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1003083306

Level:

In a certain school, grades are given according to the rules listed below: \[\begin{array}{|c|c|} \hline \text{The percentage of the points gained} & \text{grade} \\\hline 0\%\text{ to } 49\% & 1 \\\hline 50\% \text{ to } 59\% & 2 \\\hline 60\% \text{ to } 79\% & 3 \\\hline 80\% \text{ to } 89\% & 4 \\\hline 90\% \text{ to } 94\% & 5 \\\hline 95\% \text{ to } 100\% & 6 \\\hline \end{array}\] Krysia gained \( 39 \) points from the history test. There were only \( 2 \) percentage points missing for her to get grade \( 4 \). What was the total amount of points one could get from the test?

\( 50 \) points

\( 41 \) points

\( 45 \) points

\( 55 \) points

1003083305

Level:

Economists predict that in a certain country \( 10\% \) annual inflation will last for two years. What will be the percentage increase in prices in this country in two years?

by \( 21\% \)

by \( 20\% \)

by \( 10\% \)

by \( 1.21\% \)

1003083304

Level:

The initial price of ice bags was \( 24.20 \) zlotys. Now, you can buy \( 22 \) ice bags (which is \( 10\% \) more than before) for the same price. What is the percentage decrease in the price of one ice bag?

by app. \( 9\% \)

by app. \( 8\% \)

by \( 10\% \)

by \( 2.2\% \)

1003083303

Level:

One half of a number \( a \) is by \( 25\% \) smaller than one third of a number \( b \). Then the number \( b \) is

by \( 100\% \) bigger than \( a \).

by \( 200\% \) bigger than \( a \).

by \( 50\% \) bigger than \( a \).

by \( 150\% \) bigger than \( a \).

1003083302

Level:

Let \( a \) and \( c \) be positive numbers. A number \( b \) equals \( 96\% \) of the number \( 2a + b \) and \( 64\% \) of the number \( 5a + c \). It means that

\( c=70a \).

\( c=1.5a \).

\( c=14a \).

\( c=48a \).

1003083301

Level:

If a number \( 3b \) is by \( 20\% \) bigger than half of the number \( 2a + b \), then the number \( a \) is bigger than \( b \) by

\( 100\% \).

\( 80\% \).

\( 50\% \).

\( 200\% \).

1003034108

Level:

Give the result of the gradual exponentiation \(\left(\left(\left(\left(2\right)^2\right)^0\right)^3\right)^4\):

\( 1 \)

\( 0 \)

\( 4^{12} \)

\( 2^9 \)

1003076712

Level:

Let \( \sin x = a \) and \( \cos x = b \). Then \( \cos(2x) \) is equal to:

\( b^2-a^2 \)

\( 2b \)

\( 2ab \)

\( a^2-b^2 \)

1003076711

Level:

\( ABC \) is a triangle with side \( c = 27\,\mathrm{cm} \) and the angle \( \gamma = 78^{\circ} \). The radius of the circle circumscribed is:

\( 13.8\,\mathrm{cm} \)

\( 27.6\,\mathrm{cm} \)

\( 18.3\,\mathrm{cm} \)

\( 6.9\,\mathrm{cm} \)

1003076710

Level:

\( ABC \) is a triangle where the side \( b \) is \( 74\,\mathrm{cm} \) long and the angle \( \alpha = 60^{\circ} \). Find the length of its side \( c \) if you know that the area of the triangle is \( 720.9\,\mathrm{cm}^2 \).

\( 22.5\,\mathrm{cm} \)

\( 37.56\,\mathrm{cm} \)

\( 38.97\,\mathrm{cm} \)

\( 24.54\,\mathrm{cm} \)

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