C

1103067809

Level: 
C
Given the graphs of the functions \( f(x)=\frac12x^2-3 \) and \( g(x)=\frac12x \), find the solution set of the following equation. \[ \left|\frac12 x^2-3\right|=\left|\frac12 x\right| \]
\( \{ -3, -2, 2, 3 \} \)
\( \{ -2, 3 \} \)
\( \{ 2, 3 \} \)
\( \left\{ -\sqrt6, -2, \sqrt6, 3 \right\} \)

1003067805

Level: 
C
For \( x\in[-3,5] \) find the solution set of the following equation. \[ \left|(x+3)(x-5)\right|=5 \]
\( \left\{ 1-\sqrt{11},1+\sqrt{11} \right\} \)
\( \left\{ 1-\sqrt{21},1+\sqrt{21} \right\} \)
\( \{ -3, 5 \} \)
\( \left\{1-\sqrt{21}, 1-\sqrt{11},1+\sqrt{11},1+\sqrt{21} \right\} \)

1003067804

Level: 
C
For \( x\in[4,\infty) \) choose the correct form of the equation \[ \left|-x^2+3x+4\right|=\left|-2 x^2+ 11 x - 12\right| \] that does not contain an absolute value.
\( x^2-3x-4=2x^2-11x+12 \)
\( x^2-3x-4=-2x^2+11x-12 \)
\(-x^2+3x+4=2x^2-11x+12 \)
\( -x^2+3x+4=-2x^2+11x-12 \)

1003041603

Level: 
C
There are \( 30 \) students in a class, of them are \( 14 \) girls and the rest are boys. The teacher selects two students for weekly routine help. If selection is done at random, what is the probability that these students are not two girls? Round the result to two decimal places.
\( \frac{\binom{16}2+\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}79 \)
\( \frac{\binom{16}2}{\binom{30}2}\doteq 0{.}28 \)
\( \frac{\binom{14}2}{\binom{30}2}\doteq 0{.}21 \)
\( \frac{\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}51 \)