在 $\triangle ABC$ 中，若 $\tan B = \frac{\cos A}{1 + \sin A}$，则 $\tan A + 5\tan B$ 的最小值为＿＿＿＿。

已知函数 $f(x) = \text{e}^x - x - 1$，$g(x) = kx^2$． (1) 记 $h(x) = f(2x) + f(x)$，求 $h(x)$ 的最小值； (2) 记 $m(x) = f(-x) - g(x)$，若 $m(x)$ 在区间 $(0, +\infty)$ 上有唯一极值点 $x_1$ 和唯一零点 $x_2$． ① 求 $k$ 的取值范围； ② 比较 $2x_1$ 和 $x_2$ 的大小．

如图所示，一实验小车静止在光滑水平面上，其上表面有粗糙水平轨道与光滑四分之一圆弧轨道。圆弧轨道与水平轨道相切于圆弧轨道最低点，一物块静止于小车最左端，一小球用不可伸长的轻质细线悬挂于 $O$ 点正下方，并轻靠在物块左侧。现将细线拉直到水平位置时，静止释放小球，小球运动到最低点时与物块发生弹性碰撞。碰撞后，物块开始沿着小车上的轨道运动，已知细线长 $L=1.25\text{ m}$，小球质量 $m=0.2\text{ kg}$，物块、小车质量均为 $M=0.3\text{ kg}$。小车上的水平轨道长 $s=1.0\text{ m}$，圆弧轨道半径 $R=0.15\text{ m}$。小球、物块均可视为质点。不计空气阻力，重力加速度 $g$ 取 $10\text{ m/s}^2$。 (1)小球运动到最低点与物块碰撞前所受拉力的大小； (2)小球与物块碰撞后的瞬间，物块速度的大小； (3)若物块与小车水平轨道动摩擦因数 $\mu=kx(k=0.6\text{ m}^{-1}$，$x$ 为距小车左端的距离)，求物块与小车保持相对静止时与小车左端的距离(结果可保留根号)。

At the 20th Asian Games Aichi-Nagoya 2026, 17-year-old Chen Yujie of China made history. On September 25, she claimed the women's 100-meter gold medal in 11.06 seconds, setting a new Games record, beating the previous mark of 11.15 seconds set by Sri Lanka's Susanthika Jayasinghe in 2002 — a record that had stood for 24 years. The road to victory was far from smooth. In the semi-finals, Singapore's two-time Olympian Shanti Pereira clocked 11.28 seconds and became the clear favorite. Chen clocked 11.41 seconds — a solid result, though not eye-catching — to secure her place in the final. Chen later admitted she felt heavy pressure ahead of her first Asian Games final. "On the training track, my legs shook. I was afraid of a false start," she recalled. Rather than submitting to nervousness, she kept repeating to herself, "Stay calm, avoid mistakes, and run cleanly." When the starting gun went off, Chen found another gear. She turned in a brilliant final run and crossed the finish line first. Pereira took silver with a season-best 11.21 seconds, while Bahrain's Edidiong Odiong earned bronze in 11.33 seconds. For Chen, this gold serves as an early, meaningful birthday gift. She will turn 18 this December — the legal age of adulthood in China. When asked how fast she believes she can go in the years ahead, she just replied: "I have no limits." Pereira spoke highly of the rising Chinese sprinter. She said she was excited to see what Chen would do and believed Chen would keep breaking records. This remarkable win builds on Chen's earlier achievement: she won the women's 200-meter title at the 2025 Asian Athletics Championships, where she also finished ahead of Pereira. Now holding her first Asian Games gold, the teenager has set her sights higher. "I hope to show my strength at the World Championships and the Olympics. I want to leave my mark on Chinese and Asian women's sprinting," Chen shared. 24. What do we know about Chen Yujie from this article? A. She broke a 24-year-old Asian Games record. B. She made it to the final with an extraordinary result. C. She beat Shanti Pereira by 0.09 seconds in the final. D. She won her Asian Games gold medal at the age of 18. 25. What does the underlined phrase "found another gear" in Paragraph 4 mean? A. Realized her true personal limit. B. Entered a more powerful state. C. Changed her usual way of running. D. Discovered new sports equipment. 26. Why does the writer mention Chen's success at the 2025 Asian Athletics Championships? A. To stress rules vary in different competitions. B. To show her Asian Games victory was no accident. C. To explain why she felt great pressure before the final. D. To prove she once broke a Games record at that competition. 27. What message does the author want to convey? A. Young athletes can break records as long as they keep calm. B. Top-level runners often set higher goals for their own future. C. Real courage is moving forward bravely when you feel afraid. D. Constant hard work is the only secret to becoming a great athlete.

用 $8$、$2$、$3$、$4$、$7$ 组成三位数乘两位数的乘法算式，乘积最大的算式是（＿＿＿＿）。 A. $843 \times 72$ B. $832 \times 74$ C. $732 \times 84$ D. $742 \times 83$

As a kid, Jorg Massen would watch birds dive and circle overhead and wonder whether they were doing it for enjoyment. Massen, now a behavioral biologist at Utrecht University, was finally able to put that question to the test thanks to a nearby bird park. For several months each year the birds at Avifauna Bird Park are free to leave their cages at certain times every day. When the gates open, each bird decides for itself: fly out into the open sky or stay home. They get no punishment or reward either way. Among these birds were 17 pink-and-gray Galah Cockatoos (鹦鹉) that, in the wild, fly long distances to find seeds. They chose to fly for almost every 20-minute period offered, Massen reported. "Their consistent choice to fly is in line with the idea that the birds found flight rewarding," says Michael Mendl, an animal behavior researcher. The only exception was a pair of birds that skipped flying once, on a day when they had just been given new nest boxes. Massen says, "they had other activities to attend to, which are also considered joyful." After flight sessions, the Galahs searched for food, scratched and raised their crests (羽冠) more — behaviors interpreted as signs of "positive excitement resulting from free flight." And in a test designed to measure optimism, the Galahs grew more hopeful of finding their favorite treat (a walnut) when they'd had several days of free flight and more pessimistic after several days of being grounded. Animal-cognition scientists used to be hesitant to judge whether animals have conscious experiences, but researchers have become increasingly open to accepting the idea. If birds are capable of conscious experience, Mendl says, "the findings would indeed suggest that the birds enjoyed flying." For Galahs, Massen says, flight appears to be a behavior they're naturally driven to perform. Massen sees his study as part of a broader shift in animal-welfare science away from only preventing suffering and toward designing environments that let animals express the natural behaviors that seem to make them feel good. 32. What did the Galahs do during the experiment? A. They flew mainly to look for seeds. B. They waited for a reward before flying. C. They rarely turned down the chance to fly. D. They only flew when the keepers gave them food. 33. What did the test in paragraph 5 show? A. The birds grew tired of flying after many sessions. B. The birds expected fewer treats after several flights. C. The birds lost interest in their walnut treats over time. D. Flying lifted their spirits while staying in lowered them. 34. What is the significance of the study according to Massen? A. It shows a return to studying animals in the wild. B. It shows a focus on preventing animals' suffering. C. It causes a debate over whether animals belong in cages. D. It signals a move toward letting animals behave naturally. 35. Which of the following is the best title? A. Why Do Birds Fly? B. What Do Birds Want? C. Do Birds Enjoy Flying? D. Do Birds Have Consciousness?

解方程：$\frac{x}{2} - 1 = \frac{x+2}{6} + 2$

如图所示，$\triangle ABC$ 的面积是36平方厘米，圆的直径$AC=6$厘米，$BD:DC=2:1$，求阴影部分的面积。

甲、乙两厂生产某一规格的上衣和长裤，甲厂每月用16天生产上衣，14天生产长裤，正好配成448套；乙厂每月用12天生产上衣，18天生产长裤，正好配成720套. 现在两厂合并，每月最多可生产多少套？

阅读下面短文，从短文后各题所给的 A、B、C、D 四个选项中选出可以填入空白处的最佳选项。 When in university, I joined a nonprofit organization and volunteered for a project designed for the needy in Romania. From special-needs adults to homeless children, volunteers seek to provide safe ＿＿＿＿ for them. Every day, ＿＿＿＿ by 15-20 kids, I helped in the kitchen, taught English, played soccer, and even assisted in painting on a big wall. I was ＿＿＿＿ about doing a bit of everything. When talking with them, I heard about their dreams and the ＿＿＿＿ they had overcome. Our conversations were mostly done using a translation app. I was amazed how the kids had fun in the ＿＿＿＿ things. I also really appreciated how technology wasn't ＿＿＿＿ their lives. They didn't have laptops and were only ＿＿＿＿ to use phones when necessary. So I had more face-to-face time with them and I ＿＿＿＿ all the genuine conversations we had. Daniel, one of the boys who impressed me a lot, told me with quiet ＿＿＿＿ that seeing what I did here ＿＿＿＿ him to become a volunteer teacher like me. His words, and ＿＿＿＿ ones from other kids, made me realize how these experiences ＿＿＿＿ their outlooks and future plans. Helping others should never be a one-and-done action. Before I left, I made a(n) ＿＿＿＿ to come back — one I meant to keep, not a(n) ＿＿＿＿ remark. The relationships run deep, built through shared meals, long conversations and playful afternoons; I feel it a responsibility to maintain them over time. Consequently, I plan to return to ＿＿＿＿ the relationships we created. 41. A. passage B. arrival C. shelter D. ground 42. A. surrounded B. guarded C. monitored D. supported 43. A. curious B. passionate C. annoyed D. cautious 44. A. obstacles B. differences C. prejudice D. anxiety 45. A. advanced B. simple C. traditional D. novel 46. A. speeding up B. taking over C. canceling out D. catering for 47. A. required B. persuaded C. forbidden D. allowed 48. A. treasured B. desired C. shared D. designed 49. A. relief B. guilt C. pride D. envy 50. A. reminded B. enabled C. permitted D. motivated 51. A. similar B. familiar C. relevant D. reasonable 52. A. reflected B. conquered C. shook D. transformed 53. A. arrangement B. promise C. choice D. appointment 54. A. casual B. serious C. sharp D. abstract 55. A. review B. reform C. renew D. reveal