B | math4u.vsb.cz

1003055106

Level:

Given two angles $ \alpha= \frac{66}{15}\pi $ and $ \beta=\frac{*}{5}\pi $, which of the following numbers is to be substituted for $ * $ so that both angles take the same position on the unit circle?

$ 2 $

$ 1 $

$ 0 $

$ 3 $

1003055105

Level:

The measurements of angles $ \theta $ form the set $ M $: \[ M=\left\{\pi+k\frac23\pi\right\},\ k\in\{-2,-1,1,2\}.\] Calculate their sum.

$ 4\pi $

$ 0 $

$ \frac23 \pi $

$ -\frac23 \pi $

1003055104

Level:

The measures of given angles belong to the set $ M $: \[ M = \left\{ 120^{\circ} + k\,360^{\circ}\right\},\ k\in\{-1,0,1\}.\] Determine their arithmetic mean.

$ 120^{\circ} $

$ 420^{\circ} $

$ -120^{\circ} $

$ -420^{\circ} $

1003055103

Level:

Find out for which $ k\in\mathbb{Z} $ is true: \[ -\frac{11}4\pi = \frac74\pi+k\frac{\pi}2 \]

$ -9 $

$ 9 $

$ -18 $

$ 18 $

1003055102

Level:

The measure of the angle $ \theta $ meets the following conditions: \[\theta\in\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac23\pi+k\frac{\pi}3\right\},\ \theta\in\left[-\frac{\pi}2,2\pi\right].\] Choose the smallest value of $\theta$.

$ -\frac{\pi}3 $

$ -\frac{\pi}2 $

$ \frac23\pi $

$ \frac{\pi}3 $

1003055101

Level:

How many different values of $ \theta $ meet both conditions: \[\theta\in\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{3\pi}4+2k\pi\right\}\text{, }\ \theta\in[-2\pi,4\pi ] \]

$ 3 $

$ 4 $

$ 5 $

$ 2 $

1103055013

Level:

The regular pentagon $ ABCDE $ is inscribed in a circle with the center $ S $ (see the picture). Express the measure of the angle $ SAB $.

$ 54^{\circ} $

$ 72^{\circ} $

$ 36^{\circ} $

$ 108^{\circ} $

1103055012

Level:

The regular pentagon $ ABCDE $ is inscribed in a circle with the center $ S $ (see the picture). Give the measure of the angle $ ASB $.

$ 72^{\circ} $

$ 36^{\circ} $

$ 54^{\circ} $

$ 108^{\circ} $

1103055011

Level:

The picture shows the regular octagon $ ABCDEFGH $ and the equilateral triangle $ ABJ $. Give the measure of the angle $ JBC $.

$ 75^{\circ} $

$ 30^{\circ} $

$ 45^{\circ} $

$ 60^{\circ} $

1103055009

Level:

The regular hexagon $ ABCDEF $ is in the picture. The area of the triangle $ ABC $ is $ 10\,\mathrm{cm}^2 $. Calculate the length of the side of the hexagon. Round to one decimal place.

$ 4.8\,\mathrm{cm} $

$ 23.1\,\mathrm{cm} $

$ 6.3\,\mathrm{cm} $

$ 7.2\,\mathrm{cm} $

B

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