2010011002
Level:
A
Which of the following statements is not true?
\( \log_{\frac12}6=-3 \)
\( \log_{\frac12}8=-3\)
\( \log_2 \sqrt{2}=\frac12\)
\( \log_{\frac12}\frac14=2\)
A
2010011001
Level:
A
Among offered answers, choose a logarithmic form of the following equality.
\[ \sqrt{16} = 4 \]
\( \log_{16}4=\frac{1}{2}\)
\( \log_{\frac12}16=4\)
\( \log_4 \frac12=16\)
\( \log_{2}4=16\)
2010010006
Level:
A
Evaluate the following expression.
\[ ||2-4|-2\cdot |1-3||\]
\( 2\)
\( 7\)
\(6\)
\( 8\)
2010010005
Level:
A
Evaluate the following expression.
\[ ||3-4|-2\cdot |1-5||\]
\( 7\)
\( 9\)
\(6\)
\( 8\)
2010010004
Level:
A
Choose the true statement.
\( |3-7| \leq |7-3|\)
\( |4-6| > |6-4|\)
\( |1-7| < |7-1|\)
\( |2-8| = |8+2|\)
2010010003
Level:
A
Choose the true statement.
\( |3-4| \leq |4-3|\)
\( |3-6| > |6-3|\)
\( |2-7| < |7-2|\)
\( |3-8| = |8+3|\)
2010009905
Level:
A
Let \( f(x)=\frac{-3}{x} \). Find the false statement.
The function \(f\) is bounded above.
The range of \( f \) is \( \left(-\infty;0\right)\cup\left(0;\infty\right) \).
The function \( f \) is increasing on \( \left(-\infty;0\right) \).
The function \( h \) defined by \(h(x)=-f(x)\) is an odd function.
2010009803
Level:
A
Which of the following equations has exactly two solutions in the interval \( \left[ -\frac{\pi}2;\frac{\pi}{2}\right] \)?
\( 3\cos x - 2 = 0 \)
\( 3\sin x - 2 = 0 \)
\( 2\cos x - 3 = 0 \)
\( 3\cos x + 2 = 0 \)
2010009802
Level:
A
How many solutions does the equation \( \mathrm{cotg}^2\,x = 3 \) have for \( -\pi\leq x\leq \pi \)?
\( 4 \) solutions
\( 2 \) solutions
\( 8 \) solutions
\( 6 \) solutions
2010009801
Level:
A
How many solutions does the equation \( \sin^2x = 0.75 \) have for \( 0\leq x\leq 2\pi \)?
\( 4 \) solutions
\( 1 \) solution
\( 2 \) solutions
\( 3 \) solutions