3. Execute the flowchart shown in Figure 1. If the input is $n = 3$, then the output is\\
A. $\frac { 6 } { 7 }$\\
B. $\frac { 3 } { 7 }$\\
C. $\frac { 8 } { 9 }$\\
D. $\frac { 4 } { 9 }$\\
\includegraphics[max width=\textwidth, alt={}, center]{a6eae9e4-32c9-40f4-807d-a64508802a24-1_850_438_1149_1420}\\
(4) If variables $x , y$ satisfy the constraint conditions $\left\{ \begin{array} { c } x + y \geq - 1 \\ 2 x - y \leq 1 \\ y \leq 1 \end{array} \right.$, then the minimum value of $z = 3 x - y$ is\\
(A) $- 7$\\
(B) $- 1$\\
(C) $1$\\
(D) $2$\\
(5) Let the function $f ( x ) = \ln ( 1 + x ) - \ln ( 1 - x )$. Then $f ( x )$ is\\
(A) an odd function and increasing on $( 0,1 )$\\
(B) an odd function and decreasing on $(0,1)$\\
(C) an even function and increasing on $( 0,1 )$\\
(D) an even function and decreasing on $(0,1)$\\
(6) Given that the expansion of $\left( \sqrt { \mathrm { x } } - \frac { \mathrm { a } } { \sqrt { \mathrm { x } } } \right) ^ { 5 }$ contains a term with $\mathrm { x } ^ { \frac { 3 } { 2 } }$ whose coefficient is 30, then $\mathrm { a } =$\\
(A) $\sqrt { 3 }$\\
(B) $- \sqrt { 3 }$\\
(C) $6$\\
(D) $- 6$\\
(7) In the square shown in Figure 2, 10000 points are randomly thrown. The estimated number of points falling in the shaded region (where curve C is the density curve of the normal distribution $N ( 0,1 )$) is

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{a6eae9e4-32c9-40f4-807d-a64508802a24-2_337_353_826_406}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

(A) $2386$\\
(B) $2718$\\
(C) $3413$\\
(D) $4772$

Attachment: If $X \sim N \left( \mu , \sigma ^ { 2 } \right)$, then

$$\begin{aligned}
& P ( \mu - \sigma < x \leq \mu + \sigma ) = 0.6826 \\
& P ( \mu - 2 \sigma < x \leq \mu + 2 \sigma ) = 0.9544
\end{aligned}$$

(8) Points $\mathrm { A } , \mathrm { B } , \mathrm { C }$ move on the circle $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 1$, and $\mathrm { AB } \perp \mathrm { BC }$. If point P has coordinates $( 2,0 )$, then the maximum value of $| \overrightarrow { P A } + \overrightarrow { P B } + \overrightarrow { P C } |$ is\\
A. $6$\\
B. $7$\\
C. $8$\\
D. $9$\\
(9) The graph of the function $f ( x ) = \sin 2 x$ is shifted to the right by $\varphi \left( 0 < \varphi < \frac { \pi } { 2 } \right)$ units to obtain the graph of function $g ( x )$. If for $x _ { 1 }$ and $x _ { 2 }$ satisfying $\left| f \left( x _ { 1 } \right) - g \left( x _ { 2 } \right) \right| = 2$, we have $\left| x _ { 1 } - x _ { 2 } \right| _ { \min } = \frac { \pi } { 3 }$, then $\varphi =$\\
A. $\frac { 5 \pi } { 12 }$\\
B. $\frac { \pi } { 3 }$\\
C. $\frac { \pi } { 4 }$\\
D. $\frac { \pi } { 6 }$