B

1003112807

Level: 
B
The sum of the first two terms of a geometric sequence is \( 28 \) and its first term equals \( 2 \). Which of the following statements about its common ratio \( q \) is not valid?
\( q \) is an even number.
\( q > 10 \)
\( q < 28 \)
\( q \) is prime number.
\( q \) is a divisor of \( 26 \).

1003112806

Level: 
B
The sum of the first four terms of a geometric sequence is \( 0 \) and the first term equals \( 2 \). Choose the correct formula to find the eighth term.
\( a_8 = 2\cdot (-1)^7 \)
\( a_8 = 2\cdot (1)^7 \)
\( a_8 = 2\cdot 2 \)
\( a_8 = \frac02 \)
\( a_8 = 2\cdot (-2) \)

1003112804

Level: 
B
The third term of a geometric sequence is \( -5 \) and the eighth term is \( -5 \). \( s_5 \) is the sum of the first five terms and \( q \) is the common ratio of this sequence. Choose the formula which is not valid for this sequence:
\( s_5=-5\cdot\frac{q^5-1}{q-1} \)
\( s_5=-25 \)
\( s_5=5\cdot a_1 \)
\( s_5=5\cdot a_3 \)
\( s_5=5\cdot(-5) \)

1003090804

Level: 
B
Find the distance between parallel lines \( p \) and \( q \) given by their parametric equations. \begin{align*} p\colon x&=3+3t, & q\colon x&=2-3s, \\ y&=-1+t;\ t\in\mathbb{R}; & y&=1-s;\ s\in\mathbb{R}. \end{align*}
\( \frac{7\sqrt{10}}{10} \)
\( \frac{\sqrt{10}}{2} \)
\( \frac{\sqrt{10}}{5} \)
\( \frac{5\sqrt{10}}{2} \)

1003090803

Level: 
B
Find the distance between parallel lines \( p \) and \( q \), if they are given by slope-intercept form equations, where \( p \) is \( y=-3x+5 \) and \( q \) is \( y=-3x-1 \).
\( \frac{3\sqrt{10}}5 \)
\( \frac{2\sqrt{10}}5 \)
\( \frac{4\sqrt{10}}5 \)
\( \frac{\sqrt{10}}5 \)

1003090802

Level: 
B
Find the distance between parallel lines \( p \) and \( q \), if they are given by their general form equations, where \( p \) is \( 2x-4y+5=0 \) and \( q \) is \( x-2y+3=0 \).
\( \frac{\sqrt5}{10} \)
\( \frac{11\sqrt5}{10} \)
\( \frac{3}{2\sqrt5} \)
\( \frac{3\sqrt5}{10} \)

1103090801

Level: 
B
Find a general form equation of the straight line that passes through the point \( M=[2;3] \) and is parallel with the line of symmetry of the line segment \( AB \), where \( A=[-1;4] \), and \( B=\left[\frac52;-3\right] \) (see the picture).
\( x-2y+4=0 \)
\( 2x+y-7=0 \)
\( 3x+2y-12=0 \)
\( 2x-3y+5=0 \)

1103109008

Level: 
B
Let \( p \) be the line with the equation \( x-2y-1=0 \). Find the coordinates of all points lying on the line \( p \) such that their distance from the line \( y=3 \) equals to \( 1 \).
\( X_1 = \left[5;2\right]\text{, }X_2 = \left[9;4\right] \)
\( X_1 = \left[4;2\right]\text{, }X_2 = \left[8;4\right] \)
\( X_1 = \left[2;4\right]\text{, }X_2 = \left[6;4\right] \)
\( X_1 = \left[2;5\right]\text{, }X_2 = \left[4;9\right] \)