1003032401
Level:
B
Factoring the polynomial \( 625x^4-1 \) we get:
\( \left( 25x^2+1\right)(5x-1)(5x+1) \)
\( (5x-1)(5x+1)^2 \)
\( (5x-1)^4 \)
\( \left( 25x^2+1\right)(5x-1)^2 \)
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 \( m=0 \).
1003032307
Level:
A
The sum of the polynomials \( -x^3 y^2+6xy+5xy^4 \) and \( x^3-4xy^4+y^2 x^3+2xy \) is:
\( x^3+xy^4+8xy \)
\( -y^2+8xy+xy^4+y^2 x^3 \)
\( -x^3 y^2+8xy+xy^4+y^2 x^3+3x \)
\( x^3+xy^4+8x^2 y^2 \)
1003032306
Level:
A
The product \( \left(2x^2y+3xy^2\right)(x-y-4) \) equals:
\( 2x^3y+x^2y^2-3xy^3-8x^2y-12xy^2 \)
\( 2x^3y+2x^2y^2-3xy^3-8x^2y-12xy^2 \)
\( 2x^3y+3x^2y^2-3x^2y^2-8x^2y-12xy^2 \)
\( 2x^3y-x^2y^2+3xy^3-8x^2y+12xy^2 \)
1003032305
Level:
A
Simplifying the rational expressions \( \frac{(x-y)^2(p+q)^3}{2(x-y)(p+q)^4} \) we get:
\( \frac{x-y}{2(p+q)} \)
\( \frac{p+q}{2(x-y)} \)
\( 2(x-y)(p+q) \)
\( 2(x+y)(p-q) \)
1003032304
Level:
A
Reducing the rational expression \( \frac{13ab^2(c-d)}{39a^2b(c-d)^2} \) to lowest terms we get:
\( \frac{b}{3a(c-d)} \)
\( \frac{3b}{a(c-d)} \)
\( \frac{a}{3b(c-d)} \)
\( 3ab(c-d) \)
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.
1003032301
Level:
A
The polynomial \( 2x^2\left(x^2+3\right)+x^2+3 \) equals:
\( \left(2x^2+1\right)\left(x^2+3\right) \)
\( 2x^2\left(x^2+3\right) \)
\( 4x^2\left(x^2+3\right) \)
\( 2x^2\left(x^2+3\right)^2 \)
9000146708
Level:
C
Divide the following two polynomials using long division.
\[
\left (2x^{3} + x^{2} - 17x + 5\right ) : \left (x^{2} + 3x - 1\right )
\]
\(2x - 5\)
\(2x + 5\)
\(2x + 7 + \frac{2x-2}
{x^{2}+3x-1}\)
\(2x + 7 + \frac{12-40x}
{x^{2}+3x-1}\)