2010015205
Level:
A
The measures of two interior angles of a triangle are \( 61^{\circ}20' \) and \( 28^{\circ} \). What is the measure of the third interior angle?
\( 90^{\circ}40' \)
\( 33^{\circ}20' \)
\( 145^{\circ}20' \)
\( 147^{\circ}40' \)
A
2010015201
Level:
A
Interior angles of a triangle \( ABC \) are in the ratio \( \alpha:\beta:\gamma=3:5:7 \). Calculate the measures of these angles.
\( \alpha=36^{\circ};\ \beta=60^{\circ};\ \gamma=84^{\circ} \)
\( \alpha=30^{\circ};\ \beta=50^{\circ};\ \gamma=70^{\circ} \)
\( \alpha=16.5^{\circ};\ \beta=30^{\circ};\ \gamma=133.5^{\circ} \)
\( \alpha=84^{\circ};\ \beta=60^{\circ};\ \gamma=36^{\circ} \)
2010015002
Level:
A
\( KLMN \) is a square. Determine the degree measure of the angle \( NRS \) if the measure of the angle \( LSR \) is \( 110^{\circ} \).
\( 155^{\circ}\)
\( 120^{\circ} \)
\( 110^{\circ} \)
\( 135^{\circ} \)
2010015001
Level:
A
The side lengths of the rectangle \( ABCD \) are in the ratio \( AB: BC=4:3 \). Give the degree measure of the angle \( ASB \). Round the result to two decimal places.
\( 106.26^{\circ} \)
\( 73.74^{\circ} \)
\( 104.26^{\circ} \)
\( 75.74^{\circ} \)
2010012704
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\to 1}\frac{1-x^3}{x^2+3x-4} \]
\( -\frac35\)
\( -3\)
\( \frac35\)
\(0\)
2010014604
Level:
A
Among the lines in the following list (slope-intercept form) identify a line perpendicular
to the line
\[
y = \frac{2}{3}x - 1.
\]
\(y = -\frac{3}
{2}x +1\)
\(y = \frac{2}
{3}x +1\)
\(y = \frac{3}
{2}x - 1\)
\(y = -\frac{1}
{2}x + 1\)
2010014603
Level:
A
In the following list identify a line which is perpendicular to the line
\( 2x +3y -7= 0\).
\(\begin{aligned}[t] x& = 2t, &
\\y & = -11+3t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& = 1+3t, &
\\y & = 11 - 2t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2+t, &
\\y & = 3 - t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2t+7, &
\\y & = - 3t+1;\ t\in \mathbb{R}
\\ \end{aligned}\)
2010014602
Level:
A
Find the normal vector of the following line.
\[
p\colon \begin{aligned}[t] x =&1 +4t, &
\\y =& - 3 -2t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\((1;2)\)
\((4;-2)\)
\((1;-3)\)
\((-2;1)\)
2010014601
Level:
A
Find the normal vector of the line passing through the points
\(A = [1;3]\) and
\(B = [-2;5]\).
\((2;3)\)
\((-3;2)\)
\((3;-2)\)
\((2;-3)\)
2010014506
Level:
A
The function \( f \) is given by the graph. Identify which of the following statements is true.
The function \( f \) is neither increasing nor decreasing.
The function \( f \) is decreasing.
The function \( f \) is decreasing in the interval \( [ -4;1] \).
The function \( f \) is increasing.