2010005704
Level:
B
Writing the expression \( \frac{(0.25)^{-2}\cdot (x \colon y^2)^{-2} }{(2y)^4\cdot x^{-2}}\), \( x\neq0\), \( y\neq0 \) in a simplified form, we will get:
\( 1\)
\( y^{-8} \)
\( x^{-4} \)
\( \frac14 \)
B
2010005703
Level:
B
Calculate \( \left(4{.}3\cdot10^{-6}\right)\cdot\left(3\cdot10^{9}\right) \) and give the result in the scientific notation.
\( 12\,900 = 1{.}29\cdot10^4\)
\( 12\,900 = 12{.}9\cdot10^3\)
\( 12\,900 = 129\cdot10^2\)
\( 0.000\,000\,000\,000 \,001\,29= 1{.}29\cdot10^{-15}\)
2010005702
Level:
B
The number \(\sqrt[5]{(-3)^2}\cdot\left(\frac1{81}\right)^{-\frac25} \) equals:
\( 9 \)
\( -9 \)
\( 3 \)
\( -3 \)
2010005701
Level:
B
The product of the numbers \( \left(\sqrt[6]{3}\cdot 81^{\frac14}\right)^{-1} \) and \( \sqrt[3]9\cdot \sqrt{3}\) equals:
\( 1 \)
\( \frac13 \)
\( \sqrt3 \)
\( 3 \)
2010005506
Level:
B
The sum of the first \( n \) terms of a geometric sequence is \( 1 \), the common ratio is \( -3 \) and the first term equals \( \frac17 \). Find \( n \).
\( 3\)
\( 4 \)
\( 5 \)
\( 6 \)
\( 2 \)
2010005505
Level:
B
The sum of the first two terms of a geometric sequence is \( 54 \) and its first term equals \( 3 \). Which of the following statements about its common ratio \( q \) is not valid?
\( q \) is an even number.
\( q > 10 \)
\( q < 54 \)
\( q \) is a prime number.
\( q \) is a divisor of \( 51 \).
2010005504
Level:
B
Find the sum of the first five terms of the geometric sequence \( \{a_n\}_{n=1}^{\infty} \), if: \[ \begin{aligned} a_1+a_3&=-10, \\ a_1+a_2&=0. \end{aligned} \]
\( -5 \)
\( 5 \)
\( 0 \)
\( -1 \)
\( 1\)
2010005503
Level:
B
Find the first term of the geometric sequence \( \{a_n\}_{n=1}^{\infty} \), if: \[\begin{aligned} a_5\cdot a_6&=-9, \\ a_6-a_5&=6. \end{aligned} \]
\( -3 \)
\( 3 \)
\( -1 \)
\( 1 \)
\( -9 \)
2010005502
Level:
B
The sum of the first three terms of a geometric sequence is \( \frac{13}9 \) and the common ratio is \( \frac13 \). Find the sum of all the terms from the \( 3 \)rd to the \( 5 \)th of the sequence.
\( \frac{13}{81} \)
\( \frac{10}{81} \)
\( \frac1{27} \)
\( \frac{40}{81} \)
\( \frac{121}{81} \)
2010005501
Level:
B
The sum of the first and the second term of a geometric sequence is \( 2 \), the sum of the third and the fourth term is \( 18 \) and the common ratio is negative. Find the first term.
\( -1 \)
\( 1\)
\( 2 \)
\( \frac12 \)
\( -2 \)