A

1103044805

Level: 
A
Given graphs of the functions \( f(x)=-x^2-x+6 \) and \( g(x) =x^2-4x+4 \), find the domain of the equation \( \frac{-x^2-x+6}{x^2-4x+4} =-2 \).
\( \mathbb{R}\setminus\{2\} \)
\( \mathbb{R}\setminus\{-3;2\} \)
\( \mathbb{R}\setminus\{-3;-0.5;2\} \)
\( \mathbb{R}\setminus\{-2\} \)

1103044804

Level: 
A
Given graphs of the functions \( f(x) = x^2-x-6 \) and \( g(x) = x+2 \), find the domain of the equation \( \frac{x+2}{x^2-x-6}=\frac{x^2-x-6}{x+2} \).
\( \mathbb{R}\setminus\{-2;3\} \)
\( \mathbb{R}\setminus\{-2;3;4\} \)
\( \mathbb{R}\setminus\{-2\} \)
\( \mathbb{R}\setminus\{-2;4\} \)

1103044802

Level: 
A
Given graphs of the functions \( f(x)=x^2-4x \) and \( g(x) = 4x^2-16x+12 \), find the domain of the equation \( \frac{4x^2-16x+12}{x^2-4x}=6 \).
\( \mathbb{R}\setminus\{0;4\} \)
\( \mathbb{R}\setminus\{1;3\} \)
\( \mathbb{R}\setminus\{0;1;3;4\} \)
\( \mathbb{R}\setminus\{2\} \)

1103044801

Level: 
A
Given graphs of the functions \( f(x) =2x^2-2x-4 \) and \( g(x) = 2x+2 \), find the domain of the equation\( \frac{2x^2-2x-4}{2x+2} = 10 \).
\( \mathbb{R}\setminus\{-1\} \)
\( \mathbb{R}\setminus\{-1;2\} \)
\( \mathbb{R}\setminus\{-1;2;3\} \)
\( \mathbb{R}\setminus\{-1;3\} \)

1003025104

Level: 
A
The annual production of a business is recorded in the following table. Find the compound annual growth rate over the time period \( 2014 \) - \( 2017 \). (I.e., the average annual coefficient of the production growth, i.e., the ratio that provides a constant growth rate over the time period.) Round the result to four decimal places.\[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & 2014 & 2015 & 2016 & 2017 \\\hline \text{Production (pcs)} & 20\: 000 & 20\: 400& 21\: 420 & 24\: 633 \\\hline \end{array}\]
\( 1{.}0719 \)
\( 1{.}0705 \)
\( 1{.}0733 \)
\( 1{.}0727 \)

1003025103

Level: 
A
Ten workers produce the same type of components. Two workers produce one component in \( 4 \) minutes, other three workers in \( 5 \) minutes, another one worker in \( 6 \) minutes, next three workers in \( 7 \) minutes and the last one of them in \( 8 \) minutes. What is the average time needed to produce one component? Round the result to the nearest hundredth.
\( 5{.}49\,\mathrm{min} \)
\( 5{.}50\, \mathrm{min} \)
\( 5{.}65\, \mathrm{min} \)
\( 5{.}80\, \mathrm{min} \)

1003025102

Level: 
A
A car travels the first quarter of its journey at an average speed of \( 50\, \mathrm{kph} \), the second quarter at an average speed of \( 90\, \mathrm{kph} \), the third quarter at an average speed of \( 130\, \mathrm{kph} \) and the remaining one quarter at an average speed of \( 80\, \mathrm{kph} \). What is the average speed of the car during the journey? Round the result to two decimal places.
\( 77{.}97\, \mathrm{km}/\mathrm{h} \)
\( 85{.}00\, \mathrm{km}/\mathrm{h} \)
\( 87{.}50\, \mathrm{km}/\mathrm{h} \)
\( 82{.}71\, \mathrm{km}/\mathrm{h} \)

1103025101

Level: 
A
The results of the math test are shown in the graph. Based on the graph, which of the following statements is false?
The median of the scores is the same as their modus.
Half of the students had higher score than the average score.
The average score rounded to the nearest hundredth is \( 2{.}68 \).