2010016403
Level:
B
Identify the function shown in the graph.
\( f(x) = \cos 2x\)
\( f(x) = -\cos 2x\)
\( f(x) = \sin 2x\)
\( f(x) = -\sin 2x\)
Sine, cosine, tangent and cotangent
2010016405
Level:
B
In the following list identify a true statement about the function
\(f(x) =\cos x\), where
\(x\in \left[ -\frac{\pi }{2}; \frac{\pi } {2} \right] \).
The function \(f\)
is neither increasing nor decreasing.
The function \(f\)
is decreasing.
The function \(f\)
is increasing.
The function \(f\) is increasing and decreasing.
2010016406
Level:
B
In the following list identify a true statement about the function
\(f(x) =\sin x\) on the interval \(I=\left( -\frac{\pi }{2}; \frac{\pi } {2} \right) \).
The function \(f\) does not have
a minimum or maximum on \(I\).
The function \(f\) has a unique minimum and no maximum on \(I\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).
2010016407
Level:
B
Identify the transformation which transforms the graph of the function
\(g(x) =\cos (2x)\) to the graph
of the function \(f(x) =\cos (2x -1)\).
Shift of graph of \(g\)
by \(\frac{1}
{2}\) of a
unit to the right.
Shift of graph of \(g\)
by \(\frac{1}
{2}\) of a
unit to the left.
Shift of graph of \(g\)
by \(1\) unit to the left.
Shift of graph of \(g\)
by \(1\) unit to the right.
2010016408
Level:
B
Consider the function \(f(x)=\mathop{\mathrm{cotg}}\nolimits x\) with
domain restricted to the interval \( (0;\pi )\).
In the following list identify the function with domain
\(\left (0; \frac{\pi } {2}\right )\).
\(f(2\cdot x)\)
\(f(x+2)\)
\(f(x-2)\)
\(f(\frac{x}2)\)
2010016801
Level:
B
To which quadrant does the angle \( \varphi \) belong if \( \cos\varphi=0.8 \) and \( \sin\varphi < 0 \)?
IV.
I.
II.
III.
2010016802
Level:
B
Choose the true statement:
\( \sin 240^{\circ} < \sin 120^{\circ} \)
\( \cos50^{\circ} < \cos130^{\circ} \)
\( \sin 300^{\circ} < \sin 270^{\circ} \)
\( \cos330^{\circ} < \cos150^{\circ} \)
2010016803
Level:
B
The value of \( \cos\left(-\frac{28\pi}3\right) \) is the same as the value of
\( \cos\frac{4\pi}3 \).
\( \cos\frac{\pi}3 \).
\( \cos\left(-\frac{7\pi}3\right) \).
\( \cos\frac{5\pi}3 \).
2010016804
Level:
B
How many \( x \)-intercepts has the graph of the function \( f(x)=\sin 2x \) on the interval \( [ -\pi; 2\pi ] \)?
\( 7\)
\( 5\)
\( 8\)
\( 6\)
2100005408
Level:
B
Which of the graphs is the graph of the function \(f(x)=2-2\sin\left(x-\frac{\pi}{2}\right)\)?
