9000065306
Level:
A
In the arithmetic sequence given by the second term
\(a_{2} = -3\) and the
fifth term \(a_{5} = 3\)
find \(a_{11}\).
\(a_{11} = 15\)
\(a_{11} = 22\)
\(a_{11} = 19\)
\(a_{11} = 27\)
A
9000065305
Level:
A
In the arithmetic sequence given by the relations
\(a_{1} =\pi \),
\(a_{n+1} = a_{n} + 2\pi \) find
\(a_{13}\).
\(a_{13} = 25\pi \)
\(a_{13} = 27\pi \)
\(a_{13} = 26\pi \)
\(a_{13} = 24\pi \)
9000065601
Level:
A
Find the area of the region bounded by
\(x\)-axis,
graph of \(f(x) = x + 3\)
and lines \(x = -1\)
and \(x = 1\).
\(6\)
\(2\)
\(4\)
\(8\)
9000065302
Level:
A
Find the formula for the \(n\)-th
term of an arithmetic sequence with the first term
\(a_{1} = 1\) and the
second term \(a_{2} = -2\).
\(a_{n} = 4 - 3n,\ n\in\mathbb{N}\)
\(a_{n} = 1 - 2n,\ n\in\mathbb{N}\)
\(a_{n} = -2 + n,\ n\in\mathbb{N}\)
\(a_{n} = 3 + 2n,\ n\in\mathbb{N}\)
9000065610
Level:
A
Using definite integral find the area of the triangle defined by the following three
inequalities
\[
\begin{aligned}y& > 0, &
\\y& < x + 3,
\\y& < 3 - x.
\\ \end{aligned}
\]
\(\int _{-3}^{0}(x + 3)\, \mathrm{d}x +\int _{ 0}^{3}(3 - x)\, \mathrm{d}x\)
\(\int _{0}^{3}(x + 3)\, \mathrm{d}x\)
\(\int _{-3}^{3}(3 - x)\, \mathrm{d}x\)
\(\int _{-3}^{0}(3 - x)\, \mathrm{d}x +\int _{ 0}^{3}(x + 3)\, \mathrm{d}x\)
9000065501
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int (x^{3} + x^{2} - 2x)\, \mathrm{d}x
\]
\(\frac{1}
{4}x^{4} + \frac{1}
{3}x^{3} - x^{2} + c,\ c\in \mathbb{R}\)
\(\frac{1}
{4}x^{4} -\frac{1}
{3}x^{3} + x^{2} + c,\ c\in \mathbb{R}\)
\(3x^{2} + 2x - 2 + c,\ c\in \mathbb{R}\)
\(3x^{2} - 2x + 2 + c,\ c\in \mathbb{R}\)
9000065602
Level:
A
Find the area of the region bounded by
\(x\)-axis,
graph of \(f(x)= x^{2} + 3\)
and lines \(x = -2\)
and \(x = 1\).
\(12\)
\(6\)
\(8\)
\(10\)
9000065502
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int (4x + 7)\, \mathrm{d}x
\]
\(2x^{2} + 7x + c,\ c\in \mathbb{R}\)
\(2x^{2} - 7x + c,\ c\in \mathbb{R}\)
\(4 + c,\ c\in \mathbb{R}\)
\(4x^{2} + 7x + c,\ c\in \mathbb{R}\)
9000065605
Level:
A
Find the area of the region bounded by the curves
\(y = -2x\) and
\(y = -x^{2} + 3\).
\(\frac{32}
{3} \)
\(\frac{29}
{3} \)
\(\frac{31}
{3} \)
\(\frac{35}
{3} \)
9000065507
Level:
A
Given the function
\[
F(x) = \frac{1}
{4}x^{4} -\frac{2}
{3}x^{3},
\]
find the function \(f\)
such that \(F\) is
primitive to \(f\)
on \(\mathbb{R}\).
\(f(x) = x^{3} - 2x^{2}\)
\(f(x) = x^{5} - 2x^{4}\)
\(f(x) = x^{5} - 3x^{2}\)
\(f(x) = -4x^{-4} - 3x^{2}\)