1003024905
Level:
B
Which of the following functions is bounded above?
\( f(x) = -3^{-x} \)
\( f(x) = \left(\frac13\right)^{-x} \)
\( f(x) = 3^x \)
\( f(x) = \left(\frac13\right)^x \)
B
1003024904
Level:
B
Which of the following functions is decreasing?
\( f(x)=\left(\frac15\right)^x \)
\( f(x)=-5^{-x} \)
\( f(x)=\left(\frac15\right)^{-x} \)
\( f(x)=5^x \)
1003024903
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( 0 < b < 1 \), find the correct statement.
Function \( f \) is increasing.
Function \( f \) is decreasing.
Function \( f \) is nonincreasing.
Function \( f \) is nondecreasing.
1003024902
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( b > 0 \), find the correct statement.
Function \( f \) is bounded above.
Function \( f \) is bounded below.
Function \( f \) is bounded.
Function \( f \) is unbounded.
1003024901
Level:
B
Given the increasing exponential function \(f(x)=a^x\), choose the correct statement about the base \(a\).
\(a > 1\)
\(a=1\)
\(a < 1\)
\( 0 < a < 1 \)
1003020702
Level:
B
Find the solution of the inequality.
\[
\sqrt{3x^2-x+7}\geq2
\]
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\left(-\frac13;\frac73\right)\)
\(x\in\mathbb{R}\setminus\{2\}\)
1003020701
Level:
B
Find the solution of the inequality.
\[
\sqrt{-2x^2+x+5}\geq5
\]
\(x\in\emptyset\)
\(x\in[-1;5]\)
\(x\in\left(-\frac12;\frac52\right)\)
\(x\in\mathbb{R}\)
9000153702
Level:
B
The picture shows a square pyramid. The side of a base square is
\(a = 4\; \mathrm{cm}\) and the height of
the pyramid is \(v = 6\; \mathrm{cm}\).
Find the angle \(\varphi \).
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{6}
{2\sqrt{2}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 64^{\circ }46^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{6}
{2}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 71^{\circ }34^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2}
{6}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 36^{\circ }52^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{2\sqrt{10}}
{2} \mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 72^{\circ }27^{\prime}\)
9000168706
Level:
B
Which of the given points is one of the vertices of the hyperbola \(16x^{2} - 9y^{2} + 64x + 18y - 89 = 0\)?
\([-5;1]\)
\([-6;1]\)
\([-2;4]\)
\([-2;5]\)
9000153703
Level:
B
The picture shows a square pyramid. The side of a base square is
\(a = 4\; \mathrm{cm}\) and the height of
the pyramid is \(v = 6\; \mathrm{cm}\).
Find the angle \(\varphi \).
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2}
{6}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 36^{\circ }52^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{6}
{2\sqrt{2}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 64^{\circ }46^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2}
{2\sqrt{10}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 35^{\circ }6^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2\sqrt{2}}
{6} \mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 50^{\circ }29^{\prime}\)