1003037302
Level:
A
The sum of three consecutive odd numbers is twenty greater than the smallest of these numbers. Find the smallest one of the three unknown odd numbers.
\( 7 \)
\( 13 \)
\( 21 \)
\( 1 \)
A
1003037301
Level:
A
Five times the unknown number is greater by nine than one-half of the number. Find the number.
\( 2 \)
\( -2 \)
\( 1 \)
\( 10 \)
1003028905
Level:
A
Find the factored form of the equation.
\[ x^4+2x^3-3x-6=0 \]
\( \left(x^3-3\right)(x+2) = 0 \)
\( \left(x^3+3\right)(x-2) = 0 \)
\( \left(x^3-2\right)(x+3) = 0 \)
\( \left(x^3+2\right)(x-3) = 0 \)
1003028904
Level:
A
Find the factored form of the equation.
\[ x^4+2x^2=0 \]
\( x^2\left(x^2+2\right)=0 \)
\( \left(x^2-2\right)\left(x^2+2\right)=0 \)
\( \left(x^2+\sqrt2x\right)\left(x^2-\sqrt2x\right)=0 \)
\( \left(x^2+\sqrt2x\right)\left(x^2+\sqrt2x\right)=0 \)
1003028903
Level:
A
Find the factored form of the equation.
\[ x^3-2x^2-x+2=0 \]
\( (x-2)(x-1)(x+1)=0 \)
\( x(x-1)(x-2)=0 \)
\( x^2(x-2)=0 \)
\( x(x+1)(x-2)=0 \)
1003028902
Level:
A
Find the factored form of the equation.
\[ x^4+2x^2+x^3+2x=0 \]
\( x\left(x^2+2\right)\left(x+1\right)=0 \)
\( x\left(x^2+1\right)\left(x+1\right)=0 \)
\( x\left(x^2+1\right)\left(x+2\right)=0 \)
\( x\left(x^2+2\right)\left(x+2\right)=0 \)
1003028901
Level:
A
Find the factored form of the equation.
\[ x^4-16=0 \]
\( \left(x^2+4\right)\left(x-2\right)\left(x+2\right)=0 \)
\( \left(x-2\right)^2\left(x+2\right)^2=0 \)
\( \left(x-2\right)^4=0 \)
\( \left(x+4\right)\left(x-2\right)\left(x+2\right)=0 \)
1003020403
Level:
A
An ellipse has the centre at \( S=[-1;3] \), the semi major axis with the length of \( 3 \) and the semi minor axis with the length of \( 2 \). The semi major axis is parallel to \( y \) axis. The equation of the ellipse is:
\( \frac{(x+1)^2}4+ \frac{(y-3)^2}9 = 1 \)
\( \frac{(x+1)^2}9 + \frac{(y-3)^2}4 = 1 \)
\( \frac{(x-1)^2}4+ \frac{(y+3)^2}9 = 1 \)
\( \frac{(x+1)^2}4-\frac{(y-3)^2}9 = 1 \)
\( \frac{(x+1)^2}4 + \frac{(y-3)^2}9 = -1 \)
1003020402
Level:
A
The equation of an ellipse is given by \( x^2+4y^2-6x+32y+48=0 \). The length of its semi-minor axis is:
\( \frac52 \)
\( 5 \)
\( 25 \)
\( \frac{25}4 \)
\( \frac{15}2 \)
1003020401
Level:
A
The equation of an ellipse is given by \( 5x^2+9y^2-30x-18y+9=0 \). The length of its semi-major axis is:
\( 3 \)
\( 5 \)
\( 9 \)
\( \sqrt5 \)
\( 14 \)