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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
2017 national-II-science

8 maths questions

Q1 Complex Numbers Arithmetic Complex Division/Multiplication Simplification View
1. $\frac { 3 + i } { 1 + i } =$
A. $1 + 2 i$
B. $1 - 2 \mathrm { i }$
C. $2 + \mathrm { i }$
2. $A = \{ 1,2,4 \}$
$$B = \left\{ x \mid x ^ { 2 } - 4 x + m = 0 \right\}$$
If $A \cap B = \{ 1 \}$, then $B =$
A. $\{ 1 , - 3 \}$
B. $\{ 1,0 \}$
C. $\{ 1,3 \}$
D. $2 - i$
3. In the ancient Chinese mathematical classic ``Suanfa Tongzong'', there is the following problem: ``Looking from afar at a seven-story pagoda, with lights doubling at each level, totaling 381 lights, how many lights are at the top?'' This means: a seven-story pagoda has a total of 381 lights, and the number of lights at each lower level is twice that of the level above it. The number of lights at the top of the pagoda is
A. 1
B. 3
C. 5 [Figure]
Q6 Permutations & Arrangements Linear Arrangement with Constraints View
6. The number of ways to arrange 3 people in a row is
A. $12$ ways
B. $18$ ways
C. $24$ ways
D. $36$ ways [Figure] [Figure] [Figure] [Figure] [Figure]
C. C and D can know each other's scores
B. B can know all four people's scores
Q9 Conic sections Eccentricity or Asymptote Computation View
9. If the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$ has an asymptote that cuts the circle $( x - 2 ) ^ { 2 } + y ^ { 2 } = 4$ with a chord of length 2, then the eccentricity of $C$ is
A. $2$
B. $\sqrt { 3 }$
C. $\frac { 2 \sqrt { 3 } } { 3 }$
D. $\frac { \sqrt { 5 } } { 2 }$
Q10 Vectors 3D & Lines MCQ: Angle Between Skew Lines View
10. In a right triangular prism $A B C - A _ { 1 } B _ { 1 } C _ { 1 }$, $\angle A B C = 120 ^ { \circ } , A B = 2 , B C = C C _ { 1 } = 1$. The cosine of the angle between skew lines $A B _ { 1 }$ and $B C _ { 1 }$ is
A. $\frac { \sqrt { 3 } } { 2 }$
B. $\frac { \sqrt { 15 } } { 5 }$
C. $\frac { \sqrt { 10 } } { 5 }$
D. $\frac { \sqrt { 3 } } { 3 }$ [Figure]
Q12 Vectors Introduction & 2D Optimization of a Vector Expression View
12. Given that $\triangle A B C$ is an equilateral triangle with side length 2, and $P$ is a point in the plane $A B C$, the minimum value of $\overrightarrow { P A } \cdot ( \overrightarrow { P B } + \overrightarrow { P C } )$ is
A. $- 2$
B. $- \frac { 3 } { 2 }$
C. $- \frac { 4 } { 3 }$
D. $- 1$
II. Fill in the Blank: This section has 4 questions, each worth 5 points.
Q13 Discrete Probability Distributions Binomial Distribution Identification and Application View
13. The defect rate of a batch of products is 0.02. Drawing one item at a time with replacement from this batch, 100 times total, let $X$ denote the number of defective items drawn. Then $D X = $ ______
Q14 Trig Graphs & Exact Values View
14. The maximum value of the function $f ( x ) = \sin ^ { 2 } x + \sqrt { 3 } \cos x - \frac { 3 } { 4 } \left( x \in \left[ 0 , \frac { \pi } { 2 } \right] \right)$ is ______
Q15 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP View
15. For an arithmetic sequence $\left\{ a _ { n } \right\}$ with sum of first $n$ terms $S _ { n }$, if $a _ { 3 } = \frac { 3 } { 2 } , S _ { 4 } = 10$, then $\sum_{k=1}^{n} \frac { 1 } { S _ { k } } = $ ______ [Figure]
III. Solving Problems: Questions 16-23 [Figure] [Figure]