14已知數(shù)列的前項(xiàng)和比集合的子集個(gè)數(shù)少1.則 . 查看更多

 

題目列表(包括答案和解析)

請(qǐng)根據(jù)A至F各課程的介紹和個(gè)各人的情況說(shuō)明,選出符合各人要求的最佳選項(xiàng)。

A.You’ll be ready for the heated competition in the Nike Money Mesh Women’s Basketball Pants, a ventilated (透氣的)design that offers a wide range of motion.
B.Be your own avatar(。。。) in the Nike “Your Head” Women’s T-shirt, a playful design that works hard to keep sweat at bay. It uses a Dri-FIT fabric to keep sweat away to help keep you dry and comfortable.
C.It is our classic cotton skirt, sweetened with lace (花邊) at the edge. Waistband adjusts inside for a perfect fit. Jersey undershorts are attached. Just the perfect one for toddler girls aged 2-4.
D.If you want jeans with a skinny fit, or need something to fit well if you are skinny, come here! LV skinny 511 jeans. The jeans sit below the waist, with slim legs to the ankles. The jeans are our slimmest fit.
E. The Nike Air Jordan VI Retro basketball shoes will always be remembered as the sneakers that Michael wore while winning his first NBA championship. They were designed by the legendary Tinker Hatfield, and feature many fresh design elements.
F. Two jackets in one! That’s right! Adidas All-star NBA Men’s Jacket is reversible(可兩面穿的)with front welt pockets. This jacket has a classic, full-front zip and hood with colorful artistry, which is 100% Adidas.
閱讀以下人物的信息,然后匹配相應(yīng)的服裝:
46. Mary’s friend has invited her to attend a birthday party. She has asked her mom to buy a new pair of jeans for the party. She is a slim teen girl. Wearing jeans with slim legs may help her look tall and slim.
47. Jenny is going to Illinois to visit her old classmate Kate who is now a mother of a 3-year-old girl. She is looking for a gift for the little girl. She has decided to buy a lovely skirt for her. It must be very comfortable and made of cotton.
48. John is going for a camp this weekend,  but he can’t find a suitable jacket to keep warm outside and inside. So he would like to buy a new one. He wants to try something new that can be turned inside out and still be worn. In this way, he would not have to take too many things.
49. After suffering from a bad cold for a long time, Alice was advised to take exercise by her doctor. She wants to buy a T-shirt which can keep sweat away.  The T-shirt should be comfortable and keep her dry while she’s playing sports.
50. Lily’s company is going to have a basketball match and there is no doubt that Lily will be the front player. She’s looking for new sporting basketball pants and she’s a crazy Nike fan.

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下面是一篇應(yīng)用文及其應(yīng)用場(chǎng)合的信息,請(qǐng)閱讀下列應(yīng)用文和相關(guān)信息,并按照要求匹配信息。
請(qǐng)根據(jù)A至F各課程的介紹和個(gè)各人的情況說(shuō)明,選出符合各人要求的最佳選項(xiàng)。
A. A Look at American Literature
A Look at American Literature is a course which gives us a brief outline of American Literature.
B. Works of Some Famous American Writers
Works of Some Famous American Writers show us the introductions to eleven famous writers and their works and also give us some comments on the works.
C. Detailed Reading of American Literature
Detailed Reading of American Literature is a course which focuses on some important and moving details in the works of American literature. It will analyse the detail.
D. Story and Plot
It’s a course which analyses the setting of the main plots in some famous stories. The aim of this course is to help those who want to become writers in the future.
E. Characters and Life
As you know, literature comes from our life, but it’s more than our life. This course will analyze the personalities of some important characters in the world literature, and combine the analysis with our life. It will help us gain wisdom from the characters.
F. Literature Comments
The course is a study of how to write literature comments through some vivid examples.
請(qǐng)閱讀以下學(xué)生的相關(guān)信息,然后匹配他/她和擬要選擇的課:
Helen wants to become a famous writer in the future. She is eager to take a course which can help her realize her dream.
Peter was ill last term and missed a lot of lessons in American literature. He wants to take a course which can give him an outline of it.
Kate likes to read literature works and she has many opinions after reading, but she doesn’t know how to express her ideas properly.
Tommy has the basic knowledge of American literature. He wants to take a course which can help him read more famous works about American literature.
Jerry wants to write some articles to show the significance of researching literature today. He is looking for a course which can help him.
待選課程學(xué)生                        課程名稱
【小題1】 Helen              A.  A Look at American Literature
【小題2】Peter               B.  Works of Some Famous American Writers
【小題3】 Kate               C.  Detailed Reading of American Literature
【小題4】 Tommy              D.  Story and Plot
【小題5】Jerry               E.  Characters and Life
F.  Literature Comments

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根據(jù)所給的中文和括號(hào)內(nèi)的語(yǔ)法提示, 把下面句子翻譯成英語(yǔ),寫(xiě)在答題卷相應(yīng)的橫線上。
【小題1】 我覺(jué)得很奇怪他睡得那么少卻能夠干得那么賣力。(賓語(yǔ)從句)
I find ______ ________ ______ he is able to work so hard with so little sleep.
【小題2】 這兩姐妹一定是吵架了,因?yàn)樗齻兓ゲ焕聿恰?must have done)
The sisters _______ _______ _______ an argument, for they are no longer talking to each other.
【小題3】 那位老師和兩個(gè)學(xué)生參加了會(huì)議。(主謂一致)
The ________ with two ________ ________ at the meeting.
【小題4】 是什么事使他不能參加我們的會(huì)議仍然是個(gè)謎。(主語(yǔ)從句)
_______ prevented him from _______ our meeting still ______ a mystery.
【小題5】老師不用抬頭看就已經(jīng)知道是哪個(gè)學(xué)生在班上講話。(V+ing 作賓語(yǔ))
Without ______ ______ _______ her desk, the teacher already knew which student was talking in class.  

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根據(jù)句子的意思和括號(hào)里的中文提示以及首字母, 寫(xiě)出下列的單詞。要求寫(xiě)出完整單詞。
【小題1】 The Greek financial difficulties would not be easily o________(戰(zhàn)勝).
【小題2】The single mother is s________(奮力) to bring up her child alone.
【小題3】 We all i________(打算)to have DIY decorations, but our cupboards will be made by a carpenter.
【小題4】The new credit cards will be of great b________(利益) to our customers.
【小題5】 Most of the compositions written by the students were very good i___________(真正地).
【小題6】 I can say to the governor that he ___________ (誤解)the order and tried to defend himself.
【小題7】 He was a little boy, but he ___________(行為表現(xiàn))as if he was an adult.
【小題8】The government’s actions are ___________(相違的)to the public interest.
【小題9】___________(不像)most people in the office, I don’t come to work by car.
【小題10】He created a new ___________(體系)of teaching foreign languages.

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完成句子(共14空,每空0.5分,滿分7分)
【小題1】你只有在不遠(yuǎn)離河岸的條件下才能去游泳。
You can go swimming               that you don’t go too far from the river bank.
【小題2】他被委任承擔(dān)學(xué)校各方面的管理工作。
He has been        to        the school management in all respects.
【小題3】寫(xiě)一篇名為音樂(lè)的回憶的文章,字?jǐn)?shù)不限。
Write an essay of as many words as you like        the        of “Musical Memories”.
【小題4】幸福不在于擁有很多,而在于就算擁有很少也很滿足。
Happiness        not in having much, but in being        with little.
【小題5】麥克很謙虛,他把他的成功都?xì)w功于他的父母和老師們。
Mike is modest and he        a lot of his success        his parents and teachers.
【小題6】據(jù)報(bào)道中國(guó)的經(jīng)濟(jì)總量目前僅次于美國(guó)——比日本或歐洲任何一個(gè)國(guó)家都要大。
It is reported that China’s economy is now               to the United States, larger than that of Japan or any single member of the European Union.
【小題7】在上世紀(jì)90年代,他來(lái)到深圳,尋求成功的機(jī)會(huì)。
In the 1990’s, he came to Shenzhen to        his       

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1.解析:,故選A。

2.解析:∵

,

故選B。

3.解析:由,得,此時(shí),所以,,故選C。

4.解析:顯然,若共線,則共線;若共線,則,即,得,∴共線,∴共線是共線的充要條件,故選C。

5.解析:設(shè)公差為,由題意得,,解得,故選C。

6.解析:∵雙曲線的右焦點(diǎn)到一條漸近線的距離等于焦距的,∴,又∵,∴,∴,∴雙曲線的離心率是。故選B.

7.解析:∵、為正實(shí)數(shù),∴,∴;由均值不等式得恒成立,,故②不恒成立,又因?yàn)楹瘮?shù)是增函數(shù),∴,故恒成立的不等式是①③④。故選C.

8.解析:∵,∴在區(qū)間上恒成立,即在區(qū)間上恒成立,∴,故選D。

9.解析:∵

,此函數(shù)的最小值為,故選C。

10.解析:如圖,∵正三角形的邊長(zhǎng)為,∴,∴,又∵,∴,故選D。

11.解析:∵在區(qū)間上是增函數(shù)且,∴其反函數(shù)在區(qū)間上是增函數(shù),∴,故選A

12.解析:如圖,①當(dāng)時(shí),圓面被分成2塊,涂色方法有20種;②當(dāng)時(shí),圓面被分成3塊,涂色方法有60種;

③當(dāng)時(shí),圓面被分成4塊,涂色方法有120種,所以m的取值范圍是,故選A。

13.解析:做出表示的平面區(qū)域如圖,當(dāng)直線經(jīng)過(guò)點(diǎn)時(shí),取得最大值5。

學(xué)科網(wǎng)(Zxxk.Com)14.解析:∵,∴時(shí),,又時(shí),滿足上式,因此,

。

學(xué)科網(wǎng)(Zxxk.Com)15.解析:設(shè)正四面體的棱長(zhǎng)為,連,取的中點(diǎn),連,∵的中點(diǎn),∴,∴或其補(bǔ)角為所成角,∵,∴,∴,又∵,∴,∴所成角的余弦值為。

學(xué)科網(wǎng)(Zxxk.Com)16.解析:∵,∴,∵點(diǎn)的準(zhǔn)線與軸的交點(diǎn),由向量的加法法則及拋物線的對(duì)稱性可知,點(diǎn)為拋物線上關(guān)于軸對(duì)稱的兩點(diǎn)且做出圖形如右圖,其中為點(diǎn)到準(zhǔn)線的距離,四邊形為菱形,∴,∴,∴,∴,∴,∴向量的夾角為。

17.(10分)解析:(Ⅰ)由正弦定理得,,,…2分

,,………4分

(Ⅱ)∵,,∴,∴,………………………6分

又∵,∴,∴,………………………8分

!10分

18.解析:(Ⅰ)∵,∴;……………………理3文4分

(Ⅱ)∵三科會(huì)考不合格的概率均為,∴學(xué)生甲不能拿到高中畢業(yè)證的概率;……………………理6文8分

(Ⅲ)∵每科得A,B的概率分別為,∴學(xué)生甲被評(píng)為三好學(xué)生的概率為!12分

(理)∵,,!9分

的分布列如下表:

0

1

2

3

的數(shù)學(xué)期望!12分

19.(12分)解析:(Ⅰ)時(shí),

,,

    

得,   ………3分

 

 

+

0

0

+

遞增

極大值

遞減

極小值

遞增

,      ………………………6分

(Ⅱ)在定義域上是增函數(shù),

對(duì)恒成立,即 

   ………………………9分

(當(dāng)且僅當(dāng)時(shí),

               

 ………………………4分

學(xué)科網(wǎng)(Zxxk.Com)              

20.解析:(Ⅰ)∵,,∴,∵底面,∴,∴平面,∴,又∵平面,∴,∴平面,∴!4分

(Ⅱ)∵平面,∴,,∴為二面角的平面角,………………………6分

,,∴,又∵平面,,∴,∴二面角的正切值的大小為。………………………8分

(Ⅲ)過(guò)點(diǎn),交于點(diǎn),∵平面,∴在平面內(nèi)的射影,∴與平面所成的角,………………………10分

學(xué)科網(wǎng)(Zxxk.Com),∴,又∵,∴與平面所成的角相等,∴與平面所成角的正切值為!12分

解法2:如圖建立空間直角坐標(biāo)系,(Ⅰ)∵,,∴點(diǎn)的坐標(biāo)分別是,,,∴,,設(shè),∵平面,∴,∴,取,∴,∴!4分

(Ⅱ)設(shè)二面角的大小為,∵平面的法向量是,平面的法向量是,∴,∴,∴二面角的正切值的大小為!8分

(Ⅲ)設(shè)與平面所成角的大小為,∵平面的法向量是,,∴,∴,∴與平面所成角的正切值為!12分

21.(Ⅰ) 解析:如圖,設(shè)右準(zhǔn)線軸的交點(diǎn)為,過(guò)點(diǎn)


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