1003187105
Level:
B
Let \( a \) be a positive real number. Then \( |x| \geq a \)
if and only if \( x \geq a \) or \( x \leq -a \).
if and only if \( x \geq a \).
if and only if \( x \leq -a \).
if and only if \( x > 0 \).
B
1003187104
Level:
B
Let \( a \) be a positive real number. Then \( |x| \leq a \)
if and only if \( -a \leq x \leq a \).
if and only if \( x \leq a \).
if and only if \( x \geq -a \).
if and only if \( x < 0 \).
1003032401
Level:
B
Factoring the polynomial \( 625x^4-1 \) we get:
\( \left( 25x^2+1\right)(5x-1)(5x+1) \)
\( (5x-1)(5x+1)^2 \)
\( (5x-1)^4 \)
\( \left( 25x^2+1\right)(5x-1)^2 \)
1003032303
Level:
B
A car travels by \( 20\,\mathrm{km}/\mathrm{h} \) faster than a second car. The first car covers \( 260\,\mathrm{km} \) in the same time the second car covers \( 195\,\mathrm{km} \). What is the average speed of each car?
\( 80\,\mathrm{km}/\mathrm{h} \) and \( 60\,\mathrm{km}/\mathrm{h} \)
\( 100\,\mathrm{km}/\mathrm{h} \) and \( 80\,\mathrm{km}/\mathrm{h} \)
\( 90\,\mathrm{km}/\mathrm{h} \) and \( 70\,\mathrm{km}/\mathrm{h} \)
\( 120\,\mathrm{km}/\mathrm{h} \) and \( 100\,\mathrm{km}/\mathrm{h} \)
1003187309
Level:
B
Give the number which satisfies the equation \( |6x+4|+4x=0 \).
\( x=-2 \)
\( x=1 \)
\( x=2 \)
\( x=-1 \)
1003187304
Level:
B
How many solutions does the equation \( \left| |x-4|-2\right|+2=0 \) have?
\( 0 \)
\( 2 \)
\( 4 \)
\( 6 \)
1003187303
Level:
B
Find the solution set of the equation \( |x|=-x \).
\( (-\infty;0] \)
\( (-1;1) \)
\( \{-4\} \)
\( (0;+\infty) \)
1003187411
Level:
B
The solution set of the equation \( 3|51-x|-2|x-81| =0 \) is:
\( \{-9;63\} \)
\( \{63\} \)
\( \{9;63\} \)
\( \{-63;-9\} \)
1003187405
Level:
B
Choose the expression which takes only negative values.
\( -|2-4x|-1 \)
\( |-2x-5|-2 \)
\( -|2-4x|+2 \)
\( |2-x|-2 \)
1003187402
Level:
B
For a given parameter \( a\in\mathbb{R} \) the number \( \pi-\sqrt[3]5-\sqrt2+7 \) represents one of the solutions of the equation \( |2x|=2a^2 \). Which of the following numbers is also the solution of this equation?
\( \sqrt2-7+\sqrt[3]5-\pi \)
\( \sqrt{7-\pi+\sqrt[3]5+\sqrt2} \)
\( \sqrt[3]5-\pi-\sqrt2-7 \)
\( \sqrt{\pi-\sqrt[3]5-\sqrt2+7} \)