9000064501
Level:
B
Find the quadratic equation with the solution
\(x_{1, 2} =\pm 2\mathrm{i}\).
\(x^{2} + 4 = 0\)
\(x^{2} - 4\mathrm{i} = 0\)
\(x^{2} - 4 = 0\)
\(x^{2} + 4\mathrm{i} = 0\)
B
9000064502
Level:
B
Find the quadratic equation with the solution
\(x_{1, 2} = 2\pm \mathrm{i}\sqrt{2}\).
\(x^{2} - 4x + 6 = 0\)
\(3x^{2} + 4x + 2 = 0\)
\(3x^{2} - 4x + 2 = 0\)
\(x^{2} + 4x + 6 = 0\)
9000064503
Level:
B
Find the values of the real coefficients
\(a\),
\(b\) and
\(c\) such
that the quadratic equation
\[
ax^{2} + bx + c = 0
\]
has solution \(x_{1, 2} =\pm \mathrm{i}\frac{\sqrt{5}}
{3} \).
\(a = 9\text{, }b = 0\text{, }c = 5\)
\(a = 5\text{, }b = 0\text{, }c = 9\)
\(a = 9\text{, }b = 0\text{, }c = -5\)
\(a = 5\text{, }b = 0\text{, }c = -9\)
9000064504
Level:
B
Find the values of the real coefficients
\(a\),
\(b\) and
\(c\) such
that the quadratic equation
\[
ax^{2} + bx + c = 0
\]
has solutions \(x_{1, 2} = 1\pm \frac{\mathrm{i}}
{2}\).
\(a = 4\text{, }b = -8\text{, }c = 5\)
\(a = 1\text{, }b = -4\text{, }c = 5\)
\(a = 4\text{, }b = 8\text{, }c = 5\)
\(a = 1\text{, }b = 4\text{, }c = 5\)
9000064107
Level:
B
Find the tangent to the graph of the function
\(f(x) = x^{2} + 4x - 2\) parallel to
the line \(2x + y + 1 = 0\).
\(2x + y + 11 = 0\)
\(2x - y - 1 = 0\)
\(2x + y - 1 = 0\)
\(2x - y - 11 = 0\)
9000064108
Level:
B
Find the normal line to the graph of the function
\(f(x) = 2x^{2} - 7x\) parallel to
the line \(y = -x\).
\(x + y + 4 = 0\)
\(- x + y + 4 = 0\)
\(x - y - 8 = 0\)
\(x + y - 8 = 0\)
9000064109
Level:
B
Find the tangent to the graph of the function
\(f(x) = 3x^{2} - 8x + 2\) perpendicular
to the line \(x + 4y + 5 = 0\).
\(4x - y - 10 = 0\)
\(-4x + y + 1 = 0\)
\(8x - 2y + 1 = 0\)
\(-8x + 2y - 10 = 0\)
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.
\(s_{12} = 180\)
\(s_{12} = 72\)
\(s_{12} = 120\)
\(s_{12} = 168\)
9000065308
Level:
B
For the arithmetic sequence with the first term $a_1=3$ holds $a_n=27$ and the sum of the first $n$ terms is $195$. Find $n$.
\(n = 13\)
\(n = 14\)
\(n = 15\)
\(n = 16\)