Polynomials and fractions

9000146205

Level: 
A
Factor the following expression. \[ 9a^{6} - 4b^{2} \]
\(\left (3a^{3} - 2b\right )\left (3a^{3} + 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{3} - 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{2} + 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{2} - 2b\right )\)

9000146206

Level: 
A
Factor the following expression. \[ x^{2}y^{10} - 81 \]
\(\left (xy^{5} - 9\right )\left (xy^{5} + 9\right )\)
\(\left (xy^{5} - 9\right )\left (xy^{5} - 9\right )\)
\(\left (xy^{5} - 9\right )\left (xy^{2} + 9\right )\)
\(\left (xy^{5} - 9\right )\left (xy^{2} - 9\right )\)

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