1003187002
Level:
A
Evaluate the expression \( \left|\left(1-\sqrt2\right)^2 \right|+\left|\left(1+\sqrt2\right)^2\right|-|-6| \).
\( 0 \)
\( 12 \)
\( 4\sqrt2 \)
\( -4 \)
Absolute value
1003187001
Level:
B
Let \( x\in(-\infty;-4] \). The value of the expression \( \left| |x|-4\right|-2|x-4|+|10-x| \) is equal to:
\( -2 \)
\( -6 \)
\( 2 \)
\( 6 \)
1003124210
Level:
B
Which two numbers do both satisfy the equation \( |3x-3|=9 \)?
\( -2\text{, } 4 \)
\( -4\text{, } 2 \)
\( -5\text{, } 7 \)
\( -7\text{, } 5 \)
1003124209
Level:
B
Which of the given inequalities holds for \( x=2\pi \)?
\( |x+1| > 5 \)
\( |x-1| < 2 \)
\( |x+3| \leq 4 \)
\( |x-5| \geq 3 \)
1003124208
Level:
B
Assuming \( -6 < x < 0 \), the expression \( \frac{|x+6|-x+6}x \) is equal to:
\( \frac{12}x \)
\( -\frac{12}x \)
\( 2 \)
\( 0 \)
1003124207
Level:
B
On the real number line, the distance of a number \( x \) from the number \( -4 \) is given by:
\( |x+4| \)
\( |x-4| \)
\( |4x| \)
\( |x|+4 \)
1003124206
Level:
A
Simplifying \( \left|\sqrt5-3\right|-\left|2\sqrt5-4\right| \) we get:
\( -3\sqrt5+7 \)
\( -\sqrt5+1 \)
\( -3\sqrt5+1 \)
\( -\sqrt5+7 \)
1003124205
Level:
B
Assuming \( x\in(4;7) \), the expression \( |x-4|-|x-7| \) can be written in the form:
\( 2x-11 \)
\( -2x+11 \)
\( 3 \)
\( -11 \)
1003124204
Level:
B
Let \( x\neq0 \). Complete the following sentence to get a true statement. The solution set of the inequality \( \frac{|x|}x>2 \)
does not contain any integer.
contains \( 2 \) integers.
contains only natural numbers.
contains infinitely many integers.
1003124203
Level:
B
Assuming \( x < 0 \), the expression \( \bigl| |x|+2 \bigr| \) is equal to:
\( -x+2 \)
\( x+2 \)
\( -x-2 \)
\( x-2 \)