2010001602
Level:
A
Simplifying \( \left|\sqrt3-3\right|-\left|2\sqrt3-2\right| \) we get:
\( -3\sqrt3+5 \)
\( -3\sqrt3+1 \)
\( \sqrt3+5 \)
\( \sqrt3+1 \)
A
2010001601
Level:
A
Evaluate the following expression.
\[
|2-5|+|2(-3)| - |(-3)(-1)|
\]
\(6\)
\(12\)
\(-12\)
\( -6\)
2010001404
Level:
A
Find the intersection \( A\cap B' \) if \( A=(-\infty;4) \) and \(B=(-6;+\infty) \). (By \(B'\) the complement of the set \( B \) is denoted.)
\( (-\infty;-6 ] \)
\( (-6;4) \)
\( [ 4 ;+\infty) \)
\( (-6;4 ] \)
2010001403
Level:
A
Find the set difference \( A\setminus B \) for \( A=\left\{x\in \mathbb{Z}\ \colon x^2=1\right\} \) and \( B=\{0;1;2;3\} \).
\( \{-1\} \)
\( \{0;1;2;3\} \)
\( \{0;2;3\} \)
\( \emptyset\)
2010001302
Level:
A
Expand the polynomial \(\left (2x-3x^2\right )^{2} -\left (3x^2 + 2x\right )^{2}\).
\(-24x^3\)
\(0\)
\(8x^2\)
\(8x^2-24x^3\)
2010001301
Level:
A
Expand \( (x-1)(1-x+x^2)(x+1)\).
\( x^4-x^3+x-1\)
\( x^4-x^3+2x^2+x-1\)
\( x^4+x^3-x+1\)
\( x^4+x^3-2x^2+x-1\)
2010001103
Level:
A
Evaluate the definite integral. \[ \int\limits_1^3\left(\frac3x-\frac x3+x^3\right)\mathrm{d}x \]
\( \frac{56}{3}+\ln 27 \)
\( \frac{56}{3}+\ln 9 \)
\( \frac{65}{3} +\ln 27 \)
\( \frac{56}{3} \)
2010001102
Level:
A
Evaluate the definite integral. \[ \int\limits_{\frac{\pi}6}^{\frac{\pi}3}\left(\frac3{\sin^2x} -\frac6{\cos^2x}\right)\mathrm{d}x \]
\( -2\sqrt3 \)
\( 2\sqrt3 \)
\( 0 \)
\( 12\sqrt3 \)
2010001101
Level:
A
Evaluate the definite integral.
\[ \int\limits_0^1\left(4\sqrt[3]{x}-4x^3+2\mathrm{e}^x\right)\mathrm{d}x \]
\( 2\mathrm{e} \)
\( 4+2\mathrm{e} \)
\( 0 \)
\( -2\mathrm{e} \)
2010000812
Level:
A
Assuming \( y \neq 1\), \(x\neq \pm y\), simplify the expression:
\[\frac{y^2-2xy+x^2}{(1-y)(y-x)}\cdot\frac{3y^2-6y+3}{x^2-y^2}\]
\(\frac{3(y-1)}{x+y}\)
\(\frac{3(1-y)}{x+y}\)
\(\frac{3}{x+y}\)
\( 3\)