用高一数学知识给我讲一下---Here is the extracted content from the image:
**Question 4:**
已知平面 $\alpha$, 直线 $m, n$ 满足 $m \not\subset \alpha, n \subset \alpha$, 则 "$m // \alpha$" 是 "$m // n$" 的
A. 充分不必要条件
B. 必要不充分条件
C. 充分必要条件
D. 既不充分也不必要条件
**Question 5:**
在 $\triangle ABC$ 中, $\vec{AD} = \frac{2}{3}\vec{AC}$, 点 $E$ 在 $BD$ 上, 若 $\vec{AE} = x \vec{BA} + \frac{1}{3}\vec{BC}$, 则 $x = $
A. $-\frac{2}{3}$
B. $-\frac{4}{5}$
C. $-\frac{5}{6}$
D. $-\frac{6}{7}$
**Question 6:**
底面圆周长为 $2\pi$, 母线长为 4 的圆锥内切球的体积为
A. $\frac{\sqrt{15}\pi}{5}$
B. $\frac{13\pi}{25}$
C. $\frac{\sqrt{15}\pi}{25}$
D. $\frac{4\sqrt{15}\pi}{25}$
**二、多项选择题:** 本题共 2 小题, 每小题 5 分, 共 10 分. 在每小题给出的四个选项中, 有多项符合题目要求, 全部选对得 5 分, 部分选对得 2 分, 有错选得 0 分.
**Question 7:**
如图所示, 下列频率分布直方图显示了三种不同的分布形态. 图(1)形成对称形态, 图(2)形成“右拖尾”形态, 图(3)形成“左拖尾”形态, 根据所给图作出以下判断, 正确的是
A. 图(1)的平均数 = 中位数 = 众数
B. 图(2)的平均数 < 众数 < 中位数
C. 图(2)的众数 < 中位数 < 平均数
D. 图(3)的平均数 < 中位数 < 众数
**Chart/Diagram Description (for Question 7):**
Type: Three frequency distribution histograms with overlaid curves.
Main Elements:
- Three separate plots, labeled (1), (2), and (3) below the x-axis.
- Each plot has a horizontal axis (representing the variable/data) and a vertical axis (representing frequency or density, indicated by an upward arrow).
- Rectangular bars rise from the horizontal axis in each plot, forming a histogram shape.
- A curved line is drawn over the tops of the bars in each plot, illustrating the overall shape of the distribution.
- Plot (1) shows a symmetric distribution, with the bars highest in the center and decreasing symmetrically towards the left and right. The curve is bell-shaped and symmetric.
- Plot (2) shows a right-skewed distribution, with the bars highest on the left and tailing off towards the right. The curve is skewed to the right ("right-tailed").
- Plot (3) shows a left-skewed distribution, with the bars highest on the right and tailing off towards the left. The curve is skewed to the left ("left-tailed").
- Arrows on the horizontal axis indicate direction (presumably increasing values).
**Question 8:**
如图, 已知正方体 $ABCD-A_1B_1C_1D_1$, $M, N$ 分别为 $A_1D_1$ 和 $AA_1$ 的中点, 则下列四种说法中正确的是
A. $CM // AC$
B. $BD_1 \perp AC$
C. $BC_1$ 与 $AC$ 所成的角为 $60^\circ$
D. $CD$ 与 $BN$ 为异面直线
**Chart/Diagram Description (for Question 8):**
Type: Perspective drawing of a cube.
Main Elements:
- A cube is shown with vertices labeled $A, B, C, D$ on the bottom face and $A_1, B_1, C_1, D_1$ on the top face, with $A_1$ above $A$, $B_1$ above $B$, etc.
- Edges are shown as solid or dashed lines to indicate visibility.
- Point $M$ is marked as the midpoint of edge $A_1D_1$.
- Point $N$ is marked as the midpoint of edge $AA_1$.
- Lines/segments mentioned in the options are implicitly present (e.g., $CM$, $AC$, $BD_1$, $BC_1$, $CD$, $BN$).
**Other Information:**
- The bottom of the page contains text: "高一数学试题 第 2 页 (共 4 页)" (Senior 1 Mathematics Exam Paper Page 2 (Total 4 pages)).