B

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 \( -\frac25 \).
\( \left( \frac{2\log n-4}{3-5\log n}\right)_{n=1}^{\infty} \)
\( \left( \frac{4\log n-2}{3-5\log n}\right)_{n=1}^{\infty} \)
\( \left( \frac{2(\log n)^2-4}{3-5\log n}\right)_{n=1}^{\infty} \)
\( \left( \frac{2\log n-4}{3-5(\log n)^2}\right)_{n=1}^{\infty} \)
\( \left( \frac{4\log n-2}{3-5\log n}\right)_{n=1}^{\infty} \)

2010005405

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