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
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. $\frac { \sqrt { 5 } + 1 } { 2 }$
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
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. $y = a + b \ln x$
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. $y = 2 x + 1$
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. $\frac { 3 \pi } { 2 }$
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