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-III-science

17 maths questions

Q1 5 marks Probability Definitions Set Operations View
Given sets $A = \{ x \mid x - 1 \geqslant 0 \} , B = \{ 0,1,2 \}$, then $A \cap B =$
A. $\{ 0 \}$
B. $\{ 1 \}$
C. $\{ 1,2 \}$
D. $\{ 0,1,2 \}$
Q2 5 marks Complex Numbers Arithmetic Complex Division/Multiplication Simplification View
$( 1 + i ) ( 2 - i ) =$
A. $- 3 - \mathrm { i }$
B. $- 3 + \mathrm { i }$
C. $3 - i$
D. $3 + i$
Q4 5 marks Addition & Double Angle Formulae Direct Double Angle Evaluation View
If $\sin \alpha = \frac { 1 } { 3 }$, then $\cos 2 \alpha =$
A. $\frac { 8 } { 9 }$
B. $\frac { 7 } { 9 }$
C. $- \frac { 7 } { 9 }$
D. $- \frac { 8 } { 9 }$
Q5 5 marks Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
The coefficient of $x ^ { 4 }$ in the expansion of $\left( x ^ { 2 } + \frac { 2 } { x } \right) ^ { 3 }$ is
A. 10
B. 20
C. 40
D. 80
Q6 5 marks Circles Optimization on a Circle View
The line $x + y + 2 = 0$ intersects the $x$-axis and $y$-axis at points $A$ and $B$ respectively. Point $P$ is on the circle $( x - 2 ) ^ { 2 } + y ^ { 2 } = 2$. The range of the area of $\triangle ABP$ is
A. $[ 2,6 ]$
B. $[ 4,8 ]$
C. $[ \sqrt { 2 } , 3 \sqrt { 2 } ]$
D. $[ 2 \sqrt { 2 } , 3 \sqrt { 2 } ]$
Q7 5 marks Curve Sketching Identifying the Correct Graph of a Function View
The graph of the function $y = - x ^ { 4 } + x ^ { 2 } + 2$ is approximately (See figures A, B, C, D in the original paper.)
Q8 5 marks Binomial Distribution Find Parameters from Moment Conditions View
Each member of a certain group uses mobile payment with probability $p$. The payment methods of each member are independent. Let $X$ be the number of people among 10 members of the group who use mobile payment. If $D(X) = 2.4$ and $P ( X = 4 ) < P ( X = 6 )$, then $p =$
A. 0.7
B. 0.6
C. 0.4
D. 0.3
Q9 5 marks Sine and Cosine Rules Determine an angle or side from a trigonometric identity/equation View
In $\triangle ABC$, the sides opposite to angles $A, B, C$ are $a, b, c$ respectively. If the area of $\triangle ABC$ equals $\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 4 }$, then $C =$
A. $\frac { \pi } { 2 }$
B. $\frac { \pi } { 3 }$
C. $\frac { \pi } { 4 }$
D. $\frac { \pi } { 6 }$
Q10 5 marks Volumes of Revolution Volume of a 3D Geometric Solid (Pyramid/Tetrahedron) View
Points $A, B, C, D$ are on the surface of a sphere with radius 4. $\triangle ABC$ is an equilateral triangle with area $9 \sqrt { 3 }$. The maximum volume of the tetrahedron $D$-$ABC$ is
A. $12 \sqrt { 3 }$
B. $18 \sqrt { 3 }$
C. $24 \sqrt { 3 }$
D. $54 \sqrt { 3 }$
Q11 5 marks Conic sections Eccentricity or Asymptote Computation View
Let $F _ { 1 }, F _ { 2 }$ be the left and right foci of the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ $(a > 0, b > 0)$, and $O$ be the origin. A perpendicular is drawn from $F _ { 2 }$ to an asymptote of $C$, with foot of perpendicular at $P$. If $| PF_2 | = \sqrt { 6 } | OP |$, then the eccentricity of $C$ is
A. $\sqrt { 5 }$
B. 2
C. $\sqrt { 3 }$
D. $\sqrt { 2 }$
Q12 5 marks Laws of Logarithms Compare or Order Logarithmic Values View
Let $a = \log _ { 0.2 } 0.3, b = \log _ { 2 } 0.3$, then
A. $a + b < ab < 0$
B. $ab < a + b < 0$
C. $a + b < 0 < ab$
D. $ab < 0 < a + b$
Q13 5 marks Vectors Introduction & 2D Perpendicularity or Parallel Condition View
Given vectors $a = ( 1,2 ) , b = ( 2 , - 2 ) , c = ( 1 , \lambda )$. If $c \parallel ( 2a + b )$, then $\lambda = $ $\_\_\_\_$.
Q14 5 marks Differentiating Transcendental Functions Determine parameters from function or curve conditions View
The slope of the tangent line to the curve $y = ( ax + 1 ) e ^ { x }$ at the point $( 0,1 )$ is $- 2$. Then $a = $ $\_\_\_\_$.
Q15 5 marks Standard trigonometric equations Count zeros or intersection points involving trigonometric curves View
The number of zeros of the function $f ( x ) = \cos \left( 3 x + \frac { \pi } { 6 } \right)$ on $[ 0, \pi ]$ is $\_\_\_\_$.
Q16 5 marks Conic sections Focal Chord and Parabola Segment Relations View
Given point $M ( - 1, 1 )$ and parabola $C : y ^ { 2 } = 4 x$. A line through the focus of $C$ with slope $k$ intersects $C$ at points $A$ and $B$. If $\angle AMB = 90 ^ { \circ }$, then $k = $ $\_\_\_\_$.
Q17 12 marks Geometric Sequences and Series Derive General Term from Geometric Property View
In a geometric sequence $\{ a _ { n } \}$, $a _ { 1 } = 1$ and $a _ { 4 } = 4 a _ { 2 }$.
(1) Find the general term formula for $\{ a_n \}$;
(2) Let $S _ { n }$ be the sum of the first $n$ terms of $\{ a_n \}$. If $S _ { m } = 63$, find $m$.
Q18 12 marks Data representation View
To improve production efficiency, a factory conducted technological innovation activities and proposed two new production methods for completing a production task. To compare the efficiency of the two methods, 40 workers were selected and randomly divided into two groups of 20 each. The first group used the first production method, and the second group used the second production method. Based on the time (in minutes) taken by workers to complete the production task, a stem-and-leaf plot was drawn.
(1) Based on the stem-and-leaf plot, which production method has higher efficiency? Explain your reasoning.
(2) Find the median $m$ of the time taken by all 40 workers to complete the production task, and fill in the contingency table with the number of workers whose completion time exceeds $m$ and does not exceed $m$ for each production method.