9000020909
Level:
B
The sum of squares of two consecutive integers is
\(1201\).
Identify these integers.
\(24\)
and \(25\)
\(23\)
and \(24\)
\(25\)
and \(26\)
\(26\)
and \(27\)
Quadratic Equations and Inequalities
9000020409
Level:
B
One of the solutions of the quadratic equation \( x^{2} + bx - 10 = 0\) is \(x_{1} = 5\). Find the second solution \(x_{2}\) and the value of the coefficient \(b\).
\(x_{2} = -2\) and
\(b = -3\)
\(x_{2} = -3\) and
\(b = -2\)
\(x_{2} = 2\) and
\(b = 3\)
\(x_{2} = 3\) and
\(b = 2\)
9000020410
Level:
B
The quadratic equation
\[
ax^{2} + 4x + c = 0
\]
has solutions \(x_{1} = -3\)
and \(x_{2} = 5\). Find the
coefficients \(a\)
and \(c\).
\(a = -2\),
\(c = 30\)
\(a = -2\),
\(c = -30\)
\(a = 2\),
\(c = -30\)
\(a = 2\),
\(c = 30\)
9000020406
Level:
B
The ratio of the sides of a rectangle is
\(3 : 4\). The length of
the diagonal is \(100\, \mathrm{cm}\).
Find the perimeter of the rectangle.
\(280\, \mathrm{cm}\)
\(150\, \mathrm{cm}\)
\(480\, \mathrm{cm}\)
\(300\, \mathrm{cm}\)
9000020403
Level:
A
Identify an equation which does not have at least one solution in the interval
\((0,\infty )\).
\(x^{2} + 5x + 6 = 0\)
\(x^{2} - 2x - 3 = 0\)
\(x^{2} - 10x = 0\)
\(x^{2} - 10x + 24 = 0\)
9000020405
Level:
A
Identify an equation which does not have the set
\(K = \{ - 3,6\}\) as the
set of all solutions of this equation.
\(3x^{2} - 9x + 54 = 0\)
\(2x^{2} - 6x - 36 = 0\)
\(\frac{1}
{3}x^{2} - x - 6 = 0\)
\(- x^{2} + 3x + 18 = 0\)
9000021703
Level:
B
Solve the following inequality.
\[
(x - 2)^{2}\geq (x + 1)(x - 5)
\]
\(x\in \mathbb{R}\)
\(x\in \emptyset \)
\(x\in \left (-\infty , \frac{9}
{8}\right ] \)
\(x\in \left [ \frac{9}
{8},\infty \right )\)
9000021803
Level:
B
Solve the following inequality.
\[
(3x - 1)(2 - 4x) < 0
\]
\(x\in \left (-\infty , \frac{1}
{3}\right )\cup \left (\frac{1}
{2},\infty \right )\)
\(x\in \left (\frac{1}
{3}, \frac{1}
{2}\right )\)
\(x\in \left (-\infty , \frac{1}
{2}\right )\)
\(x\in \left (\frac{1}
{3},\infty \right )\)
9000022301
Level:
B
Find the solution set of the quadratic inequality.
\[
x^{2} - 8x + 16\leq 0
\]
\(\{4\}\)
\(\emptyset \)
\(\mathbb{R}\setminus \{4\}\)
\(\mathbb{R}\)
\((-\infty ,4)\cup (4,\infty )\)