2010011701
Level:
A
How many natural numbers belong to the solution set of the inequality \( |3x-7| < 5 \)?
\(3\)
\(4\)
\(2\)
\(1\)
A
2010011407
Level:
A
Find the area of the region bounded by the curves
\(y = x+1\) and
\(y = -x^{2} + 3\).
\( \frac{9}2\)
\(2\)
\(6\)
\( \frac{21}2\)
2010011406
Level:
A
Find the area of the region bounded by the graph of
\(f(x)=\sin x-1\) on
\(\left [ \frac{\pi }{2};\pi \right ] \) and
lines \(y = 0\)
and \(x =\pi \).
\( \frac{\pi}2-1\)
\( \frac{\pi}2\)
\(1\)
\( \frac{3\pi}2-1\)
2010011405
Level:
A
Find the area of the region bounded by
\(x\)-axis,
graph of \(f(x)= x^{2} + 5\)
and lines \(x = -1\)
and \(x = 2\).
\( 18\)
\(24\)
\(13\)
\( \frac{52}3\)
2010011404
Level:
A
Find the area of the triangle $ABC$ highlighted in yellow (see the picture).
\( 16\)
\(12\)
\(8\)
\( 20\)
2010011403
Level:
A
Find the area of the yellow region indicated in the picture.
\( 2\sqrt{2}\)
\( 2\sqrt{3}\)
\( \sqrt{2}\)
\( 4\sqrt{2}\)
2010011402
Level:
A
Find the area of the yellow triangle $ABC$ indicated in the picture. Read all the needed values from the picture.
\( 10.5\)
\( 36.75\)
\( 10\)
\(15.75\)
2010011401
Level:
A
Calculate the area of a plane region bounded by the graphs of the functions $f(x)=x^2-2x+2$ and $g(x)=14-x^2$.
\( \frac{125}3\)
\( \frac{19}3\)
\( \frac{93}3\)
\(75\)
2010011205
Level:
A
A diagonal of a rectangle has length of \( 26\,\mathrm{cm} \) and the perimeter of the rectangle is \( 68\,\mathrm{cm} \). Find the difference of the length and the width of the rectangle in centimeters.
\( 14 \)
\( 20 \)
\( 24 \)
\( 28\)
2010011105
Level:
A
Evaluate the following limit. (Apply L'Hospital's rule repeatedly.)
\[ \lim_{x\to0}\frac{x^4+2x^3}{x-\sin x} \]
\(12\)
\( 0\)
\( -12\)
\( 6\)
\(-6\)