Polynomials and fractions

1003032308

Level: 
A
Consider polynomials \( p(x)=(m-2)x^3+3mx^2-x+m \) and \( q(x)=x^3+m^2x^2+x+3 \).
Polynomials \( p \) and \( q \) are different for every \( m \).
Polynomials \( p \) and \( q \) are equal for \( m=3 \).
Polynomials \( p \) and \( q \) are equal for \( m=-3 \).
Polynomials \( p \) and \( q \) are equal for \( m=3 \) and for \( m=0 \).

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 \( 100\,\mathrm{km}/\mathrm{h} \)

1003032302

Level: 
A
The relationship between the time \( t \), the travelling distance \( s \) and the average speed \( v \) is expressed by the formula \( s = v\cdot t \). If the speed doubles, then the time to travel the same distance
will decrease by half.
will decrease by \( 2 \) hours.
will double.
will increase by \( 2 \) hours.