gaokao

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
2018 national-I-science

13 maths questions

Q1 5 marks Complex Numbers Arithmetic Modulus Computation View
Let $z = \frac { 1 - \mathrm { i } } { 1 + \mathrm { i } } + 2 \mathrm { i }$, then $| z | =$
A. 0
B. $\frac { 1 } { 2 }$
C. 1
D. $\sqrt { 2 }$
Q2 5 marks Inequalities Set Operations Using Inequality-Defined Sets View
Given the set $A = \left\{ x \mid x ^ { 2 } - x - 2 > 0 \right\}$, then $\mathrm { C } _ { \mathrm { R } } A =$
A. $\{ x \mid - 1 < x < 2 \}$
B. $\{ x \mid - 1 \leqslant x \leqslant 2 \}$
C. $\{ x \mid x < - 1 \} \cup \{ x \mid x > 2 \}$
D. $\{ x \mid x \leqslant - 1 \} \cup \{ x \mid x \geqslant 2 \}$
Q4 5 marks Arithmetic Sequences and Series Find Specific Term from Given Conditions View
Let $S _ { n }$ denote the sum of the first $n$ terms of an arithmetic sequence $\left\{ a _ { n } \right\}$. Given $3 S _ { 3 } = S _ { 2 } + S _ { 4 }$ and $a _ { 1 } = 2$, then $a _ { 5 } =$
A. $- 12$
B. $- 10$
C. 10
D. 12
Q5 5 marks Tangents, normals and gradients Determine unknown parameters from tangent conditions View
Let $f ( x ) = x ^ { 3 } + ( a - 1 ) x ^ { 2 } + a x$. If $f ( x )$ is an odd function, then the equation of the tangent line to the curve $y = f ( x )$ at the point $( 0,0 )$ is
A. $y = - 2 x$
B. $y = - x$
C. $y = 2 x$
D. $y = x$
Q6 5 marks Vectors Introduction & 2D Expressing a Vector as a Linear Combination View
In $\triangle A B C$, $A D$ is the median to side $B C$, and $E$ is the midpoint of $A D$. Then $\overrightarrow { E B } =$
A. $\frac { 3 } { 4 } \overrightarrow { A B } - \frac { 1 } { 4 } \overrightarrow { A C }$
B. $\frac { 1 } { 4 } \overrightarrow { A B } - \frac { 3 } { 4 } \overrightarrow { A C }$
C. $\frac { 3 } { 4 } \overrightarrow { A B } + \frac { 1 } { 4 } \overrightarrow { A C }$
D. $\frac { 1 } { 4 } \overrightarrow { A B } + \frac { 3 } { 4 } \overrightarrow { A C }$
Q8 5 marks Conic sections Vector and Dot Product Conditions on Conics View
Let the parabola $C : y ^ { 2 } = 4 x$ have focus $F$. A line through $( - 2,0 )$ with slope $\frac { 2 } { 3 }$ intersects $C$ at points $M$ and $N$. Then $\overrightarrow { F M } \cdot \overrightarrow { F N } =$
Q9 5 marks Curve Sketching Number of Solutions / Roots via Curve Analysis View
Given the function $f ( x ) = \left\{ \begin{array} { l l } \mathrm { e } ^ { x } , & x \leqslant 0 , \\ \ln x , & x > 0 , \end{array} \right.$ and $g ( x ) = f ( x ) + x + a$. If $g ( x )$ has 2 zeros, then the range of $a$ is
A. $( 0 , + \infty )$
B. $[ 0 , + \infty )$
C. $[ - 1 , + \infty )$
D. $[ 1 , + \infty )$
Q11 5 marks Conic sections Focal Distance and Point-on-Conic Metric Computation View
Given the hyperbola $C : \frac { x ^ { 2 } } { 3 } - y ^ { 2 } = 1$, with $O$ as the origin and $F$ as the right focus of $C$. A line through $F$ intersects the two asymptotes of $C$ at points $M$ and $N$. If $\triangle O M N$ is a right triangle, then $| M N | =$
A. $\frac { 3 } { 2 }$
B. 3
C. $2 \sqrt { 3 }$
D. 4
Q13 5 marks Inequalities Linear Programming (Optimize Objective over Linear Constraints) View
If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x - 2 y - 2 \leqslant 0 , \\ x - y + 1 \geqslant 0 , \\ y \leqslant 0 , \end{array} \right.$ then the maximum value of $z = 3 x + 2 y$ is $\_\_\_\_$
Q14 5 marks Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
Let $S _ { n }$ denote the sum of the first $n$ terms of the sequence $\left\{ a _ { n } \right\}$. If $S _ { n } = 2 a _ { n } + 1$, then $S _ { 6 } = \_\_\_\_$
Q15 5 marks Combinations & Selection Selection with Group/Category Constraints View
From 2 female students and 4 male students, select 3 people to participate in a science and technology competition, with at least 1 female student selected. The total number of different selection methods is $\_\_\_\_$ (Answer with numerals)
Q16 5 marks Addition & Double Angle Formulae Function Analysis via Identity Transformation View
Given the function $f ( x ) = 2 \sin x + \sin 2 x$, the minimum value of $f ( x )$ is $\_\_\_\_$
Q17 12 marks Sine and Cosine Rules Multi-step composite figure problem View
In planar quadrilateral $A B C D$, $\angle A D C = 90 ^ { \circ }$, $\angle A = 45 ^ { \circ }$, $A B = 2$, $B D = 5$.
(1) Find $\cos \angle A D B$;
(2) If $D C = 2 \sqrt { 2 }$, find $B C$.