2000005509
Level:
A
Calculate the area of a rhombus whose perimeter is \(2\,\mathrm{m}\) and lengths of its diagonals are in the ratio \(3:4\).
\(2\,400\,\mathrm{cm}^2\)
\(1\,800\,\mathrm{cm}^2\)
\(3\,600\,\mathrm{cm}^2\)
\(2\,000\,\mathrm{cm}^2\)
A
2000005506
Level:
A
The picture shows a triangle \(ABC\) with a central transversal \(EF\). The area of the trapezoid \(ABFE\) is \(24\,\mathrm{cm}^2\). What is the area of the triangle \(EFC\)?
\(8\,\mathrm{cm}^2\)
\(4\,\mathrm{cm}^2\)
\(16\,\mathrm{cm}^2\)
\(12\,\mathrm{cm}^2\)
2000005505
Level:
A
What is the perimeter of the rhombus \(ABCD\), if \(|BD|=8\,\mathrm{cm}\) and \(|\measuredangle DAB|=60^{\circ}\) (see the picture)?
\(32\,\mathrm{cm}\)
\(16\,\mathrm{cm}\)
\(28\,\mathrm{cm}\)
\(36\,\mathrm{cm}\)
2000005503
Level:
A
The diagonals of a quadrilateral \(ABCD\) are halved and perpendicular to each other. What type of quadrilateral is it?
square or rhombus
rhombus
square
rectangle or square
2000005501
Level:
A
Derive the formula for the area of a square using the length of its diagonal \(u\).
\( \frac{u^2}{2}\)
\( 4u^2\)
\( \frac{u^2}{4}\)
\( 2u^2\)
2000005301
Level:
A
In real numbers, find the solution set of the following equation.
\[\frac{x^2+1}{x^2-9}=0\]
\( \emptyset \)
\( \pm 1\)
\( \pm 3\)
\( -1\)
2000005108
Level:
A
Which of the following statements about the function \(f\) is correct? (See the picture.)
The function is one-to-one.
\(D(f)=(-4;\infty)\) and the function is bounded below.
The function has a local maximum.
The function is odd.
2000005107
Level:
A
Which of the following statements about the function \(f\) is correct? (See the picture.)
The function is bounded below.
\( H(f)=(-2;2) \)
The function is even.
The function is increasing on the interval \( (2;\infty)\).
2000005106
Level:
A
Which of the following statements is not valid for the function \(f\)? (See the picture.)
The function is one-to-one.
The function is bounded below.
\(f(-1) =2\).
The value \(-2\) doesn’t belong to the range of \(f\).
2100005105
Level:
A
The pictures show graphs of different functions \(f\). For which of the graphed functions is \(D(f) = \{2;3;4;5;6\}\)?
