9000150401
Level:
A
Evaluate the following definite integral.
\[
\int _{-3}^{1}(x^{2} + 3x)\, \text{d}x
\]
\(-\frac{8}
{3}\)
\(\frac{8}
{3}\)
\(-\frac{64}
{3} \)
\(\frac{64}
{3} \)
A
9000150402
Level:
A
Evaluate the following definite integral.
\[
\int _{-\frac{\pi }{
2} }^{ \frac{\pi }
{2} }\sin x\, \text{d}x
\]
\(0\)
\(\pi \)
\(2\)
\(1\)
9000149702
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} + 2x - 8y + 13 = 0
\]
\([-1,4]\)
\([-1,-4]\)
\([1,4]\)
\([1,-4]\)
9000148906
Level:
A
Each candidate in a tender is fluent in at least one out
of two required languages (English and French). There are
\(20\) candidates fluent
in English and \(14\)
candidates fluent in French. From these amounts
\(10\)
candidates are fluent in both languages. How many candidates are there in the
tender?
\(24\)
\(34\)
\(14\)
\(44\)
9000149703
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} - 10x - 2y + 10 = 0
\]
\([5,1]\)
\([5,-1]\)
\([-5,1]\)
\([-5,-1]\)
9000150101
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int \left (\cos x -\sin x\right )\, \mathrm{d}x
\]
\(\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(\sin x -\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x -\cos x + c,\ c\in \mathbb{R}\)
9000149704
Level:
A
Find the center of the following ellipse.
\[
9x^{2} + 4y^{2} + 54x - 32y + 109 = 0
\]
\([-3,4]\)
\([-3,-4]\)
\([3,4]\)
\([3,-4]\)
9000148904
Level:
A
Pamela needs new ski for a ski course. There are skis from six different vendors in a
shop. The shop has four different ski pairs from each vendor, but two vendors have all
products behind Pam's financial limit. How many pairs are at disposal for Pam?
\(4\cdot 4=16\)
\(4!=24\)
\(4\cdot 2=8\)
\(4 + 2=6\)
9000149705
Level:
A
Find the center of the following ellipse.
\[
16x^{2} + 9y^{2} - 32x - 54y - 47 = 0
\]
\([1,3]\)
\([1,-3]\)
\([-1,3]\)
\([-1,-3]\)
9000148910
Level:
A
The player throws a dice in a desktop game. If he gets the number
\(6\), he
throws again and his score is the sum of both numbers. Find how many possibilities
are there for the player's score.
\(5 + 6=11\)
\(2\cdot 6=12\)
\(1 + 6=7\)
\(6\cdot 6=36\)