; 4] . \end{aligned}

Choose the correct statement.

The function

f

is graphed in blue and the function

h

is graphed in green.

The function

g

is graphed in red and the function

f

is graphed in green.

The function

f

is graphed in green and the function

h

is graphed in blue.

The function

g

is graphed in green and the function

f

is graphed in blue.

2000003701

Level:

Group of mountaineers would climb the top of the mountain at an ascent speed of

400 m

per day in

10

days. However, due to the weather, they have to conquer the peak in

8

days. How many more meters per day do they have to cover?

100

meters more

80

meters more

120

meters more

90

meters more

2000003702

Level:

Four workers assembled a garden pool in

5

hours. How long would it take eight workers to do the same job?

2 h 30 \min

2 h 40 \min

2 h 20 \min

2 h 45 \min

2000003703

Level:

The pool is filled with eight equally powerful pumps in

6

hours. During the maintenance of some of the pumps, it took

24

hours to fill the pool. How many pumps were running?

2

pumps

3

pumps

4

pumps

6

pumps

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