2010008202
Level:
A
Identify the solution of the equation.
\[ 2^x+2^{x+2}+2^{x+4}=84 \]
\(x=2\)
\(x=1\)
\(x=0\)
\(x=4\)
A
2010008006
Level:
A
Compare the two definite integrals \( I_1 = \int_0^1 \left( x^3-x\right) \mathrm{d}x\) and \( I_2 = \int_1^0 \left( x-x^3\right) \mathrm{d}x\).
\( I_1 =I_2\)
\( I_1 > I_2\)
\( I_1 < I_2 \)
These integrals cannot be compared.
2010008005
Level:
A
Compare the two definite integrals \( I_1 = \int_1^2 \left( x^2-x\right) \mathrm{d}x\) and \( I_2 = \int_2^1 \left( x-x^2\right) \mathrm{d}x\).
\( I_1 =I_2\)
\( I_1 > I_2\)
\( I_1 < I_2 \)
These integrals cannot be compared.
2010008004
Level:
A
Compare the two definite integrals \( I_1 = \int_0^1 \left( x^6\cos^2x-20\right) \mathrm{d}x\) and \( I_2 = \int_0^1 \left( 20-x^6\cos^2x\right) \mathrm{d}x\).
\( I_1 < I_2\)
\( I_1 = I_2\)
\( I_1 > I_2 \)
These integrals cannot be compared.
2010008003
Level:
A
Compare the two definite integrals \( I_1 = \int_0^1 \left( 10-x^4\sin^2x\right) \mathrm{d}x\) and \( I_2 = \int_0^1 \left( x^4\sin^2x-10\right) \mathrm{d}x\).
\( I_1 > I_2\)
\( I_1 = I_2\)
\( I_1 < I_2 \)
These integrals cannot be compared.
2010008002
Level:
A
Compare the two definite integrals \( I_1 = \int_0^3 \frac{x^3}{3^x} \mathrm{d}x\) and \( I_2 = \int_3^0 \frac{x^3}{3^x}\ \mathrm{d}x\).
\( I_1 > I_2\)
\( I_1 = I_2\)
\( I_1 < I_2 \)
These integrals cannot be compared.
2010008001
Level:
A
Compare the two definite integrals \( I_1 = \int_0^2 x^5 \cdot 2^x \mathrm{d}x\) and \( I_2 = \int_2^0 x^5 \cdot 2^x \mathrm{d}x\).
\( I_1 > I_2\)
\( I_1 = I_2\)
\( I_1 < I_2 \)
These integrals cannot be compared.
2010007903
Level:
A
Choose the interval which contains all the solutions of the following quadratic
equation.
\[
6x^{2} + 13x +5 = 0
\]
\(\left(-2;-\frac12 \right]\)
\(\left[ \frac12;2 \right)\)
\(\left(-\frac32; \frac12 \right]\)
\(\left(-1;\frac53 \right]\)
2010007802
Level:
A
Find the domain of the following expression.
\[
\sqrt{\left (3x - 2 \right ) \left (4+5x\right )}
\]
\(\left(-\infty ;-\frac{4}
{5}\right] \cup \left[ \frac{2}
{3};\infty \right )\)
\(\left[ -\frac{4}
{5}; \frac{2}
{3}\right] \)
\(\left (-\infty ;-\frac{4}
{5}\right) \cup \left( \frac{2}
{3};\infty \right)\)
\(\left( -\frac{4}
{5}; \frac{2}
{3}\right) \)
2010007801
Level:
A
Identify a true statement which concerns to the following equation.
\[
2\sqrt{x+5} = x+2
\]
The solution is in the set \(\left \{x\in \mathbb{R} : -1 < x\leq - 5 \right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : 5 < x\leq 7 \right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : -4 < x\leq - 1 \right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : -1 < x\leq 2 \right \}\).