9000106206
Level:
A
In the following list find the vector having the same direction as the line passing through
the points \(A = [3,4]\)
and \(B = [5,8]\).
\((1,2)\)
\((4,2)\)
\((1,3)\)
\((2,-4)\)
A
9000106001
Level:
A
In the following list identify a vector in the direction of the following parametric
line.
\[\begin{aligned}
x =\ &1 + t, & &
\\y =\ &3 + 2t,\ t\in \mathbb{R} & &
\end{aligned}\]
\(\left (1,2\right )\)
\(\left (1,3\right )\)
\(\left (0,2\right )\)
\(\left (3,1\right )\)
9000106207
Level:
A
In the following list identify a normal vector to the line
\(p\).
\[
p\colon - x + 2y + 3 = 0
\]
\((1,-2)\)
\((2,3)\)
\((-1,3)\)
\((2,-1)\)
9000104306
Level:
A
Assuming \(a = 0\),
solve the following inequality.
\[
a\left (a - 1\right )x < 1
\]
\(x\in\mathbb{R}\)
\(x\in\mathbb{R}\setminus \{1\}\)
\(x\in\emptyset \)
\( x\in\left \{ \frac{1}
{a\left (a-1\right )}\right \}\)
9000104302
Level:
A
Assuming \(a = 0\),
solve the following inequality.
\[
2ax + 4a < 1
\]
\(\mathbb{R}\)
\(\emptyset \)
\(\left (\frac{1-4a}
{2a} ,\infty \right )\)
\(\left (-\infty , \frac{1-4a}
{2a} \right )\)
9000104308
Level:
A
Assuming \(a = \frac{1}
{2}\),
solve the following inequality.
\[
2a^{2}x - 1 > ax
\]
\(\emptyset \)
\(\mathbb{R}\)
\(\left ( \frac{1}
{a\left (2a-1\right )},\infty \right )\)
\(\left (-\infty , \frac{1}
{a\left (2a-1\right )}\right )\)
9000104309
Level:
A
Assuming \(a = -1\),
solve the following inequality.
\[
a^{2}x - 1 < a - ax
\]
\(\emptyset \)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \{- 1\}\)
\(\mathbb{R}\setminus \{ - 1,0\}\)
9000104401
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has no solution.
\[
a^{2}x + 2ax - 3a = 0
\]
\(\{ - 2\}\)
\(\{2\}\)
\(\{0\}\)
\(\{ - 3,1\}\)
9000104402
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has no solution.
\[
2a^{2}x - ax - 2a = -1
\]
\(\left \{0\right \}\)
\(\left \{\frac{1}
{2}\right \}\)
\(\left \{-\frac{1}
{2}\right \}\)
\(\left \{-\frac{1}
{2}, \frac{1}
{2}\right \}\)
9000104403
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has infinitely many solutions.
\[
3a^{2}x - 2ax + 4 = 6a
\]
\(\left \{\frac{2}
{3}\right \}\)
\(\left \{-\frac{2}
{3}\right \}\)
\(\left \{0\right \}\)
\(\left \{0, \frac{2}
{3}\right \}\)