題目列表(包括答案和解析)
請(qǐng)拼寫出符合題意的單詞;注意正確形式;若有錯(cuò)誤概不給分。
1. If Tom plans to pass the physical exam, he’d better change his _____ (態(tài)度) towards learning.
2. The brave policeman is still ______ (恢復(fù)) from his operation after fighting with the thief.
3. I would be g______ if you could give me some advice on how to write a good travel journal.
4. The successful program “Where are we going, dad?” was _____ (組織) by Hunan TV station.
5. ______ (逐漸) the children began to understand the importance of honesty.
(本題12分)根據(jù)空氣質(zhì)量指數(shù)API(為整數(shù))的不同,可將空氣質(zhì)量分級(jí)如下表:
對(duì)某城市一年(365天)的空氣質(zhì)量進(jìn)行監(jiān)測,獲得的API數(shù)據(jù)按照區(qū)間,,,,,進(jìn)行分組,得到頻率分布直方圖如圖.
(1)求直方圖中的值;
(2)計(jì)算一年中空氣質(zhì)量為良的天數(shù);
(3)某環(huán)保部門準(zhǔn)備在一年內(nèi)隨機(jī)到該城市考察兩次空氣質(zhì)量,求兩次考察空氣質(zhì)量都為良的概率(結(jié)果用分?jǐn)?shù)表示).
以下是五個(gè)應(yīng)聘者的信息
。請(qǐng)閱讀
A至F職位招聘的信息
,選出符合他們要求的最佳選項(xiàng)。選項(xiàng)中有一項(xiàng)是多余選項(xiàng)。(答案寫在答題卷上)
1.Elizabeth Nagata.
Elizabeth
once studied in a secretarial program when she was at university. She has
worked in Sumitomo Corporation as an executive assistant for eight years.
2.James Florian.
James once
worked as a salesperson and served as the director of new home sales in both
Forest Lakes and Glenmore for three years. He can speak excellent German and
English, and he is very good at dealing with people.
3.Arthur Smith.
Arthur, a
22-year-old boy, has just graduated from college. He’s got a diploma in Library
Technician Program. Wishing to have some free time, he doesn’t want to work
full time.
4.Gillian Anderson.
Gillian
graduated from the University of Manchester and got a Master’s Degree in
Library Science five years ago. As soon as she left school, she worked in St.
Bride Printing Library as a librarian. Now she is skilled in dealing with
almost everything in the library system.
5..Jerome Fingelhamm.
Jerome, aged
32, majored in computer science when he was at university. He has worked in a
software company for six years and is an expert at both software and hardware.
He got a driver’s license when he was eighteen years old.
A.
|
B.Executive Assistant Vancouver
|
C.Reference Specialist
|
D.Library Technician |
We need a
part-time library technician. Your position is responsible for library
cataloging (
編目錄), binding, ordering publications, assisting in legal research. Both
technical and reference services are required. The successful applicant should
have a Library Technician diploma (文憑).
E.
Circulation Director(
發(fā)行總監(jiān))
We are
looking for a circulation director. The successful applicant must have good
managing skills, including the ability to assign tasks to ensure the work of
the circulation department is done to the highest standard. A sales experience
of at least ten years is needed.
F. Computer
& Network Assistant
This
position is responsible for the activities related to the use of automated (
自動(dòng)化的) systems. Duties include
installing (安裝), repairing and updating software and
hardware. A driver’s license is necessary.
第二節(jié):以下是五個(gè)應(yīng)聘者的信息
。請(qǐng)閱讀
A至F職位招聘的信息
,選出符合他們要求的最佳選項(xiàng)。選項(xiàng)中有一項(xiàng)是多余選項(xiàng)。(答案寫在答題卷上)
Elizabeth Nagata.
Elizabeth once studied in a secretarial program when she was at university. She has worked in Sumitomo Corporation as an executive assistant for eight years.
James Florian.
James once worked as a salesperson and served as the director of new home sales in both Forest Lakes and Glenmore for three years. He can speak excellent German and English, and he is very good at dealing with people.
Arthur Smith.
Arthur, a 22-year-old boy, has just graduated from college. He’s got a diploma in Library Technician Program. Wishing to have some free time, he doesn’t want to work full time.
Gillian Anderson.
Gillian graduated from the University of Manchester and got a Master’s Degree in Library Science five years ago. As soon as she left school, she worked in St. Bride Printing Library as a librarian. Now she is skilled in dealing with almost everything in the library system.
.Jerome Fingelhamm.
Jerome, aged 32, majored in computer science when he was at university. He has worked in a software company for six years and is an expert at both software and hardware. He got a driver’s license when he was eighteen years old.
Sales Executive
We are looking for intelligent sales staff for our ever-growing team. Applicants must have at least one year sales experience, knowledge of English language publications and media, good English and social skills.
B. Executive Assistant Vancouver
Island Regional Library (VIRL) has an opportunity for an executive assistant. A diploma in Business Administration or a secretarial program is needed. A minimum (
最小值
) of five years’ experience as an executive assistant to an executive director is required.
C. Reference Specialist
You’re responsible for providing support for reference services in the library system. The successful applicant must have a Master’s Degree in Library Science and a minimum of three years’ experience as a professional librarian.
D. Library Technician
We need a part-time library technician. Your position is responsible for library cataloging (
編目錄
), binding, ordering publications, assisting in legal research. Both technical and reference services are required. The successful applicant should have a Library Technician diploma (
文憑
).
E. Circulation Director(
發(fā)行總監(jiān)
)
We are looking for a circulation director. The successful applicant must have good managing skills, including the ability to assign tasks to ensure the work of the circulation department is done to the highest standard. A sales experience of at least ten years is needed.
F. Computer & Network Assistant
This position is responsible for the activities related to the use of automated (
自動(dòng)化的
) systems. Duties include installing (
安裝
), repairing and updating software and hardware. A driver’s license is necessary.
第二節(jié):以下第81至85題是五個(gè)應(yīng)聘者的信息。請(qǐng)閱讀A至F職位招聘的信息,選出符合他們要求的最佳選項(xiàng)。選項(xiàng)中有一項(xiàng)是多余選項(xiàng)。(答案寫在答題卷上)
______ 81. Elizabeth Nagata.
Elizabeth once studied in a secretarial program when she was at university. She has worked in Sumitomo Corporation as an executive assistant for eight years.
______ 82.James Florian.
James once worked as a salesperson and served as the director of new home sales in both Forest Lakes and Glenmore for three years. He can speak excellent German and English, and he is very good at dealing with people.
______ 83.Arthur Smith.
Arthur, a 22-year-old boy, has just graduated from college. He’s got a diploma in Library Technician Program. Wishing to have some free time, he doesn’t want to work full time.
______ 84. Gillian Anderson.
Gillian graduated from the University of Manchester and got a Master’s Degree in Library Science five years ago. As soon as she left school, she worked in St. Bride Printing Library as a librarian. Now she is skilled in dealing with almost everything in the library system.
______ 85.Jerome Fingelhamm.
Jerome, aged 32, majored in computer science when he was at university. He has worked in a software company for six years and is an expert at both software and hardware. He got a driver’s license when he was eighteen years old.
Sales Executive
We are looking for intelligent sales staff for our ever-growing team. Applicants must have at least one year sales experience, knowledge of English language publications and media, good English and social skills.
B. Executive Assistant Vancouver
Island Regional Library (VIRL) has an opportunity for an executive assistant. A diploma in Business Administration or a secretarial program is needed. A minimum (最小值) of five years’ experience as an executive assistant to an executive director is required.
C. Reference Specialist
You’re responsible for providing support for reference services in the library system. The successful applicant must have a Master’s Degree in Library Science and a minimum of three years’ experience as a professional librarian.
D. Library Technician
We need a part-time library technician. Your position is responsible for library cataloging (編目錄), binding, ordering publications, assisting in legal research. Both technical and reference services are required. The successful applicant should have a Library Technician diploma (文憑).
E. Circulation Director(發(fā)行總監(jiān))
We are looking for a circulation director. The successful applicant must have good managing skills, including the ability to assign tasks to ensure the work of the circulation department is done to the highest standard. A sales experience of at least ten years is needed.
F. Computer & Network Assistant
This position is responsible for the activities related to the use of automated (自動(dòng)化的) systems. Duties include installing (安裝), repairing and updating software and hardware. A driver’s license is necessary.
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(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)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(shí),圓面被分成2塊,涂色方法有20種;②當(dāng)或時(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)過點(diǎn)時(shí),取得最大值5。
14.解析:∵,∴時(shí),,又時(shí),滿足上式,因此,,
∴。
15.解析:設(shè)正四面體的棱長為,連,取的中點(diǎn),連,∵為的中點(diǎn),∴∥,∴或其補(bǔ)角為與所成角,∵,,∴,∴,又∵,∴,∴與所成角的余弦值為。
16.解析:∵,∴,∵點(diǎn)為的準(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(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),
,,
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(duì)恒成立,即
………………………9分
又(當(dāng)且僅當(dāng)時(shí),)
………………………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(diǎn)做∥,交于點(diǎn),∵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(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)線與軸的交點(diǎn)為,過點(diǎn)
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