9000150405
Level:
B
Evaluate the following definite integral.
\[
\int _{-1}^{3} \frac{1}
{2x + 3}\, \text{d}x
\]
\(\ln 3\)
\(\ln 1\)
\(\ln 9\)
\(2\ln 9\)
B
9000151304
Level:
B
Find the angle \(\varphi \)
between the lines \(y = 0\)
and \(\frac{x}
{2} + \frac{y}
{3} = 1\).
\(56^{\circ }19'\)
\(13^{\circ }45'\)
\(26^{\circ }46'\)
\(81^{\circ }23'\)
9000150406
Level:
B
Evaluate the following definite integral.
\[
\int _{-3}^{2} \frac{x}
{x^{2} + 3}\, \text{d}x
\]
\(\frac{1}
{2}\ln \frac{7}
{12}\)
\(2\ln \frac{12}
{7} \)
\(2\ln \frac{7}
{12}\)
\(\frac{1}
{2}\ln \frac{12}
{7} \)
9000151309
Level:
B
Given points \(A = [-1.4]\),
\(B = [2,-2]\),
\(C = [5,-1]\), find the angle
\(\varphi \) between
the lines \(AB\)
and \(BC\).
\(81^{\circ }52'\)
\(98^{\circ }08'\)
\(61^{\circ }22'\)
\(45^{\circ }32'\)
9000151301
Level:
B
Find the angle \(\varphi \)
between the lines \(3x - 7 = 0\)
and \(x + y + 13 = 0\).
\(45^{\circ }\)
\(90^{\circ }\)
\(60^{\circ }\)
\(30^{\circ }\)
9000153304
Level:
B
Two students performed repeated measurements of the same length. After
evaluating statistical characteristics they got equal means of the length. Which of the
following statement is true? (Remark: The accuracy is determined by the coefficient of variation.)
There is not enough information to compare the accuracy of both measurements.
One of the students measured with a better accuracy than the other.
Both students did their measurements with the same accuracy.
9000151308
Level:
B
Given points \(A = [-1;4]\),
\(B = [2,-2]\) and
\(C = [5,-1]\), find the angle
\(\beta \) (the interior angle
at the vertex \(B\))
in the triangle \(ABC\).
\(98^{\circ }08'\)
\(81^{\circ }53'\)
\(76^{\circ }17'\)
\(68^{\circ }27'\)
9000149408
Level:
B
On the \(x\)-axis
find the points such that the distance from these points to the line
\(p\colon x - 2y + 2 = 0\) is
\(\sqrt{5}\).
\([3;0]\),
\([-7;0]\)
\([5;0]\)
\(\left [\sqrt{5};0\right ]\),
\(\left [-\sqrt{5};0\right ]\)
\([3;7]\)
9000149708
Level:
B
Find the vertex of the following parabola.
\[
x^{2} + 8x - 4y + 24 = 0
\]
\([-4;2]\)
\([-4;-2]\)
\([4;2]\)
\([4;-2]\)
9000149401
Level:
B
Find the distance from the point \(P = [-4;2]\)
to the line \(3x - 4y - 5 = 0\).
\(5\)
\(1\)
The line contains \(P\).
\(\sqrt{5}\)