学进去

已知函数，则下列结论正确的是（       ）

A．若，则在上递增

B．若为奇函数，则

C．若是的极值点，则

D．若和都是的零点，在上具有单调性，则的取值集合为

已知函数，为的反函数，若、的图像与直线交点的横坐标分别为，，则下列说法正确的为（       ）

A．	B．
C．	D．

已知双曲线的左，右焦点分别为，双曲线C的虚轴长为2，有一条渐近线方程为．如图，点A是双曲线C上位于第一象限内的点，过点A作直线l与双曲线的右支交于另外一点B，连接并延长交双曲线左支于点P，连接与，其中l垂直于的平分线m，垂足为D．

(1)求双曲线C的标准方程；
(2)求证：直线m与直线的斜率之积为定值；
(3)求的最小值．

已知函数.
(1)当时，求的最小值；
(2)①求证：有且仅有一个极值点；
②当时，设的极值点为，若.求证：

在中，，为内一点，，，则（       ）

A．

B．

C．

D．

阅读下面材料, 根据其内容和所给段落开头语续写两段, 使之构成一篇完整的短文。

It was a hot and dry summer. The beach near the city was crowded with a lot of people, from little kids to the aged, who planned to beat the heat in the water. They enjoyed themselves leisurely. Some were playing beach volleyball, some were making sand castles, and some were doing sunbathing.

Among them, there was a group of 10 boys aged between 12 to 15 years old trying to take an adventure. At first, they intended to hire a yacht (游艇), but due to the wind and the waves, the yacht rides were forbidden on that day. After a while, the boys decided to challenge themselves to race in the sea. They made a deal that the one who swam the fastest would win the race and deserve a huge treat from the group. Most of the boys agreed, except for a few. A boy in the group warmed them of the danger, as the waves weren’t constant. Some boys began to hesitate, but some didn’t listen to him and started their race.

Everything went so well. Suddenly, waves from the sea rose a lot and most of the boys in that young group struggled to reach the beach. However, three boys who considered themselves very brave, decided to ignore the waves and swim further out to sea for more excitement and fun.

Although many people on the beach shouted at them and asked them to swim back immediately, they continued to swim further from the beach. The wind became stronger；all of a sudden, one boy was washed away by a rising wave and the other two boys were so scared that they shouted for help and swam as fast as they could to the beach. However, no one on the beach risked his life to save the boy as the waves were so alarming；and the crowd were asked to move to a safe place.

注意: 1.续写的词数应为150左右；
2.请按如下格式在答题卡的相应位置作答。
Paragraph l: From the crowd on the beach, a young man stood out.
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Paragraph 2 : The man stood silently for a few seconds.
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How to Make Exercise a Habit

The new year is a time when it seems like everyone makes goals to work out and get fit. But by the third week of January, that all seems to go out the window. I’ve seen this happen almost every year: my workout classes are packed with fresh faces. 1． So I will share some tips on how to make exercise a habit, helping you stay healthier in the long run.

Focus on the routine and not the results

These days it feels like everyone is looking for a quick fix or fast results, particularly when it comes to health and fitness. 2． Focus on creating and enjoying the habit. Try scheduling your works alongside one of the other routines you already have in place.

3．

Everyone seems to want to set big goals of working out 4 times a week with 60-minute sessions. But realistically, if you’re not used to this, it will just be overwhelming and lead you to quit. Given this, doing workouts even as small as5-10 minutes is a good place to start.

Forget the “all or nothing” view

When it comes to exercise, the all or nothing approach does not serve you. Say you plan a workout for today, but say things get crazy at work and you miss your scheduled time. Well that doesn’t mean you’ve failed. 4． Even if you miss your workout, that doesn’t mean you’ve given up. Just remember your results are from your every effort, not matter how small.

Find joy in your workouts

5． Don’t let yourself be boxed into a certain type of workout just because it’s trendy or everyone is doing them. A workout that suits you will promote your drive and enjoyment.

A．Life happens sometimes.

B．Start with mini workouts

C．Build yourself workout time-zone

D．But in reality, it takes time for results to show.

E．Explore until you find a workout that feels like fun.

F．There is something magical that makes your plan work.

G．But after just a few weeks, they return to the regular number of people.

阅读下面材料，根据其内容和所给段落开头语续写两段，使之构成一篇完整的短文。

The day Dana and Jeff’s daughter Melody was born was nothing like they expected. The words the doctor said to them completely shook them, “Your daughter was born with a cleft lip (唇裂).” It was impossible for the couple to hide their sadness. They couldn’t believe it was true until they saw their daughter in person. Seeing her cleft made Dana and Jeff heartbroken more than anything. It broke their heart to imagine the kind of life Melody would lead in the future.

When the doctor told Dana and Jeff that their daughter’s condition was treatable with a cleft lip surgery (外科手术), the couple saw a ray of hope. Rather than feeling stressful like the first few days, they promised themselves they never wanted their daughter to suffer from that. They would support Melody as best they could.

Dana and Jeff were ready to do anything for Melody. After bringing Melody home, they immediately began looking for cleft surgery options. However, no matter where they turned, getting Melody the surgery she needed was expensive, and the various treatments and medications she needed in the following would also be much more costly than the young family could afford.

One day, however, things took a turn for the better. While browsing through a medical forum one evening, Jeff stumbled upon (意外发现) a post about a nonprofit organization that specialized in cleft lip surgeries for children. The organization, named Smileatfuture, is dedicated to providing free surgeries to families who could not afford the procedure. The couple had seen a lot of photos and read a lot of stories about children who had cleft surgeries sponsored by Smileatfuture, and the results were unbelievable. The idea that Melody could grow up with hardly a scar (伤疤) where her cleft was lit a fire under the couple. Without any hesitation, Dana and her husband reached out to Smileatfuture and handed in an application for medical aid.

注意：
1.续写词数应为150个左右；
2.请按如下格式在答题卡的相应位置作答。

Everything went more smoothly than Dana and Jeff had expected.

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The big day for Melody’s surgery finally came.

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阅读下面材料，根据其内容和所给段落开头语续写两段，使之构成一篇完整的短文。

It was a Saturday morning as I prepared to take my eight-year-old son, David, to the aquarium. His eyes were widened with excitement, and he chattered non-stop about the sea creatures we would see, the sharks, the dolphins... We boarded the bus, and after a few stops, we made ourselves comfortably seated. David gazed out the window, watching the world go by with wonder.

The bus continued its route, and with each stop, it became increasingly crowded. Passengers of varying ages and backgrounds filled the seats. David and I were engaged in a light-hearted conversation about marine life, our anticipation and joy building with each passing minute.

As we approached a mid-route bus stop, an elderly lady boarded, her movements labored and her legs visibly unsteady. The bus was full, and for a moment, there was an obvious hesitation among the passengers, each perhaps weighing the social morals against their own comfort. The elderly lady seized her walking aid, swaying slightly with each lurch of the vehicle.

Noticing the elderly lady’s struggle, David made a decision. Without a moment’s hesitation, he rose from his seat. His small hand gestured towards the elderly lady. “You can sit here, ma'am,” he said, his voice clear and sincere. The elderly lady’s face transformed with a mixture of surprise and gratitude. “Oh, thank you, boy,” she said, her voice filling up with emotion. David then took her hand gently, helping her navigate through the crowd to the seat he had left for her. With the help of David, the lady eased herself into the seat, her relief evident. I felt pride welling up within me as I watched what David had done. Looking at David, who was standing now, I saw not just the playful child he was known to be, but the empathetic and considerate young man he was growing into.

注意：
1.续写词数应为150个左右；
2.请按如下格式在答题卡的相应位置作答。

As the bus rolled on, it was filled with renewed warmth among the passengers.

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That evening, as we returned home, I couldn’t help but reflect on the true treasure of the day.

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Although Rio knew little about marketing, he succeeded ______ other more well-informed managers failed.

A．as

B．unless

C．what

D．where