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
2023 national-II

8 maths questions

Q1 5 marks Complex Numbers Arithmetic Locating Points in the Complex Plane (Quadrant/Axis) View
In the complex plane, the point corresponding to $(1+3i)(3-i)$ is located in
A. the first quadrant
B. the second quadrant
C. the third quadrant
Q2 5 marks Probability Definitions Set Operations View
Let $A=\{0,-a\}$, $B=\{1,a-2,2a-2\}$. If $A\subseteq B$, then $a=$
A. 2
B. 1
C. $\frac{2}{3}$
Q5 5 marks Conic sections Chord Properties and Midpoint Problems View
Given the ellipse $\frac{x^2}{3}+y^2=1$ with left and right foci $F_1, F_2$ respectively, the line $y=x+m$ intersects $C$ at points $A$ and $B$. If the area of $\triangle F_1AB$ is 2 times the area of $\triangle F_2AB$, then $m=$
A. $\frac{2}{3}$
B. $\frac{\sqrt{2}}{3}$
C. $-\frac{\sqrt{2}}{3}$
D. $-\frac{2}{3}$
Q6 5 marks Applied differentiation Finding parameter values from differentiability or equation constraints View
Given that the function $f(x)=a\mathrm{e}^x-\ln x$ is monotonically increasing on the interval $(1,2)$, the minimum value of $a$ is
A. $\mathrm{e}^2$
B. $\mathrm{e}$
C. $\mathrm{e}^{-1}$
D. $\mathrm{e}^{-2}$
Q7 5 marks Addition & Double Angle Formulae Half-Angle Formula Evaluation View
Given that $\alpha$ is an acute angle and $\cos\alpha=\frac{1+\sqrt{5}}{4}$, then $\sin\frac{\alpha}{2}=$
A. $\frac{3-\sqrt{5}}{8}$
B. $\frac{-1+\sqrt{5}}{8}$
C. $\frac{3-\sqrt{5}}{4}$
D. $\frac{-1+\sqrt{5}}{4}$
Q8 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 geometric sequence $\{a_n\}$. If $S_4=-5$, $S_6=21S_2$, then $S_8=$
A. 120
B. 85
C. $-85$
D. $-120$
Q10 5 marks Conic sections Focal Chord and Parabola Segment Relations View
Let $O$ be the origin of coordinates. The line $y=-\sqrt{3}(x-1)$ passes through the focus of the parabola $C: y^2=2px$ $(p>0)$ and intersects $C$ at points $M$ and $N$. Let $l$ be the directrix of $C$. Then
A. $p=2$
B. $|MN|=\frac{8}{3}$
C. the circle with $MN$ as diameter is tangent to $l$
D. $\triangle OMN$ is an isosceles triangle
Q11 5 marks Stationary points and optimisation Find critical points and classify extrema of a given function View
If the function $f(x)=a\ln x+\frac{b}{x}+\frac{c}{x^2}$ $(a\neq 0)$ has both a local maximum and a local minimum, then:
A. $bc>0$
B. $ab>0$
C. $b^2+8ac>0$
D. $ac<0$