高三第二次月考试题

湖南省长沙市第一中学2023-2024学年高三上学期第二次月考英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解“Unfortunately, 85 percent of what makes us attractive or less to mosquitoes(蚊子) is hardwired in our genetic circuit board,” says Winegard, author of The Mosquito: A Human History of Our Deadliest Predator. Still, there are ways to outsmart summer’s most annoying party crashers, especially if all you want is to enjoy an evening on your patio (露台).Know your blood typeOnly female mosquitoes feed on humans, and for good reason: The proteins in your blood help them grow and mature their eggs. “She’s just being a good mom,” Wineguard says. “People with blood type O are her top of choice. They get bitten twice as much as people with blood type A, with blood type B falling in between.”Stay cool“Mosquitoes hunt by both smell and sight,” Wineguard says. “They can smell the carbon dioxide and see the heat signature of their target.” Avoiding alcohol can keep your body temperature lower— making you harder to find — so consider choosing a cocktail instead.Wear light colorsAvoiding dark clothing can also keep you cooler, but that’s not the only reason it may offer relief. Mosquitoes, like many biting flies, are attracted to darker colors. The thinking behind this is that the animals they typically feed upon are larger, dark-bodied mammals(哺乳动物).Get rid of standing waterEven a glass of drinking water left on the deck can become a breeding ground for mosquito eggs — and mother mosquitoes lay about 100 eggs at a time. “They don’t need very much at all to breed. It can be a backyard toy , like a truck that has a bit of water in it, or a crushed pop can,” says Winegard. If you get rid of it, they’ll go somewhere else to lay their eggs.1．What’s the intention of this text?A．To introduce a new book.B．To offer professional tips.C．To analyze a study of insects.D．To suggest throwing a party.2．Why does a female mosquito feed on human blood?A．To hatch more eggs.B．To raise a large family.C．To identify blood types.D．To fully develop her body.3．What can we learn about mosquitoes according to Winegard?A．They can trace the smell of alcohol.B．They have energy-locating abilities.C．They feed off dark-bodied animals.D．They need abundant water to breed.The Malaysian actress, Michelle Yeoh, 60, shared some wisdom with the American Film Institute’s newest graduating class in a speech as she accepted an honorary doctorate of fine arts at the class of 2022 graduation ceremony.She recalled her early years in the industry. After an injury dashed her dreams of going into ballet, Yeoh bounced back at a gym where several stuntmen(特技替身演员)trained and ended up learning some tricks of the trade from them.“The first thing they taught me what to do was to tuck and roll, then how to fall on my side, and then how to fall on my back. And after a while, it dawned on me that they were teaching me how to fall,” she recalled. “And they said to me, ‘How are you going to go up if you don’t know how to come down?’” “That lesson sticks with me to this day. I had to learn how to fall. Well, you could say I learned it in my bones, literally,” Yeoh added.The actress mentioned jumping off a 20-foot highway overpass for one stunt, in which she over-rotated (旋转), causing her back to fold in half and a stunt went wrong. “I didn’t land properly, but I completed the scene,” she said.“These moments taught me perseverance, courage and humility,” she said. “They also taught me to hone my skills and eventually progress to the point where I was running on rooftops and jumping onto moving trains. I’m not asking you all to do that, okay? What I want to share with you today is that our slips and stumbles(绊跌)are the secrets to our flight. Trust me, that’s part of the deal. Success without failure is called luck. It cannot really be repeated or relied upon. It is from failure that we learn and grow,” Yeoh continued.The Crazy Rich Asians star concluded her speech: “Be courageous, take chances, break barriers, be proud of what makes you unique.” “And most importantly, don’t be afraid to fall, for you are learning to fly,” Yeoh said.4．What can we learn about Michelle Yeoh from the first two paragraphs?A．She was tricked by several stuntmen.B．She was passionate about working out in a gym.C．She won a doctor’s degree in fine arts despite her old age.D．She was terribly defeated by an injury and discouraged in her early years.5．What lesson did Michelle Yeoh learn from the stuntmen?A．God helps those who help themselves.B．Misfortune might be a blessing in disguise.C．Successful people are learning experiences with others.D．The greatest glory is not in never falling, but in rising every time we fall.6．What does the underlined word “hone”in paragraph 5 mean?A．Believe.B．Sharpen.C．Restore.D．Dominate. 7．What are the keys to our success according to the text?A．Mistakes and failure.B．Luck and humility.C．Courage and pride.D．Opportunities and skills.“It’s a natural question,”Dr. Holt-Lunstad said the “ideal”number of friends. “Just like we have guidelines and recommendations for the amount of sleep we get and how physically active we are, this is health relevant.” While she and other friendship researchers admit there aren’t many studies that have specifically tackled the question of how many friends people should aim for, those that have been done offer a range.Dr. Degges-white recently conducted a survey of 297 adults, which has not been published or subject to peer review but found that 55 percent of participants believed two to three close friends was ideal, while 31 percent thought four to six was was the goal. But friendship and intimacy are subjective, and there isn’t a widely used scale researchers share to define those concepts across studies. It’s also unclear how social media factors into all of this, as research suggests the size of a person’s online network may not have any meaningful impact on their perceived well-being.While friendship research offers some standards, it may be more useful for most of us to consider if you need more friends. Dr. Marisa Franco recommends starting with a fairly obvious but powerful question: Do I feel lonely? “Also, different people bring out different parts of us. So when you have a larger friend group, you’re able to experience this side of yourself that loves golf, and this side that loves cars,” she added. “If you feel like your identity has sort of shrunk, or you’re not feeling quite like yourself, that might indicate youneed different types of friends.”Of course, making friends in adulthood isn’t always easy. Research shows people struggle with it because they find it difficult to trust new people. For those reasons, it is often easier to start by reawakening old relationships. The amount of time you actually spend with your friends matters, too. Franco suggests that on average, very close friendships tend to take around 200 hours to develop. But spending time with friends you feel ambivalent (情绪复杂的) about — because they’re unreliable, critical, competitive or any of the many reasons people get under our skin — can be bad for your health.8．Which statement would Dr. Holt-Lunstad probably agree with?A．Healthy friendships contribute to quality sleep.B．There have been guidelines for making friends.C．Two to six close friends may be the most ideal.D．Friendships can be crucial factor in well-being.9．How was Dr. Degges-White’s survey?A．It summarized the statistics in previous studies.B．It set standards on the exact number of friends.C．It distinguished between friendship and intimacy.D．It dismissed the influences of social media factors.10．According to Franco, you have to make new friends if _________.A．your friend circle is large enough B．you have a wide range of hobbiesC．your personal identities are restricted D．you lead an unhappy adulthood life 11．What matters in maintaining close friendships according to Franco?A．Quantities of time.B．Meeting frequency.C．Your healthy moods.D．Personalities of friends.Many robots track objects by “sight” as they work with them, but optical (视觉的) sensors can’t take in an item’s entire shape when it’s in the dark or partially blocked from view. Now a new low-cost technique lets a robotic hand “feel” an unfamiliar object’s form — and skillfully handle it based on this information alone.Roboticist, Xiaolong Wang in University of California, San Diego and his team wanted to find out if complex coordination (协调) could be achieved in robotics using only simple touch data. The researcher attached 16 contact sensors, each costing about $12, to the palmand fingers of a four -fingered robot hand. These sensors simply indicate if an object is touching the hand or not. “While one sensor doesn’t catch much, a lot of them can help you capture different aspects of the object,” Wang says. In this case, the robot’s task was to rotate (旋转) items placed in its palm.The researchers first connected a large volume of touch data as a virtual robot hand practiced rotating objects, including ball. Using binary contact information (“touch” or “no touch”) from each sensor, the team built a computer model that determines an object’s position at every step of the handling process and moves the fingers to rotate it smoothly and stably.Next they transferred this capability to operate a real robot hand, which successfully manipulated (操纵) previously unencountered objects such as apples, tomatoes, soup cans and rubber ducks. Transferring the computer model to the real world was relatively easy because the binary sensor data were so simple; the model didn’t rely on accurate measurements.Digging into what the robot hand perceives, Wang and his colleagues found that it can re-create the entire object’s form from touch data, informing its actions. He and his team are set to present thier handiwork at an international conference called Robotics: Science and Systems.New York University’s Lerrel Pinto, who studies robots’ interactions with the real world, wonders whether the system would become less effective at more complicated tasks including opening a bottle cap. Wang’s group aims to tackle more complex movements in future work as well as to add sensors in places such as the sides of the fingers. The researchers will also try adding vision to improve touch data for handling complicated shapes.12．What may contribute to the ineffectiveness of the optical sensors?A．Poor visibility.B．Blocked roads.C．Complicated tasks.D．Inaccurate calculation.13．What do paragraphs 3-4 focus on?A．Stimulating the robot fingers to move the items steadily.B．Increasing the precision of touch of the robot hand.C．Comparing the computer world with the real circumstances.D．Testing if touch information can facilitate the formation of the object shape. 14．What is the attitude of Lerrel Pinto towards the system?A．Neutral.B．Suspicious.C．Favorable.D．Pessimistic.15．What is the best title for the text?A．Robotics: Science and SystemB．New Robot Rotates Items SkillfullyC．New Robot Hand Works by Feel, Not SightD．From the Computer Model to the Real Robot Hand二、七选五Which is more important for people, book learning or experience? Some have spent their lives studying and gradually acquiring valuable deep knowledge. They are afraid to start andthe book, make mistakes, and learn from this experience.The debate between book learning and experience has been going on for a long time. There is no clear “right answer” yet, but there is strong evidence that experience gives us important skills that can’t be learned in books.17 Of course, reading the best books on learning gives someone knowledge, but experience gives know-how. It comes from practicing again and again. Professionals can make themselves because they devote their work, practice, and time to obtaining this position instead of managing to read books only. This distinguishes them from all the others.Reading more books about something doesn’t lead to success. You can acquire a lot of knowledge by reading, but there are also ways to accumulate knowledge through experience. Knowledge is theoretical, but experience is distinguished by the fact that you can put into practice what you have learned in a book. 18Book learning to understand a concept is important. But if you can’t understand the application of the concept in real time, the concept is useless. Experience allows you to put the learned concepts into practice. 19 You can’t effectively learn important skills without applying these concepts to real life.Certainly, the experience can lead to failure. But you can also learn from that failure and lead to success. 20 Therefore, experience is your greatest ally(盟友) in professional development if you want to understand the theory behind the concept, become an expert inthis field, keep the technique in mind, and gain valuable insights through failure.A．In contrast, others don’t worry about anything.B．You can learn a lot from books on self-learning.C．Of course, with these concepts, experience is acquired.D．This is valuable knowledge that is not found in any book.E．It is also an opportunity to test and challenge your knowledge.F．Through experience, you can also learn how to interact with people.G．Neither scientists nor doctors have read books only and become experts.三、完形填空Growing up in New Delhi, I saw Barbie as more than just a doll. She was the centralbedroom floor.As much as I loved Barbie, our time together could only last so long. Eventually, I grew 23 that I still played with my Barbie dolls while my middle-school friends had all moved onto more “mature” 24 . Barbie became similar with being a fake, “plastic” girl, whose bright pink clothing 25 my friends and me.By the tender age of 12, my friends and I had become 26 all girlish things, and Barbie topped our list of items to grow out of. Every 27 we took up instead seemed either gender-neutral or traditionally masculine (男子气概). For a 28 period I took up watching football to look cool (say exactly a month).Looking back, I feel like we were missing the point: Barbie was simply a blank canvas upon which to draw our ideas. It was our own 29 that we had come to abuse her for wearing pink clothes and having blond hair. That is why I appreciate the way the Barbie movie is being 30 . The movie 31 and Barbie’s bright pink colors are everywhere — there are 100 or more co-brand products, and you can get everything Barbie-pink from sports facilities to make-up and shoes. In Malibu, there is a pink hotel 32 after Barbie’s pink Dream House.In an interview, the director Gerwig said the team had many meetings just to settle on the correct 33 of pink for the movie — one that was beautiful but “not too fashionable”, she said, “because when I was a little girl, I loved the pinkest, brightest things”,without a hint of the 34 that I and my peers had of Barbie all those years ago, which would have been really important to me as an adolescent girl who often felt 35 in her femininity (女子气质).21．A．theme B．character C．argument D．conflict 22．A．assigned B．gathered C．created D．staged 23．A．embarrassed B．satisfied C．curious D．aware 24．A．peers B．hobbies C．ladies D．companies 25．A．involved B．caught C．offended D．connected 26．A．worried about B．passionate for C．content with D．dismissive of 27．A．appointment B．journey C．recreation D．challenge 28．A．difficult B．contemporary C．brief D．spare 29．A．fault B．memory C．experience D．selection 30．A．marketed B．captured C．illustrated D．filmed 31．A．settings B．promotions C．results D．witnesses 32．A．operated B．managed C．organized D．modeled 33．A．symbol B．design C．image D．shade 34．A．imagination B．judgment C．ignorance D．appreciation 35．A．interrupted B．sympathetic C．unsettled D．familiar四、用单词的适当形式完成短文阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

天津市耀华中学2025届高三语文上学期其次次月考试题本试卷考试时间150分钟，总分150分。

第Ⅰ卷一、(12分)阅读下面一段文字，完成下面1~2题。

那位看管敦煌莫高富的道士总是惊惶．担心，认为自己做了错事。

那些洋人一次一次地来，说着不着．边际的大话，在拱手作．揖间，用看似正值的理由把经卷运走了，__________，确定会露．马脚，出大乱子。

他把祖宗的家产给卖了，觉得自己是________子孙，壁画上那些普度众生的菩萨也在始终盯着他。

他确定报官，就算被朝廷抓了去，也认罪________，哪怕是杀头的罪名。

他不想接着被这些物件拖累．了，要尽．早上报，于是给当地官府呈上了拜帖．，上报了实情。

他庆幸自己的隐私尚未走漏．，可以全身而退。

经过很多的繁文缛．节，朝廷用两个月的工．夫将这些经卷运走了。

以后的日子，他时常量上土山眺望．．，沙漠始终到遥远的天涯，仿佛有两条深深地车辙。

1．文中加点字的字音和字形，全都正确的一组是A．惊惶( huáng)担心不着(zháo)边际作(zuò)揖B．正值(dāng) 露(lòu)马脚拖累(lěi)C．尽(jǐn)早拜帖(tiě) 走漏(lòu)D．繁文缛(rù)节工(gōng)夫瞭(liáo)望2．依次填入文中横线处的词语，最恰当的一项是A．长此以往不肖服法漫延B．久而久之不肖伏法扩散C．长此以往不孝伏法漫延D．久而久之不孝服法扩散3．下列各句中没有语病的一句是A．通过仪器来视察世界开阔了人们的视野，由此也变更了我们对物质世界的相识。

B．他们一向致力于救助校内留守儿童的工作取得了重大进展，得到了社会的普遍欢迎。

C．白鳍豚与拉河豚，恒河豚是当今世界上仅存的淡水豚类，又是数量最少的一种，我们确定要对白鳍豚加以爱护。

D．抱着成为优秀舞蹈演员的想法，我们的歌舞剧也成型了，所以，在青春时期，我们至少要有一两个幻想。

2024南开中学高三数学第二次月考一．选择题：在每小题给出的四个选项中，只有一项是符合题目要求的．1. 设集合{}ln A x y x ==，{}21B y y x ==+，则()R A B ⋂=ð（ ）A. ()0,1 B. (]0,1 C. [)0,1 D. []0,12. 设数列{}n a 的公比为q ，则“10a >且01q <<”是“{}n a 是递减数列”的（ ）A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件3. 函数()2cos e ex x x x f x -+=-的大致图像为（ ）A. B.C. D.4. 设5log 2a =，ln 2b =，0.20.5c -=，则a ，b ，c 的大小关系为（ ）A. a c b <<B. a b c <<C. b<c<aD. c a b <<5. 设n S 为正项等比数列{}n a 的前n 项和，5a ，33a ，4a 成等差数列，则84S S 的值为（ ）A. 116 B. 117 C. 16D. 176. 已知35a b =且211a b +=，则a 的值为（ ）A. 3log 15 B. 5log 15 C. 3log 45 D. 5log 457. 我国古代数学名著《九章算术》中记载“今有羡除，下广六尺，上广一丈，深三尺，末广八尺，无深，袤七尺．问积几何?”这里的“羡除”，是指由三个等腰梯形和两个全等的三角形围成的五面体．在图1所示羡除中，////AB CD EF ，10AB =，8CD =，6EF =，等腰梯形ABCD 和等腰梯形ABFE 的高分别为7和3，且这两个等腰梯形所在的平面互相垂直．按如图2的分割方式进行体积计算，得该“羡除”的体积为（ ）A. 84B. 66C. 126D. 1058. 记()n a τ表示区间[],n n a 上的偶数的个数．在等比数列{}n a n -中，14a =，211a =，则()4a τ=（ ）A. 39B. 40C. 41D. 429. 将函数πsin 24y x ⎛⎫=+ ⎪⎝⎭图象上所有点向右平移π4个单位长度，得到函数()y g x =的图象，则（ ）A. ()g x 为奇函数 B. ()3πcos 24g x x ⎛⎫=- ⎪⎝⎭C. ()g x 最小正周期为2πD. ()g x 的单调递增区间为5πππ,π88k k ⎡⎤-+-+⎢⎥⎣⎦，Zk ∈二．填空题：本大题共6小题，每小题5分，共30分．试题中包含两个空的，答对1个的给3分，全部答对的给5分．10. 设i 是虚数单位，()12a i i bi +=+（,a b ∈R ），则b a -=_____．11. 在5223x x ⎛⎫- ⎪⎝⎭的展开式中，x 的系数是______．12. 已知直线():20l y kx k =->与圆221x y +=相切，且被圆()()2240x y a a ++=>截得的弦长为k =______；=a ______．13. 锐角α，β满足2π23αβ+=，tan tan 22αβ=-α和β中的较小角等于______．14. D 为ABC 的边AB 一点，满足2AD DB = ．记CA a = ，CB b = ，用a ，b 表示CD = ______；若的的1CD = ，且ABC 的面积为98，则ACB ∠的最小值为______．15. 若二次函数()()2121f x ax b x a =+---在区间[]2,3上存在零点，则22a b +的最小值为______．三．解答题：本大题共5小题，共60分．解答应写出文字说明，证明过程或演算步骤．16. 在ABC 中，,,A B C 对应的边为,,a b c .已知1cos 2a C cb +=.（Ⅰ）求A ；（Ⅱ）若4,6b c ==，求cos B 和()cos 2A B +的值.17. 如图，在直三棱柱111ABC A B C -中，AB BC ⊥，12AB BC BB ===，D 为棱AB 中点．M 为线段1BC 的中点．（1）求证：1//BC 平面1ACD ；（2）求平面1ACD 与平面1C DC 的夹角的余弦值；（3）求点M 到平面1ACD 的距离．18. 椭圆22221x y a b+=的左、右顶点分别为A ，B ，上顶点为()0,2C ，左、右焦点分别为1F ，2F ，且1AF ，12F F ，1F B 成等比数列．（1）求椭圆的方程；（2）过1F 的直线l 与椭圆交于M ，N 两点，直线CM ，CN 分别与x 轴交于P ，Q 两点．若CMN CPQ S S =△△，求直线l 的斜率．19. 已知数列{}n a 是首项为1的等差数列，数列{}n b 是公比不为1的等比数列，满足122a a b +=，233a a b +=，454a a b +=．（1）求{}n a 和{}n b 的通项公式；的（2）求数列{}n n a b 的前n 项和n S ；（3）若数列{}n d 满足11d =，1n n n d d b ++=，记12nk n i k d T b ==∑．是否存在整数m ，使得对任意*n ∈N 都有212n n nd mT b ≤-<成立？若存在，求出m 的值；若不存在，说明理由．20. 已知函数()2e xf x a x =-，0a >且1a ≠．（1）当e a =时，求曲线()y f x =在1x =处的切线方程；（2）若1a >，且()f x 存在三个零点1x ，2x ，3x ．（i ）求实数a 的取值范围；（ii ）设123x x x <<，求证：1233x x x ++>．的2024南开中学高三数学第二次月考一．选择题：在每小题给出的四个选项中，只有一项是符合题目要求的．【1题答案】【答案】A【2题答案】【答案】A【3题答案】【答案】A【4题答案】【答案】B【5题答案】【答案】D【6题答案】【答案】C【7题答案】【答案】A【8题答案】【答案】C【9题答案】【答案】B二．填空题：本大题共6小题，每小题5分，共30分．试题中包含两个空的，答对1个的给3分，全部答对的给5分．【10题答案】【答案】3．【11题答案】【答案】720【12题答案】【答案】①. ②. 4【13题答案】【答案】π6##30︒【14题答案】【答案】 ① 1233a b + ②. π2【15题答案】【答案】125三．解答题：本大题共5小题，共60分．解答应写出文字说明，证明过程或演算步骤．【16题答案】【答案】（Ⅰ）π3A =（Ⅱ）1114-【17题答案】【答案】（1）证明见解析；（2； （3.【18题答案】【答案】（1）22154x y += （2）12-或0【19题答案】【答案】（1）21n a n =-，2n n b =（2）()12326n n S n +=-⋅+（3）存在5m =，理由见解析【20题答案】【答案】（1）e e 0x y -+=（2）（i）1a <<，（ii ）证明见解析.。

长郡中学2025届高三月考试卷（二）物理本试题卷分选择题和非选择题两部分，共8页。

时量75分钟。

满分100分。

第I卷选择题（共44分）一、选择题（本题共6小题，每小题4分，共24分。

每小题只有一项符合题目要求）1. 2024年8月郑钦文斩获巴黎奥运会网球女单冠军。

关于网球运动中蕴含的力学知识，若忽略空气阻力，以下说法正确的是（ ）A. 球在空中飞行时，受重力和推力的作用B. 球撞击球拍时，球拍对球的力大于球对球拍的力C. 球的速度越大，惯性越大D. 球在空中飞行时，处于失重状态【答案】D【解析】【详解】A．球在空中飞行时，只受重力作用，不受推力，故A错误；B．球撞击球拍时，由牛顿第三定律可知球拍对球的力等于球对球拍的力，故B错误；C．球的惯性由质量决定，与速度无关，故C错误；D．球在空中飞行时，只受重力，则处于完全失重状态，故D正确。

故选D。

2. 探月工程中，“嫦娥三号”探测器的发射过程可以简化如下：卫星由地面发射后，进入地月转移轨道，经过P点时变轨进入距离月球表面100公里的圆形轨道1，在轨道1上经过Q点时变轨进入椭圆轨道2，轨道2与月球表面相切于M点，月球车将在M点着陆月球。

下列说法正确的是（）A. “嫦娥三号”在轨道1上的速度比月球的第一宇宙速度大B. “嫦娥三号”在地月转移轨道上经过P 点的速度比在轨道1上经过P 点时大C. “嫦娥三号”在轨道1上的运动周期比在轨道2上的小D. “嫦娥三号”在轨道1上经过Q 点时的加速度小于在轨道2上经过Q 点时的加速度【答案】B 【解析】【详解】A ．月球的第一宇宙速度等于近月轨道的环绕速度，根据解得由于轨道1的半径大于近月卫星的半径，则“嫦娥三号”在轨道1上的速度比月球的第一宇宙速度小，故A 错误；B ．地月转移轨道变轨到轨道1是由高轨道变轨到低轨道，需要在两轨道切点P 位置减速，即“嫦娥三号”在地月转移轨道上经过P 点的速度比在轨道1上经过P 点时大，故B 正确；C ．根据开普勒定律可知由于轨道1的半径大于轨道2的半长轴，则“嫦娥三号”在轨道1上的运动周期比在轨道2上的大，故C 错误；D ．根据解得22Mm v G m r r=v =33122212r a T T =2MmGma r =卫星与月心间距相等，加速度大小相等，即“嫦娥三号”在轨道1上经过Q 点时的加速度等于在轨道2上经过Q 点时的加速度，故D 错误。

河北省石家庄市第一中学2025届高三下学期第二次月考-数学试题试卷请考生注意：1．请用2B 铅笔将选择题答案涂填在答题纸相应位置上，请用0．5毫米及以上黑色字迹的钢笔或签字笔将主观题的答案写在答题纸相应的答题区内。

写在试题卷、草稿纸上均无效。

2．答题前，认真阅读答题纸上的《注意事项》，按规定答题。

一、选择题：本题共12小题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1．已知我市某居民小区户主人数和户主对户型结构的满意率分别如图和如图所示，为了解该小区户主对户型结构的满意程度，用分层抽样的方法抽取30%的户主进行调查，则样本容量和抽取的户主对四居室满意的人数分别为A ．240，18B ．200，20C ．240，20D ．200，182．阿基米德（公元前287年—公元前212年），伟大的古希腊哲学家、数学家和物理学家，他死后的墓碑上刻着一个“圆柱容球”的立体几何图形，为纪念他发现“圆柱内切球的体积是圆柱体积的23，且球的表面积也是圆柱表面积的23”这一完美的结论.已知某圆柱的轴截面为正方形，其表面积为24π，则该圆柱的内切球体积为( ) A ．43π B ．16πC ．163π D ．323π 3．定义在R 上函数()f x 满足()()f x f x -=，且对任意的不相等的实数[)12,0,x x ∈+∞有()()12120f x f x x x -<-成立，若关于x 的不等式()()()2ln 3232ln 3f mx x f f mx x --≥--++在[]1,3x ∈上恒成立，则实数m 的取值范围是（ ） A ．1ln6,126e ⎡⎤+⎢⎥⎣⎦B ．1ln3,126e ⎡⎤+⎢⎥⎣⎦C ．1ln3,23e ⎡⎤+⎢⎥⎣⎦D ．1ln6,23e ⎡⎤+⎢⎥⎣⎦4．已知A 类产品共两件12,A A ，B 类产品共三件123,,B B B ，混放在一起，现需要通过检测将其区分开来，每次随机检测一件产品，检测后不放回，直到检测出2件A 类产品或者检测出3件B 类产品时，检测结束，则第一次检测出B 类产品，第二次检测出A 类产品的概率为（ ） A ．12B ．35C ．25D ．3105．函数()y f x =()x R ∈在(]1∞-，上单调递减，且(1)f x +是偶函数，若(22)(2)f x f -> ，则x 的取值范围是（ ） A ．（2，+∞） B ．（﹣∞，1）∪（2，+∞） C ．（1，2） D ．（﹣∞，1）6．已知复数，则的共轭复数在复平面对应的点位于（ ）A ．第一象限B ．第二象限C ．第三象限D ．第四象限7．以下四个命题：①两个随机变量的线性相关性越强，相关系数的绝对值越接近1；②在回归分析中，可用相关指数2R 的值判断拟合效果，2R 越小，模型的拟合效果越好； ③若数据123,,,,n x x x x 的方差为1，则1232+1,2+1,2+1,,2+1n x x x x 的方差为4；④已知一组具有线性相关关系的数据()()()11221010,,,,,,x y x y x y ，其线性回归方程ˆˆˆy bx a =+，则“()00,x y 满足线性回归方程ˆˆˆybx a =+”是“1210010x x x x +++= ，1210010y y y y ++=”的充要条件；其中真命题的个数为( ) A ．4B ．3C ．2D ．18．函数f x x 2()cos(2)3π=+的对称轴不可能为（ ） A ．65x π=-B ．3x π=-C ．6x π=D ．3x π=9．已知集合{}10,1,0,12x A xB x -⎧⎫=<=-⎨⎬+⎩⎭，则A B 等于（ ） A ．{}11x x -<<B ．{}1,0,1-C ．{}1,0-D ．{}0,110．已知数列{}n a 中，121,2a a ==，且当n 为奇数时，22n n a a +-=；当n 为偶数时，()2131n n a a ++=+．则此数列的前20项的和为（ ）A ．1133902-+B ．11331002-+C ．1233902-+D ．12331002-+11．已知直三棱柱中111ABC A B C -，120ABC ∠=︒，2AB =，11BC CC ==，则异面直线1AB 与1BC 所成的角的正弦值为（ ）． A ．32B ．105 C ．155D ．6312．若函数()222y sin x ϕϕπ⎛⎫< ⎪⎝+⎭=的图象经过点012π⎛⎫⎪⎝⎭，，则函数()()()22f x sin x cos x ϕϕ=-+-图象的一条对称轴的方程可以为( )A ．24x π=-B ．3724x π=C ．1724x π=D ．1324x π=-二、填空题：本题共4小题，每小题5分，共20分。

黑龙江省实验中学2024-2025学年高三学年上学期第二次月考数学试题考试时间：120分钟 总分：150分 命题人：高三数学备课组一､单项选择题（共8小题，每小题5分，共40分，在每小题给出的四个选项中，只有一项符合要求）1.若集合，其中且，则实数的取值范围是（ ）A. B. C. D.2.“”是“”的（ ）A.充要条件 B.既不充分又不必要条件C.必要不充分条件 D.充分不必要条件3.已知复数满足，则复数的共轭复数在复平面内对应的点位于（）A.第一象限B.第二象限C.第三象限D.第四象限4.若正数满足，则的最小值为（ ）A.3 B.6 C.9 D.125.已知函数的定义域为，且，若函数的图象与函数的图象有交点，且交点个数为奇数，则（ ）A. B.0 C.1 D.26.在中，，设点为的中点，在上，且，则（ ）A.16B.12C.8D.7.已知函数在上有且仅有两个零点，则正数的取值范围是（ ）A. B. C. D.{}230,A xmx m =->∈R ∣2A ∈1A ∉m 33,42⎛⎤ ⎥⎝⎦33,42⎡⎫⎪⎢⎣⎭33,42⎛⎫ ⎪⎝⎭33,42⎡⎤⎢⎥⎣⎦5π12α=22cos sin αα-=z ()22i (1i)z -=+z z ,a b 1232ab a b =++ab ()y f x =R ()()f x f x -=()y f x =()2log 22x x y -=+()0f =1-ABC V π6,4,2BC AB CBA ∠===D AC E BC 0AE BD ⋅= BC AE ⋅= 4-()445sin cos 8f x x x ωω=+-π0,4⎛⎤⎥⎝⎦ω48,33⎛⎤ ⎥⎝⎦48,33⎡⎫⎪⎢⎣⎭816,33⎛⎤ ⎥⎝⎦816,33⎡⎫⎪⎢⎣⎭8.在中，内角所对的边分别为.已知的外接圆半径是边的中点，则长为（ ）B.C.二､多项选择题（共3小题，每小题6分，共18分，在每小题给出的四个选项中，有多项符合题目要求，全部选对的得6分，部分选对得部分分，有错选得0分）9.函数的部分图象如图所示，则（）A.该图像向右平移个单位长度可得的图象B.函数的图像关于点对称C.函数的图像关于直线对称D.函数在上单调递减10.已知是平面上的三个非零向量，那么（ ）A.若，则B.若，则C.若，则与的夹角为D.若，则在方向上的投影向量相同ABC V ,,A B C ,,a b c 222π,24,3A b c ABC =+=V R D =AC BD 1+()()πsin 0,0,2f x A x A ωϕωϕ⎛⎫=+>>< ⎪⎝⎭π63sin2y x =()y f x =π,06⎛⎫- ⎪⎝⎭()y f x =5π12x =-()y f x =2ππ,36⎡⎤--⎢⎥⎣⎦,,a b c ()()a b c b c a ⋅=⋅ a ∥ca b a b +=- 0a b ⋅= a b a b ==+ a a b - π3a b a c ⋅=⋅ ,b c a11.定义在上的函数满足，则（ ）A.是周期函数B.C.的图象关于直线对称D.三､填空题（共3小题，每小题5分，共15分）12.已知，则__________.13.若数列满足，则__________.14.已知函数及其导函数的定义域均为，且为偶函数，若时，，且，则不等式的解集为__________.四､解答题（本大题共5个小题，共77分，解答应写出文字说明，证明过程或演算步骤）15.（本题满分13分）在中，内角，C 所对的边分别为.已知.（1）求角的大小；（2）若且，求的外接圆半径.16.（本题满分15分）在中，角所对的边分别为，设向量.（1）求函数的最小值；（2）若，求的面积.17.（本题满分15分）R ()f x ()()()()()322,6,12f x f x f f x f x f ⎛⎫++=+=-=⎪⎝⎭()f x ()20240f =()f x ()21x k k =-∈Z 20241120242k k f k=⎛⎫-= ⎪⎝⎭∑πsin 6x ⎛⎫+= ⎪⎝⎭ππcos 2cos 233πcos 2sin cos 3x x x x x ⎛⎫⎛⎫+-- ⎪ ⎪⎝⎭⎝⎭=⎛⎫+ ⎪⎝⎭{}n a 21111,1n na a a +==-985a =()f x ()f x 'ππ,22⎛⎫-⎪⎝⎭()f x 0x ≥()()tan f x f x x ≥'π23f ⎛⎫= ⎪⎝⎭()1cos f x x <ABC V ,A B ,,a b c 12cos sin 2sin sin B C A B =+C 32a b c +=3a =ABC V ABC V ,,A B C ,,a b c ()()()π2π2sin ,cos ,cos sin ,,,63m A A A n A A A f A m n A ⎡⎤=+=-=⋅∈⎢⎥⎣⎦ ()f A ()0,sin f A a B C ==+=ABC V已知锐角的三个内角，C 所对的边为.（1）求角的大小；（2）求的取值范围.18.（本题满分17分）已知函数.（1）当时，求的极值；（2）若，当时，恒成立，求的取值范围.19.（本题满分17分）已知函数.（1）当时，设，求在处的切线方程；（2）当时，求的单调区间；（3）证明：若曲线与直线有且仅有两个交点，求的取值范围.ABC ,A B ()()(),,,cos cos cos cos sin sin a b c A B A B C C A +-=B 222a c b+()()()22ln 1f x ax a x x a =-+++∈R 1a =()f x ()12,0,x x ∞∀∈+12x x ≠()()12122f x f x x x ->--a ()log a a x f x x =e a =()()e 1F x xf x -=()F x 1x =2a =()f x ()y f x =21y a =a。

海南省文昌中学2024-2025学年高三上学期第二次月考数学试题一、单选题1．已知集合{23}M xx =-<<∣，{}2540N x x x =-+>∣，则M N ⋃=（ ） A ．(2,1)-- B ．(2,4)-C ．(,1)(4,)-∞+∞UD ．(,3)(4,)-∞⋃+∞2．若复数z 满足(13i)3i z -=-（i 为虚数单位），则z 的模z =（ ）A ．35B ．1CD ．53．“2π3α=”是“1cos 2α=-”的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件D ．既不充分也不必要条件4．已知函数()()()1,0ln e 2,0f x x f x x x ⎧->⎪=⎨-++≤⎪⎩，则()2024f 的值为（ ）A ．1-B ．0C ．1D ．25．已知0.43a =，0.5log 4b =，πcos 18c ⎛⎫=- ⎪⎝⎭，则（ ）A ．c b a >>B ．b a c >>C ．c a b >>D ．a c b >>6．已知函数()()21,0lg ,0x x f x x x ⎧+≤⎪=⎨>⎪⎩，若函数()()g x f x b =-有三个不同的零点，则实数b 的取值范围为（ ） A ．(0,1]B ． 0,1C ．(0,)+∞D ．(1,)+∞7．若cos 0,,tan 222sin παααα⎛⎫∈= ⎪-⎝⎭，则tan α=（ ）A B C D 8．挂钟的时针和分针从凌晨0时起到下午14点所在的14小时内，分针与时针会重合（ ）次（注意：0时开始的那次重合不计算在内）A ．11B ．12C ．13D ．14二、多选题9．已知正数x ，y 满足2x y +=，则下列选项正确的是（ ） A ．11x y+的最小值是4B ．xy 的最大值是1C ．22x y +的最小值是1D ．(1)x y +的最大值是9410．已知函数()sin()f x A x ωϕ=+（0A >，0ω>，π||2ϕ<）的部分图象如图所示，则下列说法正确的是（ ）A ．1ω=B ．函数()f x 的图象关于直线5π12x =-对称 C ．函数()f x 图象向右平移π3个单位后得到函数5π()2cos 26g x x ⎛⎫=- ⎪⎝⎭的图像D ．函数()f x 在区间115π,π1212⎛⎫-- ⎪⎝⎭上是减函数11．对于已知函数32()3f x x x ax b =-++，下列论述正确的有（ ）A ．若9a =-，则函数()y f x =的单调递减区间为(1,3)-B ．若函数()y f x =在区间(0,)+∞上是增函数，则4a ≥C ．当3a =，0b =时，函数()f x 图像的对称轴为2x =D ．当0a =，2b =时，函数()f x 图像的对称中心为(1,0)三、填空题12．函数()f x 是定义在R 上的奇函数，当0x >时，2()log f x x =，则(4)f -=．13．如图是某个函数()y f x =的图象在[0,2]x ∈的一段图像．写出函数()y f x =在[0,2]x ∈时满足图象的一个解析式()f x =（写出一个即可）．14．设()cos sin x x f ααα=-（其中N x +∈，α为任意角），则求下列： （1）当4x =时，且π0,3α⎡⎤∈⎢⎥⎣⎦时，()f α的取值范围为；（2）当8x =时，且π0,3α⎡⎤∈⎢⎥⎣⎦时，()f α的取值范围为．四、解答题15．某公园为了提升公园形象，提高游客旅游的体验感，他们更新了部分设施，调整了部分旅游线路.为了解游客对新措施是否满意，随机抽取了100名游客进行调查，男游客与女游客的人数之比为2:3，其中男游客有35名满意，女游客有15名不满意.(1)完成22⨯列联表，依据表中数据，以及小概率值0.05α=的独立性检验，能否认为游客对公园新措施满意与否与性别有关?(2)从被调查的游客中按男、女分层抽样抽取5名游客.再随机从这5名游客中抽取3名游客征求他们对公园进一步提高服务质量的建议，其中抽取男游客的人数为X .求出X 的分布列及数学期望.参考公式：22()()()()()n ad bc a b c d a c b d χ-=++++，其中n a b c d =+++.参考数据：16．已知函数()2()cos cos sin f x x x x x =+-．(1)求函数()f x 的最小正周期和单调递增区间； (2)若把()y f x =的图像先向右平移π6个单位，再向上平移1个单位，得到()y g x =的图像，则当[0,2π]x ∈时，求使得()2gx =时所有x 的取值．17．在锐角ABC V 中，内角A ，B ，C 的对边分别为a ，b ，c ，已知2(cos cos)cos ca Bb A C+=． (1)求角C ；(2)若c =ABABC V 的面积S ．18．已知双曲线222:1(0)x C y a a-=>的焦距为1A ，2A ，过点(4,0)T 的直线l 与双曲线C 的右支交于M ，N 两点．(1)求双曲线的方程； (2)若直线MN MN ； (3)记直线1A M ，2A N 的斜率分别为1k ，2k ，证明：12k k 是定值． 19．已知函数()ln (2)f x x mx b b =+->， (1)若1m =-，3b =时，求()f x 的极值； (2)若2m =时，①证明：()f x 有唯一零点a ，且(1,)a b ∈；②若我们任取1(1,)x a ∈开始，实施如下步骤：在()()11,x f x 处作曲线()f x 的切线，交x 轴于点()2,0x ；在()()22,x f x 处作曲线()f x 的切线，交x 轴于点()3,0x ；……．在()(),n n x f x 处作曲线()f x 的切线，交x 轴于点()1,0n x +；可以得到一个数列{}n x ，它的各项都是()f x 不同程度的零点近似值．设()1n n x g x +=，求()n g x 的解析式（用n x 表示1n x +）；并证明：当1(1,)x a ∈，总有1n n x x a +<<．。

深圳外国语学校2024-2025学年度高三第一学期第二次月考数学试题试卷共4页，卷面满分150分，考试用时120分钟.注意事项：1.答卷前，考生务必将自己的姓名､准考证号码填写在答题卡上.2.作答时，务必将答案写在答题卡上.写在本试卷及草稿纸上无效.3.考试结束后，将答题卡交回.一､选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中，只有一个选项是正确的.请把正确的选项填涂在答题卡相应的位置上.1.已知集合，则（ ）A.B.C.D.2.已知命题，则命题的否定为（ ）A. B.C. D.3.设函数在区间上单调递减，则实数的取值范围是（ ）A. B. C.D.4.函数的图象大致为（）A. B.C. D.5.设正实数满足，则当取得最小值时，的最大值为（ ）A.1B.2C.3D.46.已知函数的定义域为是偶函数，是奇函数，则的值为{{},21x A xy B y y ====+∣∣A B ⋂=(]1,2(]0,1[]1,2[]0,2:1,1p x x ∀>>p 1,1x x ∀><1,1x x ∀≤>1,1x x ∃>≤1,1x x ∃≤≤()()3x x a f x -=30,2⎛⎫⎪⎝⎭a (),1∞--[)3,0-(]0,1[)3,∞+()1cos ex x xf x -=a b c ､､2240a ab b c -+-=c ab 236a b c+-()f x (),e xy f x =+R ()3e xy f x =-()ln3f（ ）A.B.3C.D.7.已知三倍角公式，则的值所在的区间是（ ）A. B. C. D.8.已知函数，若对于任意的实数与至少有一个为正数，则实数的取值范围是（ ）A.B.C. D.二､多选题：本题共3小题，每小题6分，共18分.在每小题给出的选项中，有多项符合题目要求.全部选对得6分，部分选对的得部分分，选对但不全的得部分分，有选错的得0分.9.下列说法正确的是（）A.若函数定义域为，则函数的定义域为B.若定义域为的函数值域为，则函数的值域为C.函数与的图象关于直线对称D.成立的一个必要条件是10.若，则下列不等式一定成立的是（ ）A. B.C. D.11.已知定义在上的偶函数和奇函数满足，则（ ）A.的图象关于点对称B.是以8为周期的周期函数C.D.三､填空题：本题共3小题，每小题5分，共15分.731031133sin33sin 4sin ααα=-sin10 11,43⎛⎫⎪⎝⎭11,54⎛⎫ ⎪⎝⎭11,65⎛⎫ ⎪⎝⎭11,76⎛⎫ ⎪⎝⎭()()()22241,f x mx m x g x mx =--+=(),x f x ()g x m ()0,2()0,8[)2,8(),0∞-()f x []1,3()21f x +[]0,1R ()f x []1,5()21f x +[]0,215xy ⎛⎫= ⎪⎝⎭5log y x =-y x =a b >1a b ->log 1a b >a b <1ab a b+>+11a b a b ->-11a b a b+<+R ()f x ()g x ()()21f x g x ++-=()f x ()2,1()f x ()()8g x g x +=20241(42)2025k f k =-=∑12.已知函数，则__________.13.已知函数且，若函数的值域是，则实数的取值范围是__________.14.若，则的最大值为__________.四､解答题：本题共5小题，共77分.解答应写出文字说明､证明过程或演算步骤.15.（本小题满分13分）设函数（1）求曲线在点处的切线方程；（2）设，若函数有三个不同零点，求c 的取值范围.16.（本小题满分15分）记的角的对边分别为，已知.（1）求；（2）若点是边上一点，且，求的值.17.（本小题满分15分）如图，四棱锥中，底面是边长为2的菱形，，已知为棱的中点，在底面的投影为线段的中点，是棱上一点.（1）若，求证：平面；（2）若，确定点的位置，并求二面角的余弦值.18.（本小题满分17分）已知函数.（1）函数与的图像关于对称，求的解析式；()cos2f x x =066lim x f x f xππ∆→⎛⎫⎛⎫+∆-⎪ ⎪⎝⎭⎝⎭=∆()223,2(06log ,2a x x x f x a x x ⎧-++≤=>⎨+>⎩1)a ≠()f x (],4∞-a ()e 1xa xb ≥++()1a b +()32.f x x ax bx c =+++().y f x =()()0,0f 4a b ==()f x ABC V ,,A B C ,,a b c sin sin sin A B Cb c a b-=++A D BC ,2AB AD CD BD ⊥=sin ADB ∠P ABCD -ABCD π3ABC ∠=E AD P H EC M PC 2CM MP =PE ∥MBD ,PB EM PC EC ⊥=M B EM C --()()()2ln 1cos 2g x x x =--+--()f x ()g x 1x =-()f x（2）在定义域内恒成立，求a 的值；（3）求证：，.19.（本小题满分17分）设集合，其中.若集合的任意两个不同的非空子集，都满足集合的所有元素之和与集合的元素之和不相等，则称集合具有性质.（1）试分别判断在集合与是否具有性质P ，不必说明理由；（2）已知集合具有性质P .①记，求证：对于任意正整数，都有；②令，，求证：；（3）在（2）的条件下，求的最大值.()1f x ax -≤2111ln 42nk n f k =+⎛⎫-< ⎪⎝⎭∑*n ∈N {}()12,,,3n S a a a n =≥ *,1,2,,i a i n ∈=N S A B ､A B S P {}11,2,3,4S ={}21,2,4,8S ={}12,,,n S a a a = 121kik i aa a a ==+++∑L k n ≤121kk i i a =≥-∑12i i i d a -=-1kk ii D d==∑0k D ≥12111na a a +++深圳外国语学校2025届高三第二次月考数学答案一､选择题：题号1234567891011答案ACDADDCBACBDABC二､填空题12. 13.14.三､解答题15.解：（1）由，得.因为，，所以曲线在点处的切线方程为.（2）当时，，所以.令，得，解得或.与在区间上的情况如下：所以，当且时，⎫⎪⎪⎭e2()32f x x ax bx c =+++()232f x x ax b =++'()0f c =()0f b '=()y f x =()()0,0f y bx c =+4a b ==()3244f x x x x c =+++()2384f x x x =++'()0f x '=23840x x ++=2x =-23x =-()f x ()f x '(),-∞+∞x(),2-∞-2-22,3⎛⎫-- ⎪⎝⎭23-2,3⎛⎫-+∞ ⎪⎝⎭()f x '+0-0+()f x Zc]3227c -Z0c >32027c -<存在，，，使得.由的单调性知，当且仅当时，函数有三个不同零点.16.（1）由及正弦定理得，整理得，所以由余弦定理得：因为，所以.（2），记，则.在中，.①在中，由正弦定理得.②由①②及得，解得.由，解得.17.（1）设，因为底面是边长为2的菱形，所以，对角线BD 平分，又为棱的中点，所以，在中，根据角平分线性质定理得，又，所以，所以，，平面，且平面平面.()14,2x ∈--222,3x ⎛⎫∈--⎪⎝⎭32,03x ⎛⎫∈- ⎪⎝⎭()()()1230f x f x f x ===()f x 320,27c ⎛⎫∈ ⎪⎝⎭()3244f x x x x c =+++sin sin sin A B C b c a b -=++a b cb c a b-=++222a b c bc =++2221cos ,22b c a A bc +-==-()0,πA ∈2π3A =π6DAC BAC BAD ∠=∠-∠=ADB α∠=π6C DAC αα∠=-∠=-Rt ABD V cos AD BD α=ADC V ππsinsin 66AD CDα=⎛⎫- ⎪⎝⎭2CD BD =cos 2ππsin sin 66αα=⎛⎫- ⎪⎝⎭4=tan α=22πtan cos 1,0,2αααα⎛⎫=+=∈ ⎪⎝⎭sin α=sin ADB ∠=BD CE N ⋂=ABCD CD AB =ADC ∠E AD 2CD AB DE ==ADC V 2CN CDNE DE==2CM MP =2CM MP =2CN CMNE MP==MN ∴∥PE PE ⊄MBD MN ⊂,MBD PE ∴∥MBD（2）平面，且平面，，因为，所以，在中，，，所以是等边三角形，又为棱的中点，所以，平面，平面，所以平面平面，又平面平面，平面ABCD ，平面，又平面，，又，平面，平面，且平面，.因为P 在底面的投影H 为线段的中点，所以，又所以为等边三角形，故为中点，所以在底面上的投影为的中点.在中，，，以为原点，分别以为轴，以过点且与平面垂直的直线为轴建立空间直角坐标系，所以，，设是平面的一个法向量，则，令，则，即，平面，是平面的一个法向量，PH ⊥ ABCD BC ⊂ABCD PHBC ∴⊥π3ABC∠=2π3BCD ∠=ACD V CD AB =π3ABC ∠=ACD V E AD BC CE ⊥PH ⊥ ABCD PH⊂PCE PCE ⊥ABCD PCE ⋂ABCD =CE BC ⊂BC ∴⊥PEC EM ⊂PEC BC EM ∴⊥PB EM ⊥ ,,PB BC B PB BC ⋂=⊂PBC EM ∴⊥PBC PC ⊂PBC EM PC ∴⊥EC PC PE =PC CE =PCE V MPC M ABCD CH CDE V CE ===3,2CEAD PH ⊥== C ,CB CE ,x y C ABCD z ()()()30,0,0,2,0,0,,4C B E M ⎛⎫⎪ ⎪⎝⎭()32,,4EB ME ⎛⎫∴==- ⎪ ⎪⎝⎭(),,n x y z = EBM 0203004n EB x n ME y z ⎧⋅=⇒=⎪⎨⋅=⇒-=⎪⎩ 2y =x z ==2,n =BC ⊥ PEC ()2,0,0CB ∴=PEC因为二面角是一个锐角，所以二面角18.（1）依题意，设图像上任意一点坐标为，则其关于对称的点在图像上，则，则，故，；（2）令，，则在在恒成立，又，且在上是连续函数，则为的一个极大值点，，，下证当时，在恒成立，令，，当，，在上单调递增，当，，在上单调递减，故，在上恒成立，又，则时，恒成立，综上，.（3）由（2）可知：，则，即，则，又由（2）可知：在上恒成立，则在上恒成立且当且仅当时取等，令，，则，cos ,n CB n CB n CB⋅∴===⋅B EMC --B EM C --()f x ()00,x y 1x =-()002,x y --()g x 000()(2)y f x g x ==--0000()(2)2ln(1)cos f x g x x x =--=++0(1)x >-()()2ln 1cos f x x x =++()1x >-()()()12ln 1cos 1h x f x ax x x ax =--=++--()1x >-()0h x ≤(1,)x ∈-+∞()00h =()h x (1,)x ∈-+∞0x =()h x 2()sin 1h x x a x '=--+(0)202h a a '=-=⇒=2a =()0h x ≤(1,)x ∈-+∞()ln(1)x x x ϕ=+-1()111x x x x ϕ'=-=-++()1,0x ∈-()0x ϕ'>()x ϕ()1,0-(0,)x ∈+∞()0x ϕ'<()x ϕ()0,∞+()()00x ϕϕ≤=()ln 1x x ≤+(1,)-+∞cos 1x ≤2a =()()()()12ln 1cos 10h x f x ax x x x ⎡⎤=--=+-+-⎦≤⎣2a =()12f x x -≤11111222f k k ⎛⎫⎛⎫--≤-⎪ ⎪⎝⎭⎝⎭1122f k k⎛⎫-≤ ⎪⎝⎭211111122122nk n f k n n n =+⎛⎫⎛⎫-≤+++ ⎪ ⎪++⎝⎭⎝⎭∑ ()ln 1x x ≤+()1,-+∞ln 1x x ≤-()0,∞+1x =(0,1)1nx n =∈+*N n ∈1ln1111n n n n n -<-=+++即，则，综上，，即证19.（1）对于集合，因为，故集合的元素和相等，故不具有性质.对于，其共有15个非空子集：，，各集合的和分别为：，，它们彼此相异，故具有性质.（2）①因为具有性质，故对于任意的，也具有性质，否则有两个非空子集，它们的元素和相等，而也是的子集，故不具有性质，矛盾.注意到共有个非空子集，每个子集的元素和相异，且子集的和最大为，最小为，故.②因为，故，由①可得，故.（3）不妨设，设，则，由（2）可得，且.而11ln ln ln(1)ln 11n n n n n n n +<-==+-++111ln(1)ln ln(2)ln(1)ln(2)ln(21)122n n n n n n n n n+++<+-++-+++--++ ln(2)ln ln 2n n =-=21112ln 2ln 42nk n f k =+⎛⎫-<= ⎪⎝⎭∑{}11,2,3,4S =1423+=+{}{}1,4,2,31S P {}21,2,4,8S ={}{}{}{}{}{}{}{}{}{}8,,,,,,1,2481,21,41,82,42,,,84,{}{}{}{}{}1,2,41,2,81,4,82,4,81,2,4,8,,,,59610121,2,4,8,3,,,,,7,11,13,14,152S P {}12,,,n a a a P k {}12,,,k a a a P {}12,,,k a a a ,A B ,A B {}12,,,n a a a {}12,,,n a a a P {}12,,,k a a a 21k -12k a a a +++ 1a 1221kk a a a +++≥- 12i i i d a -=-()112122k k k D a a a -=+++-+++ ()1221k k a aa =+++-- ()12210kk a a a +++--> 0k D ≥12n a a a <<< 1121112122111112112222n n n n n n a a a a a a a a a ---⎛⎫+++-+++=+++ ⎪--⎝⎭- 112i i ic a -=10i i c c +->12i i i d a -=-10kk ii D d==≥∑112112211222122n n n n n n a a a c d c d c d a a a ---+++=+++-- ()()()112213321n n n c D c D D c D D c D D -=+-+-++-，故，当且仅当时等号成立，即此时任意的正整数，即故此时时等号成立，故的最大值为.()()()121232110n n n n n c c D c c D c c D c D --=-+-++-+≥ 111211*********n n n a a a --+++≤+++=- 120n D D D ==== k 1221kk a a a ++=-1111,222kk k k a a --==-=12k k a -=12111n a a a +++ 1122n --。

河北省衡水市2024-2025学年高三上学期第二次调研考试（9月月考）英语试题一、阅读理解Below are some strategies that can be employed in class to engage students in learning activities.Think — Pair — ShareThis technique is popular in the lower elementary grades to encourage speaking and listening skills. First, ask students to think about their response to a question, and then ask them to pair up with another person, usually someone nearby. The pair discuss their response, and then they share that response with a larger group.FishbowlA fishbowl is organized with two four student groups who sit facing each other in the center of the room. All the other students sit in a circle around them. Those students seated in the center discuss the question. Students on the outside circle take notes. In a variation, students on the outside may provide quick notes known as “fish food” by passing them to students on the inside for use in their discussion.Concentric CirclesOrganize students into two circles, one outside circle and one inside circle so that each student on the inside is paired with a student on the outside. The teacher poses a question to the whole group. Each pair discuss how to respond. After this brief discussion, the students on the outside circle move one space to the right. This will mean each student will be part of a new pair. The teacher can have them share the results of that discussion or pose a new question.PyramidStudents begin this strategy in pairs and respond to a discussion question with a single partner. At a signal from the teacher, the first pair join another pair which creates a group of four. These groups of four share their ideas. Next, the groups of four move to form groups of eight in order to share their best ideas. This grouping can continue until the whole class is joined up in one large discussion.1．Which strategy can a teacher adopt if he doesn’t want all the students to speak?A．Think — Pair — Share.B．Fishbowl.C．Concentric Circles.D．Pyramid.2．What’s a unique aspect of Concentric Circles?A．Students change partners.B．Students respond to a question.C．Students pass notes to each other.D．Students take turns to present their ideas. 3．How does Pyramid work?A．Best ideas are collected for a presentation.B．One group combines with another with each step.C．The whole class work together to carry out a project.D．Groups of four move around the classroom to share ideas.Malonga was born in Brazzaville, Congo, where his grandmother owned a restaurant. His love for food and cooking started there. He spent his teenage years in Germany and he started his career working in top European restaurants.In 2015, he competed in the French Top Chef TV show as the first Black chef to do so. When it came time to open his own restaurant, he took a two - year tour of the African continent, seeking inspiration.He opened Meza Malonga in 2020. Dinners at Meza Malonga have no menu — the meal changes based on seasonally available ingredients(食材)and what’s exciting Malonga at the moment. Giant windows open onto the hills of Kigali. The chefs present each course. There’s nobody yelling(大喊), “Yes chef!” and Malonga pointedly refers to “our restaurant… our menu… our project.” His longest employee is Frank Buhigiro, who says “The way we work is like we are family. You know, we don’t have pressure because we get time to think and create.”The restaurant is only open for eight months out of the year. For the other four months, Malonga and his team travel the continent. They experience different African cuisines first - hand, and source unique ingredients. But it’s more driven, more intense, than just sourcing. Malonga has visited 48 African countries, eating his way across the continent. Upon returning to Kigali, he brings back new flavors as souvenirs(纪念品). He describes new tastes like a shiny new toy. “Right now, I’m eating cassava leaves — I love it!”Malonga wants to carve out a space for African food in the global fine dining scene. Something he thinks is increasingly possible based on how people travel. Now, he says, people book trips not based on where they sleep, but where they eat.4．What gave Malonga his early inspiration for his career?A．A European cooking show.B．A famous chef in Germany.C．His book about African cuisine.D．His grandmother’s restaurant.5．In what way is Meza Malonga unique?A．It combines dining with traveling.B．It has a fixed menu that never changes.C．Diners can choose their own ingredients.D．The chefs present each course to the diners.6．What’s the working atmosphere like in Meza Malonga?A．Easy and simple.B．Warm and relaxing.C．Formal but exciting.D．Positive but tense.7．What is the main purpose of Malonga and his team’s travels across Africa?A．To enhance their team spirit.B．To search for designs for toy souvenirs.C．To experience cuisines and source ingredients.D．To seek suitable locations for opening new restaurants.Ernesto Gomez’s journey into ornithology (鸟类学) began with a childhood encounter with scarlet macaws as they flew past him in the green rainforest of Chiapas, Mexico. This experience fired a lifelong passion for birds and conservation, leading him to specialize in ornithology and join Pronatura Península deY ucatán (PPY), an environmental conservation group in Mexico.Gomez’s work is supported by Fish and Wildlife Service grant programs that improves wetland habitats for migratory birds and promotes environmental education and research. One of Gomez’s key projects involves restoring and managing wetland habitats in the Yucatan Peninsula, which has led to the return of several species. These efforts not only support bird populations butalso reduce the vulnerability of coastal communities by improving their capacity to adapt to environmental risks.Community engagement is central to PPY’s success, with the annual Toh Festival being a key example. This festival, named after a bird of cultural significance, hosts a variety of bird-related activities from March to November, including birding marathons, photo expeditions (探险), contests, tours, and workshops. These events inspire community members to appreciate and protect the region’s rich biodiversity.As a nature photographer, Gomez approaches his work with respect for the wildlife, aiming to remain careful to avoid disturbing the birds. His photography serves a higher purpose, creating media communications that support PPY’s environmental education and community outreach initiatives. His images not only record the beauty of birds but also provide a window into their world, inspiring people to learn more about the challenges they face and the habitats they depend on.Ernesto Gomez proved to us the power of photography to inspire and educate. His work ensures that the beauty of Yucatan’s birds and habitats continues to inspire, reminding us of the vital link between people and nature.8．Where did Ernesto Gomez’s interest in ornithology come from?A．An encounter with scarlet macaws.B．A documentary on wetland conservation.C．A photography exhibition about Mexican forests.D．An educational program onenvironmental science.9．What does the underlined word “vulnerability” mean in paragraph 2?A．The stability of regional biodiversity.B．The quality of being weak and easily hurt.C．The capability of managing wetland habitats.D．The probability of being adaptive to environmental risks.10．What is a primary purpose of the Toh Festival?A．To raise funds for conservation projects.B．To engage people in bird-related activities.C．To promote bird - watching as a tourism activity.D．To recognize the work of nature photographers.11．How do Gomez’s photos contribute to PPY’s mission?A．By providing visual documentation for scientific research.B．By attracting birding marathoners to the Yucatan Peninsula.C．By creating media communications for environmental education.D．By encouraging people to face the challenges of environmental conservation.Albino redwoods, with their slightly shining white appearance, are a rare sight in California’s coastal forests. Despite lacking chlorophyll, which is used to photosynthesize(光合作用), these trees have managed to survive, puzzling researchers for over a century. However, a recent study by biologist Zane Moore from the University of California in Davis may have uncovered the secret to their existence.Redwoods rank among the tallest organism on earth and claim an existence of some 3,500 years. They are known for their complex root systems that allow them to communicate and share nutrients during tough times. Researchers have seen this firsthand by introducing dye to trees on one side of an area of redwoods and tracing it all the way to the further reaches. In summer, they become more independent, and those unable to sustain themselves are cut off from the shared system in the autumn needle drop.So, if albino red woods can’t photosynthesize, why are they able to stick around? Moore’s research suggests that albino redwoods survive by tapping into the communal root system and absorbing sugars from healthier neighbors. Contrary to the belief that they are parasites(寄生植物), Moore’s findings indicate a symbiotic(共生) relationship.Albino redwoods tend to grow in less healthy conditions and have been found to contain high levels of poisonous heavy metals in their leaves. Moore theorizes that these trees are not only surviving but also serving a purpose by acting as a “reservoir(水库) for poison”, thus protecting their healthier counterparts. This discovery could potentially make it possible to use albino redwoods in polluted areas to safeguard other trees.The study highlights the interconnectedness of trees and their ability to look out for one another, forming bonds and even recognizing their offspring. Moore’s research emphasizes the importance of considering the entire community of trees, rather than focusing on individuals, to understand what’s happening in the forest.12．What can be learned about redwoods?A．They depend on each other for nutrition in tough times.B．They have unusually strong roots that can reach very far.C．How they photosynthesize has puzzled researchers for long.D．How they communicate among individuals remains a secret.13．How do albino redwood s survive?A．They become parasites of other tree species.B．They rely on the fallen needles for their growth.C．They have developed an alternative method of photosynthesis.D．They absorb sugars from the root system of healthier redwoods.14．What role do albino redwood s play in the forest ecosystem?A．They transport water for the forest.B．They act as a source of food for other plants.C．They protect other redwood trees by absorbing poison.D．They are responsible for the reproduction of the redwood species.15．What’s the best title of the text?A．Albino Redwoods May be the Result of PollutionB．Albino Redwoods May Survive to Help Nearby TreesC．Symbiotic Relationship is Built among Albino RedwoodsD．Researchers Discovered Complex Root System of Albino RedwoodsMischief Night, also known by various names like Devil’s Night and Cabbage Night, is a tradition that has changed over time in the United States and Canada. Historically, Halloween pranks(恶作剧)were performed on October 31st. 16 However, by the 1920s and 1930s, these pranks changed into more serious acts of destruction, possibly due to the social tensions of the Great Depression.In an effort to deal with this destructive behavior, parents and community leaders encouraged the tradition of trick-or-treat. 17 This shift effectively moved the mischief from October 31st to October30th.The custom of Mischief Night is particularly popular in areas with a history of Irish and Scottish immigration, such as the northeastern United States and English-speaking communities inCanada. 18According to a Cambridge Online Survey of World Englishes, 74% of Americans surveyed do not have a specific name for this night. 19 East Michigan referred to it as Devil’s Night, parts of New Jersey and New York as Mischief Night, and Washington State as Devil’s Eye. A similar study conducted by Harvard University a decade ago revealed other names like Gate Night, which involved opening farmers’ gates to let livestock roam free.20 The term Cabbage Night, for instance, originates from an old Scottish tradition where young women would use cabbages in fortune- telling rituals on All Hallows’ Eve, leading to a tradition of throwing cabbages at neighbors’ homes. Despite the decline in the use of specific names, Mischief Night continues to be a part of local traditions.A．Yet, regional names do exist.B．They offered candy to children in costumes as an alternative.C．The origins of these names have long been a topic of discussion.D．They involved light - hearted tricks such as throwing eggs at houses.E．Children had great fun but parents were concerned about the serious destruction.F．The data suggest that the specific names for this night are gradually fading away. G．However, it is less common in the South, West, and French-speaking regions of Canada.二、完形填空My friend Julie and I had completed an incredibly complicated set of instructions which led us to our comfortable room in Tokyo. The next morning, still with a white wine hangover from celebratory night, we 21 a most unexpected sensation: The whole room was shaking from side to side. My friend Julie was up and screaming “what’s happening?” I was very 22 but my mind was 23 .“I think it’s an earthquake,” I said.I staggered (踉跄) out of 24 and noticed a helpful guide page which was 25 on the small table that I hadn’t noticed before.The room stopped shaking and then started again like a 26 sailor. The cups were shaking and I was feeling rather 27 . Sure enough, the guide page had a section on what todo in an earthquake. It 28 that all buildings in Tokyo were earthquake-proof, but if you were worried, the door frames could 29 you as they were all reinforced (强化的) steel.We didn’t feel particularly protected. Julie rushed downstairs to seek 30 , but she was me t with a shrug (耸肩) from the old lady there who simply 31 that Japan sometimes shakes.Although the center of the earthquake was off the coast of the Ogasawara Islands, it 32 the whole of Japan and the aftershocks were felt as far away as India and Nepal. I was 33 that it got so little international 34 . It didn’t cause a tsunami and no nuclear power plants were affected — but it was still a crazy 35 .21．A．caught up with B．put up with C．looked forward to D．woke up to 22．A．curious B．careful C．dizzy D．calm 23．A．working B．disturbed C．slow D．blank 24．A．reach B．bed C．place D．sight 25．A．actually B．previously C．accidentally D．accordingly 26．A．worried B．seasoned C．drunken D．scared 27．A．sick B．easy C．tired D．sleepy 28．A．proved B．noted C．ensured D．predicted 29．A．interest B．bother C．support D．protect 30．A．comfort B．approval C．fortune D．assistance 31．A．replied B．complained C．hoped D．denied 32．A．panicked B．moved C．shook D．troubled 33．A．skeptical B．anxious C．surprised D．fortunate 34．A．business B．cooperation C．privilege D．attention 35．A．action B．experience C．idea D．game三、单词拼写36．The change of seasons is a natural (现象).(根据汉语提示单词拼写)四、语法填空37．She decided to take an (addition) course to enhance her skills in data analysis.(所给词的适当形式填空)38．The rapid (respond) of the firefighters helped to minimize the damage caused by the fire. (所给词的适当形式填空)39．A (type) day for a student might involve attending classes, studying, and participating in extracurricular activities. (所给词的适当形式填空)五、单词拼写40．The fundamental (原则) of good nutrition is to consume a balanced diet that includes a variety of fruits, vegetables, and proteins. (根据汉语提示单词拼写)六、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

2023届福建省龙岩第一中学高三上学期第二次月考数学试题一、单选题1．已知{}1,0,1,3,5A =-，{}230B x x =-<，则R A B =ð（ ） A ．{}0,1 B ．{}1,1,3-C ．{}1,0,1-D ．{}3,5【答案】D【分析】由题意求出B ，R B ð，由交集的定义即可得出答案.【详解】因为{}230B x x =-<32x x ⎧⎫=<⎨⎬⎩⎭， 所以R B =ð32x x ⎧⎫≥⎨⎬⎩⎭，所以A R B =ð{}3,5.故选：D. 2．若5:11xp x -≤+，则p 成立的一个充分不必要条件是（ ） A ．21x -<≤- B ．12x -≤≤ C ．15x ≤≤ D ．25x <<【答案】D【分析】先求出分式不等式的解集，进而结合选项根据充分不必要条件的概念即可求出结果. 【详解】因为511xx -≤+，即51011x x x x -+-≤++，因此4201x x -≤+等价于()()42+10+10x x x -≤≠⎧⎨⎩，解得2x ≥或1x <-，结合选项可知p 成立的一个充分不必要条件是25x <<， 故选：D.3．已知函数()()2ln 16f x x x =++-，则下列区间中含()f x 零点的是（ ）A ．()0,1B ．()1,2C ．()2,3D ．()3,4【答案】C【分析】分别求出()0f 、()1f 、()3f 、()4f 的值，即可判断其正负号，利用零点存在定理则可选出答案.【详解】由题意知：()0ln1660f =-=-<，()231ln2+16ln3+462ln 32ln0e f f =-<-==-=<（）， ()ln3+96ln3303f =-=+>，()ln4+166ln 40041f =-=+>. 由零点存在定理可知()f x 在区间()2,3一定有零点. 故选：C.4．如图是杭州2022年第19届亚运会会徽，名为“潮涌”，钱塘江和钱江潮头是会徽的形象核心，绿水青山展示了浙江杭州山水城市的自然特征，江潮奔涌表达了浙江儿女勇立潮头的精神气质，整个会徽形象象征着新时代中国特色社会主义大潮的涌动和发展.如图是会徽的几何图形，设弧AD 长度是1l ，弧BC 长度是2l ，几何图形ABCD 面积为1S ，扇形BOC 面积为2S ，若122l l =，则12S S =（ ）A ．1B ．2C ．3D ．4【答案】C【分析】通过弧长比可以得到OA 与OB 的比，接着再利用扇形面积公式即可求解 【详解】解：设AOD θ∠=，则12,l OA l OB θθ=⋅=⋅，所以122l OAl OB==，即2OA OB =， 所以12221222111222231122OA l OB l OB l OB l S S OB l OB l ⋅-⋅⋅-⋅===⋅⋅， 故选：C5．已知22sin sin ,cos cos 33αβαβ-=--=，且π,0,2αβ⎛⎫∈ ⎪⎝⎭，则ta n()αβ-的值为（ ）AB．CD．【答案】B【分析】将条件的两个式子平方相加可得()8922cos αβ--=，然后可得()5os 9c αβ-=，再由2sin sin 03αβ-=-<，π,0,2αβ⎛⎫∈ ⎪⎝⎭，可得()π,02αβ⎛⎫-∈- ⎪⎝⎭，从而可求出()in s αβ-=，由商式关系可求得()an t αβ-=【详解】由2sin sin 3αβ-=-，得22sin 2sin sin sin 49ααββ-+=，由2cos cos 3αβ-=，得22cos 2cos cos cos 49ααββ-+=，两式相加得，()8922cos αβ--=，所以可得()5os 9c αβ-=，因为2sin sin 03αβ-=-<，π,0,2αβ⎛⎫∈ ⎪⎝⎭，所以()π,02αβ⎛⎫-∈- ⎪⎝⎭，所以()in s αβ-=()an t αβ-=故选：B6．已知()()2222cos 1ln 4f x x x =-⋅，则函数()f x 的部分图象大致为（ ）A ．B ．C ．D ．【答案】A【分析】利用二倍角余弦公式化简()2f x 的表达式，令()20t x t =≠，可得()f x 的解析式，再判断函数()f x 的奇偶性，可排除选项C 、D ，最后根据0x +→时，()0f x <即可求解.【详解】解：()()()()22222cos 1ln 4cos 2ln 2f x x x x x =-⋅=⋅，令()20t x t =≠，则()2cos ln f t t t =⋅()0t ≠，所以()2cos ln f x x x =⋅()0x ≠，定义域关于原点对称，因为()()()()22cos ln cos ln f x x x x x f x -=-⋅-=⋅=，所以()f x 为偶函数，图象关于y 轴对称，故排除选项C 、D ；又0x +→时，因为2cos 0,ln 0x x ><，所以()2cos ln 0f x x x =⋅<，所以排除选项B ，选项A 正确； 故选：A.7．已知()22231,0log ,0x x x f x x x ⎧++≤⎪=⎨>⎪⎩，函数()()g x f x b =+有四个不同的零点1234,,,x x x x ，且满足：1234x x x x <<<.则下列结论中不正确的是（ ） A ．10b -<< B ．341x x =C ．3112x ≤< D ．1232x x +=-【答案】A【分析】作出()f x 图象，利用函数有四个不同的交点求出10b -≤<，A 错误； 根据二次函数的对称轴求出1232x x +=-可判断D ；数形结合结合对数运算得到341x x =可判断B ；数形结合求出231log 0x -≤<，解得3112x ≤<，可判断C. 【详解】如图，作出()f x 图象，若y ＝－b 与()y f x =有四个交点，需01b <-≤，则10b -≤<，故A 错误；这四个交点的横坐标依次为1234,,,x x x x ，因为抛物线2231y x x =++的对称轴为34x =-，所以1232x x +=-，故D 正确；因为2324log log x x -=，即2324log log 0x x +=，所以341x x =，故B 正确；()(]323log 0,1f x x =-∈，即231log 0x -≤<，所以3112x ≤<，故C 正确.故选：A.8．已知13sin 2,ln 2,2a b c -===，则a ，b ，c 的大小关系是( ) A ．c b a << B ．a b c <<C ．b a c <<D ．b c a <<【答案】D【分析】判断sin2和2πsin3的大小，比较a 与34、b 与34、c 与34的大小可判断a 与b 大小关系及b 与c 大小关系，判断aca 与c 大小关系，从而可判断a 、b 、c 大小关系．【详解】2π3sin2sin34a =>=>， 4333344443e e 2e 2lne ln24⎛⎫=>⇒>⇒=> ⎪⎝⎭，即b 34<，∴a >b ；∵3131322264-⎛⎫== ⎪⎝⎭，3327464⎛⎫= ⎪⎝⎭，∴13324->，c b ∴>；∵62764=⎝⎭，6131162464-⎛⎫== ⎪⎝⎭，132->，a c ∴>； a cb ∴>>． 故选：D ．【点睛】本题关键是利用正弦函数的值域求出sin2的范围，以34两个值作为中间值，比较a 、b 、c 与中间值的大小即可判断a 、b 、c 的大小．二、多选题9）A ．2252cos cos 1212ππ⎛⎫- ⎪⎝⎭ B ．1tan151tan15+︒-︒C．cos15︒︒ D ．16sin10cos20cos30cos40︒︒︒︒【答案】ABD【分析】对于A ，采用降幂公式，结合特殊角三角函数，可得答案； 对于B ，根据特殊角三角函数，结合正切的和角公式，可得答案； 对于C ，根据辅助角公式，结合特殊角三角函数，可得答案； 对于D ，根据积化和差公式，结合特殊角三角函数，可得答案.【详解】对于A ，2251cos 1cos 55662cos cos 2cos cos12122266ππππππ⎛⎫++ ⎪⎛⎫-=-=- ⎪ ⎪⎝⎭⎪⎝⎭=，故A 正确； 对于B ，()1tan15tan 45tan15tan 4515tan 6031tan151tan 45tan15++==+==--，故B 正确；对于C ，13cos153sin152cos15sin1522⎛⎫-=- ⎪ ⎪⎝⎭()()()2sin30cos15cos30sin152sin 30152sin152sin 4530=-=-==-()212sin 45cos30cos 45sin 302222⎛⎫=-== ⎪ ⎪⎝⎭C 错误； 对于D ，16sin10cos 20cos30cos 40 ()116sin 30sin 10cos30cos 402⎡⎤=⨯+-⎣⎦ 8sin30cos30cos 408sin10cos30cos 40=-()18408sin 40sin 20cos 402⎡⎤=-⨯+-⎣⎦404sin 40cos 404sin 20cos 40=-+()1402sin804sin 60sin 202⎡⎤=-+⨯+-⎣⎦402sin8032sin 20=-+-404sin50cos303=-+ )cos 40sin 503=-+)cos 40cos 403=-+=D 正确；故选：ABD.10．已知0a >，0b >，且4a b +=，则下列结论正确的是（ ） A ．4ab ≤ B ．111a b+≥ C ．2216a b +≥ D ．228a b +≤【答案】AB【分析】根据基本不等式进行逐一判断即可.【详解】A ：因为0a >，0b >，所以4a b ab +≥≤，当且仅当2a b ==时取等号，故本选项正确；B ：因为0a >，0b >，所以有11111()(2)(21444a b b a a b a b a b b a ++=+=++≥+=+，当且仅当2a b ==时取等号，故本选项正确；C ：因为228a b +≥=，当且仅当2a b ==时取等号，所以本选项不正确；D ：因为0a >，0b >，所以有22282a b a b +≤≤+≥，当且仅当2a b ==时取等号，所以本选项不正确，故选：AB11．已知函数()()3sin 222f x x ππϕϕ⎛⎫=+-<< ⎪⎝⎭的图像关于直线3x π=对称，则（ ）A ．函数12f x π⎛⎫+ ⎪⎝⎭为奇函数B ．函数()f x 在,32ππ⎡⎤⎢⎥⎣⎦上单调递增C ．函数()f x 的图像向右平移()0a a >个单位长度得到的函数图像关于6x π=对称，则a的最小值是3πD ．若方程()f x a =在2,63ππ⎡⎤⎢⎥⎣⎦上有2个不同实根12,x x ，则12x x -的最大值为2π【答案】AC【分析】根据题意得6πϕ=-，()3sin 26f x x π⎛⎫=- ⎪⎝⎭，再结合三角函数的图像性质依次分析各选项即可得答案.【详解】解：因为函数()()3sin 222f x x ππϕϕ⎛⎫=+-<< ⎪⎝⎭的图像关于直线3x π=对称，所以，2,Z 32k k ππϕπ⨯+=+∈，解得,Z 6k k πϕπ=-+∈，因为22ππϕ-<<，所以6πϕ=-，即()3sin 26f x x π⎛⎫=- ⎪⎝⎭，所以，对于A 选项，函数3sin 212f x x π⎛⎫+= ⎪⎝⎭，是奇函数，故正确；对于B 选项，当,32x ππ⎡⎤∈⎢⎥⎣⎦时，25,626x πππ-⎡⎤∈⎢⎥⎣⎦，由于函数sin y x =在5,26ππ⎡⎤⎢⎥⎣⎦上单调递减，所以函数()f x 在,32ππ⎡⎤⎢⎥⎣⎦上单调递减，故错误；对于C 选项，函数()f x 的图像向右平移()0a a >个单位长度得到的函数图像对应的解析式为()3sin 226g x x a π⎛⎫=-- ⎪⎝⎭，若()g x 图像关于6x π=对称，则22,Z 662a k k ππππ⨯--=+∈，解得,Z 62k a k ππ=-+∈， 由于0a >，故a 的最小值是3π，故正确； 对于D 选项，当2,63x ππ⎡⎤∈⎢⎥⎣⎦时，672,66x πππ⎡⎤⎢⎥⎣⎦-∈，故结合正弦函数的性质可知，若方程()f x a =在2,63ππ⎡⎤⎢⎥⎣⎦上有2个不同实根12,x x ，不妨设12x x <，则12x x -取得最大值时满足1266x ππ-=且25266x ππ-=， 所以，12x x -的最大值为3π，故错误.故选：AC12．已知1a b >>，则（ ） A ．ln ln a b b a > B ．11ea ba b-<C ．11e b a ->D ．若m b b n =+，则m a a n >+ 【答案】BC【分析】根据各个选项中的不等式，通过构造新函数，利用导数判断其单调性，再结合特例法进行判断即可.【详解】因为1a b >>，所以ln ln ln ln b aa b b a b a>⇔>， 设函数ln ()(1)xf x x x=>，21ln ()x f x x -'=，当(1,e)x ∈时，()0f x '>，函数()f x 单调递增， 当(e,)x ∈+∞时，()0f x '<，函数()f x 单调递减， 所以A 选项错误；因为1a b >>，所以由111111eln ln ln ln a ba ab a b b a b a b -<⇔-<-⇔->-， 设函数1()ln g x x x =-，211()g x x x '=+，当,()0x ∈+∞时，()0g x '>，函数()g x 单调递增，所以B 选项正确；因为111eln 1ba a b->⇔>-，设函数1()ln 1h a a a ⎛⎫=-- ⎪⎝⎭，所以21()a h a a -'=，当()1,a ∞∈+时，()0'>h a ，函数()h a 单调递增， 当()0,1a ∈时，()0h a '<，函数()h a 单调递减，所以()(1)0h a h >=，即11ln 10ln 1a a a a ⎛⎫-->⇒>- ⎪⎝⎭，因为1a b >>，所以111111a b a b <⇒->-，因此11ln 11a a b>->-，所以C 选项正确. 令2,0b m ==，则有1n =-，又令3a =，所以01,2m a a a n ==+=， 显然不成立，所以D 选项错误， 故选：BC【点睛】方法点睛：不等式是否成立可以通过构造函数利用导数的性质来进行判断.三、填空题13．已知角θ的终边经过点(2,1)P -，则22cos 2sin cos 2θθθ-=___________.【答案】23【分析】利用三角函数定义求出tan θ，再利用二倍角公式化简，结合齐次式法计算作答.【详解】因角θ的终边经过点(2,1)P -，则1tan 2θ=-，所以2222222222112()cos 2sin cos 2sin 12tan 221cos 2cos sin 1tan 31()2θθθθθθθθθ-⨯----====----. 故答案为：2314．函数()xe f x x =的单调递减区间是__________.【答案】和（或写成和）【详解】试题分析：由题意得22(1)()x x x xe e e x f x x x-='-=，令()0f x '<，解得0x <或01x <<，所以函数的递减区间为和．【解析】利用导数求解函数的单调区间．15．已知函数(1)y f x =+的图象关于直线3x =-对称，且对R x ∀∈都有()()2f x f x +-=，当2(]0,x ∈时，()2f x x =+.则(2022)f =___________. 【答案】2-【分析】根据给定条件，推理论证出函数()f x 的周期，再利用周期性计算作答. 【详解】因函数(1)y f x =+的图象关于直线3x =-对称，而函数(1)y f x =+的图象右移1个单位得()y f x =的图象，则函数()y f x =的图象关于直线2x =-对称，即(4)()f x f x --=，而对R x ∀∈都有()()2f x f x +-=，则(4)()2f x f x --+-=，即R x ∀∈，(4)()2f x f x +=-+，有(8)(4)2f x f x +=-++[()2]2()f x f x =--++=，因此函数()y f x =是周期函数，周期为8，又当2(]0,x ∈时，()2f x x =+， 所以(2022)(25382)(2)2(2)242f f f f =⨯-=-=-=-=-. 故答案为：2-16．已知函数()sin cos (0,0)f x x a x a ωωω=+>>图像的两条相邻对称轴之间的距离小于,3f ππ⎛⎫= ⎪⎝⎭()6f x f π⎛⎫≤⎪⎝⎭，则ω的最小值为___________. 【答案】13【分析】先由对称轴间的距离确定了1ω>，再利用()6f x f π⎛⎫≤ ⎪⎝⎭得到2,Z 62k k πωπϕπ+=+∈，依次利用诱导公式与基本关系式求得tan 6πω⎛⎫⎪⎝⎭、cos 6πω⎛⎫ ⎪⎝⎭、sin 6πω⎛⎫⎪⎝⎭的a 关于表达式，求出a 的值，进而得到121,Z k k ω=+∈，即可得到结果. 【详解】()()sin cos f x x a x x ωωωϕ=+=+，tan a ϕ=， 因为两条相邻对称轴之间的距离小于π，即2T π<，故22T ππω=<，所以1ω>， 因为()f x 在6x π=处取得最大值，所以2,Z 62k k πωπϕπ+=+∈，即2,Z 26k k ππωϕπ=+-∈，所以1tan tan 2tan 2626tan 6k a ππωππωϕππω⎛⎫⎛⎫=+-=-== ⎪ ⎪⎛⎫⎝⎭⎝⎭ ⎪⎝⎭， 所以1tan 6a πω⎛⎫= ⎪⎝⎭，因为3f π⎛⎫= ⎪⎝⎭3πωϕ⎛⎫+=⎪⎝⎭，即sin 3πωϕ⎛⎫+= ⎪⎝⎭所以sin sin 2sin cos 3326266k πωπωππωππωπωϕπ⎛⎫⎛⎫⎛⎫⎛⎫+=++-=+= ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭所以sin tan cos 666πωπωπω⎛⎫⎛⎫⎛⎫=⨯= ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭又2222sin cos 166πωπω⎛⎫⎛⎫+=+= ⎪ ⎪⎝⎭⎝⎭，解得23a =，又0a >，所以a =1sin 62πω⎛⎫= ⎪⎝⎭，又tan 06πω⎛⎫> ⎪⎝⎭，所以2,Z 66k k πωππ=+∈，解得121,Z k k ω=+∈，又1ω>，所以ω的最小值为13.故答案为：13.四、解答题17．已知a ，b ，c 分别为ABC 内角A ，B ，C 的对边，且满足2225,sin 2sin 8b c a bc C B +-==． （1）求cos A ；（2）若ABC 的周长为6ABC 的面积．【答案】（1）516；（2【解析】（1）由余弦定理可求得cos A ；（2）根据正弦定理可得2c b =，再由已知和余弦定理可求得2b =，根据三角形的面积可求得答案.【详解】解：（1）因为22258b c a bc +-=，所以2225cos 216b c a A bc +-==；（2）因为sin 2sin C B =，所以2c b =．由余弦定理得2222152cos 4a b c bc A b =+-=，则a =，因为ABC 的周长为636b =2b =，所以ABC 的面积为122b b ⨯⨯【点睛】方法点睛：（1）在解三角形中，如果题设条件是关于边的二次形式，我们可以利用余弦定理化简该条件；（2）如果题设条件是关于边的齐次式或是关于内角正弦的齐次式，那么我们可以利用正弦定理化简该条件；（3）如果题设条件是边和角的混合关系式，那么我们也可把这种关系式转化为角的关系式或边的关系式.（4）与三角形有关的最值问题，我们可以利用基本不等式来求最值或利用正弦定理把边转化为关于角的三角函数式，再利用三角变换和正弦函数、余弦函数的性质求最值或范围.18．已知函数()2ππ2sin sin cos cos 44f x x x x x x ⎛⎫⎛⎫=+-+ ⎪ ⎪⎝⎭⎝⎭.(1)求()f x 的对称中心，并求当π0,2x ⎛⎫∈ ⎪⎝⎭时，()f x 的值域；(2)若函数()g x 的图像与函数()f x 的图像关于y 轴对称，求()g x 在区间()0,π上的单调递增区间.【答案】(1)对称中心：π1π,622k ⎛⎫-+ ⎪⎝⎭，k ∈Z ，值域：12⎛⎤- ⎥⎝⎦(2)5π11π,1212⎛⎫ ⎪⎝⎭【分析】（1）根据三角恒等变换，化简函数()f x ，再结合正弦型函数的对称中心公式，即可得到对称中心，结合正弦函数的图像即可求得其值域.（2）由（1）中()f x 的解析式，根据对称变换即可得到函数()g x 的解析式，再结合正弦型函数的单调区间即可求得结果.【详解】(1)因为函数()2ππ2sin sin cos cos 44f x x x x x x ⎛⎫⎛⎫=+-+ ⎪ ⎪⎝⎭⎝⎭222cos x x x x x x ⎫=+⎪⎪⎝⎭⎝⎭()221cos 2cos sin 22xx x x +=-+π1232x ⎛⎫++ ⎪⎝⎭令π2π,3x k k +=∈Z ，解得ππ62k x =-+，即对称中心π1π,622k k ⎛⎫-+∈ ⎪⎝⎭Z ，当π0,2x ⎛⎫∈ ⎪⎝⎭时，则ππ4π2,333x ⎛⎫+∈ ⎪⎝⎭，再结合三角函数图像可得()12f x ⎛⎤∈- ⎥⎝⎦所以，函数对称中心：π1π,622k ⎛⎫-+ ⎪⎝⎭，k ∈Z ，值域：12⎛⎤- ⎥⎝⎦.(2)因为函数()g x 的图像与函数()f x 的图像关于y 轴对称，则()()π1232g x f x x ⎛⎫=-=-++ ⎪⎝⎭，令ππ3π2π22π232k x k +≤-+≤+，k ∈Z ，解得7ππππ,1212k x k k -+≤≤-+∈Z 当1k =时，即为5π11π,1212⎛⎫ ⎪⎝⎭所以当()0,πx ∈时，()g x 的单调递增区间：5π11π,1212⎛⎫⎪⎝⎭.19．为进一步奏响“绿水青山就是金山银山”的主旋律，某旅游风景区以“绿水青山”为主题，特别制作了旅游纪念章，决定近期投放市场，根据市场调研情况，预计每枚该纪念章的市场价y （单位：元）与上市时间x （单位：天）的数据如下表：(1)根据上表数据，从下列函数中选取一个恰当的函数描述每枚该纪念章的市场价y 与上市时间x 的变化关系并说明理由：①(0)y ax b a =+≠，②()20y ax bx c a =++≠，③()log 0,0,1b y a x a b b =≠>≠，④(0)ay b a x=+≠； (2)利用你选取的函数，求该纪念章市场价最低时的上市天数及最低市场价；(3)利用你选取的函数，若存在()10,x ∈+∞，使得不等式()010f x k x -≤-成立，求实数k 的取值范围．【答案】(1)选择()20y ax bx c a =++≠，理由见解析(2)当该纪念章上市10天时，市场价最低，最低市场价为每枚70元 (3)k ≥【分析】(1)由表格数据分析变量x 与变量y 的关系，由此选择对应的函数关系；(2)由已知数据求出函数解析式，再结合函数性质求其最值；(3)不等式可化为()17010210x k x -+≤-，由条件可得()min 17010210x k x ⎡⎤-+≤⎢⎥-⎣⎦，利用函数的单调性求()17010210y x x =-+-的最小值，由此可得k 的取值范围． 【详解】(1)由题表知，随着时间x 的增大，y 的值随x 的增大，先减小后增大，而所给的函数(0)y ax b a =+≠，()log 0,0,1b y a x a b b =≠>≠和(0)ay b a x=+≠在(0,)+∞上显然都是单调函数，不满足题意，故选择()20y ax bx c a =++≠．(2)把()2,102，()6,78，()20,120分别代入2y ax bx c =++，得42102,36678,40020120,a b c a b c a b c ++=⎧⎪++=⎨⎪++=⎩解得12a =，10b =-，120c = ∴()221110120107022y x x x =-+=-+，,()0x ∈+∞． ∴当10x =时，y 有最小值，且min 70y =．故当该纪念章上市10天时，市场价最低，最低市场价为每枚70元． (3)令()()()1701010210f xg x x x x ==-+--(10,)x ∞∈+， 因为存在()10,x ∈+∞，使得不等式()0g x k -≤成立， 则()min k g x ≥．又()()17010210g x x x =-+-在(10,10+上单调递减，在()10++∞上单调递增，∴ 当10x =+()g x 取得最小值，且最小值为(10g +=∴k ≥20．己知函数21()2ln (21)(0)2f x x ax a x a =-+->．(1)若曲线(=)y f x 在点(1,(1))f 处的切线经过原点，求a 的值；(2)设2()2g x x x =-，若对任意(0,2]s ∈，均存在(0,2]t ∈，使得()()f s g t <，求a 的取值范围．【答案】(1)=4a ； (2)(0,1ln 2)-.【分析】（1）利用导数的几何意义求切线方程（含参数a ），由切线过原点求出a 的值； （2）利用导数研究()f x 的单调性并求出(0,2]上的最大值，由二次函数性质求()g x 在(0,2]上的最大值，根据已知不等式恒（能）成立求参数a 的范围.【详解】(1)由21()2ln (21)(0)2f x x ax a x a =-+->，可得2()21f x ax a x '=-+-．因为(1)2211f a a a '=-+-=+，13(1)21122f a a a =-+-=-，所以切点坐标为3(1,1)2a -，切线方程为：()311(1)2a y a x ⎛⎫--=+- ⎪⎝⎭， 因为切线经过(0,0)，所以3112aa -=+，解得=4a ． (2)由题知()f x 的定义域为(0,)+∞，21()[(21)2]f x ax a x x'=----，令()f x '=2(21)20ax a x ---=，解得1x a=-或=2x ， 因为0,a >所以10a-<，所以12a-<， 令()0f x '>，即2(21)20ax a x ---<，解得：12x a-<<，令()0f x '<，即2(21)20ax a x --->，解得：1x a<-或2x >，所以()f x 增区间为(0,2)，减区间为(2,)+∞．因为()22()211g t t t t =-=--，所以函数()g t 在区间(0,2]的最大值为0， 函数()f s 在(0,2)上单调递增，故在区间(0,2]上max ()(2)2ln 222f s f a ==+-， 所以2ln 2220a +-<，即ln 210a +-<，故1ln 2a <-， 所以a 的取值范围是(0,1ln 2)-.21．如图，在三棱柱111ABC A B C -中，1112,,AB AC AA AB AC A AB A AC ===⊥∠=∠，D 是棱11B C 的中点.(1)证明：1AA BC ⊥；(2)若三棱锥11B A BD -1A BD 与平面11CBB C 所成锐二面角的余弦值.【答案】(1)证明见解析【分析】（1）作出辅助线，由三线合一证明线线垂直，进而证明线面垂直，得到BC ⊥平面1AAO ，从而证明1AA BC ⊥；（2）作出辅助线，由三棱锥的体积求出1A H =用空间向量求解二面角；方法二：作出辅助线，找到二面角的平面角，再求解余弦值. 【详解】(1)取BC 中点O ，连接AO ，1AO ,1AC,因为AB AC =,所以AO BC ⊥,因为11A AB A AC ∠=∠，11,AB AC AA AA ==，所以11A AB A AC ≅，所以11A B AC =，所以1AO BC ⊥， 因为1AOAO O =，1,AO AO ⊂平面1AAO ， 所以BC ⊥平面1AAO ， 因为1AA ⊂平面1AAO ， 所以1AA BC ⊥；(2)连接OD ，则平面1AAO 即为平面1AA DO ， 由（1）知BC ⊥平面1AA DO ，因为BC ⊂平面ABC ，且BC ⊂平面11BCC B ， 故平面1AA DO ⊥平面ABC ，平面1AA DO ⊥平面11BCC B ，过O 作1OM A D ⊥于M ，则OM ⊥平面ABC ，过1A 作1A H OD ⊥于H ，则1A H ⊥平面11BCC B ，因为11DO BB AA ∥∥知DO BC ⊥，在ABC中：2,AB AC BC ===所以1112BDB S DB DO =⋅△所以111111113B A BD A BDB BDB A A V V S h --==⋅==△，所以11A A H h = 法一：设MOD α∠=，则1DA H α∠=，在1Rt A HD △中11cos A H A D α===所以sin cos DM DO OM OD αα=⋅==⋅=又1A D M 为线段1A D 的中点，以O 为原点，分别以,,OA OB OM 分别为x ，y ，z 轴正方向建立空间直角坐标系，1(0,A B C A ⎝⎭，1,2222B D ⎛⎛ ⎝⎭⎝⎭， 设面1A BD 的法向量为()1111,,x n y z =，则有111111*********n BA xn BD x⎧⋅==⎪⎪⎨⎪⋅=-=⎪⎩，两式相减得：10x =，所以110=，令12z =，可得：1y = 所以1(0,7,2)n =，设面11CBB C 的法向量为()2222,,n x y z =，则有221122220202n CB n CB ⎧⋅==⎪⎨⋅=-=⎪⎩， 解得：20y =，令21z =，解得：2x =所以2(7,0,1)n=， 设锐二面角为θ，则有1212cos 4n n n n θ⋅===+⋅. 法二：过H 做HE BD ⊥，连接1A E ，1A H ⊥面11BCC B，1A H DB ∴⊥，则DB ⊥面1AHE ，1A E BD ∴⊥，则1A EH ∠即为所求二面角.在1Rt A DH △中，11A H A D =12DH =，在Rt DOB 中，2,DO OB DB == 由RtRt DEHDOB 可得：HE DHOB DB=，HE ∴=，则1A E =11cos HE A EH A E ∴∠===22．己知函数()e sin 1(0)x f x a x a =-->在区间(0,)π内有唯一极值点1x ． (1)求实数a 的取值范围；(2)证明：()f x 在区间(0,)π内有唯一零点2x ，且212x x <． 【答案】(1)(1,)∈+∞a (2)证明见解析【分析】（1）根据极值点的定义，求导，进而求导函数的零点，研究零点左右与零大小关系，可得答案；（2）由（1）明确函数的单调区间，分别在两个单调区间上，利用零点存在性定理，证明零点唯一存在，根据单调性证明不等式成立. 【详解】(1)()e cos x f x a x '=-，①当01a <≤时，因为()0,x π∈，所以cos 1a x <，1e e x π<<，()0f x '>，()f x 在()0,π上单调递增，没有极值点，不合题意，舍去；②当1a >时，令()=()g x f x '，则()e sin x g x a x '=+，因为()0,x π∈，所以()0g x '>，所以()f x '在()0,π上递增，又因为(0)10f a '=-<，2e 02f ππ⎛⎫'=> ⎪⎝⎭，所以()f x '在()0,π上有唯一零点1x ，且10,2x π⎛⎫⎪⎝⎭∈，所以()10,x x ∈，()0f x '<；1,2x x π⎛⎫∈ ⎪⎝⎭，()0f x '>，所以()f x 在()0,π上有唯一极值点，符合题意. 综上，(1,)∈+∞a .(2)由（1）知1a >，所以,2x ππ⎡⎫∈⎪⎢⎣⎭时，()e cos 0x f x a x '=->，所以()10,x x ∈，()0f x '<，()f x 单调递减；()1,x x π∈，()0f x '>，()f x 单调递增，所以()10,x x ∈时，()(0)0f x f <=，则()10f x <，又因为()e 10f ππ=->， 所以()f x 在()1,πx 上有唯一零点2x ，即()f x 在(0,)π上有唯一零点2x .因为()112211112e sin 21e 2sin cos 1x xf x a x a x x =--=--，由（1）知()10f x '=，所以11e cos x a x =，则()112112e 2e sin 1x x f x x =--，构造2()e 2e sin 1,0,2t tp t t t π⎛⎫=--∈ ⎪⎝⎭，所以()2()2e 2e (sin cos )2e e sin cos t t t tp t t t t t '=-+=--，记()e sin cos ,0,2tt t t t πϕ⎛⎫=--∈ ⎪⎝⎭，则()e c o s s i n t t t t ϕ'=-+，显然()t ϕ'在0,2π⎛⎫⎪⎝⎭上单调递增，所以()(0)0t ϕϕ''>=，所以()t ϕ在0,2π⎛⎫ ⎪⎝⎭上单调递增，所以()(0)0t ϕϕ>=，所以()0p t '>，所以()p t 在0,2π⎛⎫⎪⎝⎭上单调递增，所以()(0)0p t p >=，所以()()1220f x f x >=，由前面讨论可知：112x x π<<，12x x π<<，且()f x 在()1,x x π∈单调递增，所以122x x >.【点睛】在利用导数证明不等式成立时，一定明确单调区间，在同一单调区间上，由函数值的大小关系，可得自变量的大小关系，探究函数的单调性，可通过研究导数过着导数中部分代数式所构成函数的单调性，求其最值，可得函数的单调性.。

2022-2023学年度高三第二次月考 数学试题第I 卷一、单选题1．已知集合，则（ ） A ．[]4,1--B ．[)4,3-C ．[)1,3-D ．[]1,3-2．已知函数()2ln 1f x mx x =++的图像在()()1,1f 处的切线过点()2,8，则m =（ ）A ．53B ．2C ．3D ．43．已知，条件，条件，则是的 A ．充分不必要条件 B ．必要不充分条件 C ．充要条件 D ．既不充分也不必要条件4．若函数()21ln 2f x x ax x =--在区间()1,2内有最小值，则实数a 的取值范围为（ ） A ．()0,1B ．12,23⎛⎫ ⎪⎝⎭C ．30,2⎛⎫ ⎪⎝⎭D ．31,2⎛⎫ ⎪⎝⎭5．已知定义在R 上的函数为偶函数，当时，则不等式的解集为 A ．1,2⎛⎤-∞ ⎥⎝⎦B ．(],2∞-C ．[)2,∞+D ．1,2⎡⎫+∞⎪⎢⎣⎭6．函数()()()21ln 2ln 2x f x x x -=+--的大致图象是（ ）A ．B ．C ．D ．7．若0pq ≠，直线1y px =+与曲线3e qx y -=相切于点()00,x y ，则0x =（ ）二、多选题三、填空题15．已知有偶函数()f x ，奇函数()g x ，且有()()e xf xg x +=，则()f x 的值域为____________.16．已知函数()f x 的导函数为()f x '，若()(),e 0,1e 1xx f x f <'∀∈-=-R ，则关于x的不等式()ln 1f x x >-的解集为______.四、解答题17．已知R a ∈，集合R M =，{}2230N x ax ax =+-<(1)若1a =，求集合N （用区间表示）； (2)若M N ，求实数a 的取值范围. 18．已知函数，且．求：(1)a 的值及曲线()y f x =在点(1,(1))f 处的切线方程； (2)函数()f x 在区间[]0,2上的最大值． 19．已知函数，(1)若[]1,1x ∃∈-，方程()0f x m -=有解，求实数m 的取值范围；(2)若对任意的[]11,4x ∈，总存在[]21,4x ∈，使得()()12f x g x ≤，求实数a 的取值范围； (3)设()()()h x f x g x =+，记()M a 为函数()h x 在[]0,1上的最大值，求()M a 的最小值.20．已知函数333()log log (9)f x x x=⋅.(1)求函数()f x 的值域； (2)求不等式()4f x <-的解集.21．为进一步奏响“绿水青山就是金山银山”的主旋律，某旅游风景区以“绿水青山”为主题，特别制作了旅游纪念章，并决定近期投放市场.根据市场调研情况，预计每枚纪念章的市场价y （单位：元）与上市时间x （单位：天）的数据如下表. 上市时间x /天 2632 市场价y /元148 6073(1)①0ay b a =+≠①log 0,0,1y a x a b b =≠>≠，①变化关系（无需说明理由），并求出该函数的解析式；(2)利用你选取的函数，求该纪念章市场价最低时的上市天数及每枚纪念章的最低市场价.22．已知()e 1,()(1)1(0,e x f x a ax g x a x a =-+=-+≠为自然对数的底数). (1)讨论函数()f x 的单调性； (2)若函数有两个不同零点，求证：参考答案：M N x=-{|故选：C.【分析】结合导数求出切线方程，将【详解】由，必定存在极值点，由24a =+>2x <，故只需要32a <<. 2yx 为增函数，为偶函数，所以，故11x --所以()f x 的值域为[)1,+∞.故答案为：16．()0,e【分析】构造函数()()e x g x f x =-，结合已知不等式及导数与单调性关系可求()g x 的单调性，结合函数的单调性即可求解不等式.【详解】令()()e x g x f x =-，则()()e x g x f x ''=-，因为对(),e 0x x f x ∀-'∈<R ，所以函数()g x 在R 上单调递减，又因为()1e 1f =-，所以(1)1g =-，则有ln (ln )(ln )e (ln )x g x f x f x x =-=-，所以(ln )(ln )f x g x x =+，由()ln 1f x x >-可得(ln )1g x x x +>-，即(ln )1(1)g x g >-=，所以ln 1x <，解得0e x <<，所以关于x 的不等式()ln 1f x x >-的解集为(0,e)， 故答案为：17．(1)()3,1N =-，(2)(]3,0-.【分析】（1）代入1a =，解一元二次不等式，将解集写成区间形式即可；（2）若M N ，表示不等式恒成立，所以分成0a =和0a ≠两种情况讨论，求解不等式，即可得到实数a 的取值范围．【详解】（1）当1a =时，由2230x x +-<，得(1)(3)0x x -+<，解得31x -<<，所以()3,1N =-.（2）①当0a =时，此时30-<成立，①当0a ≠时，因为2230ax ax +-<的解集为R ，所以20Δ4120a a a <⎧⎨=+<⎩，解得30a -<<4a时，g综上，a的取值范围为()9,⎫+∞⎪⎭（1）由对数运算法则化简函数式后，把log x 作为一个整体，解一元二次不等式，然后再解对数不等式可得．()9,⎫+∞⎪⎭.*N 天时，市场价最低，最低市场价为每枚）根据表中数据的关系可选则()()00t ϕϕ>=，即()()00m t m ''>=，①()m t 在()0,∞+上单调递增，①()()00m t m >=，即()2e 20t t t -++>成立，①122x x +>.【点睛】方法点睛：利用导数证明不等式问题，方法如下：（1）直接构造函数法：证明不等式()()f x g x >（或()()f x g x <）转化为证明()()0f x g x ->（或()()0f x g x -<），进而构造辅助函数()()()h x f x g x =-； （2）适当放缩构造法：一是根据已知条件适当放缩；二是利用常见放缩结论；（3）构造“形似”函数，稍作变形再构造，对原不等式同解变形，根据相似结构构造辅助函数.。

高三语文月考试题答案和解析一、现代文阅读1．【答案】A【解析】A项“上下章在思想上也几乎没有任何联系”有误，原文是“上下章几乎没有任何联系”，侧重的是说篇幅上，思想上还是有联系的。

2．【答案】C【解析】C项“只有聪明的读者才能发掘出诗的言外之意和书的行间之意”并不成立，作者引用“好诗‘言有尽而意无穷’”意在说明正是中国哲学家把自己丰富的思想寄予在精炼简短语言中，读者才可能读出新意来。

3．【答案】D【解析】中国哲学家表达自己思想的方式强调暗示但并不意味着对语言作用的排斥，原文也无此表述，由后文“它可以与《老子》原书对照着读，也可以对人们理解原书大有帮助，但是它永远不能取代原书”也可看出D项表述的不妥。

二、古代诗文阅读（一）文言文阅读（19分）4．B（饵：诱捕）5．B（排除②③⑥，②是徐文长的游历与创作，③是徐文长才思敏捷，⑥是徐文长因狂疾自残）6．C（“在酒筵上对胡公出语不敬”有误，应是“和尚行为不轨，徐文长在喝酒时偶尔对胡公提起”）7．（1）如果要聘我为幕客，必须用接待宾客的礼节，（并且）不规定时间，让我能自由进出。

（2）文长都大声地呵斥，把他们看作奴才，以和他们结交为耻辱而不来往，因此他的名声没有流传出越地以外。

（二）古代诗歌阅读（11分）8．这两句诗描写了秋风微拂，树叶掉落、花瓣飞舞的景象。

作者融情于景，用“鸟惊”“花翔”的情感化描写，传达出作者因秋风吹动而内心惊动、思绪飘远的思乡之情。

9．作者身在异乡，在秋风中，思乡之情油然而生。

醉酒后听到吴人的歌声，心里产生错觉，误认为梦中回到了故乡。

此字化无形为有形，生动传神地表达了作者的思乡之情。

10．(1) 百步九折萦岩峦以手抚膺坐长叹(2) 耳得之而为声取之无禁(3)己所不欲勿施于人三、文学类文本阅读（25分）11. (1)【答案】D（3分）B （2分）A（1分）。

【解析】本题主要考查学生对小说有关内容的分析和概括能力。

A．万众瞩目”有夸张意，而选项中的表意属于写实；题目还有吸引读者的作用。

山东实验中学2024年高三下学期第二次月考试题英语试题试卷请考生注意：1．请用2B铅笔将选择题答案涂填在答题纸相应位置上，请用0．5毫米及以上黑色字迹的钢笔或签字笔将主观题的答案写在答题纸相应的答题区内。

写在试题卷、草稿纸上均无效。

2．答题前，认真阅读答题纸上的《注意事项》，按规定答题。

第一部分（共20小题，每小题1.5分，满分30分）1．---I’m sure Andrew will win the first prize in the final.---I think so. He _____ for it months.A．is preparing B．has been preparing C．was preparing D．had been preparing2．The farmer used wood to build a house ________ to store grain.A. thatB. in whichC. whichD. what3．If you ___________ to my advice carefully, you would n’t have made such a terrible mistake.A．listened B．have listenedC．would listen D．had listened4．The foreigners here are greatly impressed by the fact that _______ people from all walks of life are working hard for ________ new Tianjin.A．/; a B．/; theC．a; a D．the; the5．The people succeeded because they understood that you can’t let your failures _________ you ——you have to let your failures teach you.A．define B．declineC．qualify D．simplify6．They have leading experts in this field, and that's ____ they've made important progress.A．where B．why C．whether D．who7．My daughter, _________ all kinds of meat, would not like to eat any vegetable, which worries me a lot. A．devoted to B．addicted to C．accustomed to D．exposed to8．－Do you really mean it when you say he will a good president?A．judge B．duit C．turn D．Serve9．________about the man wearing sunglasses during night that he was determined to follow him.A．So curious the detective wasB．So curious was the detectiveC．How curious was the detectiveD．How curious the detective was10．Jane is not good at sports，but when it to cooking，she’s excellent．A．happens B．comes C．does D．occurs11．_____ the plant once a week if you are to get fruit in the autumn.A．Watered B．Watering C．To water D．Water12．Many netizens are impressed with the excuse given by a teacher for quitting her job ______ she owes the world a visit.A．because B．that C．where D．why13．—I’m burnt out as I’ve been working on my essay all the time.—____________. You’ll surely make it.A．Don’t put on airs B．Give me a breakC．Don’t get on my nerve D．Hang in there14．---We want someone to design the new art museum for me.---_____ the young fellow have a try?A．Shall B．May C．Will D．Need15．—Jenny，how did your math exam go?—I thought I ________，but in fact I came in the top 10% in the class.A．might have failed B．couldn’t have failed C．should have failed D．mustn’t have failed16．—I'm going to order chicken and salad．What about you?—.I'll have the same.A．I'm afraid not B．It's up to youC．That sounds good to me．D．That depends17．Had Mary not been hurt in the car accident, ________ the next week’s marathon.A．she would run B．she would have runC．she will run D．she must have run18．As to the long-term effects of global warming some believe that the damage has been done,______________________.A．otherwise we take steps to make up nowB．now that we take steps to make upC．whether we take steps to make up now or notD．unless we take steps to make up now19．English is a language shared by several diverse cultures, _________ uses it differently.A．all of which B．each of which C．all of them D．each of them20．During the period of recent terrorist activities, people _____ not to touch an unattended bag.A．had always been warned B．were always being warnedC．are always warning D．always warned第二部分阅读理解（满分40分）阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项。

深圳2024-2025学年度高三第一学期第二次月考物理试题（答案在最后）卷面满分100分，考试用时75分钟。

注意事项：1.答卷前，考生务必将自己的姓名、准考证号码填写在答题卡上。

2.作答时，务必将答案写在答题卡上。

写在本试卷及草稿纸上无效。

3.考试结束后，将答题卡交回。

一、单项选择题：本题共7小题，每小题4分，共24分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1.深中通道是国家重大工程和世界级跨海集群工程，全长约24千米，北距虎门大桥约30千米，小明计划周末从家坐车去深圳宝安机场，他事先用导航软件搜索路线，若选择走A路线，经过虎门大桥，路程约103千米，耗时约1小时50分钟；若选择走B路线，经过深中通道，路程约53千米，耗时约1小时10分钟，假设汽车实际行驶路程和时间与导航软件预计的相同，则下列说法正确的是（）A.汽车通过两条路线的平均速度相同B.汽车通过A路线的平均速度更大C.汽车通过A路线的位移更大D.汽车通过A路线的平均速率更大2.如图，潜艇从海水的高密度区驶入低密度区过程称为“掉深”。

图a，某潜艇在高密度区水平向右匀速航行；t=0时，该捞艇开始“掉深”，图b为其竖直方向的速度时间图像，水平速度v保持不变。

若以水平向右为x轴，竖直向下为y轴，则带艇“掉深”后的0~30s内。

能大致表示其运动轨迹的图形是（）A. B.C. D.3.2023年的春晚舞蹈《锦绣》，艺术地再现了古代戍边将士与西域各民族化干戈为玉帛并建立深厚友谊的动人故事。

图（a ）是一个优美且难度极大的后仰动作，人后仰平衡时，可粗略认为头受到重力G 、肌肉拉力2F 和颈椎支持力1F 。

如图（b ），若弯曲后的头颈与水平方向成60︒角，2F 与水平方向成45︒角，则可估算出1F 的大小为（）A.)1G +B.)1G -C.)2GD.)2G -4.图甲是北京冬奥会单板滑雪大跳台比赛项目中运动员在空中姿态的合成图。

比赛场地分为助滑区、起跳台、着陆坡和终点区域四个部分。

湖南省邵阳市邵东市第一中学2024-2025学年高三上学期第二次月考英语试题一、阅读理解Investment CompetitionAbout the CompetitionThe Wharton Global High School Investment Competition is a free, online investment simulation (模拟) for high school students(9th to 12th grade)and teachers. Students work in teams of four to seven, guided by a teacher as their advisor (顾问). Together, they learn about teamwork, communication, risk, companies and industry analysis and many other important aspects of investing.Teams examine a brief case study featuring a potential client and are tasked with working closely to meet that client’s long term investment goals. Equipped with an approved stock list and the Wharton Investment Simulator (WInS), which allows them to simulate (模拟) stock trading, students develop an investment strategy, analyze sectors and companies, and build a portfolio (投资组合) using $ 100 ,000 in virtual cash provided by WInS over the course of 10 weeks. Winners are selected on the strength of their team strategies, not on the growth of their portfolios.Results Final reports are reviewed by a team of judges, who select 50 semi-finalist teams. Those teams are invited to present their strategies to a panel of expert judges at the virtual semifinals. The top 10 teams from the semifinals move on to the final of the competition, the Global Finale, at Wharton in Philadelphia.Please RememberOnce advisors register for the competition, they will receive a confirmation email with instructions to set up their student team accounts on WInS, our trading platform. Student team accounts must be set up no later than September 20, 2023. In order to complete the registration form, advisors will need to:•Choose the username and password for their advisor accounts.•Provide their school-issued email address, as well as a back-up email address where all competition communications will be sent.1．What’s the function of WInS?A．Offering virtual cash.B．Studying some brief cases.C．Making people win business.D．Understanding clients’ requirements. 2．What can we know about the Global Finale?A．All final reports must be delivered to it.B．It’s the highest level of the competition.C．It’s a final graded by clients’ opinions.D．About fifty teams can participate in it.3．What should advisors do after registering for the competition?A．Send a confirmation email to judges.B．Guide students to create their own accounts.C．Ensure team members are from the same school.D．Build the student team accounts on the specific platform.In the mid-1990s, Tom Bissell taught English as a volunteer in Uzbekistan. He left after seven months, physically broken and having lost his mind. A few years later, still attracted to the country, he returned to Uzbekistan to write an article about the disappearance of the Aral Sea.His visit, however, ended up involving a lot more than that. Hence this book, Chasing the Sea: Lost Among the Ghosts of Empire in Central Asia, which talks about a road trip from Tashkent to Karakalpakstan, where millions of lives have been destroyed by the slow drying up of the sea. It is the story of an American travelling to a strange land, and of the people he meets on his way: Rustam, his translator, a lovely 24-year-old who picked up his colorful English in California, Oleg and Natasha, his hosts in Tashkent, and a string of foreign aid workers.This is a quick look at life in Uzbekistan, made of friendliness and warmth, but also its darker side of society. In Samarkand, Mr Bissell admires the architectural wonders, while on his way to Bukhara he gets a taste of police methods when suspected of drug dealing. In Ferghana, he attends a mountain funeral(葬礼)followed by a strange drinking party. And in Karakalpakstan, he is saddened by the dust storms, diseases and fishing boats stuck miles from the sea.Mr Bissell skillfully organizes historical insights and cultural references, making his tale a well-rounded picture of Uzbekistan, seen from Western eyes. His judgment and references are decidedly American, as well as his delicate stomach. As the author explains, this is neither a travel nor a history book, or even a piece of reportage. Whatever it is, the result is a fine and vividdescription of the purest of Central Asian traditions.4．What made Mr Bissell return to Uzbekistan?A．His friends' invitation.B．His interest in the country.C．His love for teaching.D．His desire to regain health.5．What does the underlined word “that” in paragraph 2 refer to?A．Developing a serious mental disease.B．Taking a guided tour in Central Asia.C．Working as a volunteer in Uzbekistan.D．Writing an article about the Aral Sea.6．Which of the following best describes Mr Bissell's road trip in Uzbekistan?A．Romantic.B．Eventful.C．Pleasant.D．Dangerous. 7．What is the purpose of this text?A．To introduce a book.B．To explain a cultural phenomenon.C．To remember a writer.D．To recommend a travel destination.The launch of a tool to record a vanishing Greek dialect drew attention back this week to one of the great extinctions of the modern world: nine languages are believed to be disappearing every year. Romeyka, which is spoken by an ageing population of a few thousand people in the mountain villages near Turkey’s Black Sea coast, separated from modern Greek thousands of years ago. It has no written form. For linguists, it is a“ living bridge” to the ancient Greek world, the loss of which would clearly be a blow.But some languages are in even bigger trouble, with 350 that have fewer than 50 native speakers and 46 that have just one. A cooperation between Australian and British institutions paints the situation in distinct colours, with a language stripes chart, devised to illustrate the accelerating decline in each decade between 1700 and today. Its authors predict that between 50% and 90% of the world’s 7,000 languages will be extinct by 2150. Even now, half of the people on the planet speak just 24 of them.The history of languages has always been linked to colonialism (殖民主义) and political persecution (迫害), which scatter populations as well as controlling them. The Endangered Languages Alliance (ELA) has tracked down and mapped hundreds of dying languages in NewYork, which is an unexpected discovery. These dialects are supposed to be found in remote rural areas. Among ELA’s more shocking discoveries is that, of 700 surviving speakers of Seke, which originated in a cluster of mountain villages in Nepal, more than 150 can be traced to two apartment buildings in Brooklyn district of New York.From Sami reindeer herders across the Arctic to Australia’s Indigenous (土著的) peoples, the ways in which people express themselves hide secret messages about ancient ways of living in nature. Both a will and a way are needed if they are to survive. By simply honouring their existence, linguists play an important role. Ken Hale, an activist who is strongly for preserving endangered languages famously argued that losing any language was “like dropping a bomb on the Louvre”.8．What does “Romeyka” in Paragraph 1 refer to?A．An extinct ancient Greek language.B．A language with very few written words.C．A disappearing dialect related to ancient Greek.D．A popular dialect loved by the young generation.9．Why are the numbers used in Paragraph 2?A．To show the importance of the dialects.B．To conclude the diversity of the dialects.C．To explain different ways to protect dialects.D．To illustrate the tendency of fast dying dialects.10．What can we infer from Paragraph 3?A．Seke is a place in the mountains of Nepal.B．People assume fewer dialects exist in big cities.C．Nepal and New York were twin cities many years ago.D．ELA is not surprised to trace an original Nepal dialect to Brooklyn.11．What does Ken Hale’s quote mean?A．The extinction of a dialect is a great loss.B．Bombing Louver is a disaster to any language.C．Ancient ways of living are kept secret in Louvre.D．Languages are to survive simply by honoring them.In the threatening trouble of climate change, growing commercial crops on solar farms is a potentially efficient use of agricultural land that can both increase commercial food production and improve solar panel performance and longevity(寿命), according to a new Cornell research.“We now have, for the first time, a physics-based tool to estimate the costs and benefits of co-locating solar panels and commercial agriculture in terms of increased power conversion efficiency and solar-panel longevity, ” said lead author Henry Williams, a doctoral student in Cornell Engineering.“There is potential for agrivoltaic (农业光伏) systems-where agriculture and solar panels coexist-to provide increased passive cooling through taller panel heights, more reflective ground cover and higher evapotranspiration (蒸散) rates compared to traditional solar farms,” said Max Zhang, professor in the Sibley School of Mechanical and Aerospace Engineering, “We can generate renewable electricity and conserve farmland through agrivoltaic systems.” In New York, for example, about 40% of solar farm capacity has been developed on agricultural lands, while about 84% of land suitable for solar development is agricultural, according to a previous research study from Zhang’s group.The engineers showed that solar panels mounted over vegetation reveal surface temperature drops compared to those built over bare ground. Solar panels were mounted 4 meters above a cotton crop and the solar panels showed temperature reductions by up to 10 degrees Celsius, compared with those mounted a half-meter above bare soil.“As you decrease the solar panel operating temperature, you can increase efficiency and improve the longevity of your solar panels, ” said Williams, “We’re showing double benefits. On one hand, you have food production for farmers, and on the other hand, we’ve shown improved longevity and improved conversion efficiency for solar developers.”“Up to this point, most of the benefits from agrivoltaic systems have been around areas with abundant sunshine, ” said Zhang, “This research is taking a step toward evaluating the application of agrivoltaics in climates representative of the Northeastern U. S. in relaxing the land-use competition it faces.”12．What does the new Cornell research convey?A．Growing commercial crops can relieve climate change.B．It’s costly to improve solar panel performance and longevity.C．Commercial agriculture can increase power conversion efficiency.D．The coexistence of solar panels and commercial crops is mutually beneficial.13．Why does the author list the figures in paragraph 3?A．To show the promising future of agrivoltaics.B．To indicate the lack of solar farms in New York.C．To tell agricultural lands are based on solar farms.D．To demonstrate agricultural farms are more developed.14．What can be inferred from the last paragraph?A．The Northeastern US is rich in agricultural lands.B．Hot climate zones are ideal for developing agrivoltaics.C．The research made a breakthrough in land-use competition.D．The application of agrivoltaics in Northeastern US proved practical.15．Which is a suitable title for the text?A．Approaches to Tackling World Climate ChangeB．Methods of Increasing Agricultural ProductionC．Agrivoltaics Have Been Well Received in the USD．Growing Crops at Solar Farms Generates Higher EfficiencySETTING A GOAL OF PAINTINGYou’ll find that having a clear goal when you go out painting will make you a better painter, faster. 16 The goals are as follows.Explore an area. 17 . When in Scotland for the first time, I didn’t know what to paint. So, rather than making finished paintings, I focused on just sketching (素描) the things that were new to me. It’s a relaxing approach to painting, and it helps you get familiar with a strange land.18 . It’s like exploring, but with more focus. On my Scotland trip, I became fond ofa beautiful, ancient stone bridge and knew I wanted to make a big painting of it when I got home. I collected color studies in gouache (水粉画), pencil sketches and photos. Once home, where I had all the tools and materials ready, I was able to create that larger work.Work on a skill or problem. This is usually a workshop goal, but you can do it on your own.If you don’t understand color temperature, consider making color studies in different temperature.19 : Is it true that white in shadow is darker than black in light? See for yourself by observing and painting such a situation.Create a finished painting. This can be a difficult task compared to the others. You have to be at the top of your game, employing good design, good color and good edge treatment. I usually do this for open-air contests or when I’m practicing for one. Many artists, however, often enjoy bringing a painting fully to completion at the scene. 20A．Have a good tripB．Gather reference materialsC．Before this you’d better make a planD．This is what I do if I’m in unfamiliar areaE．Or you may have a question you want to answerF．It takes experience, time and energy and plenty of coffeeG．Consider having one of four simple goals before heading out二、完形填空As a first-generation Asian immigrant (移民) who had grown up in poverty, I knew I was beyond 21 to be admitted into Harvard. I loved books, but it never crossed my mind to become a(n) 22 of any sort. I didn’t 23 to have unrealistic dreams.Still, something 24 me. My deskmate had 25 our friendship recently. There wasn’t a dramatic fight or disagreement. He had 26 moved on to new friends. I felt an ache in my chest that 27 night. I started doodling (涂鸦) on my notepad and then, suddenly, my hand started writing words. I’d written a poem about him. There on the page was the truth about how much it hurt to 28 him.That tiny poem was a 29 that rooted in my heart. I realized I could possibly become a writer and from that moment on, it was all I 30 to do. So I changed my field of study to English. I 31 my first short stories while I was still a student. I went on to write my first novel, Girl in Translation, which became an international 32 and is taught in schools around the world.That night, I learned that art isn’t a 33 . It’s at the core of what makes us human. Although I’d believed that immigrants couldn’t afford to be 34 , I understood then that we had always been the ultimate artists, 35 ourselves again and again as we try to adapt to a new landscape.21．A．innocent B．fortunate C．dependent D．voluntary 22．A．surgeon B．lawyer C．artist D．engineer 23．A．expect B．regret C．agree D．refuse 24．A．bothered B．inspired C．interested D．satisfied 25．A．adapted to B．shown off C．broken off D．referred to 26．A．unwillingly B．cautiously C．helplessly D．simply 27．A．fancy B．peaceful C．happy D．lonely 28．A．marry B．upset C．lose D．desert 29．A．romance B．seed C．secret D．shadow 30．A．hesitated B．resolved C．declined D．pretended 31．A．bought B．borrowed C．priced D．published 32．A．gap B．effort C．challenge D．bestseller 33．A．necessity B．luxury C．game D．reality 34．A．practical B．reliable C．energetic D．creative 35．A．rescuing B．recreating C．recovering D．relaxing三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

湖南省湖南师范大学附属中学2024-2025学年高三上学期第二次月考英语试题一、阅读理解The Virgin Islands National Park is a tropical (热带的) paradise on the island of St. John,which covers more than half of the small island.It is surrounded by the Atlantic Ocean to the north and the Caribbean Sea to the south,where the climate is warm all year.The island's white sand beaches and clear blue seas are considered to be among the most beautiful in the Caribbean,gaining reputation and popularity among visitors across the world.How the national park was formedLaurence Rockefeller was an American millionaire,businessman and conservationist.He visited St.John in the 1950s. He quickly fell in love with the island's clean, pure beauty.He first purchased a small resort there, Caneel Bay. He also purchased more than 2,000 hectares of the island and donated it to the government.That donation created the U.S.Virgin Islands National Park.It was officially opened as a national park on December 1, 1956.How to get to the parkThe only way to reach the park is by boat. Some people arrive on their own sailboats. Others come in on large cruise ships.Visitors also arrive on water taxis from the island of St. Thomas.What to do at the parkFrom the tropical hills to the blue waters,there are many things to do at the Virgin Islands National Park. Visitors enjoy fishing,camping,sailing,scuba diving, snorkeling (浮潜), and bird watching. Of all of the park's beaches, Trunk Bay Beach is said to be the most striking. Below the clear blue water is a 200-meter snorkeling path. Hawksnest Beach is also a popular place for snorkeling. Near the shore are three small reefs of Elkhorn Coral. The Elkhorn Coral gets its name from its shape. The reef looks similar to the huge horns (角) of an animal called elk. It is a very rare kind of reef.Scientists say it is in danger of becoming extinct.The Virgin Islands National Park is often called America's paradise. It protects St. John's pristine nature, and preserves the record of human history in the Caribbean.Don't hesitate! Come here and put yourself in the paradise!1．What is most likely attractive to tourists when they visit the Virgin Islands National Park?A．Its tropical climate.B．Its location.C．Its beautiful scenery.D．Its activity.2．What can we learn about the Virgin Islands National Park?A．An animal called elk is at risk of becoming dying out.B．Visitors can choose any means of transportation to get to the park.C．Laurence's donation greatly contributed to the foundation of the park.D．There is a 200-meter snorkeling path beneath the water of the Hawksnest Beach. 3．Where is the text probably taken from?A．A speech script.B．A travel brochure.C．An academic essay.D．A geographic journal.Boeing’s Starliner spacecraft landed in a New Mexico desert late on Friday,months after its original departure date and without the two astronauts it carried when it launched in early June.The Nasa astronauts Suni Williams and Butch Wilmore should have flown the Starliner back to Earth in June, a week after launching in it.But thruster (推进器) failures and helium (氦气) leaks marred their ride. Instead, they will remain at the International Space Station (ISS) for the rest of the year and will return in February aboard the SpaceX Dragon spacecraft.Nasa ultimately decided it was too risky to return Williams and Wilmore on the Starliner. So the capsule contains their empty seats and blue spacesuits along with some old station equipment.After Nasa’s space shuttles were retired more than a decade ago, Nasa hired Boeing and SpaceX for orbital (轨道的) taxi service. Boeing ran into so many problems on its first test flight with no one onboard in 2019 that it had to repeat it. The 2022 do-over uncovered even more flaws and the repair bill topped $1.5bn.The Starliner finally blasted into space on 5 June from Florida’s Cape Canaveral Space Force Station after unsuccessful launches on 6 May and 1 June. On the first launch attempt,a problem was found with a valve (阀门) on the second stage,or upper portion, of the rocket. On the second,a computer tripped an automatic hold just three minutes and 50 seconds from liftoff. Thatwas later attributed to a single ground power supply fault within one of the launch control computers.Even after it successfully launched,helium leaks continued to trouble the spacecraft. As the Starliner approached the ISS, two leaks were detected but Nasa determined the spacecraft remained stable. What started as an eight-day mission dragged on for three months after the leaks and faulty thrusters raised safety concerns.However, Nasa and Boeing officials insisted that the astronauts were not trapped and that the technical difficulties did not threaten the mission. “We’ll come home when we’re ready,” Steve Stich, Nasa’s commercial crew program manager, said in the press conference in July.4．What does the underlined word “marred” in paragraph 2 mean?A．Underwent.B．Stimulated.C．Facilitated.D．Blocked.5．What do we know about Boeing’s spacecraft launches?A．They were filled with delays and setbacks.B．Starliner’s initial launch went smoothly.C．The 2019 manned spaceflight was a failure D．Reasons of the problems were still unidentified.6．Why didn’t the two astronauts come back to Earth on time?A．Because the project went over the original budget.B．Because they were both in serious health conditions.C．Because it was dangerous to take the Starliner then.D．Because Nasa officials failed to reach an agreement.7．What can be implied according to the last two paragraphs?A．The two astronauts would come back soon.B．Officials considered the situation within control.C．Nasa officials were pessimistic and pressed.D．The mission would be completed in 3 months.Actor Alicia Silverstone worried fans on social media recently. While on a trip to England, she posted a TikTok video of herself tasting a kind of poisonous berries she found along a sidewalk. Silverstone, who appeared in the 1995 movie Clueless, said she thought the fruit was atomato. But when she bit into it and found that it had an unusual taste, she realized that it was not the common food.Plant expert, Jessica Damiano, recently wrote about poisonous plants that look like common foods for the Associated Press. She said the fruit that looked like a tomato appears to have been a Jerusalem cherry.Often sold as a houseplant, all parts of the Jerusalem cherry are poisonous.The American Society for the Prevention of Cruelty to Animals says the plant is not only harmful to humans but also to dogs, cats and horses.Eating large amounts can be deadly. Silverstone was lucky because she did not swallow the berries. She was also lucky because the berries were reddish orange, which meant they were ripe. While all parts of the Jerusalem cherry are poisonous, the plant’s unripe berries can be especially dangerous.They can cause problems with the central nervous and gastrointestinal (肠胃的) systems.The Jerusalem cherry is not the only toxic plant that looks like a safe one.The poisonous Carolina horsenettle fruit also looks like a tomato. It is also known as devil’s potato to add to the confusion.The Virginia creeper fruit also looks like blueberries, and it can be deadly if eaten.Wild parsnip has flowers like a carrot and leaves like parsley (欧芹). Simply touching it can cause a skin problem. Creeping buttercup looks like flat-leaf parsley. It can cause severe stomach pain,vomiting (呕吐) and heart problems. And Canadian moonseed can be confused with wild grape. However, its taste is so bitter that you would likely spit it out before swallowing it. This is a good thing because eating it can lead to death.If you think you have swallowed a toxic plant by mistake, contact a poison control center in your area or your doctor immediately. There is additional information on the website .Damiano advises using common sense with plants you find in the wild. If you are not completely sure that something is food, do not eat it.8．What is the purpose of the first paragraph?A．To present the author’s argument.B．To introduce the topic of the article.C．To raise the public’s attention of wild plants.D．To popularize the knowledge of medical science.9．Why was Silverstone thought to be fortunate?A．The berries she had a bite were ripe.B．She found the fruit she ate was a tomato.C．She had a good knowledge of wild plants.D．The amount of the berries she consumed was large.10．According to the description,what plants can be most harmful to people?A．Carolina horsenettle and wild parsnip.B．Virginia creeper and creeping buttercup.C．Wild parsnip and Canadian moonseed.D．Canadian moonseed and Virginia creeper.11．What may be the suitable measure if someone mistakenly swallows a poisonous plant?A．Spitting it out as quickly as possible.B．Making an appointment with their doctor.C．Getting in touch with the local authority instantly.D．Searching for the relevant information on the Internet.Superhuman artificial intelligence has played a role in our life. When it comes to playing games like chess, or solving difficult scientific challenges like predicting protein structures, computers are well ahead of humans. But we have one superpower they aren’t close to mastering: mind reading.We are blessed with a mysterious ability to reason the goals, desires and beliefs of others, a crucial skill that means we can anticipate other people’s actions and the consequences of our own. If AIs are to become truly useful in everyday life — to cooperate effectively with us or to understand that a child might run into the road after a bouncing ball — we have to give them this gift that evolution has given us to read other people's minds.In psychology, the ability to infer another’s mental state is referred to as theory of mind. In humans, this capacity develops at a very young age. How to reproduce the capability in machines is far from clear, though. One of the main challenges is context. For instance, if someone asks whether you are going for a run and you reply “it’s raining”, they can quickly conclude the answer is no. But this requires huge amounts of background knowledge about running, weather and human preferences.Besides, whether humans or AI, the theory of mind is supposed to emerge naturally from one’s own learning process. Building prior knowledge into AI makes it reliant on our imperfect understanding of theory of mind. In addition, AI may be capable of developing approaches we could never imagine. There can be many forms of theory of mind that we don’t know about simply because we live in a human body that has certain types of senses and a certain ability to think.But we might still want AI to have a more human-like form of theory of mind. Humans can clearly explain their goals to each other using common language and ideas. While letting AI form the theory of mind in their learning process is likely to lead to developing more powerful AI, plainly building in shared ways to represent knowledge may be crucial for humans to trust and communicate with AI.It is important to remember, though, that the pursuit of machines with theory of mind is about more than just building more useful robots. It is also a stepping stone on the path towards a deeper goal for AI and robotics research: building truly self-aware machines. Whether we will ever get there remains to be seen. But along the way thinking about other people and other agents, we are on the path to learning to think about ourselves.12．According to the passage,which of the following contexts can AI understand well?A．When asked where an object is, a naughty kid points in the wrong direction.B．When a teacher asks for a boy’s homework, he answers “my dog ate it” .C．When you are treated with a hotpot for dinner, you reply “a sore throat” .D．When a mom tells her kid milk is good for health, the kid drinks it up.13．Which statement will the author agree with most about theory of mind?A．Humans’ theory of mind is far from perfect.B．Humans limit AI’s theory of mind to an extent.C．AI’s theory of mind development has been totally decoded.D．Shared forms of theory of mind result in more powerful AI.14．What is the author’s attitude toward truly self-aware machines?A．Ambiguous B．Conservative.C．Skeptical.D．Approving.15．Which would be the best title for the passage?A．AI’s Theory of Mind Will Define Our FutureB．AI with Its Own Theory of Mind Is ExpectedC．AI’s Theory of Mind — a Blessing or Suffering to HumansD．Theory of Mind Bridges the Gap Between Humans and AIEnsuring that your home is as energy-efficient as it can possibly be is essential. Take the steps listed below,and you'll be living in an energy-efficient home in no time.16 To stop it in its tracks,you must invest in having your house insulated (隔热的). Taking such action may demand some cost in advance, but it will be sure to save you over f100 a year when it comes to your energy bills.The old boilers (锅炉) are not as energy-efficient as the very latest models in this field.17 By investing in a top of the line boiler, you'll no doubt tap into a number of savings. What's more,making this kind of investment will also be sure to lower your home's carbon emissions.Only when you know how much energy you use can you take action to be less wasteful and more resourceful in this instance. 18 To assist you in taking on this extremely important challenge, you might want to consider fitting an energy monitor in your home. 19 But if you're lucky,your electricity provider will give you one for free.This monitor will provide you and your family with constant updates on the amount of energy you are using on a day-to-day basis.With just a few years to go until climate change alters earth forever, now is the time for you to play your part in protecting the planet that you live in. 20A．Generally, this type of device will cost between f25 and f40.B．It means you should try to keep track of energy consumption.C．The investment demanded in this case is of great significance.D．By putting the above advice into practice,you'll be green soon.E．Taking such action will help you adjust to climate change better.F．Most of your home's wasted energy will escape through your roof.G．It might be high time to update yours if you haven't done so for years二、完形填空Not long into my career in journalism,I realized I was in need of some slow, 21 adventure.The kind of fun that required little planning,zero stress and a lot of time. The kind of time you often didn't get in a 22 .And that's when I 23 a secret.Washington,D．C．,the city where I live,is full of hidden fossils.In my overstimulated life,I began to 24 fossils.Many of the local sites are within 80 miles south of the capital along the Potomac River,so fossil hunting 25 removes me from the city.It is a visual game,requiring 26 and focus. Spotting recognizable shapes in the wild is like thinking over a broken 27 in the sediment(沉积物).Is it a tooth,a bone or a shell?I'm looking for the 28 end pieces.Thankfully,my 29 phone service in these places holds back the rest of the world while I'm finding another one.And I know the fossils aren't demanding my 30 attention because they have nothing but time.Once,I took a bottle-cap-sized trilobite(三叶虫)fossil into the newsroom and placed it within my sight.It was something I wanted to 31 throughout the day. Turning over that piece of rock is a way to 32 me outside for a moment and to a time before humans arrived and 33 cities on top of those lands.Thinking about geological time makes me feel brief and remarkable,like the little trilobite.My worried mind 34 .I realize a lot of stressful details don't matter.My 35 shifts.Maybe I don't need to take that phone call right this minute. 21．A．dangerous B．low-risk C．historical D．romantic 22．A．house B．car C．newsroom D．school 23．A．revealed B．hid C．guarded D．discovered 24．A．seek B．search C．purchase D．modify 25．A．gradually B．physically C．eventually D．typically 26．A．patience B．strength C．training D．courage 27．A．dream B．image C．resource D．puzzle 28．A．obvious B．expensive C．rare D．impressive 29．A．precious B．conventional C．poor D．clear 30．A．scholarly B．public C．extra D．immediate31．A．avoid B．notice C．introduce D．display 32．A．touch B．hold C．seize D．transport 33．A．built B．explored C．conquered D．found 34．A．takes off B．settles down C．goes blank D．runs out 35．A．standpoint B．question C．standard D．task三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

衡阳市八中2024届高三第2次月考数学试题命题人：刘瑶 审题人：颜军注意事项：本试卷满分为150分，时量为120分钟一､单选题（本大题共8小题，每题5分，共40分）1. 若集合{}{}202,1A x x B x x =≤≤=<，则A B = （）A. {}01x x ≤< B. {}12x x <≤C. {}02x x <≤ D. {0x x >或}1x <-2. 在复平面内，复数12i2i-+对应的点的坐标为( )A. (0,1)- B. ()0,1 C. 43,55⎛⎫-⎪⎝⎭ D. 43,55⎛⎫⎪⎝⎭3. 定义在R 上的偶函数()f x 满足：对任意的1x ，212[0,)()x x x ∈+∞≠，有2121()()0f x f x x x -<-，则（ ）．A. (3)(2)(1)f f f <-<B. (1)(2)(3)f f f <-<C. (2)(1)(3)f f f -<< D. (3)(1)(2)f f f <<-4. 已知等差数列{}n a 的公差为d ，前n 项和为n S ，则“0d >”是“322n n n n S S S S ->-”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5. 某校高三有1000人参加考试，统计发现数学成绩近似服从正态分布N (105，σ2)，且成绩优良（不低于120分）的人数为360，则此次考试数学成绩及格（不低于90分）的人数约为（ ）A. 360B. 640C. 720D. 7806.椭圆(22213x y a a +=>的左、右焦点分别为1F ，2F ，A 为上顶点，若12AF F △的面积为12AF F △的周长为（ ）A. 8B. 7C. 6D. 5..7. 设函数()()()eln xf x ax m ax x =--（其中e 为自然对数的底数），若存在实数a 使得()0f x <恒成立，则实数m 的取值范围是（ ）A 21,e ⎛⎫+∞⎪⎝⎭B. 1,e ⎛⎫+∞ ⎪⎝⎭C. ()2e ,+∞D. 21,e ⎛⎫-∞ ⎪⎝⎭8. 如图，在三棱锥S ABC -中，2SA SC AC AB BC =====，二面角S AC B --的正切值是，则三棱锥S ABC -外接球的表面积是（ ）A. 12πB. 4πC.D.π二､多选题（本大题共4小题，每题5分，共20分）9. 已知向量(1,3),(2,4)a b ==-，则下列结论正确的是（ ）.A. ()a b a+⊥B. |2|a b +=C. 向量,a b的夹角为34π D. b 在a10. 设等比数列{}n a 的前n 项和为n S ，前n 项积为n T ，若满足101a <<，740401a a ⋅>，()()20232024110a a --<，则下列选项正确的是（）A. {}n a 为递减数列B. 202320241S S +<C. 当2023n =时，n T 最小D. 当1n T >时，n 的最小值为404711. 已知函数()cos22sin f x x x =+，则（ ）A. 函数()f x 在区间,62ππ⎛⎫⎪⎝⎭上单调递增.B. 直线2x π=是函数()f x 图象的一条对称轴C. 函数()f x 值域为31,2⎡⎤⎢⎥⎣⎦D. 方程()()()0,2πf x a x =∈最多有8个根，且这些根之和为8π12. 已知直线():2l y k x =+交y 轴于点P ，圆()22:21M x y -+=，过点P 作圆M 的两条切线，切点分别为A ，B ，直线AB 与MP 交于点C ，则（ ）A. 若直线l 与圆M相切，则k =B. 当2k =时，四边形PAMB的面积为C. 直线AB 经过一定点D. 已知点7,04Q ⎛⎫⎪⎝⎭，则CQ 为定值三､填空题（本大题共4题，每小题5分，共20分）13. 在数学中，有一个被称为自然常数（又叫欧拉数）的常数e 2.71828≈．小明在设置银行卡的数字密码时，打算将自然常数的前6位数字2，7，1，8，2，8进行某种排列得到密码．如果排列时要求两个2相邻，两个8______个．14. 曲线()()e xf x x a =+在点()()0,0f 处的切线与直线12y x =-垂直，则=a ______.15. 底面ABCD 为菱形且侧棱⊥AE 底面ABCD 的四棱柱被一平面截取后得到如图所示的几何体.若4,3DA DH DB AE CG =====.则三棱雃F BEG -的体积为__________.16. 设0a >，平行于x 轴直线:l y a =分别与函数2x y =和12x y +=的图像交于点A ，B ，若函数2x y =的图像上存在点C ，满足ABC V 为等边三角形，则a =_________．四､解答题（本大题共6小题，共70分）的的17. 已知△ABC 的内角A ，B ，C 的对边分别为a ，b ，c ，若△ABC ，1AB AC ⋅=-且>c b ．（1）求角A 的大小；（2）设M 为BC 的中点，且AM =，求a 的长度．18. 某工艺品加工厂加工某工艺品需要经过a ，b ，c 三道工序，且每道工序的加工都相互独立，三道工序加工合格率分别为34，12，12．三道工序都合格的工艺品为特等品；恰有两道工序合格的工艺品为一等品；恰有一道工序合格的工艺品为二等品；其余为废品．（1）求加工一件工艺品不是废品的概率；（2）若每个工艺品为特等品可获利300元，一等品可获利100元，二等品将使工厂亏损20元，废品将使工厂亏损100元，记一件工艺品经过三道工序后最终获利X 元，求X 的分布列和数学期望．19. 在图1中，ABC V 为等腰直角三角形，90B Ð=°，AB =，ACD V 为等边三角形，O 为AC 边的中点，E 在BC 边上，且2EC BE =，沿AC 将ACD V 进行折叠，使点D 运动到点F 的位置，如图2，连接FO ，FB ，FE ，使得4FB =．（1）证明：FO ⊥平面ABC ．（2）求二面角E FA C --的余弦值．20. 若数列{}n A 满足21n n A A +=，则称数列{}n A 为“平方递推数列”．已知数列{}n a 中，19a =，点()1,n n a a +在函数2()2f x x x =+的图象上，其中n 为正整数，（1）证明：数列{}1n a +是“平方递推数列”，且数列(){}lg 1n a +为等比数列；（2）设()lg 1,24n n n b a c n =+=+，定义,,*,,a ab a b b a b ≤⎧=⎨>⎩，且记*n n n d b c =，求数列{}n d 的前n 项和n S ．21. 已知双曲线()2222:10,0x y C a b a b-=>>的右焦点，右顶点分别为F ，A ，()0,B b ，1AF =，点M 在线段AB上，且满足BM =OM 的斜率为1，O 为坐标原点.（1）求双曲线C 的方程.（2）过点F 的直线l 与双曲线C 的右支相交于P ，Q 两点，在x 轴上是否存在与F 不同的定点E ，使得EP FQ EQ FP ⋅=⋅恒成立？若存在，求出点E 的坐标；若不存在，请说明理由.22. 已知函数()1ln f x x a x x ⎛⎫=-- ⎪⎝⎭，0a >.（1）讨论()f x 极值点的个数；（2）若()f x 恰有三个零点()123123,,t t t t t t <<和两个极值点()1212,x x x x <.（ⅰ）证明：()()120f x f x +=；（ⅱ）若m n <，且ln ln m m n n =，证明：()()1231e ln 1mm n n t t t -->+.。