9000104302
Level:
A
Assuming \(a = 0\),
solve the following inequality.
\[
2ax + 4a < 1
\]
\(\mathbb{R}\)
\(\emptyset \)
\(\left (\frac{1-4a}
{2a} ;\infty \right )\)
\(\left (-\infty ; \frac{1-4a}
{2a} \right )\)
A
9000104306
Level:
A
Assuming \(a = 0\),
solve the following inequality.
\[
a\left (a - 1\right )x < 1
\]
\(x\in\mathbb{R}\)
\(x\in\mathbb{R}\setminus \{1\}\)
\(x\in\emptyset \)
\( x\in\left \{ \frac{1}
{a\left (a-1\right )}\right \}\)
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.
\[
a^{2}x - 1 < a - ax
\]
\(\emptyset \)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \{- 1\}\)
\(\mathbb{R}\setminus \{ - 1;0\}\)
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.
\[
3a^{2}x - 2ax + 4 = 6a
\]
\(\left \{\frac{2}
{3}\right \}\)
\(\left \{-\frac{2}
{3}\right \}\)
\(\left \{0\right \}\)
\(\left \{0; \frac{2}
{3}\right \}\)
9000104404
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has infinitely many solutions.
\[
a^{2}x + 1 = a^{2} + ax
\]
\(\left \{1\right \}\)
\(\left \{-1;1\right \}\)
\(\left \{0\right \}\)
\(\left \{-1\right \}\)
9000104405
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has a unique solution.
\[
a^{3}x + 3 = 3a^{2}x + a
\]
\(\mathbb{R}\setminus \left \{0;3\right \}\)
\(\left \{0\right \}\)
\(\left \{0;3\right \}\)
\(\mathbb{R}\setminus \left \{3\right \}\)
9000101601
Level:
A
Expand \((1 + x)\left (x^{2} + x - 1\right )(1 - x)\).
\(- x^{4} - x^{3} + 2x^{2} + x - 1\)
\(x^{4} - x^{3} + 2x^{2} + x + 1\)
\(- x^{4} + x^{3} - 1\)
\(x^{4} + x^{3} - 2x^{2} + x - 1\)
9000101604
Level:
A
Expand the polynomial \(\left (2x^{2} + 4x\right )^{2} -\left (4x - 2x^{2}\right )^{2}\).
\(32x^{3}\)
\(0\)
\(32x^{3} - 8x\)
\(32x^{3} - 32x^{2} + 8x\)