1103040110
Level:
B
The picture shows a hyperbola drawn in the rectangular coordinate system. What is the major axis of this hyperbola?
The \( y \)-axis
The segment \( AB \)
The segment \( EF \)
The \( x \)-axis
B
1103040109
Level:
B
The picture shows a hyperbola drawn in the rectangular coordinate system. What is the minor axis of this hyperbola?
The \( y \)-axis
The segment \( EF \)
The \( x \)-axis
The segment \( AB \)
1103040108
Level:
B
A parabola in the rectangular coordinate system is shown in the picture. What is the vertex form equation of this parabola?
\( x^2 = 4(y-1) \)
\( x^2 = 4(y+1) \)
\( y^2 = 4(x-1) \)
\( y^2 = 4(x+1) \)
1103040105
Level:
B
A parabola is given by the picture. What is the parameter of this parabola?
The distance of the point \( F \) from the line \( d \)
The distance of points \( V \) and \( F \)
A half of the segment \( DV \)
Two times the distance of the point \( F \) from the line \( d \)
1103040104
Level:
B
The picture shows a hyperbola drawn in the rectangular coordinate system. What is the eccentricity of this hyperbola?
The distance of points \( S \) and \( F \)
The distance of points \( S \) and \( A \)
The distance of points \( A \) and \( B \)
The distance of points \( E \) and \( F \)
1003024102
Level:
B
The equation of a parabola is given by \( 3y^2+x-12y+14=0 \). Find the equation of its directrix.
\( x=-\frac{23}{12} \)
\( x=\frac{23}{12} \)
\( y=-\frac{23}{12} \)
\( y=\frac{23}{12} \)
\( x=-\frac{11}{6} \)
1003024101
Level:
B
The equation of a hyperbola with the center \( S=[-1,3] \), the focus \( F=[4,3] \), and the vertex \( A=[2,3] \) is given by:
\( \frac{(x+1)^2}{9}-\frac{(y-3)^2}{16} =1 \)
\( \frac{(x-1)^2}{9}-\frac{(y+3)^2}{16} =1 \)
\( \frac{(x+1)^2}{9}+\frac{(y-3)^2}{16} =1 \)
\( \frac{(x-1)^2}{16}-\frac{(y+3)^2}{9} =1 \)
\( \frac{(y-3)^2}{16}-\frac{(x+1)^2}{9} =1 \)
1003044607
Level:
B
Identify the solution of the equation.
\[ 16\cdot16^{\sqrt{2x+5}}-65\cdot4^{\sqrt{2x+5}}+4=0 \]
\( x=-2 \)
\( x_1=-\frac12,\ x_2=2 \)
\( x_1=\frac1{16},\ x_2=4 \)
\( x_1=-4,\ x_2=-\frac1{16} \)
1003044606
Level:
B
How many solutions does the following equation have?
\[ 7^{\sqrt x}+7^{1-\sqrt x}=8 \]
Exactly two solutions
Exactly one solution
No solutions
Infinitely many solutions
1003044605
Level:
B
Identify the solution of the equation.
\[ 3^{2x-2}-244\cdot3^{x-5}=-3^{-3} \]
\( x_1=-3,\ x_2=2 \)
\( x_1=-2,\ x_2=3 \)
\( x_1=\frac1{27},\ x_2=9 \)
\( x_1=-9,\ x_2=-\frac1{27} \)