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Papers (66)
2025
national-I 19 national-II 18 national-I_eol 19
2024
beijing 21 national-II 19 national-I_github 19
2023
national-A-science 18 national-B-science 16 national-II 8
2022
national-A-arts 15 national-A-science 14 national-B-arts 20 national-B-science 17 national-I 19 national-II 7
2021
national-A-arts 19 national-A-science 18 national-I 14 national-II 12
2020
national-I-arts 20 national-I-science 9 national-II-science 17 national-III-arts 22 national-III-science 16 shanghai 17
2019
beijing-science 15 national-I-arts 13 national-I-science 12 national-I-science_gkztc 14 national-II-arts 13 national-II-science 9 national-II-science_gkztc 13 national-III-arts 14 national-III-science 16 national-III-science_gkztc 14
2018
national-I-arts 14 national-I-science 13 national-II-arts 20 national-II-science 18 national-III-science 17
2017
national-I-arts 13 national-I-science 14 national-II-arts 15 national-II-science 8
2016
national-I 7
2015
anhui-arts 14 beijing-arts 15 beijing-science 13 chongqing-arts 20 chongqing-science 15 fujian-science 18 hubei-arts 16 hubei-science 15 hunan-arts 21 hunan-science 11 jiangsu 19 national-II-arts 15 national-II-science 16 shaanxi-science 17 sichuan-arts 15 sichuan-science 21 tianjin-arts 17 tianjin-science 17 zhejiang-arts 15 zhejiang-science 15
Unknown
sample_questions 7
2015 national-II-arts

15 maths questions

Q1 Inequalities Set Operations Using Inequality-Defined Sets View
1. Given sets $A = \{ x \mid - 1 < x < 2 \} , B = \{ x \mid 0 < x < 3 \}$, then $A \cup B =$
A. $( - 1,3 )$
B. $( - 1,0 )$
C. $( 0,2 )$
D. $( 2,3 )$
Q2 Complex Numbers Arithmetic Systems of Equations via Real and Imaginary Part Matching View
2. If $a$ is a real number and $\frac { 2 + a i } { 1 + i } = 3 + i$, then $a =$
A. $- 4$
B. $- 3$
C. $3$
D. $4$
Q3 Data representation View
3. Based on the bar chart of China's annual carbon dioxide emissions (in units of 10,000 tons) from 2004 to 2013 shown below, which of the following conclusions is incorrect? [Figure]
A. Year-on-year comparison shows that 2008 had the most significant effect in reducing carbon dioxide emissions
B. China's efforts to control carbon dioxide emissions showed results in 2007
C. Since 2006, China's annual carbon dioxide emissions have shown a decreasing trend
D. Since 2006, China's annual carbon dioxide emissions are positively correlated with the year
Q4 Vectors Introduction & 2D Dot Product Computation View
4. Given $\vec { a } = ( 0 , - 1 ) , \vec { b } = ( - 1,2 )$, then $( 2 \vec { a } + \vec { b } ) \cdot \vec { a } =$
A. $- 1$
B. $0$
C. $1$
D. $2$
Q5 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
5. Let $S _ { n }$ be the sum of the first $n$ terms of an arithmetic sequence $\left\{ a _ { n } \right\}$. If $a _ { 1 } + a _ { 3 } + a _ { 5 } = 3$, then $S _ { 5 } =$ [Figure] [Figure]
A. $5$
B. $7$
C. $9$
D. $11$
Q7 Circles Inscribed/Circumscribed Circle Computations View
7. Given three points $A ( 1,0 ) , B ( 0 , \sqrt { 3 } ) , C ( 2 , \sqrt { 3 } )$, the distance from the circumcenter of $\triangle A B C$ [Figure]
to the origin is
A. $\frac { 5 } { 3 }$
B. $\frac { \sqrt { 21 } } { 3 }$
C. $\frac { 2 \sqrt { 5 } } { 3 }$
D. $\frac { 4 } { 3 }$
Q9 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
9. Given a geometric sequence $\left\{ a _ { n } \right\}$ satisfying $a _ { 1 } = \frac { 1 } { 4 } , a _ { 3 } a _ { 5 } = 4 \left( a _ { 4 } - 1 \right)$, then $a _ { 2 } =$
A. $2$
B. $1$
C. $\frac { 1 } { 2 }$
D. $\frac { 1 } { 8 }$
Q11 Curve Sketching Identifying the Correct Graph of a Function View
11. As shown in the figure, the rectangle's edge, is the midpoint, point moves along the edge, and moves with, denote, express the sum of distances from the moving point to two points as a function of, then the graph of is approximately
[Figure]
A.
[Figure]
B.
[Figure]
C.
[Figure]
D.
Q12 Modulus function Solving inequalities involving modulus View
12. Let $f ( x ) = \ln ( 1 + | x | ) - \frac { 1 } { 1 + x ^ { 2 } }$. The range of $x$ for which $f ( x ) > f ( 2 x - 1 )$ holds is
A. $\left( \frac { 1 } { 3 } , 1 \right)$
B. $\left( - \infty , \frac { 1 } { 3 } \right) \cup ( 1 , + \infty )$
C. $\left( - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)$
D. $\left( - \infty , - \frac { 1 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , + \infty \right)$
II. Fill-in-the-Blank Questions: This section contains 4 questions, 5 points each, 20 points total
Q13 Exponential Functions Parameter Determination from Conditions View
13. Given that the graph of function $f ( x ) = a x ^ { 3 } - 2 x$ passes through the point $( - 1,4 )$, then $a = $ $\_\_\_\_$ .
Q14 Inequalities Linear Programming (Optimize Objective over Linear Constraints) View
14. If $x , y$ satisfy the constraint conditions $\left\{ \begin{array} { c } x + y - 5 \leq 0 \\ 2 x - y - 1 \geq 0 \\ x - 2 y + 1 \leq 0 \end{array} \right.$, then the maximum value of $z = 2 x + y$ is $\_\_\_\_$ .
Q15 Conic sections Equation Determination from Geometric Conditions View
15. A hyperbola passes through the point $( 4 , \sqrt { 3 } )$ and has asymptote equations $y = \pm \frac { 1 } { 2 } x$. The standard equation of this hyperbola is $\_\_\_\_$ .
Q16 Differentiating Transcendental Functions Determine parameters from function or curve conditions View
16. The tangent line to the curve $y = x + \ln x$ at the point $( 1,1 )$ is tangent to the curve $y = a x ^ { 2 } + ( a + 2 ) x + 1$. Then $a = $ $\_\_\_\_$ .
III. Solution Questions
17 (This question is worth 12 points). In $\triangle A B C$, $D$ is a point on $BC$, $AD$ bisects $\angle B A C$, and $B D = 2 D C$.
(1) Find $\frac { \sin \angle B } { \sin \angle C }$; (II) If $\angle B A C = 60 ^ { \circ }$, find $\angle B$.
Q18 Data representation View
18. (This question is worth 12 points). A company randomly surveyed 40 users from regions $A$ and $B$ respectively to understand user satisfaction with its products. Based on user satisfaction scores, a frequency distribution histogram of user satisfaction scores in region $A$ and a frequency distribution table of user satisfaction scores in region $B$ were obtained.
Frequency Distribution Histogram of User Satisfaction Scores in Region A [Figure]
Satisfaction Score Interval\multicolumn{5}{|c|}{Frequency Distribution Table of User Satisfaction Scores in Region B}
Frequency$[ 50,60 )$$[ 60,70 )$$[ 70,80 )$$[ 80,90 )$$[ 90,100 ]$
2814106

(I) Draw the frequency distribution histogram of user satisfaction scores in region $B$ on the answer sheet, and compare the mean and dispersion of satisfaction scores in the two regions through this histogram (no need to calculate specific values, just provide conclusions); [Figure] (II) Based on user satisfaction scores, user satisfaction levels are divided into three categories:
Satisfaction ScoreBelow 7070 to 89At least 90
Satisfaction LevelDissatisfiedSatisfiedVery Satisfied

Estimate which region has a higher probability that a user's satisfaction level is dissatisfied, and explain the reasoning.
Q20 Conic sections Equation Determination from Geometric Conditions View
20. (This question is worth 12 points). The ellipse $C : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ has eccentricity $\frac { \sqrt { 2 } } { 2 }$, and the point $( 2 , \sqrt { 2 } )$ lies