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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
2020 national-I-science

9 maths questions

Q1 5 marks Complex Numbers Arithmetic Modulus Computation View
If $z = 1 + \mathrm { i }$, then $\left| z ^ { 2 } - 2 z \right| =$
A. 0
B. 1
C. $\sqrt { 2 }$
D. 2
Q2 5 marks Inequalities Set Operations Using Inequality-Defined Sets View
Let sets $A = \left\{ x \mid x ^ { 2 } - 4 \leqslant 0 \right\}$, $B = \{ x \mid 2 x + a \leqslant 0 \}$, and $A \cap B = \{ x \mid - 2 \leqslant x \leqslant 1 \}$. Then $a =$
A. $- 4$
B. $- 2$
C. 2
D. 4
Q3 5 marks Solving quadratics and applications Finding a ratio or relationship between variables from an equation View
The Great Pyramid of Khufu in Egypt is one of the ancient wonders of the world. Its shape can be viewed as a regular square pyramid. The area of a square with side length equal to the height of the pyramid equals the area of one lateral triangular face of the pyramid. Then the ratio of the height of the lateral triangle to the base of the square is
A. $\frac { \sqrt { 5 } - 1 } { 4 }$
B. $\frac { \sqrt { 5 } - 1 } { 2 }$
C. $\frac { \sqrt { 5 } + 1 } { 4 }$
D. $\frac { \sqrt { 5 } + 1 } { 2 }$
Q4 5 marks Conic sections Focal Distance and Point-on-Conic Metric Computation View
Let $A$ be a point on the parabola $C : y ^ { 2 } = 2 p x$ ($p > 0$). The distance from point $A$ to the focus of $C$ is 12, and the distance to the $y$-axis is 9. Then $p =$
A. 2
B. 3
C. 6
D. 9
Q5 5 marks Linear regression View
A student research group at a school conducted an experiment to study the relationship between the germination rate $y$ of a certain crop seed and temperature $x$ (in units of ${}^{\circ}\mathrm{C}$). Under 20 different temperature conditions, seed germination experiments were performed. From the experimental data $\left( x _ { i } , y _ { i } \right)$ ($i = 1,2 , \cdots , 20$), a scatter plot was obtained. From this scatter plot, between $10^{\circ}\mathrm{C}$ and $40^{\circ}\mathrm{C}$, which of the following four regression equation types is most suitable as the regression equation type for the germination rate $y$ and temperature $x$?
A. $y = a + b x$
B. $y = a + b x ^ { 2 }$
C. $y = a + b e ^ { x }$
D. $y = a + b \ln x$
Q6 5 marks Tangents, normals and gradients Find tangent line equation at a given point View
The equation of the tangent line to the graph of $f ( x ) = x ^ { 4 } - 2 x ^ { 3 }$ at the point $( 1 , f ( 1 ) )$ is
A. $y = - 2 x - 1$
B. $y = - 2 x + 1$
C. $y = 2 x - 3$
D. $y = 2 x + 1$
Q7 5 marks Trig Graphs & Exact Values View
Let the function $f ( x ) = \cos \left( \omega x + \frac { \pi } { 6 } \right)$ on $[ - \pi , \pi ]$ have a graph as shown. Then the smallest positive period of $f ( x )$ is
A. $\frac { 10 \pi } { 9 }$
B. $\frac { 7 \pi } { 6 }$
C. $\frac { 4 \pi } { 3 }$
D. $\frac { 3 \pi } { 2 }$
Q8 5 marks Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions View
The coefficient of $x ^ { 3 } y ^ { 3 }$ in the expansion of $\left( x + \frac { y ^ { 2 } } { x } \right) ( x + y ) ^ { 5 }$ is
A. 5
B. 10
C. 15
D. 20
Q9 5 marks Trig Proofs Trigonometric Equation Constraint Deduction View
Given $\alpha \in ( 0 , \pi )$ and $3 \cos 2 \alpha - 8 \cos \alpha = 5$, then $\sin \alpha =$
A. $\frac { \sqrt { 5 } } { 3 }$
B. $\frac { 2 } { 3 }$
C. $\frac { 1 } { 3 }$
D. $\frac { \sqrt { 5 } } { 9 }$