C

1003049204

Level: 
C
Let \( f(x)=|x| \). Identify which of the statements is false.
\( \forall a\text{, }b\in\mathbb{R}\colon f(a+b)=f(a)+f(b) \)
\( \forall a\text{, }b\in\mathbb{R}\colon f(a\cdot b)=f(a)\cdot f(b) \)
\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon f(\frac ab)=\frac{f(a)}{f(b)} \)
\( \forall a\in\mathbb{R}\colon f(a)=f(-a) \)

1003049203

Level: 
C
Identify which of the statements is false.
\( \forall a\text{, }b\in\mathbb{R}\colon |a+b|=|a|+|b| \)
\( \forall a\text{, }b\in\mathbb{R}\colon |a\cdot b|=|a|\cdot|b| \)
\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon|\frac ab|=\frac{|a|}{|b|} \)
\( a\in\mathbb{R}\colon |a|=|-a| \)

1003028402

Level: 
C
Let \( f(x)=\frac{2x-4}{x^2-4} \). Which of the statements about the domain and the range of the function \( f \) is true?
\( -2\notin D(f) \wedge -2\in H(f) \)
\( -2\in D(f) \wedge -2\notin H(f) \)
\( -2\in D(f) \wedge -2\in H(f) \)
\( -2\notin D(f) \wedge -2\notin H(f) \)

1003055509

Level: 
C
Mr. Nowak deposited \( 2000 \) zlotys into his savings account at an annual interest rate of \( 4.5\% \), compounded annually. At the end of the year, the \( 19\% \) tax of the interest was deducted. What was the amount of the money deducted?
\( 17.10 \) zlotys
\( 19 \) zlotys
\( 38 \) zlotys
\( 85.50 \) zlotys

1103055010

Level: 
C
In the regular hexagon \( ABCDEF \), \( G \) and \( H \) are the midpoints of \( AB \) and \( CD \). What part of the area of the hexagon is covered by the area of the quadrilateral \( BCHG \)? The area of the quadrilateral corresponds to the shaded region in the figure.
\( \frac5{24} \)
\( \frac15 \)
\( \frac1{28} \)
\( \frac5{36} \)

1103055001

Level: 
C
The picture shows an intersection of two streets. Two water carts passed the intersection while sprinkling entire surface of the street. Each of the carts continued along the street it came. Determine how many square meters of the streets surface were sprinkled twice?
\( 96\,\mathrm{m}^2 \)
\( 48\,\mathrm{m}^2 \)
\( 124\,\mathrm{m}^2 \)
\( 140\,\mathrm{m}^2 \)

1003031104

Level: 
C
Dan and Jane took a bike trip. Dan rode for \( 3 \) hours at constant speed. Jane rode for half an hour longer at the speed of \( 4\,\mathrm{kph} \) less than Dan’s speed. Identify, which of the following statements about Dan’s speed is true.
The speed is less than \( 28\,\mathrm{kph} \).
The speed is greater than \( 28\,\mathrm{kph} \).
The speed is less than \( 20\,\mathrm{kph} \).
The speed is greater than \( 24\,\mathrm{kph} \).

1003031103

Level: 
C
Five litres of a quality wine in by yourself provided bottles cost more than three and a half litres of the same wine in a bigger wine container. The container price is \( 150\,\mathrm{CZK} \). Complete the next statement so that it is true. The price of one litre of this quality wine is
greater than \( 100\,\mathrm{CZK} \).
less than \( 100\,\mathrm{CZK} \).
greater than \( 350\,\mathrm{CZK} \).
greater than \( 500\,\mathrm{CZK} \).