B

1103083109

Level: 
B
The graphs of the quadratic functions \( f \) and \( g \) are shown in the picture. The graph of \( g \) is the reflection of the graph of \( f \) about \( y \)-axis. Identify which of the following statements about \( f \) and \( g \) is true.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the linear term only.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the quadratic term only.
The equations of \( f \) and \( g \) differ in in the sign of the coefficient at the absolute term only.
None of the statements above is true.

1103083107

Level: 
B
The quadratic functions \( f \) and \( g \) that have the same vertex \( V \) are graphed in the picture. The graph of \( g \) is the reflection of the graph of \( f \) in the vertex \( V \). Also, both the graphs are symmetric across \( y \)-axis. Identify the true statement about \( f \) and \( g \).
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the quadratic term only.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the linear term only.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the absolute term only.
None of the statements above is true.

1003035910

Level: 
B
Find the limit of the sequence \( \left( \left( -\frac23 \right)^n \right)_{n=1}^{\infty} \).
\( \lim\limits_{n\rightarrow\infty}\left( -\frac23 \right)^n=0 \)
\( \lim\limits_{n\rightarrow\infty}\left( -\frac23 \right)^n=-\infty \)
\( \lim\limits_{n\rightarrow\infty}\left( -\frac23 \right)^n=-\frac23 \)
\( \lim\limits_{n\rightarrow\infty}\left( -\frac23 \right)^n=-\frac32 \)
\( \lim\limits_{n\rightarrow\infty}\left( -\frac23 \right)^n \) does not exist.

1003035909

Level: 
B
Find the limit of the sequence \( \left(\left( -\frac32 \right)^n \right)_{n=1}^{\infty} \).
\( \lim\limits_{n\rightarrow\infty}\left( -\frac32 \right)^n \) does not exist.
\( \lim\limits_{n\rightarrow\infty}\left( -\frac32 \right)^n = \infty \)
\( \lim\limits_{n\rightarrow\infty}\left( -\frac32 \right)^n = 0 \)
\( \lim\limits_{n\rightarrow\infty}\left( -\frac32 \right)^n = -\infty \)
\( \lim\limits_{n\rightarrow\infty}\left( -\frac32 \right)^n = -\frac32\)

1003035908

Level: 
B
Find the limit of the sequence \( \left(\left( \frac23 \right)^n\right)_{n=1}^{\infty} \).
\( \lim\limits_{n\rightarrow\infty}\left( \frac23 \right)^n =0 \)
\( \lim\limits_{n\rightarrow\infty}\left( \frac23 \right)^n =-\infty \)
\( \lim\limits_{n\rightarrow\infty}\left( \frac23 \right)^n =\frac{16}{81} \)
\( \lim\limits_{n\rightarrow\infty}\left( \frac23 \right)^n =\frac23 \)
\( \lim\limits_{n\rightarrow\infty}\left( \frac23 \right)^n \) does not exist.

1003035907

Level: 
B
Find the limit of the sequence \( \left(\left( \frac32 \right)^n \right)_{n=1}^{\infty} \).
\( \lim\limits_{n\rightarrow\infty}\left( \frac32 \right)^n =\infty \)
\( \lim\limits_{n\rightarrow\infty}\left( \frac32 \right)^n =\frac32 \)
\( \lim\limits_{n\rightarrow\infty}\left( \frac32 \right)^n =\frac{81}{16} \)
\( \lim\limits_{n\rightarrow\infty}\left( \frac32 \right)^n = 0\)
\( \lim\limits_{n\rightarrow\infty}\left( \frac32 \right)^n \) does not exist.

1003082305

Level: 
B
Let \( [x,y]\in\mathbb{R}\times\mathbb{R} \), \( z_1 = 5 + xy\,\mathrm{i} \) and \( z_2 = x + y - 4\,\mathrm{i} \). Find all \( [x,y] \) such that \( z_1 \) and \( z_2 \) are the complex conjugates.
\( [x,y] \in\left\{[4,1],[1,4]\right\} \)
\( [x,y]\in\left\{[6,1],[9,4]\right\} \)
\( [x,y]\in\left\{[4,9],[1,6]\right\} \)
\([x,y]\in\left\{[-4,9],[-1,6]\right\} \)
\( [x,y]\in\left\{[6,-1],[9,-4]\right\} \)

1003082303

Level: 
B
Given the complex numbers \( a=6\sqrt2\left(\cos\frac{\pi}3+\mathrm{i}\cdot\sin\frac{\pi}3\right) \), \( b=3\sqrt2\left(\cos\frac56\pi+\mathrm{i}\cdot\sin\frac56\pi\right) \) and \( c=2\left(\cos240^{\circ}+\mathrm{i}\cdot\sin240^{\circ}\right) \), evaluate \( \frac a{b\cdot c} \).
\( \cos\frac{\pi}6+\mathrm{i}\cdot\sin\frac{\pi}6 \)
\( \cos\frac{11}6\pi+\mathrm{i}\cdot\sin\frac{11}6\pi \)
\( 4\left(\cos\frac{\pi}6\pi+\mathrm{i}\cdot\sin\frac{\pi}6\pi\right) \)
\( 4\left(\cos⁡\frac{11}6\pi+\mathrm{i}\cdot\sin\frac{11}6\pi\right) \)