1. This examination lasts 120 minutes. The test paper has 4 pages with a total score of 150 points. The answer sheet has 2 pages.

2. Before answering, write your name and admission number on the front of the answer sheet, and write your name on the back. Paste the verified barcode in the designated position on the answer sheet.

3. All answers must be filled in or written on the answer sheet in the area corresponding to the question number. Do not misalign. Answers written on the test paper will receive no credit.

11. The content of the chapters ``Lines in the Coordinate Plane'' and ``Conic Sections'' in the textbook embodies that the essence of analytic geometry is $\_\_\_\_$ $\_\_\_\_$.

13. Among the following propositions about lines $l$, $m$ and planes $\alpha$, $\beta$, the true proposition is
A. If $l \subset \beta$ and $\alpha \perp \beta$, then $l \perp \alpha$.
B. If $l \perp \beta$ and $\alpha \parallel \beta$, then $l \perp \alpha$.
C. If $l \perp \beta$ and $\alpha \perp \beta$, then $l \parallel \alpha$.
D. If $\alpha \cap \beta = m$ and $l \parallel m$, then $l \parallel \alpha$.

7. The Shanghai World Expo 2010 opens at 9:00 AM and stops admitting visitors at 8:00 PM. In the flowchart on the right, $S$ represents the total number of visitors reported on the official website of the Shanghai World Expo at each whole hour, and $a$ represents the number of visitors admitted in the 1 hour before the hourly report. Then [Figure]
The blank execution box should be filled with $\_\_\_\_$ $\mathrm { S } \leftarrow \mathrm { S } + \mathrm { a }$.

10. In an $n \times n$ matrix $\left( \begin{array} { c c c c c c c } 1 & 2 & 3 & \cdots & n - 2 & n - 1 & n \\ 2 & 3 & 4 & \cdots & n - 1 & n & 1 \\ 3 & 4 & 5 & \cdots & n & 1 & 2 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ n & 1 & 2 & \cdots & n - 3 & n - 2 & n - 1 \end{array} \right)$, let $a _ { i j }$ denote the entry in the $i$-th row and $j$-th column ($i , j = 1,2 \cdots , n$). When $n = 9$, $a _ { 11 } + a _ { 22 } + a _ { 33 } + \cdots + a _ { 99 } = $ $\_\_\_\_$ $45$. Analysis: $a _ { 11 } + a _ { 22 } + a _ { 33 } + \cdots + a _ { 99 } = 1 + 3 + 5 + 7 + 9 + 2 + 4 + 6 + 8 = 45$

11. The Shanghai Expo 2010 park opens at 9:00 and stops admitting visitors at 20:00. In the flowchart on the right, $S$ represents the total number of visitors reported by the Shanghai Expo official website at each whole hour, and $a$ represents the number of visitors admitted in the 1 hour before the whole hour report. Then the blank execution box should be filled with $\_\_\_\_$.

12. In an $n \times n$ matrix $\left( \begin{array} { c c c c c c c } 1 & 2 & 3 & \cdots & n - 2 & n - 1 & n \\ 2 & 3 & 4 & \cdots & n - 1 & n & 1 \\ 3 & 4 & 5 & \cdots & n & 1 & 2 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ n & 1 & 2 & \cdots & n - 3 & n - 2 & n - 1 \end{array} \right)$ , [Figure]
Let the number in the $i$-th row and $j$-th column be denoted as $a _ { i j } ( i , j = 1,2 , \cdots , n )$ . When $n = 9$ , $a _ { 11 } + a _ { 22 } + a _ { 33 } + \cdots + a _ { 99 } =$ $\_\_\_\_$.

12. As shown in the figure, in a square piece of paper $ABCD$ with side length 4, the diagonals $AC$ and $BD$ intersect at $O$. Triangle $AOB$ is cut off, and the remaining part is folded along $OC$ and $OD$ so that $OA$ and $OB$ coincide. Then the volume of the tetrahedron with vertices $A$, $B$, $C$, $D$, and $O$ is $\_\_\_\_$ $\frac { 8 \sqrt { 2 } } { 3 }$.
Analysis: The folded solid is a regular triangular pyramid with base edge length 4 and lateral edge length $2 \sqrt { 2 }$, with height $\frac { 2 \sqrt { 6 } } { 3 }$. Therefore, the volume of the tetrahedron is $\frac { 1 } { 3 } \times \frac { 1 } { 2 } \times 16 \times \frac { \sqrt { 3 } } { 2 } \times \frac { 2 \sqrt { 6 } } { 3 } = \frac { 8 \sqrt { 2 } } { 3 }$ [Figure]

16. C; 17. C; 18. D.

III. Solution Problems

19. The original expression $= \lg ( \sin x + \cos x ) + \lg ( \cos x + \sin x ) - \lg ( \sin x + \cos x ) ^ { 2 } = 0$ . 20. (1) When $n = 1$ , $a _ { 1 } = - 14$ ; when $n \geq 2$ , $a _ { n } = S _ { n } - S _ { n - 1 } = - 5 a _ { n } + 5 a _ { n - 1 } + 1$ , so $a _ { n } - 1 = \frac { 5 } { 6 } \left( a _ { n - 1 } - 1 \right)$ , Since $a _ { 1 } - 1 = - 15 \neq 0$ , the sequence $\left\{ a _ { n } - 1 \right\}$ is a geometric sequence;
(2) From (1): $a _ { n } - 1 = - 15 \cdot \left( \frac { 5 } { 6 } \right) ^ { n - 1 }$ , we get $a _ { n } = 1 - 15 \cdot \left( \frac { 5 } { 6 } \right) ^ { n - 1 }$ , thus $S _ { n } = 75 \cdot \left( \frac { 5 } { 6 } \right) ^ { n - 1 } + n - 90 \left( n \in \mathbf { N } ^ { * } \right) ;$ Solving the inequality $S _ { n } < S _ { n + 1 }$ , we get $\left( \frac { 5 } { 6 } \right) ^ { n - 1 } < \frac { 2 } { 5 } , n > \log _ { \frac { 5 } { 6 } } \frac { 2 } { 25 } + 1 \approx 14.9$ , when $n \geq 15$ , the sequence $\left\{ S _ { n } \right\}$ is monotonically increasing; Similarly, when $n \leq 15$ , the sequence $\left\{ S _ { n } \right\}$ is monotonically decreasing; therefore when $n = 15$ , $S _ { n }$ attains its minimum value. 21. (1) Let the slant height of the cylindrical lantern be $l$ , then $l = 1.2 - 2 r ( 0 < r < 0.6 ) , S = - 3 \pi ( r - 0.4 ) ^ { 2 } + 0.48 \pi$ , so when $r = 0.4$ , $S$ attains its maximum value of approximately $1.51$ square meters;
(2) When $r = 0.3$ , $l = 0.6$ , establishing a spatial rectangular coordinate system, we obtain $\overrightarrow { A _ { 1 } B _ { 3 } } = ( - 0.3,0.3,0.6 )$ , $\overrightarrow { A _ { 3 } B _ { 5 } } = ( - 0.3 , - 0.3,0.6 )$ ,
Let the angle between vectors $\overrightarrow { A _ { 1 } B _ { 3 } }$ and $\overrightarrow { A _ { 3 } B _ { 5 } }$ be $\theta$ , then $\cos \theta = \frac { \overrightarrow { A _ { 1 } B _ { 3 } } \cdot \overrightarrow { A _ { 3 } B _ { 5 } } } { \left| \overrightarrow { A _ { 1 } B _ { 3 } } \right| \cdot \left| \overrightarrow { A _ { 3 } B _ { 5 } } \right| } = \frac { 2 } { 3 }$ , therefore the angle formed by the skew lines containing $A _ { 1 } B _ { 3 }$ and $A _ { 3 } B _ { 5 }$ is $\arccos \frac { 2 } { 3 }$ . 22. (1) $x \in ( - \infty , - \sqrt { 2 } ) \cup ( \sqrt { 2 } , + \infty )$ ;
(2) For any two distinct positive numbers $a$ and $b$ , we have $a ^ { 3 } + b ^ { 3 } > 2 a b \sqrt { a b } , ~ a ^ { 2 } b + a b ^ { 2 } > 2 a b \sqrt { a b }$ . Since $\left| a ^ { 3 } + b ^ { 3 } - 2 a b \sqrt { a b } \right| - \left| a ^ { 2 } b + a b ^ { 2 } - 2 a b \sqrt { a b } \right| = ( a + b ) ( a - b ) ^ { 2 } > 0$ , we have $\left| a ^ { 3 } + b ^ { 3 } - 2 a b \sqrt { a b } \right| > \left| a ^ { 2 } b + a b ^ { 2 } - 2 a b \sqrt { a b } \right|$ , that is, $a ^ { 3 } + b ^ { 3 }$ is farther from $2 a b \sqrt { a b }$ than $a ^ { 2 } b + a b ^ { 2 }$ ;
(3) $f ( x ) = \left\{ \begin{array} { l l } | \sin x | , & x \in \left( k \pi + \frac { \pi } { 4 } , k \pi + \frac { 3 \pi } { 4 } \right) \\ | \cos x | , & x \in \left( k \pi - \frac { \pi } { 4 } , k \pi + \frac { \pi } { 4 } \right) \end{array} \right.$ , Properties: $1 ^ { \circ }$ $f ( x )$ is an even function, its graph is symmetric about the $y$-axis; $2 ^ { \circ }$ $f ( x )$ is a periodic function with minimum positive period $T = \frac { \pi } { 2 }$ ; $3 ^ { \circ }$ The function $f ( x )$ is monotonically increasing on the interval $\left( \frac { k \pi } { 2 } - \frac { \pi } { 4 } , \frac { k \pi } { 2 } \right]$ and monotonically decreasing on the interval $\left[ \frac { k \pi } { 2 } , \frac { k \pi } { 2 } + \frac { \pi } { 4 } \right)$ , $k \in \mathbf { Z }$ ; $4 ^ { \circ }$ The range of the function $f ( x )$ is $\left( \frac { \sqrt { 2 } } { 2 } , 1 \right]$ . 23. (1) $M \left( \frac { a } { 2 } , - \frac { b } { 2 } \right)$ ;
(2) From the system of equations $\left\{ \begin{array} { l } y = k _ { 1 } x + p \\ \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \end{array} \right.$ , eliminating $y$ gives the equation $\left( a ^ { 2 } k _ { 1 } ^ { 2 } + b ^ { 2 } \right) x ^ { 2 } + 2 a ^ { 2 } k _ { 1 } p x + a ^ { 2 } \left( p ^ { 2 } - b ^ { 2 } \right) = 0$ , Since the line $l _ { 1 } : y = k _ { 1 } x + p$ intersects the ellipse $\Gamma$ at points $C$ and $D$ , we have $\Delta > 0$ , that is, $a ^ { 2 } k _ { 1 } ^ { 2 } + b ^ { 2 } - p ^ { 2 } > 0$ , Let $C \left( x _ { 1 } , y _ { 1 } \right)$ , $D \left( x _ { 2 } , y _ { 2 } \right)$ , and the midpoint of $C D$ be $\left( x _ { 0 } , y _ { 0 } \right)$ , then $\left\{ \begin{array} { l } x _ { 0 } = \frac { x _ { 1 } + x _ { 2 } } { 2 } = - \frac { a ^ { 2 } k _ { 1 } p } { a ^ { 2 } k _ { 1 } ^ { 2 } + b ^ { 2 } } \\ y _ { 0 } = k _ { 1 } x _ { 0 } + p = \frac { b ^ { 2 } p } { a ^ { 2 } k _ { 1 } ^ { 2 } + b ^ { 2 } } \end{array} \right.$ , From the system of equations $\left\{ \begin{array} { l } y = k _ { 1 } x + p \\ y = k _ { 2 } x \end{array} \right.$ , eliminating $y$ gives the equation $\left( k _ { 2 } - k _ { 1 } \right) x = p$ , Since $k _ { 2 } = - \frac { b ^ { 2 } } { a ^ { 2 } k _ { 1 } }$ , we have $\left\{ \begin{array} { l } x = \frac { p } { k _ { 2 } - k _ { 1 } } = - \frac { a ^ { 2 } k _ { 1 } p } { a ^ { 2 } k _ { 1 } ^ { 2 } + b ^ { 2 } } = x _ { 0 } \\ y = k _ { 2 } x = \frac { b ^ { 2 } p } { a ^ { 2 } k _ { 1 } ^ { 2 } + b ^ { 2 } } = y _ { 0 } \end{array} \right.$ , Therefore $E$ is the midpoint of $C D$ ;
(3) Steps for constructing points $P _ { 1 }$ and $P _ { 2 }$ : $1 ^ { \circ }$ Find the midpoint $E \left( - \frac { a ( 1 - \cos \theta ) } { 2 } , \frac { b ( 1 + \sin \theta ) } { 2 } \right)$ of $P Q$ , $2 ^ { \circ }$ Find the slope of line $O E$ as $k _ { 2 } = - \frac { b ( 1 + \sin \theta ) } { a ( 1 - \cos \theta ) }$ , $3 ^ { \circ }$ From $\overrightarrow { P P _ { 1 } } + \overrightarrow { P

7. If the front view of a cone (as shown in the figure) is a triangle with sides $3, 3, 2$, then the lateral surface area of the cone is $\_\_\_\_$

9. If variables $x, y$ satisfy the conditions $\left\{ \begin{array}{c} 3x - y \leq 0 \\ x - 3y + 5 \geq 0 \end{array} \right.$, then the maximum value of $z = x + y$ is $\_\_\_\_$

1 Emphasizing Fundamentality and Highlighting Logical Reasoning Ability

Mathematics is an important means of cultivating rational thinking. The logical thinking inherent in mathematics, the reasoning methods taught, and the analytical abilities trained are all indispensable in the process of individual development and the construction of cognitive structures. These all reflect the role of mathematics as a foundational discipline.
The mathematics examination utilizes the characteristics of the discipline to deeply examine logical reasoning ability. In 2014, the College Entrance Examination made examining logical reasoning ability the primary task of test design, using mathematical knowledge as a vehicle. Questions examining logical reasoning ability account for more than $50\%$ of the test.
In 2014, the examination center conducted specialized research on innovative test design and developed logic questions to examine logical reasoning ability. One province each from the eastern, central, and western regions was selected for pilot testing, with high school seniors from provincial key schools, municipal key schools, and general schools sampled for testing. The test results showed that logic questions more effectively examine logical thinking ability. In post-exam discussions, students found logic questions interesting and enjoyed them very much. The questions do not depend on specific mathematical knowledge, are accessible to all examinees, and embody fairness. Teachers believed that such questions effectively examine logical thinking ability and could be introduced in future college entrance examinations.
To deeply examine logical reasoning ability, logic questions appeared for the first time in the 2014 College Entrance Examination mathematics papers. The questions presented a life-like scenario of three students discussing city tourism. Through dialogue among students A, B, and C, relevant information was provided, requiring examinees to accurately extract useful information from textual descriptions (dialogue), utilize the logical relationships within, conduct rigorous logical reasoning, and ultimately make correct judgments, reflecting the direction of college entrance examination reform.
Example 1: Three students A, B, and C are asked whether they have visited cities A, B, and C.
\begin{displayquote} A says: I have visited more cities than B, but I have not visited City B;
B says: I have not visited City C;
C says: We three have visited the same city. \end{displayquote}
From this, it can be determined that B has visited the city/cities of $\_\_\_\_$. After the examination, examinees and teachers responded enthusiastically to the logic questions, believing that such questions effectively examined students' logical reasoning and judgment ability by embedding logic problems in vivid dialogue contexts. The questions were novel and engaging, with plain and easy-to-understand language, close to life, and of practical significance, reflecting the idea that mathematics originates from life. The questions help increase students' interest in learning mathematics and provide good guidance for cultivating students' logical thinking ability in middle school teaching and enhancing students' ability to solve practical problems. They reflect the New Curriculum Standard's emphasis on stimulating students' learning interest from practice, valuing independent learning, and combining theory with practice.

2 Enhancing Practicality and Strengthening Examination of Innovative Application Consciousness

Mathematics originates from life and practice. Mathematical knowledge is a powerful tool for solving practical problems, and mathematical ability is a mathematical literacy that every citizen must possess. The examination of innovative application ability in the college entrance examination requires examinees to combine materials from daily life, other disciplines, and learning practice to discover and raise problems; apply learned mathematical knowledge and thinking methods to think independently, explore and research, analyze and solve problems.
Paying attention to real social hot topics is an important characteristic of the 2014 College Entrance Examination mathematics papers. Through solving social hot topics, the papers examine the ability to apply mathematical tools and methods to solve practical problems. The examination papers closely integrate with social reality and examinees' actual lives, reflecting the tremendous role and application value of mathematics in solving practical problems, and embodying the characteristics of strengthening application and practicality in college entrance examination reform.
The 2014 national papers used ``air quality,'' a social hot topic, as the background: According to historical data, the probability that air quality is excellent on a given day is 0.75, the probability that it is excellent for two consecutive days is 0.6. If today's air quality is excellent, what is the probability that tomorrow's air quality will be excellent? The papers require examinees to apply statistical and probability methods to forecast tomorrow's weather, helping examinees understand the application value of statistics and probability.
The papers broadened the sources of test materials, extensively involving many aspects of social life. The 2014 mathematics papers involved backgrounds such as rural residents' per capita net income, participation in public welfare activities, and product quality indicators. These questions are grounded in reality, close to examinees' lives, allowing examinees to deeply feel that mathematics is alive and all around them, with mathematical thinking permeating their lives.
Example 2: Four students each choose one day from Saturday and Sunday to participate in public welfare activities. The probability that both Saturday and Sunday have students participating in public welfare activities is
(A) $\frac{1}{8}$
(B) $\frac{3}{8}$
(C) $\frac{5}{8}$
(D) $\frac{7}{8}$
The questions examine basic knowledge and methods of probability, testing examinees' ability to apply mathematical tools and methods to analyze practical problems and solve them. They guide examinees to pay attention to mathematical problems in life and strengthen their application consciousness of mathematics.
Example 3: The data for per capita net income $y$ (in units of thousand yuan) of rural residents' families in a certain region from 2007 to 2013 is shown in Table 1:
\begin{table}[h]
Table 1

Year	2007	2008	2009	2010	2011	2012	2013
Year Code $t$	1	2	3	4	5	6	7
Per Capita Net Income $y$	2.9	3.3	3.6	4.4	4.8	5.2	5.9

\end{table}
(I) Find the linear regression equation of $y$ with respect to $t$; (II) Using the regression equation from (I), analyze the changes in per capita net income of rural residents' families in this region from 2007 to 2013, and predict the per capita net income of rural residents' families in this region for 2015.
The questions use rural residents' per capita net income, an important socioeconomic indicator, as the vehicle, providing data from a certain region from 2007 to 2013. Examinees are required to establish a linear regression equation, achieving the goal of examining students' ability to establish linear regression equations based on data, while also examining students' understanding of the practical significance of the slope of the regression line. The questions originate from reality, are close to life, combine theory with practice, and help examinees understand the application value of statistics and probability.

3 Improving Comprehensiveness and Examining General Mathematical Methods

An important characteristic of mathematical test design is strengthening the comprehensiveness of test questions and emphasizing the examination of general mathematical methods, avoiding special problem-solving techniques. Mathematical ideas and methods are abstractions and generalizations of mathematical knowledge at a higher level, capable of being transferred and widely applied to related disciplines and social life. The general methods examined in the college entrance examination include both specific mathematical methods such as mathematical induction, completing the square, undetermined coefficients, substitution, and identity methods, as well as logical methods such as analysis, synthesis, induction, deduction, proof by contradiction, and exhaustion. These methods play important roles in problem-solving.
In test design, one question serves as a vehicle to present to examinees a class of problems. By solving this question, examinees master the general method for solving this class of problems, enabling them to draw inferences about other cases and solve many similar new problems. For example, the probability and statistics question in the 2014 standard A papers for liberal arts appears to be about calculating the median and probability for departments A and B, but actually aims to help examinees master the following mathematical thinking: when facing estimation problems for populations with many individuals, the first step is to obtain a sample using a reasonable sampling method, the second step is to estimate the characteristics of the sample, and finally use this to estimate the population and make predictions.
Deeply examining the flexibility of thinking is another prominent characteristic of test questions. When designing college entrance examination questions, full consideration is given to individual differences in examinees' mathematical abilities. The vast majority of questions have multiple solution methods and approaches rather than a single one. Examinees with strong foundations and abilities can find concise paths through deep thinking and solve problems quickly, while examinees with average foundations and moderate abilities can solve problems using basic methods, though the solutions may be more tedious and time-consuming. For example, many multiple-choice questions only require sketching and rough estimation to eliminate incorrect options and make correct choices; most solution questions have multiple solution methods. Through such design, a thinking platform is provided for examinees of different foundations and abilities, while also providing excellent examinees with a broad space to flexibly apply mathematical knowledge and thinking methods to solve problems.
Example 4: Given that $A$, $B$, $C$ are three points on circle $O$, if $\overrightarrow{AO} = \frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC})$, then the angle between $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is $\_\_\_\_$. This question combines knowledge of circles to examine the concept and geometric meaning of vectors, testing examinees' ability to skillfully apply the fundamental theorem of plane vectors, calculate vector sums and dot products using definitions, and find vector angles by combining plane geometry knowledge. It also examines examinees' ability to use the coordinate method to calculate vector sums and dot products and find vector angles. The question organically combines numbers and shapes, with flexible and diverse solution methods, reflecting the general principles and methods of mathematics, particularly the idea of combining numbers and shapes.
Approach 1. By the parallelogram law of vector addition and $\overrightarrow{AO} = \frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC})$, the center $O$ is the midpoint of segment $BC$. That is, $BC$ is a diameter of circle $O$, so the angle between $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is $90^{\circ}$.
Approach 2. From $\overrightarrow{AB} = \overrightarrow{AO} + \overrightarrow{OB}$, $\overrightarrow{AC} = \overrightarrow{AO} + \overrightarrow{OC}$. Also from $\overrightarrow{AO} = \frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC})$, we get $\overrightarrow{OB} + \overrightarrow{OC} = 0$, meaning the center $O$ is the midpoint of segment $BC$. Therefore, $BC$ is a diameter of circle $O$, so the angle between $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is $90^{\circ}$.
Approach 3. From $\overrightarrow{AO} = \frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC})$ we get $\overrightarrow{OB} = \overrightarrow{OA} + \overrightarrow{AB} = -\frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC}) + \overrightarrow{AB} = \frac{1}{2}(\overrightarrow{AB} - \overrightarrow{AC})$.
Since $A$, $B$ are points on circle $O$, we know $|\overrightarrow{OB}| = |\overrightarrow{OA}|$, that is, $\left|\frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC})\right| = \left|\frac{1}{2}(\overrightarrow{AB} - \overrightarrow{AC})\right|$.
Therefore $\overrightarrow{AB} \cdot \overrightarrow{AC} = 0$. So the angle between $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is $90^{\circ}$.
Approach 4. Establish a rectangular coordinate system with $O$ as the origin, $\overrightarrow{OA}$ as the positive $x$-axis direction, and $|\overrightarrow{OA}|$ as the unit length. Then $A(1,0)$.
Let $B(x_1, y_1)$, $C(x_2, y_2)$. Then $\overrightarrow{AO} = (-1,0)$, $\overrightarrow{AB} = (x_1 - 1, y_1)$, $\overrightarrow{AC} = (x_2 - 1, y_2)$.
From $\overrightarrow{AO} = \frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC})$ we get $\left\{\begin{array}{l} -1 = \frac{1}{2}(x_1 + x_2) - 1, \

1. Before answering, you must fill in your name and seat number in the designated places on the test paper and answer sheet, and carefully verify that the name and seat number on the barcode pasted on the answer sheet match your name and seat number. You must also fill in your name and the last two digits of your seat number on the back of the answer sheet in the designated place.

Given sets $A = \{ 1,2,3 \} , B = \{ 1,3 \}$, then $\mathrm { A } \cap \mathrm { B } =$
(A) $\{ 2 \}$
(B) $\{ 1,2 \}$
(C) $\{ 1,3 \}$
(D) $\{ 1,2,3 \}$

1. Before answering, write your name and admission ticket number on both the examination paper and answer sheet, and paste the barcode of your admission ticket at the designated position on the answer sheet. Use a 2B pencil to fill in the box after test paper type A on the answer sheet.

1. Before answering, candidates must fill in their admission ticket number and name on the answer sheet. Candidates should carefully verify that the barcode on the answer sheet shows the correct ``admission ticket number, name, and examination subject'' that match their own admission ticket number and name.

1. This test paper is divided into Section I (Multiple Choice) and Section II (Non-Multiple Choice). Section I is on pages 1-3, and Section II is on pages 3-5.

1. Before answering, candidates must use a 0.5 mm black pen to write their name, seat number, candidate number, county/district, and subject category in the designated positions on the answer sheet and test paper.

1. Before answering, candidates must use a 0.5 mm black pen to write their name, seat number, candidate number, county/district, and subject category in the designated positions on the answer sheet and test paper.

1. Let set $A = \{ x \mid - 1 < x < 2 \}$ and set $B = \{ x \mid 1 < x < 3 \}$. Then $A \cup B =$
(A) $\{ x \mid - 1 < x < 3 \}$
(B) $\{ x \mid - 1 < x < 1 \}$
(C) $\{ x \mid 1 < x < 2 \} \{ x \mid 2 < x < 3 \}$
(D)

2. For Section I, after selecting the answer for each question, use a 2B pencil to blacken the corresponding answer option on the answer sheet. If you need to make changes, erase it cleanly with an eraser and then select another answer option.