9000068706
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = x + 14\),
\(a_{2} = x + 2\) and
\(a_{3} = x - 4\) into
three consecutive numbers of a geometric series.
\(x = 10\)
\(x = 5\)
\(x = 2.5\)
\(x = 2\)
\(x = -5\)
B
9000068709
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} =\log x\),
\(a_{2} = 2 +\log x\) and
\(a_{3} = 4\log x\) into
three consecutive numbers of a geometric series.
\(x = 100\)
\(x = 1\)
\(x =\log 2\)
\(x = 2\)
\(x = 10\)
9000068710
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = 10^{2x+2}\),
\(a_{2} = 10^{4x+1}\) and
\(a_{3} = 10^{12}\) into
three consecutive numbers of a geometric series.
\(x = 2\)
\(x = 4\)
\(x = 10^{2}\)
\(x = \frac{1}
{2}\)
\(x = \frac{1}
{100}\)
9000068701
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = 10^{2}\),
\(a_{2} = 10^{3}\) and
\(a_{3} = x\) into
three consecutive numbers of a geometric series.
\(x = 10\: 000\)
\(x = 1\: 000\)
\(x = 1\: 900\)
\(x = 1\: 990\)
\(x = 100\: 000\)
9000068702
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = -12\),
\(a_{2} = x\) and
\(a_{3} = -48\) into
three consecutive numbers of a geometric series.
\(x = -24\)
\(x = 0\)
\(x = 6\)
\(x = 12\)
\(x = -2\)
9000068703
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = -x\),
\(a_{2} = -5\) and
\(a_{3} = 5\) into
three consecutive numbers of a geometric series.
\(x = -5\)
\(x = 0\)
\(x = 5\)
\(x = -10\)
\(x = 10\)
9000065904
Level:
B
Evaluate the following integral on the interval \((0;+\infty)\).
\[
\int \frac{x^{3} + 2x}
{x^{2}} \, \text{d}x
\]
\(\frac{1}
{2}x^{2} + 2\ln |x| + c,\ c\in \mathbb{R}\)
\(x +\ln |x| + c,\ c\in \mathbb{R}\)
\(\frac{1}
{4}x^{4} + 4x^{2} +\ln |x^{2}| + c,\ c\in \mathbb{R}\)
\(2x^{2} + 2 +\ln |x^{2}| + c,\ c\in \mathbb{R}\)
9000066002
Level:
B
Evaluate the following integral on \(\mathbb{R}\).
\[
\int x\sin x\, \mathrm{d}x
\]
\(- x\cos x +\sin x + c,\ c\in \mathbb{R}\)
\(- x\cos x -\sin x + c,\ c\in \mathbb{R}\)
\(x\cos x +\sin x + c,\ c\in \mathbb{R}\)
\(x\cos x -\sin x + c,\ c\in \mathbb{R}\)
9000064110
Level:
B
Identify a true statement related to the function
\(f(x) = \frac{x-1}
{x+1}\).
The tangent at \(T = [-3;2]\)
is parallel to \(x - 2y + 1 = 0\).
The tangent at \(T = [-3;2]\)
contains the point \(A = \left [1;-4\right ]\).
The slope of the tangent at \(T = [-3;2]\)
is \(2\).
The tangent at \(T = [-3;2]\) is
perpendicular to \(x + 2y + 1 = 0\).
9000065307
Level:
B
In the arithmetic sequence given by the first term
\(a_{1} = 4\) and the common
difference \(d = 2\)
find the sum of the first twelve terms of the sequence.
\(s_{12} = 180\)
\(s_{12} = 72\)
\(s_{12} = 120\)
\(s_{12} = 168\)