9000065607
Level:
A
Find the area of the region bounded by the curves
\(y = 3^{x}\),
\(y = 3^{-x}\) and
\(y = 3\).
\(6 -\frac{4}
{\ln 3}\)
\(3 -\frac{2}
{\ln 3}\)
\(3 + \frac{4}
{\ln 3}\)
\(6 -\frac{2}
{\ln 3}\)
A
9000065509
Level:
A
Given the function
\[
F(x) = x + \frac{9}
{2}x^{2} + 9x^{3} + \frac{27}
{4} x^{4},
\]
find the function \(f\)
such that \(F\) is
primitive to \(f\)
on \(\mathbb{R}\).
\(f(x) = (1 + 3x)^{3}\)
\(f(x) = (1 + 3x)^{2}\)
\(f(x) = 1 + 3x + 3x^{2} + 3x^{3}\)
\(f(x) = (1 + 3x)^{4}\)
9000065301
Level:
A
Find the recurrence equations for the arithmetic sequence with the first term
\(a_{1} = 4\) and the common
difference \(d = -2\).
\(a_{1} = 4,\ a_{n+1} = a_{n} - 2,\ n\in\mathbb{N}\)
\(a_{1} = 4,\ a_{n+1} = a_{1} - 2,\ n\in\mathbb{N}\)
\(a_{n} = 4 + a_{n+2},\ n\in\mathbb{N}\)
\(a_{n+1} = a_{n} + 2,\ n\in\mathbb{N}\)
9000065603
Level:
A
Find the area of the region bounded by the curves
\(y = 0\),
\(y = x^{3}\),
\(x = 1\) and
\(x = 3\).
\(20\)
\(22\)
\(24\)
\(26\)
9000065303
Level:
A
Find the recurrence equations for the arithmetic sequence with the second term
\(a_{2} = 7\) and the common
difference \(d = 4\).
\(a_{1} = 3,\ a_{n} = a_{n-1} + 4,\ n\in\mathbb{N}\)
\(a_{1} = 7,\ a_{n+1} = a_{n} + 4,\ n\in\mathbb{N}\)
\(a_{n} = 7 + a_{n+4},\ n\in\mathbb{N}\)
\(a_{n+1} = a_{n} + 7,\ n\in\mathbb{N}\)
9000065609
Level:
A
Find the area of the region bounded by the curves
\(y = -x + 3\),
\(y = x^{2} - 3x\).
\(\frac{32}
{3} \)
\(8\)
\(\frac{8}
{3}\)
\(\frac{16}
{3} \)
9000065304
Level:
A
Find the first term \(a_{1}\) and
the common difference \(d\) of the
arithmetic sequence \((5 + 2n)_{n=1}^{\infty }\).
\(a_{1} = 7,\ d = 2\)
\(a_{1} = 5,\ d = 2\)
\(a_{1} = 3,\ d = -2\)
\(a_{1} = 2,\ d = 5\)
9000064505
Level:
A
Find the factorization of the following quadratic polynomial in the set of polynomial
with complex valued coefficients.
\[
2x^{2} + 32
\]
\(2(x + 4\mathrm{i})(x - 4\mathrm{i})\)
\(2(x - 4\mathrm{i})^{2}\)
\((x + 4\mathrm{i})(x - 4\mathrm{i})\)
\(2(x + 4\mathrm{i})^{2}\)
9000065309
Level:
A
The arithmetic sequence satisfies \(a_{26} = 58\)
and \(a_{21} = 43\). Find the
first term \(a_{1}\) and
the common difference \(d\)
of this sequence.
\(a_{1} = -17,\ d = 3\)
\(a_{1} = -1,\ d = 5\)
\(a_{1} = 1,\ d = 15\)
\(a_{1} = -1,\ d = 3\)
9000064507
Level:
A
Solve the following quadratic equation in the complex plane.
\[
4x^{2} + 12 = 0
\]
\(x_{1, 2} =\pm \mathrm{i}\sqrt{3}\)
\(x_{1, 2} =\pm 3\)
\(x_{1, 2} =\pm 3\mathrm{i}\)
\(x_{1, 2} =\pm \sqrt{3}\)