1003019902
Level:
A
Find the solution of the equation.
\[
\sqrt{x^2-4x+3}=\sqrt{x^2-6x+3}
\]
\(x\in\{0\}\)
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\mathbb{R}\setminus\{0\}\)
A
1003019901
Level:
A
Find the solution of the equation.
\[
\sqrt{-3x^2+2x+5}=3
\]
\(x\in\emptyset\)
\(x\in[-2,2]\)
\(x\in\{-2,2\}\)
\(x\in\mathbb{R}\)
1003020001
Level:
A
Find the sum of the roots of the equation.
\[
4x^2+2x=0
\]
\(-\frac12\)
\(0\)
\(2\)
\(-2\)
1003019801
Level:
A
Find the domain of the expression.
\[
\frac{x^2+4x-5}{-3x^2-19x+14}
\]
\(\mathbb{R}\setminus\left\{-7,\frac23\right\}\)
\(\mathbb{R}\setminus\left\{7,-\frac23\right\}\)
\(\left(7,-\frac23\right)\)
\(\left(-7,\frac23\right)\)
9000153803
Level:
A
Find the number of mutually different triangles such that all
three sides of each triangle are mutually different and each side is
\(2\),
\(3\),
\(4\) or
\(5\).
\(3\)
\(4\)
\(14\)
\(16\)
9000153806
Level:
A
Determine the number of three-digit positive integers that can be formed using the digits \(2\),
\(3\),
\(4\) and
\(5\). The digits can be used repeatedly.
\(64\)
\(24\)
\(256\)
\(81\)
9000154808
Level:
A
Little John plays a dice game against Robin Hood. To win, he needs to get the sum of \(8\) by rolling two dice. What is the probability that he wins over Robin right on the first roll? Round your result to three decimal places.
\(0{.}139\)
\(0{.}194\)
\(0{.}806\)
\(0{.}778\)
9000375401
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has a unique solution.
\[
a^{3}x + 4a - 1 = a^{2}x + 3
\]
\(\mathbb{R}\setminus \{0,1\}\)
\(\mathbb{R}\setminus \{ - 1,1\}\)
\(\mathbb{R}\setminus \{0\}\)
\(\mathbb{R}\setminus \{ - 1,0\}\)
9000375404
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has infinitely many solutions.
\[
a^{2}x + 2ax - 3x = a - 2
\]
\(\emptyset \)
\(\left \{-3,1\right \}\)
\(\left \{-3,1,2\right \}\)
\(\left \{0\right \}\)
9000375405
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has a unique solution.
\[
a^{2}x + 6x = a + 1 - 5ax
\]
\(\mathbb{R}\setminus \left \{-3,-2\right \}\)
\(\mathbb{R}\setminus \left \{2,3\right \}\)
\(\mathbb{R}\setminus \left \{-1,2,3\right \}\)
\(\mathbb{R}\setminus \left \{-3,-2,1\right \}\)