1003049201
Level:
B
Let \( f(x)=2|2x+3|-|x|\left|\frac12-x\right|\). Identify which of the following function values is the highest.
\( f(2) \)
\( f(0) \)
\( f(-1.5) \)
\( f(3.5) \)
B
1003055609
Level:
B
Determine the truth value of the statement \( \exists k\in\mathbb{Z}\colon k^2 < 0\).
It is a false statement.
It is a true statement.
It is not a statement.
It is impossible to determine whether it is a true or a false statement.
1003055608
Level:
B
Determine the truth value of the statement \( \forall x\in\mathbb{R}\colon x^2+1>0 \).
It is a true statement.
It is a false statement.
It is not a statement.
It is impossible to determine whether it is a true or a false statement.
1003055607
Level:
B
Find a false statement.
\( (5 < -10) \vee (4 < 3) \)
\( (3\in\mathbb{N})\Leftrightarrow (3\in\mathbb{Z} ) \)
\( (2 > 0)\vee(3=5) \)
\( \left(8^2 = 16 \right) \Rightarrow \left(8^2 = 15 \right) \)
1003055606
Level:
B
Identify a true proposition.
\( (2 < 5)\wedge(4 < 5) \)
\( (0 < -1)\vee (8 >10) \)
\( (3 < 5) \Rightarrow (8\leq -10) \)
\( (5 < 10) \Leftrightarrow ( 8\div3=5) \)
1003055605
Level:
B
Which of the following expressions is a proposition?
\( 5^2=25 \)
\( 10^2 \)
\( (a-b)^2 - (a+b)^2 \)
Is it raining today?
1103030505
Level:
B
The vectors \( \vec{u} \) and \( \vec{v} \) are given by the figure. Find cosine of the angle \( \varphi \) between \( \vec{u} \) and \( \vec{v} \).
Help: Use the dot product of the given vectors.
\( \cos\varphi=-\frac9{17} \)
\( \cos\varphi=\frac9{17} \)
\( \cos\varphi=\frac{\sqrt{17}}{2\sqrt{13}} \)
\( \cos\varphi=-\frac{\sqrt{17}}{2\sqrt{13}} \)
1103030504
Level:
B
The vectors \( \vec{u} \) and \( \vec{v} \) are given by the figure. Find cosine of the angle \(\varphi \) between \( \vec{u} \) and \( \vec{v} \).
Help: Use the dot product of the given vectors.
\( \cos\varphi=\frac{13\sqrt{10}}{50} \)
\( \cos\varphi=\frac{970}{50} \)
\( \cos\varphi=\frac{3\sqrt{10}}{10} \)
\( \cos\varphi=\frac{\sqrt{10}}{5} \)
1103030503
Level:
B
Find the coordinates of the vectors \( \vec{u} \) and \( \vec{v} \) given by the picture and evaluate their dot product.
\( \vec{u}=(-8,-7,9),\ \ \vec{v} =(8,7,9),\ \ \vec{u}\cdot\vec{v} = -32 \)
\( \vec{u}=(-8,-7,9),\ \ \vec{v} =(8,7,9),\ \ \vec{u}\cdot\vec{v} = 0 \)
\( \vec{u}=(-8,-7,9),\ \ \vec{v} =(8,7,9),\ \ \vec{u}\cdot\vec{v} = (-64,-49,81) \)
\( \vec{u}=(8,7,-9),\ \ \vec{v} =(-8,-7,-9),\ \ \vec{u}\cdot\vec{v} = (-64,-49,81) \)
1103030502
Level:
B
Find the coordinates of the vectors \( \vec{u} \) and \( \vec{v} \) given by the picture and evaluate their dot product.
\( \vec{u}=(-3,6),\ \ \vec{v} =(-9,-6),\ \ \vec{u}\cdot\vec{v} = -9 \)
\( \vec{u}=(3,-6),\ \ \vec{v} =(9,6),\ \ \vec{u}\cdot\vec{v} = -9 \)
\( \vec{u}=(-3,6),\ \ \vec{v} =(-9,-6),\ \ \vec{u}\cdot\vec{v} = 9 \)
\( \vec{u}=(3,-6),\ \ \vec{v} =(9,6),\ \ \vec{u}\cdot\vec{v} = 0 \)