gaokao

2019 national-II-science

8 maths questions

Let $A = \left\{ x \mid x ^ { 2 } - 5 x + 6 > 0 \right\} , B = \{ x \mid x - 1 < 0 \}$, then $A \cap B =$
A. $( - \infty , 1 )$
B. $( - 2,1 )$
C. $( - 3 , - 1 )$
D. $( 3 , + \infty )$
Q2 5 marks Complex Numbers Arithmetic Locating Points in the Complex Plane (Quadrant/Axis) View
Let $z = - 3 + 2 i$. Then in the complex plane, the point corresponding to $\bar { z }$ is located in
A. the first quadrant
B. the second quadrant
C. the third quadrant
D. the fourth quadrant
Q3 5 marks Vectors Introduction & 2D Dot Product Computation View
Given $\overrightarrow { A B } = ( 2,3 ) , \overrightarrow { A C } = ( 3 , t ) , | \overrightarrow { B C } | = 1$, then $\overrightarrow { A B } \cdot \overrightarrow { B C } =$
A. - 3
B. - 2
C. 2
D. 3
Q5 5 marks Measures of Location and Spread View
A speech competition has 9 judges who each give an original score for a contestant. When determining the contestant's final score, the highest and lowest scores are removed from the 9 original scores, leaving 7 valid scores. Compared with the 9 original scores, the numerical characteristic that remains unchanged for the 7 valid scores is
A. median
B. mean
C. variance
D. range
Q6 5 marks Exponential Functions Ordering and Comparing Exponential Values View
If $a > b$, then
A. $\ln ( a - b ) > 0$
B. $3 ^ { a } < 3 ^ { b }$
C.$a ^ { 3 } - b ^ { 3 } > 0$
D. $| a | > | b |$
Let $\alpha , \beta$ be two planes. Then a necessary and sufficient condition for $\alpha \parallel \beta$ is
A. There are infinitely many lines in $\alpha$ that are parallel to $\beta$
B. There are two intersecting lines in $\alpha$ that are parallel to $\beta$
C. $\alpha$ and $\beta$ are both parallel to the same line
D. $\alpha$ and $\beta$ are both perpendicular to the same plane
Q8 5 marks Conic sections Confocal or Related Conic Construction View
If the focus of the parabola $y ^ { 2 } = 2 p x \ ( p > 0 )$ is a focus of the ellipse $\frac { x ^ { 2 } } { 3 p } + \frac { y ^ { 2 } } { p } = 1$, then $p =$
A. 2
B. 3
C. 4
D. 8
Q9 5 marks Trig Graphs & Exact Values View
Among the following functions, which one has period $\frac { \pi } { 2 }$ and is monotonically increasing on the interval $\left( \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$?
A.$f ( x ) = | \cos 2 x |$
B.$f ( x ) = | \sin 2 x |$
C.$f ( x ) = \cos | x |$
D.$f ( x ) = \sin | x |$