B

1003023307

Level: 
B
The radian measure of the angle \( \theta \) is \( \frac{\pi}3 \). How many values from the set \( M = \left\{\frac43\pi; \frac73\pi; \frac83\pi; \frac{13}3\pi; -\frac53\pi; \frac{61}3\pi; -\frac{61}3\pi \right\} \) are the measures of angles coterminal to \( \theta \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 4 \)
\( 5 \)
\( 6 \)
\( 3 \)

1003023306

Level: 
B
The radian measure of the angle \( \theta \) is \( \frac{\pi}2 \). What is the sum of all the radian measures of the angles coterminal to \( \theta \) from the interval \( [-5\pi; 5\pi] \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \frac52\pi \)
\( 0 \)
\( 3\pi \)
\( \pi \)

1003030905

Level: 
B
Let \( f(x)=|x-1|-2|x| \). Identify which of the following statements is true.
The function \( f \) is bounded above and is not bounded below.
The function \( f \) is bounded below and is not bounded above.
The function \( f \) is bounded.
The function \( f \) is neither bounded above nor bounded below.

1103030902

Level: 
B
A part of the graph of the function \( f(x)=\frac4x \) is shown in the picture. Identify which of the following statements is true.
The function \( g \) defined by \( g(x)=\left|f(x)\right| \) is bounded below.
The function \( f \) is bounded below.
The function $h$ defined by \( h(x)=-f(x) \) is bounded below.
The function $m$ defined by \( m(x)=f(x)+4 \) is bounded below.

1103061301

Level: 
B
Let \( ABC \) be a triangle (see the picture). Find the standard form equations of the lines \( t \), \( v \) and \( o \), where \( t \) contains the median to \( AB \), \( v \) contains the altitude to \( AB \) and \( o \) is the line of symmetry of \( AB \). Choose the option with all equations correct.
\( t\colon 2x+y-10=0 ;\ v\colon 4x+y-16=0;\ o\colon 4x+y-20=0 \)
\( t\colon 2x+y-10=0;\ v\colon x-4y+13=0;\ o\colon x-4y-5=0 \)
\( t\colon x-2y-5=0;\ v\colon 4x+y-16=0;\ o\colon 4x+y-20=0 \)
\( t\colon x-2y-5=0;\ v\colon x-4y+13=0;\ o\colon x-4y-5=0 \)

1003047510

Level: 
B
Choose the sequence with the limit equal to \( 0 \).
\( \left(\frac{3(\log n)^2+2\log n-1}{5(\log n)^3+2(\log n)^2+2}\right)_{n=1}^{\infty} \)
\( \left(\frac{3(\log n)^3+2\log n-1}{5(\log n)^3+2(\log n)^2+2}\right)_{n=1}^{\infty} \)
\( \left(\frac{3(\log n)^4+2\log n-1}{5(\log n)^3+2(\log n)^2+2}\right)_{n=1}^{\infty} \)
\( \left(\frac{3(\log n)^3+2\log n-5}{5(\log n)^3-3(\log n)^2-2}\right)_{n=1}^{\infty} \)
\( \left(\frac{3(\log n)^2+2\log n-1}{2(\log n)^2+2}\right)_{n=1}^{\infty} \)

1003047509

Level: 
B
Choose the sequence with the limit equal to \( -\frac25 \).
\( \left( \frac{2\log n-4}{3-5\log n}\right)_{n=1}^{\infty} \)
\( \left( \frac{4\log n-2}{3-5\log n}\right)_{n=1}^{\infty} \)
\( \left( \frac{2(\log n)^2-4}{3-5\log n}\right)_{n=1}^{\infty} \)
\( \left( \frac{2\log n-4}{3-5(\log n)^2}\right)_{n=1}^{\infty} \)
\( \left( \frac{4\log n-2}{3-5\log n}\right)_{n=1}^{\infty} \)