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
\(x_{1, 2} = 2\pm \mathrm{i}\sqrt{2}\).
\(x^{2} - 4x + 6 = 0\)
\(3x^{2} + 4x + 2 = 0\)
\(3x^{2} - 4x + 2 = 0\)
\(x^{2} + 4x + 6 = 0\)
9000063607
Level:
B
Find the following limit.
\[
\lim _{n\to \infty } \frac{1}
{\log 10^{n}}
\]
\(0\)
\(1\)
\(10\)
\(\infty \)
9000063608
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\frac{2^{n} + 3^{n}}
{3^{n}}
\]
\(1\)
\(2\)
\(3\)
\(\infty \)
9000063806
Level:
B
Consider the sequence \(a_{n+1} = a_{n} - 2a_{n-1}\)
with \(a_{3} = 0\)
and \(a_{4} = -16\).
Find \(a_{2} - a_{1}\).
\(4\)
\(16\)
\(- 4\)
\(8\)
9000063302
Level:
B
Differentiate the following function.
\[
f(x)= (3x^{2} + 2)^{3}
\]
\(f'(x) = 18x(3x^{2} + 2)^{2},\ x\in \mathbb{R}\)
\(f'(x) = 18x(3x^{2} + 2),\ x\in \mathbb{R}\)
\(f'(x) = 18x^{2}(3x + 2)^{2},\ x\in \mathbb{R}\)
\(f'(x) = 108x^{2},\ x\in \mathbb{R}\)
9000064101
Level:
B
Find the slope of the tangent to the graph of
\(f(x) = x^{2} + 3x - 2\) at the
point \([1,2]\).
\(-\frac{1}
{5}\)
\(5\)
\(- 5\)
\(\frac{1}
{5}\)
9000063410
Level:
B
Solve the following equation.
\[
x + \frac{x}
{3} + \frac{x}
{9} + \frac{x}
{27}+\cdots = 18
\]
\(x = 12\)
\(x = 6\)
\(x = 18\)
\(x = 24\)
9000064102
Level:
B
Find the tangent to the graph of the function
\(f(x) = \frac{x+1}
{x-1}\) at the
point \([2,3]\).
\(2x + y - 7 = 0\)
\(2x - y - 1 = 0\)
\(- 2x + y + 1 = 0\)
\(x + 2y - 9 = 0\)
9000063801
Level:
B
We are given the sequence \(\left (an + b\right )_{n=1}^{\infty }\).
This sequence satisfies \(a_{2} = 2\)
and \(a_{4} = 8\). Use this
information to find \(a\).
\(a = 3\)
\(a = 1\)
\(a = 2\)
\(a = 4\)