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看二零二三年全国假卷最难的选择题,这个题怎么办?其实很简单,我们看拿到一个椭圆,首先判断 x 型还是 y 型, 这一定是 x 型,因为 x 方下面大,然后写出 a 方和 b 方,当然你也可以不用写减,因为是选择题, a 方等于几啊?等于九,所以 a 等于三, b 方等于六, b 等于根号六, c 方等于 a 方,减 b 方 c 等于根号三。然后画图 坠,把图稍微画的大一点。 x 型椭圆稍微画的大一点,不用太标准。 那我们看 f 一, f 二为左右焦点,这是 f 一,这是 f 二, p 点为椭圆上一点,我们一般点在第一象限 cruising 角 f e p f 二。好,我们知道这个角度 求 o p, 这是 o 点。其实这道题有很多的解法, 我们用我们平时教的最常规最常规最常规的方法来讲,移动点到两定点,距离之和等于长处二 a, 我的习惯是设边长为 m n, 当然了, f e f 二是焦距二 c 二倍根号三,这是我们名门学府张超带你学高中数学这本书里面讲的最基本的方法,不要用套路 来。移动点到两定点,距离之和等于长数二 a, 那 m 加 n 不就等于二 a 吗? 当然二 a 就是六,有两焦点用,定义有直角 购物定理不是直角用余弦定理。很简单,我肯定要用余弦定理。所以零边的平方和 减对边的平方二得四三 c 十二除以二倍,零边就等于五分之三。 一是怎么化减?讲了一万遍了,平方和二是搭配 c, m 方加 n 方加二 m n 等于三十六,那不就是三十六减二 m n 吗? 二是区分母,你看 m 方加 n 方减去十 十二等于五分之六倍 m n。 好,它俩相等怎么办?很简单,三十六减二, m n 等于十二,加上五分之六倍 m n, 你走三十六减十二等于几啊?二十四,这是五分之十,那不就是五分之十六吗? 你不用想了,他们都有八来,同时乘以八分之一,三五分之二 m n, 那你看 m n 出来没有? 三五一十五,二分之十五。那既然 m n 出来了,那 m 方加 n 方不也出来了吗?你看等于几? 二分之十五乘以二十五,三十五减十五等于二十一。这就是最基本的化解一个最基础的考题。一天到晚抱怨难难难,我说让你把每个题目做三遍,你为什么不听呢? 来求 o p, 我们看 o p 怎么办?其实你就不用想 o 是什么点,终点,那这个 o p 不就是中线吗?所以这个 也很容易用我们书上讲的中线定理来求中线的长度。 怎么办?你看,不要跑,你要为全国的学生服务,躲起来干嘛?好书就不能掩盖,你看 o 为 f 一 f 二的终点 不做了。那你看 p u 项链等于什么?不就等于二分之一 p f 一项链加 p f 二项链吗? 项链的平方等于项链的魔方,一平方不就出魔了吗?不就出长度了吗?所以 p o 的平方就是 p o 的魔方,等于四分之一倍 p f 一的平方就是 p f 一的魔方,加 p f 二的平方就是 p f 二的魔方。 加两倍的 p f 一乘 p f 二, p f 一向量乘 p f 二向量向量相乘等于膜膜 q n 加角,那不是 p f 一的膜 p f 二膜 q n 加角吗? q n 加角五分之三。 来,我们看,四分之一不变 m 方加音方我刚刚已经求过了二十一,这都顺理成章的事情。二倍 m n 就是十五, 十五乘以三四十五,四十五除以五九,所以就等于四分之二三十。 人家求 o p 一定不要忘了开方,所以 o p 的膜等于几啊?等于二分之二三十。 当你一天到晚抱怨难的时候,你为什么不能脚踏实地的去努力?高考只有二十二个题, 抓住二十二个题的模板,做透做熟,数学变得很简单。

这是二零二三年普通高等学校招生全国统一考试英语科听力部分。 could you please tell me how i can get to the student dorm building sure turn left when you walk out of this register office pass the bookstore and you'll see it we couldn't ask for a better day could we barbara, i know steve there isn't a cloud in the sky i love this time of year me too the flowers are beautiful but calling for rain though we got any plans this weekend we might start with our vegetable garden then the barbecue sounds fun but i still want to go fishing with george lisa i saw jack this morning you mean the former designer of our company what's he doing these days he said he's got a new job as an art reporter do you often go to the student union andrew pretty much once in a while i meet friends there and i spend a lot of time organizing activities in different clubs or associations what do you think terry well, it has one more bedroom than the last flat and the sitting room is big but there is not enough cupboard space in the kitchen it's cheaper than the last one we saw and it is in a good neighborhood well, maybe we'll have to see if the agent has anything else to show us what do you think terry well, it has one more bedroom than the last flat and the sitting room is big but there is not enough cupboard space in the kitchen it's cheaper than the last one we saw and it is in a good neighborhood well, maybe we'll have to see if the agent has anything else to show us thank you mrs johnson for what you've shared with our listeners now please tell us do you sometimes feel worried about your daughter now that she's grown up oh, i worry about her like all parents do after she graduated from medical school, she went to volunteer medical service in africa wow, that's okay, if communication was fine, but if there was no internet or telephone connection we could sometimes go two weeks without getting in touch with each other that often worries me thank you missus johnson for what you've shared with our listeners now, please tell us do you sometimes feel worried about your daughter now that she's grown up, oh, i worry about her like all parents do after she graduated from medical school she went to volunteer medical service in africa wow, that's okay if communication was fine, but if there was no internet or telephone connection we could sometimes go two weeks without getting in touch with each other that often worries me now sell yourself in a minute, please i graduated from university two years ago and have since been working in an accounting company apart from the knowledge and skills related to my major i'm really good with computers i have a large amount of experience working with big data i think i'm well qualified for the accountant position here good, why did you choose this company? peterson has been my dream company all along you value progress and focus on the quality of work more than the quantity the flexible working hours and working from home is also attractive uh huh, what do you think is your biggest weakness well, when i work i often concentrate so much on what i'm doing that i may have a hard time dealing with things that come up unexpectedly that may be annoying to some people all right, thank you very much now sell yourself in a minute please i graduated from university two years ago and have since been working in an accounting company apart from the knowledge and skills related to my major i'm really good with computers i have a large amount of experience working with big data i think i'm well qualified for the accountant position here good why did you choose this company? peterson has been my dream company all along you value progress and focus on the quality of work more than the quantity the flexible working hours and working from home is also attractive uh huh, what do you think is your biggest weakness well when i work i often concentrate so much on what i'm doing that i may have a hard time dealing with things that come up unexpectedly that may be annoying to some people all right thank you very much so robert i guess you must be well into your third decade as a writer how is life treating you fourth decade as a writer hmm let me get my calculator out well, i guess i've been writing novels since the nineteen eighties so you're right but i have been writing all my life and to answer your question life has been treating me excellently can i ask you about your childhood were you a bookish child in a strange way i was a non reader until i turned nine i used to play basketball in the school yards of brooklyn my father was a high school teacher of physics and chemistry and he was a big reader he would bring books back from his high school library one day i read the last chapter of a book the title of which i've long since forgotten i liked it so much that i started reading the remainder interestingly i read the chapters backwards until i got to the beginning i really loved the experience and i soon became an eager reader then my father would bring piles of books, home from the library and i would read them all and they were all fiction i must add that i started reading the books from the start as opposed to working backwards so robert, i guess you must be well into your third decade as a writer how is life treating you fourth decade as a writer hmm, let me get my calculation later out well, i guess i've been writing novels since the 1980s so you're right but i have been writing all my life and to answer your question life has been treating me excellently can i ask you about your childhood were you a bookish child in a strange way i was a non reader until i turned nine i used to play basketball in the school yards of brooklyn, my father was a high school teacher of physics and chemistry and he was a big reader he would bring books back from his high school library one day, i read the last chapter of a book the title of which i've long since forgotten i liked it so much that i started reading the remainder interestingly i read the chapter's backwards until i got to the beginning i really loved the experience and i soon became an eager reader then my father would bring piles of books, home from the library and i would read them all and they were all fiction i must add that i started reading the books from the start as opposed to working backwards hello, i'm maxim vengarov and i'm very happy to share with you my connection with open chicafsky competition it was june nineteen eighty six when i came to moscow to participate in open tikovsky competition at the age of ten from cheleapinsk, this was actually the turning point of my life then i attended a world music festival in berlin, and it was interesting to say that a kid made his break through already at the age of ten, and that was me now as a judge of the competition i can see clearly the huge challenges facing the musicians in the competition where else can you see young players playing within ten days, classical works and russian traditional music before coming to the final stage as a musician it's important to give maximum attention and time to your own reflections of your own feelings so what i'm really looking for in the competition is to meet someone who can touch me musically i want to see the seed at least the seed of the great tree that can grow i would go for this violinist i would go for this musician hello, i'm maxim vengarov and i'm very happy to share with you my connection with open chicafsky competition it was june nine nineteen eighty six when i came to moscow to participate in open tykovsky competition at the age of ten from chelyapinsk, this was actually the turning point of my life then i attended a world music festival in berlin, and it was interesting to say that a kid made his break through already at the age of ten, and that was me now as a judge of the competition, i can see clearly the huge challenges facing the musicians in the competition, where else can you see young players playing within ten days, classical works and russian traditional music before coming to the final stage as a musician it's important to give maximum attention and time to your own reflections of your own feelings so what i'm really looking for in the competition is to meet someone who can touch me musically i want to see the seed at least the seed of the great tree that can grow i would go for this violinist i would go for this musician。 第二节到此结束。 could you please tell me how i can get to the student dorm building sure turn left when you walk out of this register office pass the bookstore and you'll see it we couldn't ask for a better day could we barbara, i know steve there isn't a cloud in the sky i love this time of year me too the flowers are beautiful but calling for rain though we got any plans this weekend we might start with our vegetable garden then the barbecue sounds fun but i still want to go fishing with george lisa, i saw jack this morning you mean the former designer of our company what's he doing these days? he said he's got a new job as an art reporter do you often go to the student union? andrew pretty much once in a while i meet friends there and i spend a lot of time organizing activities in different clubs or associations what do you think terry well, it has one more bedroom than the last flat and the sitting room is big but there is not enough cupboard space in the kitchen it's cheaper than the last one we saw and it is in a good neighborhood well, maybe we'll have to see if the agent has anything else to show us thank you missus johnson for what you've shared with our listeners now please tell us do you sometimes feel worried about your daughter now that she's grown up oh, i worry about her like all parents do after she graduated from medical school she went to volunteer medical service in africa wow, that's okay if communication was fine, but if there was no internet or telephone connection we could sometimes go two weeks without getting in touch with each other that often worries me now sell yourself in a minute please i graduated from university two years ago and have since been working in an accounting company apart from the knowledge and skills related to my major i'm really good with computers i have a large amount of experience working with big data i think i'm well qualified for the accountant position here good why did you choose this company? peterson has been my dream company all along you value progress and focus on the quality of work more than the quantity the flexible working hours and working from home is also attractive uh huh, what do you think is your biggest weakness well, when i work i often concentrate so much on what i'm doing that i may have a hard time dealing with things that come up unexpectedly that may be annoying to some people all right thank you very much so robert i guess you must be well into your third decade as a writer how is life treating you fourth decade as a writer hmm let me get my calculator out well, i guess i've been writing novels since the 1980s so you're right but i have been writing all my life and to answer your question life has been treating me excellently can i ask you about your childhood were you a bookish child in a strange way, i was a non reader until i turned nine i used to play basketball in the school yards of brooklyn, my father was a high school teacher of physics and chemistry and he was a big reader he would bring books back from his high school library one day, i read the last chapter of a book the title of which i've long since forgotten i liked it so much that i started reading the remainder interestingly i read the chapters backwards until i got to the beginning i really loved the experience and i soon became an eager reader then my father would bring piles of books home from the library and i would read them all and they were all fiction i must add that i started reading the books from the start as opposed to working backwards hello, i'm maxim vengarov and i'm very happy to share with you my connection with open tykovsky competition it was june nineteen eighty six when i came to moscow to participate in open tykovsky competition at the age of ten from chaleapinsk this was actually the turning point of my life then i attended a world music festival in berlin and it was interesting to say that a kid made his break through already at the age of ten and that was me now as a judge of the competition i can see clearly the huge challenges facing the musicians in the competition where else can you see young players playing within ten days, classical works and russian traditional music before coming to the final stage as a musician it's important to give maximum attention and time to your own reflections of your own feelings so what i'm really looking for in the competition is to meet someone who can touch me musically i want to see the seed at least the seed of the great tree that can grow i would go for this violinist, i would go for this musician。

全国统一考试英语科听力部分现在你有五秒钟的时间阅读第一小题的有关内容。 jenny, you can just drop me here but we're two streets away from the office it's fine i had a big breakfast and feel like a bit of walk hello, george, you look tired didn't sleep well last night, no, not at all i had to work flat out to meet the project deadline now, i'm really feeling a bit run down john can't we go someplace and talk it's so noisy in here well, there's a small park across the street it's usually not crowded at this time of day we've got to do something about the neighbor's dog why has he been into your flower garden again the flower garden, the garbage can and yesterday he started digging holes in the yard hello, we have a reservation in the name of mr jones is there any table by the window sorry, we've got this corner table for you it's quiet here not close to the door。 听下面一段对话,回答第六和第七两个小题。现在你有十秒钟的时间阅读这两个小题。 dave don't forget we are invited out to dinner tonight, oh, yeah, i almost forgot what time seven thirty we should leave the house by six, thirty, you know how bad the traffic is that time of night its informal isn't it yeah you can wear your new sports jacket the one i got you as an anniversary gift okay, well, i've got to go i'll try to get home a little earlier today, good dave don't forget we are invited out to dinner tonight oh, yeah, i almost forgot what time seven thirty we should leave the house by six, thirty you know how bad the traffic is that time of night it's informal isn't it yeah you can wear your new sports jacket the one i got you as an anniversary gift okay well, i've got to go i'll try to get home a little earlier today good! 听下面一段对话,回答第八和第九两个小题。现在你有十秒钟的时间阅读这两个小题。 we need to decide exactly when we're going to move any suggestions i think july would be the best time our sales are always down that month we could move all the office equipment at a weekend do everything at once i think a weekend's too short maybe we should do it department by department? what do you mean well each week a different department would move that way there would always be people here to handle customer inquiries phone calls and so on hmm that's a good idea we need to decide exactly when we're going to move any suggestions i think july would be the best time our sales are always down that month we could move all the office equipment at a weekend do everything at once i think a weekend's too short maybe we should do it department by department? what do you mean well each week a different department would move that way there would always be people here to handle customer inquiries phone calls and so on hmm that's a good idea。 听下面一段对话,回答第十至第十二、 三个小题。现在你有十五秒钟的时间阅读这三个小题。 so mister peter cells i'd be curious to know what were the early connections in your life that led you into the art field my grandfather was an art dealer in munich they had a great museum in munich, he took me to the museum and i responded very strongly to what i saw on the walls there, i learned about art from him, i learned about looking at art from him, i think that's what really got me started then many years later after i got out of the army, i went to study art history at the university of chicago tell us more about your experiences of looking at art with your grandfather well, we looked at the famous paintings by the great artists like rembrandt, watacelli and albrecht douter ruben's paintings were my favorites yes, i remember these things this was when i was between ten and fifteen when i was fourteen i was so anxious to see more art that friend of mine and i bicycled across the alps to see venice that was a big adventure so mister peter sells i'd be curious to know what were the early connections in your life that led you into the art field my grandfather was an art dealer in munich they had a great museum in munich he took me to the museum and i responded very strongly to what i saw on the walls there i learned about art from him, i learned about looking at art from him, i think that's what really got me started then many years later after i got out of the army, i went to study art history at the university of chicago tell us more about your experiences of looking at art with your grandfather well, we looked at the famous paintings by the great artists like rembrandt, watacelli and albrecht dora ruben's paintings were my favorites yes, i remember these things this was when i was between ten and fifteen when i was fourteen i was so anxious to see more art that a friend of mine and i bicycled across the alps to see venice that was a big adventure。 听下面一段对话,回答第十三至第十六四个小题。现在你有二十秒钟的时间阅读这四个小题。 hi, john haven't seen you for ages hi, susan fancy meeting you here on the train how is your college life? what can i say i've survived what happened well early last march i started doing a part time job in a law firm a few weeks before i had started writing my term paper i thought i could finish it by august that was a pretty good idea trying to have some work experience for the first three weeks you know i tried i got up early and worked for an hour on my paper before going to work, but work was so fun i met tons of new people and soon i couldn't find even a minute for my paper so i had to quit my part time job and finally finished my paper in october well, it's never too late to mend it's kind of hard to find a balance between what you have to do and what you want to do yeah it's really important for me to balance study and work and i think i should learn to exercise some self control hi john haven't seen you for ages hi, susan fancy meeting you here on the train how is your college life? what can i say i've survived what happened well early last march i started doing a part time job in a law firm a few weeks before i i had started writing my term paper i thought i could finish it by august that was a pretty good idea trying to have some work experience for the first three weeks you know i tried i got up early and worked for an hour on my paper before going to work, but work was so fun i met tons of new people and soon i couldn't find even a minute for my paper so i had to quit my part time job and finally finished my paper in october well, it's never too late to mend it's kind of hard to find a balance between what you have to do and what you want to do yeah it's really important for me to balance study and work, and i think i should learn to exercise some self control。 听下面一段独白,回答第十七至第二十四个小题。 现在你有二十秒钟的时间阅读这四个小题。 being an athlete is very fun, painful and exciting every time i come to the track i feel like i'm out of this place this is botswana national stadium this is where i train when i saw usain bolt running in twenty twelve london olympics i was amazed just watching him run got me motivated i quit being a chess player and started to run。