1003177804
Level:
C
Choose the solution set of the given inequality.
\[ \left| |x-5|+2\right| > 3 \]
\( (-\infty;4)\cup(6;\infty) \)
\( (-\infty;-4)\cup(6;\infty) \)
\( (6;\infty) \)
\( (-\infty;-5)\cup(6;\infty) \)
C
1003177801
Level:
C
Choose the domain of the expression \( \sqrt{|x-3|-4} \).
\( (-\infty;-1]\cup[7;\infty) \)
\( (-1;3]\cup[7;\infty) \)
\( [7;\infty) \)
\( (-\infty;1)\cup(7;\infty) \)
1003158902
Level:
C
The length of a rectangle is \( 4\,\mathrm{cm} \) and width is \( x\,\mathrm{cm} \). The rectangle is divided by vertical crossing line into two parts so that one part is a square with the side of \( x\,\mathrm{cm} \) (see the picture). What is the maximum area of the remaining part of the rectangle?
\( 4\,\mathrm{cm}^2 \)
\( 2\,\mathrm{cm}^2 \)
\( 16\,\mathrm{cm}^2 \)
\( 1\,\mathrm{cm}^2 \)
1003158901
Level:
C
An object is moving with a constant deceleration in a straight line. Displacement \( s \) (in metres) in time \( t \) (in seconds) is modelled by \( s=24t-3t^2 \). Find the displacement of the object from the moment it starts to decelerate until it stops.
\( 48\,\mathrm{m} \)
\( 144\,\mathrm{m} \)
\( 16\,\mathrm{m} \)
\( 96\,\mathrm{m} \)
1003118110
Level:
C
Let \( \frac{u\sqrt5}{5-\sqrt5}=\frac{\frac{5+\sqrt5}{\sqrt5+1}}{1-\sqrt5} \). What is the reciprocal of \( u \)?
\( \frac1u=-\frac{\sqrt5}5 \)
\( \frac1u = \frac1{\sqrt5} \)
\( \frac1u = \frac5{\sqrt5} \)
\( \frac1u = -\sqrt5 \)
1003118109
Level:
C
Which of the following numbers has the same unit digit as the number \( 555^{555} \)?
\( 10^{555}+5 \)
\( \frac{10^{555}}5 \)
\( 5\cdot10^{555} \)
\( 10^{555}+10^{555} \)
1003118108
Level:
C
The value of \( \sqrt{5\left(222^2+111^2\right)} \) is:
\( 555 \)
\( 111\sqrt5 \)
\( \sqrt{15} \)
\( \sqrt{1110^2-555^2} \)
1003118105
Level:
C
The number \( \frac1{\left(2-\sqrt3\right)^3} \) is equal to:
\( 26+15\sqrt3 \)
\( 27+24\sqrt3 \)
\( 14+7\sqrt3 \)
\( 27+30\sqrt3 \)
1003118104
Level:
C
Simplify \(\sqrt[4]{\left(\sqrt3-\sqrt2\right)^4}+\sqrt[4]{\left(\sqrt2-\sqrt5\right)^4}+\sqrt[3]{\left(\sqrt3-\sqrt5\right)^3} \).
\( 2\sqrt3-2\sqrt2 \)
\( 2\sqrt5 - 2\sqrt2 \)
\( 2\sqrt3-2\sqrt5 \)
\( 2\sqrt5-2\sqrt3 \)
1003118101
Level:
C
Which of the following inequalities describes a correct relationship between the numbers \( a \), \( b \), \( c \) if \( a=4^{2^4} \), \( b=3^{4^3} \), \( c=2^{3^4} \)? (Hint: Barring parentheses, \( x^{y^z} \) is equivalent to \( x^{\left(y^z\right)} \).)
\( a < c < b \)
\( b < a < c \)
\( a < b < c \)
\( b < c < a \)