9000146705
Level:
A
Expand the following expression.
\[
(3 - 2a)^{2} - (3a - 4)(3a + 4)
\]
\(- 5a^{2} - 12a + 25\)
\(- 5a^{2} - 12a - 7\)
\(- 5a^{2} + 25\)
\(- 5a^{2} - 7\)
A
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?
\(24\)
\(34\)
\(14\)
\(44\)
9000146706
Level:
A
Expand the following polynomial.
\[
(2x + 3)^{2} - (2 - x)^{2}
\]
\(3x^{2} + 16x + 5\)
\(3x^{2} + 8x + 13\)
\(3x^{2} + 13\)
\(3x^{2} + 5\)
9000150101
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int \left (\cos x -\sin x\right )\, \mathrm{d}x
\]
\(\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(\sin x -\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x -\cos x + c,\ c\in \mathbb{R}\)
9000148902
Level:
A
There are four paths from a city to the top of nearby mountain. Find the number of
possible treks from the city to the mountain and back, if it is required to use one
path up and another one down.
\(4\cdot 3=12\)
\(4\cdot 4=16\)
\(4 + 3=7\)
\(2\cdot 4=8\)
9000141909
Level:
A
Given the function \(h\),
find \(\lim _{x\to \infty }h(x)\).
\[
h(x)=\begin{cases}
-\frac1{x-1} & \text{if } x< 1,\\
-(x-1)^2+2 & \text{if } x\geq 1
\end{cases}
\]
\(-\infty \)
\(1\)
\(0\)
\(\infty \)
Does not exist
9000141910
Level:
A
Given the function \(h\),
find \(\lim _{x\to -\infty }h(x)\).
\[
h(x)=\begin{cases}
-\frac1{x-1} & \text{if } x< 1,\\
-(x-1)^2+2 & \text{if } x\geq 1
\end{cases}
\]
\(0\)
\(2\)
\(\infty \)
\(-\infty \)
Does not exist
9000146701
Level:
A
Expand the following polynomial.
\[
2 - (2x + 1) + x(5 - 2x) - 3(x - 2)
\]
\(- 2x^{2} + 7\)
\(- 2x^{2} + 9\)
\(- 2x^{2} - 3\)
\(- 2x^{2} - 5\)
9000146702
Level:
A
Expand the following expression.
\[
a - 4(2 - a) - a(5a + 1) + 2a(3 - 2a)
\]
\(- 9a^{2} + 10a - 8\)
\(- 9a^{2} + 12a - 8\)
\(- 9a^{2} + 2a - 8\)
\(- 9a^{2} + 4a - 8\)
9000146203
Level:
A
Expand the following expression.
\[
\left (x^{5} -\sqrt{2}y\right )^{2}
\]
\(x^{10} - 2\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} - 2\sqrt{2}x^{5}y - 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y - 2y^{2}\)