B

9000022306

Level: 
B
Using the graph of the function \(f(x)= -x^{2} - 2x + 8\) solve the following inequality. \[ -x^{2} - 2x + 8\leq 5 \]
\(\left (-\infty ,-3\right ] \cup \left [ 1,\infty \right )\)
\(\left (-\infty ,-4\right ] \cup \left [ 2,\infty \right )\)
\(\left [ -3,1\right ] \)
\(\left [ -4,2\right ] \)

9000022308

Level: 
B
Using graphs of the functions \(f(x)= -2x^{2} + 3x + 4\) and \(g(x) = x\) solve the following quadratic inequality. \[ -2x^{2} + 3x + 4\geq x \]
\(\left [ -1,2\right ] \)
\(\{ - 1,2\}\)
\(\left (-1,2\right )\)
\(\left (-\infty ,-1\right )\cup \left (2,\infty \right )\)

9000022309

Level: 
B
Using graphs of the functions \(f(x) = x^{2} + x - 1\) and \(g(x) = -\frac{1} {2}x\) solve the following quadratic inequality. \[ x^{2} + x - 1 > -\frac{1} {2}x \]
\(\left (-\infty ,-2\right )\cup \left (\frac{1} {2},\infty \right )\)
\(\left (-2, \frac{1} {2}\right )\)
\(\left [ -2, \frac{1} {2}\right ] \)
\(\left (-\infty ,-2\right ] \cup \left [ \frac{1} {2},\infty \right )\)

9000022803

Level: 
B
Establish the values of the parameter \(t\) which ensure that the equation \[ x^{2} + tx + t + 8 = 0 \] with an unknown \(x\) has complex solutions with a nonzero imaginary part.
\(\left (-4,8\right )\)
\(\left [ -4,8\right ] \)
\(\left (-\infty ,-4\right )\cup \left (8,\infty \right )\)
\(\left (-\infty ,-4\right ] \cup \left [ 8,\infty \right )\)

9000022904

Level: 
B
Find the values of a real parameter \(t\) which ensure that the following system has a unique solution. \[ \begin{alignedat}{80} 2x & + &y & + &t & = - &2 & & & & & & & & \\ - 4x & - 2 &y & + &1 & = &0 & & & & & & & & \\\end{alignedat}\]
\(t\in \emptyset \)
\(t\in \mathbb{R}\)
\(t = 3\)
\(t = 1\)
\(t\in \mathbb{R}\setminus \{3\}\)

9000022905

Level: 
B
Find the values of a real parameter \(t\) which ensure that the following system has a unique solution. \[ \begin{alignedat}{80} tx & + &y & + &3 & = 0 & & & & & & \\4x & - 2 &y & + &1 & = 0 & & & & & & \\\end{alignedat}\]
\(t\in \mathbb{R}\setminus \{ - 2\}\)
\(t\in \mathbb{R}\)
\(t = -2\)
\(t\in \emptyset \)

9000022906

Level: 
B
Find the values of a real parameter \(t\) which ensure that the following system has a unique solution \([a,b]\) such that both \(a\) and \(b\) are positive real numbers. \[ \begin{alignedat}{80} a & - &tb & = - &2 & & & & & & \\a & + 2 &tb & = &0 & & & & & & \\\end{alignedat}\]
\(t\in \emptyset \)
\(t\in \mathbb{R}^{+}\)
\(t\in \mathbb{R}^{-}\)
\(t = 0\)
\(t\in \mathbb{R}\)