9000072805
Level:
B
The following numbers form a geometric sequence. The third term satisfies
\(a < 0\). Find
\(x\).
\[
x\, ,\ 5\, ,\ a\, ,\ 25
\]
\(-\sqrt{5}\)
\(\sqrt{5}\)
\(- 5\)
\(1\)
B
9000076002
Level:
B
In the following list identify a set of a numbers which give remainder
\(2\) after division by
\(5\), i.e. the numbers can
be written in the form \(5k + 2\),
\(k\in \mathbb{N}_{0}\).
\(37,\ 42,\ 102\)
\(5,\ 10,\ 15\)
\(17,\ 27,\ 100\)
\(29,\ 47,\ 60\)
\(41,\ 55,\ 62\)
9000073001
Level:
B
Consider a geometric sequence \((a_{n})_{n=1}^{\infty }\).
Let \(q\) be the quotient
and \(s_{n}\) be the sum
of the first \(n\)
terms. Given \(a_{1} = 2\)
and \(q = 2\),
find the sum of the first five terms of the sequence.
\(s_{5} = 62\)
\(s_{5} = 18\)
\(s_{5} = 32\)
\(s_{5} = -59\)
9000076003
Level:
B
In the following list identify a set of a numbers which give remainder
\(1\) after division by
\(11\), i.e. the numbers can
be written in the form \(11k + 1\),
\(k\in \mathbb{N}_{0}\).
\(56,\ 122,\ 221\)
\(21,\ 32,\ 48\)
\(18,\ 88,\ 115\)
\(34,\ 55,\ 70\)
\(45,\ 56,\ 65\)
9000072702
Level:
B
The following numbers form an arithmetic sequence. Find
\(x\).
\[
10\, ,\ 20\, ,\ x
\]
\(x = 30\)
\(x = 40\)
\(x = -20\)
\(x = -10\)
9000076004
Level:
B
In the following list identify a set such that each element of this set is a divisor of
\(256\).
\(1,\ 128,\ 256\)
\(1,\ 64,\ 123\)
\(4,\ 8,\ 104\)
\(1,\ 12,\ 128\)
\(16,\ 30,\ 64\)
9000072704
Level:
B
We are given five consecutive terms of an arithmetic sequence. Find
\(x\).
\[
4\, ,\ a\, ,\ 8\, ,\ b\, ,\ x
\]
\(x = 12\)
\(x = 10\)
\(x = 14\)
\(x = 16\)
9000076005
Level:
B
In the following list identify a set such that each element of this set is a divisor of
\(1\: 260\).
\(1,\ 36,\ 42\)
\(4,\ 8,\ 630\)
\(12,\ 18,\ 26\)
\(16,\ 315,\ 1\: 260\)
\(1,\ 17,\ 256\)
9000072706
Level:
B
We are given five consecutive terms of an arithmetic sequence. Find
\(x\).
\[
5\, ,\ a\, ,\ b\, ,\ x\, ,\ 6
\]
\(x = 5.75\)
\(x = 5.5\)
\(x = 5.8\)
\(x = 5\frac{2}
{3}\)
9000070702
Level:
B
Differentiate the following function.
\[
f(x) = (x^{2} - 3x + 2)^{\frac{1}
{2} }
\]
\(f^{\prime}(x) = \frac{2x-3}
{2\sqrt{x^{2 } -3x+2}},\ x\in \mathbb{R}\setminus \left [ 1,2\right ] \)
\(f^{\prime}(x) = \frac{2x-3}
{2\sqrt{x^{2 } -3x+2}},\ x\in \mathbb{R}\setminus \left (1,2\right )\)
\(f^{\prime}(x) = (4x - 6)\sqrt{x^{2 } - 3x + 2},\ x\in \mathbb{R}\setminus \left [ 1,2\right ] \)
\(f^{\prime}(x) = (4x - 6)\sqrt{x^{2 } - 3x + 2},\ x\in \mathbb{R}\setminus \left (1,2\right )\)