2010008405
Level:
A
Consider the equation
\[
x^{2}(1 - q) + 2x + 1 + q = 0
\]
with the real parameter \(q\).
Solve the equation for \(q = -1\).
\(\left \{-1;0\right \}\)
\(\left \{-1;1\right \}\)
\(\left \{0;1\right \}\)
\(\emptyset \)
A
2010008402
Level:
A
Find all the values of the parameter \(k\) so that the solution of the following equation is positive.
\[
kx -2= 3x -k
\]
\(k\in (2;3)\)
\(k\in (0;\infty )\)
\(k\in (3;\infty )\)
\(k\in (-\infty;2 )\)
2010008401
Level:
A
Find all the values of the parameter \(k\) so that the solution of the following equation is bigger than \(6\).
\[
2x - 9 = \frac{7x - 3k}
{3}
\]
\(k\in (-\infty;11 )\)
\(k\in \{11\}\)
\(k\in (11;\infty )\)
\(k\in (-\infty;13 )\)
2010008303
Level:
A
Three merchants were selling the same product for the same price. Successively they adjusted the prices as follows:
(a) Merchant A first increased the price of the product by \(5\%\), but later reduced it by \(10\%\).
(b) Merchant B first reduced the price of the product by \(2\%\) and later reduced it again, this time by \(3\%\).
(c) Merchant C adjusted the price of the product only once. He cheapened the product by \(10\%\).
Which merchant offers the product for the highest price after price adjustments?
Merchant B
Merchant A
Merchant C
All merchants will sell the product for the same price.
2010008302
Level:
A
During epidemic the towns reported the ratios of ill citizens (see the table). Which town had the biggest number of ill citizens on 1$^{\mathrm{st}}$ July.
\[\begin{array}{|c|c|c|} \hline \text{Town} & \text{Total population} & \text{Ratio of ill citizens on 1\(^{\mathrm{st}}\) July 2020} \\\hline A & 8\,000 & 4.0\% \\\hline B & 64\,000 & 0.5\% \\\hline C & 320\,000 & 0.1\% \\\hline \end{array}\]
All towns had the same number of ill citizens.
The biggest number of ill citizens was in the town A.
The biggest number of ill citizens was in the town B.
The biggest number of ill citizens was in the town C.
2010008301
Level:
A
Three companies made a commitment to donate a portion of their annual profit to charity (see the table). Which company did donate the biggest sum?
\[\begin{array}{|c|c|c|} \hline \text{Company} & \text{Annual profit} & \text{Ratio from annual profit} \\\hline A & 6\,000\,000 & 4.0\% \\\hline B & 12\,000\,000 & 2.0\% \\\hline C & 48\,000\,000 & 0.5\% \\\hline \end{array}\]
All companies donated the same sum.
The biggest donor was the company A.
The biggest donor was the company B.
The biggest donor was the company C.
2010008213
Level:
A
Which of the given numbers is the product of all the solutions of the following exponential equations?
\begin{align*} 3^{x+1}-3^{x}-3^{x-1}&=15\\ 3^{x+2}-3^{x}&=72 \end{align*}
\( 4\)
\( -1\)
\( 1\)
\( 2\)
2010008205
Level:
A
Identify the solution of the equation.
\[ 3\cdot 25^x-2\cdot 5^{x}-1=0\]
\(x=0\)
\(x=\frac12\)
\(x=-\frac{1}{2}\)
\(x=4\)
2010008204
Level:
A
Identify the solution of the equation.
\[ 4^x+2\cdot 16^{x}-1=0\]
\(x=-\frac{1}{2}\)
\(x=\frac12\)
\(x=0\)
\(x=4\)
2010008203
Level:
A
Identify the solution of the equation.
\[ 3^x+3^{x+1}+3^{x+3}=93 \]
\(x=1\)
\(x=2\)
\(x=0\)
\(x=4\)