1003162302
Level:
C
Find all the values of the real parameter \( m \) such that \( f(x)=-2(x-m)^2+3 \) is an even function.
\( m=0 \)
\( m=3 \)
\( m=-3 \)
\( m\in(-\infty,\infty) \)
C
1003162301
Level:
C
Find all the values of the real parameter \( a \) such that \( f(x)=ax^2-2 \) is decreasing on \( (0,\infty) \).
\( a\in(-\infty,0) \)
\( a\in(0,\infty) \)
\( a\in[2,+\infty) \)
\( a\in(-\infty,2] \)
1003160903
Level:
C
The graph of a linear function \( f \) passes through the point \( \left[4\sqrt3,2\right] \) and it makes an angle of \( 30^{\circ} \) with the positive direction of \( x \)-axis measured anticlockwise. Choose the correct form of the function \( f \), such that the given property is preserved.
\( f(x)=\frac{\sqrt3}3x-2 \)
\( f(x)=\sqrt3x-10 \)
\( f(x)=\frac{\sqrt3}3x+2 \)
\( f(x)=\sqrt3x+10 \)
1003160902
Level:
C
Suppose \( f \) is a linear function. If the value of the independent variable \( x \) increases by \( 4 \), the function value decreases by \( 12 \). Choose the correct form of the function \( f \), such that the given property is preserved.
\( f(x)=-3x \)
\( f(x)=3x \)
\( f(x)=3x-12 \)
\( f(x)=-\frac13x \)
1003160901
Level:
C
Suppose \( f \) is a linear function. If the value of the independent variable \( x \) increases by \( 6 \), the function value increases by \( 18 \). Choose the correct form of the function \( f \), such that the given property is preserved.
\( f(x)=3x+1 \)
\( f(x)=-3x \)
\( f(x)=\frac13x+18 \)
\( f(x)=\frac13x \)
1003163004
Level:
C
Find the sum of all the roots of the given equation.
\[ \Bigl| |x-4|-9\Bigr|=0 \]
\( 8 \)
\( 18 \)
\( 6 \)
\( 4 \)
1003163002
Level:
C
Find all \( t \), \( t\in\mathbb{R} \), such that the following equation with the variable \( x \) has more than two solutions.
\[ \Bigl| |3-x|-3\Bigr|=t \]
\( t\in(0,3] \)
\( t\in\{0,3\} \)
\( t\in\{3\} \)
\( t\in[1,3] \)
1003108307
Level:
C
Choose the triple of points, such that the graph of any of the functions \( f(x)=ax^2+c \), where \( a\in\mathbb{R}\setminus{0} \), \( c\in\mathbb{R} \), does not pass through all three points.
\( [-2,5] \), \( [2,1] \), \( [0,3] \)
\( [-2,5] \), \( [2,5] \), \( [0,3] \)
\( [-2,5] \), \( [2,5] \), \( [0,7] \)
\( [-2,5] \), \( [0,0] \), \( [1,1] \)
1103148606
Level:
C
If an object moving with an initial velocity \( v_0 \) is slowing down at a constant deceleration \( a \), then the distance \( s \) travelled while decelerating is described by the formula \( s=v_0t-\frac12at^2 \), where \( t \) is time of decelerating. Choose the graph, which could represent the dependency of the distance \( s \) on the time \( t \).
1103148605
Level:
C
Suppose, an object, that is in rest, starts to accelerate with the constant acceleration \( a \). The distance \( s \) travelled by the object in time \( t \) is given by the formula \( s=\frac12at^2 \). You can see the graph of the distance \( s \) on the time \( t \) dependency in the picture. Find the acceleration \( a \) of the object.
\( 8\frac{\mathrm{m}}{\mathrm{s}^2} \)
\( 16\frac{\mathrm{m}}{\mathrm{s}^2} \)
\( 4\frac{\mathrm{m}}{\mathrm{s}^2} \)
\( 2\frac{\mathrm{m}}{\mathrm{s}^2} \)