已知平面向量 $\vec{a}=(m,5)$ 在向量 $\vec{b}$ 上的投影向量为 $(2,1)$，则 $|\vec{a}|=$ ______。

已知函数 $f(x) = \log_{\frac{1}{2}} \frac{1-kx}{1+x} (k > 0)$ 是奇函数。 (1) 求实数 $k$ 的值； (2) 解关于 $x$ 的不等式 $f(2x-1) + f(x) > 0$。

记 $\triangle ABC$ 是内角 $A, B, C$ 的对边分别为 $a, b, c$。已知 $b^2 = ac$，点 $D$ 在边 $AC$ 上，$BD \sin \angle ABC = a \sin C$。 (1) 证明：$BD = b$； (2) 若 $AD = 2DC$，求 $\cos \angle ABC$。

记 $\triangle ABC$ 的内角 $A, B, C$ 的对边分别为 $a, b, c$，已知 $\frac{\cos A}{1 + \sin A} = \frac{\sin 2B}{1 + \cos 2B}$。 (1) 若 $C = \frac{2\pi}{3}$，求 $B$； (2) 求 $\frac{a^2 + b^2}{c^2}$ 的最小值。

已知函数 $f(x)=x-a\ln x$，$a\in\mathbf{R}$． (1) 若 $a=2$： (i) 求 $f(x)$ 的极值点； (ii) 证明：当 $x\in(2,4)$ 时，$f(x)<f(4-x)$； (2) 若 $a<0$，$f(x)>2af'(x)$ 恒成立，求 $a$ 的取值范围．

**Realizing your potential** Senior high school is \_\_\_\_\_\_ world full of challenges, such as new subjects, new experiences and new ways of \_\_\_\_\_\_ (think). \_\_\_\_\_\_ you work hard to rise to the challenges, you will have the opportunity to acquire great knowledge and enjoy personal \_\_\_\_\_\_ (grow). At senior high school, you should try your best to discover your potential. To \_\_\_\_\_\_ (full) realize your potential, you ought to make the most of your school resources. Of equal importance \_\_\_\_\_\_ (be) your good study habits, positive \_\_\_\_\_\_ (attitude) and useful skills. As a senior high school student, you must be active and \_\_\_\_\_\_ (responsibility). In time you will find \_\_\_\_\_\_ growing into a well-rounded person. It's very important for you \_\_\_\_\_\_ (make) continuous efforts to train your mind \_\_\_\_\_\_ develop your character. Senior high school will help you grow, realize your great potential and become confident.

【篇章一】\nMy first day at senior high school\nI've just finished my first day of senior high school and I really enjoyed it. I ______ (tell) that schoolwork will present more of a challenge in the years ahead, and that ______ teachers will hold us to higher standards. This means I'll have to put a lot of effort into my studies. I'll also need to be very careful about ______ (balance) my schoolwork and hobbies. This is all quite new and different ______ my life at junior high school, I'm sure I'll rise to all these ______ (challenge).\nIn fact, I'm looking forward to being more ______ (independence) and responsible for my own learning. There is so much knowledge I need to acquire, so I'll work ______ (hard) than ever. I also plan to take advantage of every opportunity ______ (improve) my communication skills. I'll make more friends by joining some clubs. I have confidence in ______ (I) ability to do well at senior high school!\n\n【篇章二】\nGrammar\nGoals are important in many ways. ______ (set) goals gives you a focus in life. By setting goals now, you are deciding ______ you want to achieve in the future. Then you know where you are going in life and can work hard to get there. Setting goals also helps you develop good ______ (habit). To realize your goals, you need to have a good plan, manage your time well and pay attention to details. Finally, setting goals makes you more confident. When you achieve a goal, you see ______ result of your hard work and know how much progress you have made.\nIt is important to set goals that can be achieved. That is to say, you should set goals ______ (base) on your abilities and skills. Try to break big goals down into small ones to make them ______ (easy) to reach. You will be proud of ______ (you) when you realize each small goal. It is also a good idea to put your goals where you can see them, which will remind you ______ what you are working for and keep you focused.\nA goal is a dream that ______ (need) action. As a result of your action, your dream will come true and ______ (hopeful) you will live a happy life.

如图，$\angle A=70^\circ$，$\angle B=40^\circ$，$\angle C=30^\circ$，则 $\angle D+\angle E=$（ ） A. $30^\circ$ B. $40^\circ$ C. $60^\circ$ D. $70^\circ$

8. (1) 列车原来的速度是 $36\text{ km/h}$，在一段下坡路上加速度为 $0.2\text{ m/s}^2$，列车行驶到下坡路末端时，速度增加到 $54\text{ km/h}$。求列车通过这段下坡路所用的时间；\n(2) 以 $72\text{ km/h}$ 的速度行驶的列车在驶近一座石拱桥时做匀减速直线运动（如图），加速度的大小是 $0.1\text{ m/s}^2$，列车减速行驶 $2\text{ min}$ 后的速度是多少？

已知集合 $A = \{x \mid x^2 - 6x + 5 \le 0\}$，$B = \{x \mid x^2 - mx + 4 \ge 0\}$，若“$x \in A$”是“$x \in B$”的充分条件，则实数 $m$ 的取值范围为（ ） A. $[5, +\infty)$ B. $(-\infty, 4]$ C. $[4, 5]$ D. $(-\infty, 4] \cup [5, +\infty)$