2000006801
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequalities is it?
\(y \geq x+1\)
\(y \geq x-1\)
\(y \leq x+1\)
\(y \leq x-1\)
Systems of linear equations and inequalities
2000006802
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequality is it?
\(y \leq -2x\)
\(y \geq -2x\)
\(y \leq -\frac{x}2\)
\(y \geq -\frac{x}2\)
2000006803
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequality is it?
\[\begin{aligned}
y &\leq x+2
\\y &\geq x -2
\end{aligned}\]
\[\begin{aligned}
y &\leq x-2
\\y &\geq x+2
\end{aligned}\]
\[\begin{aligned}
y &\leq 2x+2
\\y &\geq 2x -2
\end{aligned}\]
\[\begin{aligned}
y &\leq 2x-2
\\y &\geq 2x +2
\end{aligned}\]
2000006804
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequalities is it?
\[\begin{aligned}
y &\leq x
\\y &\geq -x
\end{aligned}\]
\[\begin{aligned}
y &\leq - x
\\y &\geq x
\end{aligned}\]
\[\begin{aligned}
y &\leq x
\\y &\leq -x
\end{aligned}\]
\[\begin{aligned}
y &\geq x
\\y &\geq -x
\end{aligned}\]
2010006504
Level:
C
How many solutions has the inequality in \( \mathbb{N}\times\mathbb{N} \)? (Hint: Solve the inequality graphically.)
\[ 3y\leq -2x+4 \]
\( 0 \)
\(2\)
\(3\)
infinity
2010011201
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which inequality is it?
\( y \geq -\frac32x+\frac{7}2 \)
\( y \leq -\frac32x+\frac{7}2 \)
\( y > -\frac32x+\frac{7}2 \)
\( y < -\frac32x+\frac{7}2 \)
2010011202
Level:
C
Students registered for sports camps. For the biking camp registered by \( 12 \) students more than for the boating camp. After some time one of the students switched his registration from the boating camp to the biking camp. Now, there is three times more bikers than boaters. How many students registered originally for the biking camp?
\( 20 \)
\( 21 \)
\( 7 \)
\( 8 \)
9000022901
Level:
C
An arrow has been shot at the angle
\(60^{\circ }\) at the
speed \(10\, \mathrm{m}\, \mathrm{s}^{-1}\).
Find the time when the height equals to the horizontal distance from the take-off
point. Hint: The position is given by the equations
\(x = v_{0}t\cdot \cos \alpha \),
\(y = v_{0}t\cdot \sin \alpha -\frac{1}
{2}gt^{2}\). Use
\(g = 10\, \mathrm{m}\, \mathrm{s}^{-2}\) as an
acceleration of gravity.
\(\left (\sqrt{3} - 1\right )\, \mathrm{s}\)
\(\left (\sqrt{3} + 1\right )\, \mathrm{s}\)
\(\sqrt{3}\, \mathrm{s}\)
\(\left (\sqrt{2} - 1\right )\, \mathrm{s}\)
\(\left (\sqrt{2} + 1\right )\, \mathrm{s}\)
9000026001
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x +\phantom{ 3}y\leq &3 & &
\\y - 2x < & - 1 & &
\end{aligned}\]
blue
red
green
yellow
9000026002
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x + y > &2 + x & &
\\y + 1\leq &x + 1 & &
\end{aligned}\]
green
red
yellow
blue