B | math4u.vsb.cz

1103055107

Level:

The figure shows a directional rosette that can be used to determine a marching angle. (The initial arm always faces north and the terminal arm determines the direction of the march, so the measure of the angle increases from north to east). Give the degree measure of the marching angle if the march is directed southwest.

$ 225^{\circ} $

$ 135^{\circ} $

$ -225^{\circ} $

$ -45^{\circ} $

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} $

B

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