4. Use a 2B pencil to answer multiple-choice questions, and use a black pen, marker, or ballpoint pen to answer non-multiple-choice questions. I. Fill-in-the-Blank Questions (Total Score: 48 points, 4 points each) 1. If $\operatorname { tg } \alpha = \frac { 1 } { 2 }$, then $\operatorname { tg } \left( \alpha + \frac { \pi } { 4 } \right) =$ $\_\_\_\_$. 2. A parabola has vertex at $(2,0)$ and directrix $x = -1$. Its focus is at $\_\_\_\_$. 3. Let $A = \left\{ 5 , \log _ { 2 } ( a + 3 ) \right\}$ and $B = \{ a , b \}$. If $A \cap B = \{ 2 \}$, then $A \cup B =$ $\_\_\_\_$. 4. For a geometric sequence $\left\{ a _ { n } \right\} ( n \in \mathbb{N} )$ with common ratio $q = - \frac { 1 } { 2 }$, if $\lim _ { n \rightarrow \infty } \left( a _ { 1 } + a _ { 3 } + a _ { 5 } + \cdots + a _ { 2 n - 1 } \right) = \frac { 8 } { 3 }$, then $a _ { 1 } =$ $\_\_\_\_$.
4. Use a 2B pencil to answer multiple-choice questions, and use a black pen, marker, or ballpoint pen to answer non-multiple-choice questions.
I. Fill-in-the-Blank Questions (Total Score: 48 points, 4 points each)\\
1. If $\operatorname { tg } \alpha = \frac { 1 } { 2 }$, then $\operatorname { tg } \left( \alpha + \frac { \pi } { 4 } \right) =$ $\_\_\_\_$.\\
2. A parabola has vertex at $(2,0)$ and directrix $x = -1$. Its focus is at $\_\_\_\_$.\\
3. Let $A = \left\{ 5 , \log _ { 2 } ( a + 3 ) \right\}$ and $B = \{ a , b \}$. If $A \cap B = \{ 2 \}$, then $A \cup B =$ $\_\_\_\_$.\\
4. For a geometric sequence $\left\{ a _ { n } \right\} ( n \in \mathbb{N} )$ with common ratio $q = - \frac { 1 } { 2 }$, if $\lim _ { n \rightarrow \infty } \left( a _ { 1 } + a _ { 3 } + a _ { 5 } + \cdots + a _ { 2 n - 1 } \right) = \frac { 8 } { 3 }$, then $a _ { 1 } =$ $\_\_\_\_$.\\