A

1103021702

Level: 
A
Given the triangle \( ABC \) (see the picture), where \( \alpha:\beta=5:7 \) and the angle \( \gamma \) is by \( 42^{\circ} \) smaller than the angle \( \omega \), calculate the measure of \( \gamma \).
\( 108^{\circ} \)
\( 42^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)

1003021701

Level: 
A
Interior angles of a triangle \( ABC \) are in the ratio \( \alpha:\beta:\gamma=2:4:6 \). Calculate the measures of these angles.
\( \alpha=30^{\circ},\ \beta=60^{\circ},\ \gamma=90^{\circ} \)
\( \alpha=20^{\circ},\ \beta=40^{\circ},\ \gamma=60^{\circ} \)
\( \alpha=15^{\circ},\ \beta=30^{\circ},\ \gamma=135^{\circ} \)
\( \alpha=90^{\circ},\ \beta=60^{\circ},\ \gamma=30^{\circ} \)

1003027304

Level: 
A
Choose a pair of functions, \( f_1 \) and \( f_2 \), that are antiderivatives of the same function on \( \mathbb{R} \).
\( f_1(x) = 3+\sin x\text{, }f_2(x)=\cos\left(\frac32\pi+x\right) \)
\( f_1(x) = 5+\sin x\text{, }f_2(x)=-\cos x \)
\( f_1(x) = \sin(x+\pi)\text{, }f_2(x)=\sin x \)
\( f_1(x) = \cos x\text{, }f_2(x)=-\cos x \)