題目列表(包括答案和解析)
(本題12分)定義在R上的函數(shù),已知在上有最小值3。
(1)求的單調(diào)區(qū)間;
(2)求在上的最大值。
下面來自哥本哈根的一則報道:
COPENHAGEN:No matter what the outcome of the UN climate change conference is, China will remain committed(盡…義務(wù))to achieving the emission reduction targets(減排目標(biāo))it has said for itself, Premier Wen Jiabao said on Friday.
“We will honor our word with real action,”Wen told 119 heads of state and government attending the UN climate change conference,or COP 15.
Before the conference began,China announced that it would reduce its carbon intensity emission by 40 and 45 percent by 2020.
Wen then met US President Barack Obama for nearly an hour in what a White House official described as a“step forward”.“But Obama refused to commit to new emission cuts, a move that many said could have saved the struggling climate talks.
假如你叫李華,在看完這則報道后用英語給出席“哥本哈根聯(lián)合國世界氣候變化大會”(Copenhagen)The 15th United Nations Climate Change Conference,or COP 15的各國首腦寫封信,代表中國的中學(xué)生陳述你們對世界環(huán)境問題的關(guān)注和對本次大會的期待。文章應(yīng)包括以下要點的內(nèi)容,不必逐字翻譯,字?jǐn)?shù)在120左右.
1.經(jīng)濟發(fā)展決不能以犧牲環(huán)境為代價,降低排放,減少溫室效應(yīng)(green house effect)是本世紀(jì)人類面對的最大挑戰(zhàn).(challenge)
2.幾十年來,中國政府在改善環(huán)境方面的努力有目共睹,本次大會,中國提出了最高的減排目標(biāo),起了帶頭作用.
3.自己親身體驗到了學(xué)校周邊自然環(huán)境的變化.
4.發(fā)達國家應(yīng)當(dāng)有勇氣承擔(dān)更多的責(zé)任
5.作為未來的主人,真誠希望各國的領(lǐng)導(dǎo)人立即行動起來,共同合作,不要把問題留給下一代人.
開頭已寫出:
Dear Sirs/madams,
As Chinese teenagers,we are most concerned about the opening of COP 15 in Copenhagen
閱讀下面短文,然后按要求寫一篇150詞左右的英語短文
In China,with one or two parents going out to earn money,many children are left in their hometown in the countryside.These children are called “l(fā)eftover children”.A large number of leftover children have emerged since 1978,and the statistics showed in 2004,the total was 22 million.
Usually their grandparents or their parents’ friends or relatives look after these leftover children.Sometimes they are brought up by one of their parents at home.In most cases,their guardians are not quite educated.To them,making sure that the children are healthy and fed well is the most important task,and that the children are safe and sound is considered to have done a good job.But they seldom care about children’s study,their psychological needs,or mental demands.Neither do they spend some time teaching kids how to develop good habits.
Therefore,for most of the time,the leftover children can’t get emotional support from their parents,which can result in so many problems.
【寫作內(nèi)容】
1.以約30個詞概括短文的要點;
2.然后以約120個詞就“如何關(guān)心農(nóng)村留守兒童(leftover children)的成長?”的主題發(fā)表看法,并包括如下要點:
(1)農(nóng)村留守孩子存在的原因;
(2)你認(rèn)為他們面臨的最大困難是什么;
(3)解決留守兒童問題的關(guān)鍵是什么;
(4)提出解決問題的措施。
【寫作要求】
1.你可以使用實例或其他論述方法支持你的論點,也可以參照閱讀材料的內(nèi)容,但不能直接引用原文的句子;
2.題目自定。
【評分標(biāo)準(zhǔn)】
概括準(zhǔn)確,語言規(guī)范,內(nèi)容合適,篇章連貫。
近來你班上同學(xué)關(guān)系不太融洽,老師要求你在班會上就“友誼”發(fā)表講話,鼓勵大家要珍惜友誼,包括如下內(nèi)容:
1. 友誼是人與人的關(guān)系,交朋友是人的本性(instinct);
2. 友誼的作用:有困難時友誼如何給我們予幫助;成功時朋友可以分享幸福;
3. 友誼是我們的最大快樂之一,在人生道路上沒有得到友誼,就沒有真正地?fù)碛猩睢?/p>
4. 號召大家要珍惜友誼。
【寫作要求】
只能使用5個句子表達全部內(nèi)容。
讀寫任務(wù)(共1小題,滿分25分)
在全國“兩會”上,“農(nóng)村留守兒童” 問題成為人大代表和政協(xié)委員普遍關(guān)注的熱門話題之一。請閱讀下面的短文,然后按照要求寫一篇150詞左右的英語短文。
In China, with one or two parents going out to earn money, many children are left in their hometown in the countryside. These children are called “l(fā)eftover children”. A large number of leftover children have emerged since 1978, and the statistics showed in 2004, the total is 22 million.
Usually their grandparents or their parents’ friends or relatives look after these leftover children. Sometimes they are brought up by one of their parents at home. In most cases, their guardians are not quite educated. To them, making sure that the children are healthy and fed well is the most important task, and that the children are safe and sound is considered to have done a good job. But they seldom care about children’s study, their psychological needs, or mental demands. Neither do they spend some time teaching kids how to develop good habits.
Therefore, for most of the time, the leftover children can’t get emotional support from their parents, which can result in so many problems.
[寫作內(nèi)容]
1. 以大約30個詞概括短文的內(nèi)容。
2. 然后以約120個詞就“如何關(guān)心農(nóng)村留守兒童(leftover children)的成長?”的主題發(fā)表看法,并包括如下要點:
1)農(nóng)村留守孩子存在的原因是什么。
2)你認(rèn)為他們面臨的最大困難是什么。
3)解決留守孩子問題的關(guān)鍵是什么, 提出解決問題的措施。
[寫作要求]
1. 你可以使用實例或其他論述方法支持你的論點,也可以參照閱讀材料的內(nèi)容,但不能直接引用閱讀材料的句子。
2. 題目自定。
[評分標(biāo)準(zhǔn)]
概括準(zhǔn)確、語言規(guī)范、內(nèi)容合適、篇章連貫。
_______________________________________________________________________________________________________________________________________________________________________________________________________________
1.解析:,故選A。
2.解析:∵
,
故選B。
3.解析:由,得,此時,所以,,故選C。
4.解析:顯然,若與共線,則與共線;若與共線,則,即,得,∴與共線,∴與共線是與共線的充要條件,故選C。
5.解析:設(shè)公差為,由題意得,;,解得或,故選C。
6.解析:∵雙曲線的右焦點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:∵、為正實數(shù),∴,∴;由均值不等式得恒成立,,故②不恒成立,又因為函數(shù)在是增函數(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)或時,圓面被分成2塊,涂色方法有20種;②當(dāng)或時,圓面被分成3塊,涂色方法有60種;
③當(dāng)時,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)過點時,取得最大值5。
14.解析:∵,∴時,,又時,滿足上式,因此,,
∴。
15.解析:設(shè)正四面體的棱長為,連,取的中點,連,∵為的中點,∴∥,∴或其補角為與所成角,∵,,∴,∴,又∵,∴,∴與所成角的余弦值為。
16.解析:∵,∴,∵點為的準(zhǔn)線與軸的交點,由向量的加法法則及拋物線的對稱性可知,點為拋物線上關(guān)于軸對稱的兩點且做出圖形如右圖,其中為點到準(zhǔn)線的距離,四邊形為菱形,∴,∴,∴,∴,∴,∴向量與的夾角為。
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,
,,
由得, 或 ………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),
對恒成立,即
………………………9分
又(當(dāng)且僅當(dāng)時,)
………………………4分
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)過點做∥,交于點,∵平面,∴為在平面內(nèi)的射影,∴為與平面所成的角,………………………10分
∵,∴,又∵∥,∴和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)線與軸的交點為,過點
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