篇一：2000年全国高考文科数学试题及其解析
2000年普通高等学校招生全国统一考试
数 学（文史类）
本试卷分第I卷（选择题）和第II卷（非选择题）两部分。第I卷1至2页。第II卷3至9页。共150分。考试时间120分钟。
第I卷（选择题 60分）
注意事项：
1．答第I卷前，考生务必将自己的姓名、准考证号、考试科目用铅笔涂写 在答题卡上。
2．每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需 改动，用橡皮擦干净后，再选涂其它答案，不能答在试题卷上。
3．考试结束，监考人将本试卷和答题卡一并收回。 参考公式：
三角函数的积化和差公式
1
sin?cos???sin??????sin??????
21
cos?sin???sin??????sin??????
21
cos?cos???cos??????cos??????
21
sin?sin????cos??????cos??????
2
正棱台、圆台的侧面积公式
1
S台侧??c??c?l
2
其中c?、c分别表示上、下底面周长，l表示斜高或母线长 台体的体积公式
1
V台体?S??S?S?Sh
3
其中S?、S分别表示上、下底面积，h表示高
一、选择题：本大题共12小题；第每小题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)设集合A={x|x∈Z且－10≤x≤－1}，B={x|x∈Z且|x|≤5}，则A∪B中的元素个数是
( )
（A）11
（B） 10
（C）16
（D）15
(2)在复平面内，把复数3－3i对应的向量按顺时针方向旋转
?
，所得向量对应的复数是3
( ) （A）2
（B）－23i
（C）3－3i
(D)3+3i
(3)一个长方体共一顶点的三个面的面积分别是2，，6，这个长方体对角线的长是
( ) (A)2
(B) 32
(C)6
(D)6
(4)已知sinα>sinβ，那么下列命题成立的是( )
(A)若α、β是第一象限角，则cosα>cosβ(B)若α、β是第二象限角，则tgα>tgβ (C)若α、β是第三象限角，则cosα>cosβ(D)若α、β是第四象限角，则tgα>tgβ (5)函数y=－xcosx的部分图像是 (
)
(6)《中华人民共和国个人所得税法》规定，公民全月工资、薪金所得不超过800元的部分不必纳税，超过800元的部分为全月应纳税所得额，此项税款按下表分段累进计算：
某人一月份应交纳此项税款26．78元，则他的当月工资、薪金所得介于( ) （A）800～900元 （B）900～1200元 （C）1200～1500元 (D)1500～2800元 (7)若a>b>1，P=lga?lgb，Q=
(A)R<P<Q
1?a?b?(lga+lgb)，R=lg??，则 2?2?
(C)Q<P<R
( ) (D)P<R<Q
(B) P<Q<R
(8)已知两条直线l1：y=x，l2：ax－y=0，其中a为实数．当这两条直线的夹角在(0，
?
)内12
变动时，a的取值范围是 ( )
(A)(0，1)
(B) (
3，) (C)(，1) ∪(1，3)(D)(1，3) 33
(9)一个圆柱的侧面展开图是一个正方形，这个圆柱的全面积与侧面积的比是( )
(A)
1?2?
2?
(B)
1?4?
4?
(C)
1?2?
?
(D)
1?4?
2?
(10)过原点的直线与圆x2+y2+4x+3=0相切，若切点在第三象限，则该直线的方程是( )
(A)y=x
(B) y=－3x
(C)y=
3
x 3
(D)y=－
x 3
(11)过抛物线y=ax2(a>0)的焦点F作一直线交抛物线于P、Q两点，若线段PF与FQ的长分别是p、q，则
11
?等于 ( ) pq
(B)
(A)2a
1 2a
(C)4a (D)
4 a
(12)如图，OA是圆锥底面中心O到母线的垂线，OA绕轴旋转一周所得曲面将圆锥分成体积相等的两部分，则母线与轴的夹角的余弦值为( )
(A)
1
2
(B)
11 (C) 22
(D)
1
2
第II卷（非选择题 90分）
注意事项：
1．第II卷共7页，用钢笔或圆珠笔直接答在试题卷中。 2．答卷前将密封线内的项目填写清楚。
二．填空题：本大题共4小题；每小题4分，共16分，把答案填在题中横线上.
(13)乒乓球队的10名队员中有3名主力队员，派5名参加比赛，3名主力队员要安排在第一、三、五位置，其余7名队员选2名安排在第二、四位置，那么不同的出场安排共有___________种(用数字作答) x2y2
??1的焦点为F1、F2，点P为其上的动点．当∠F1PF2为钝角时，点P横(14)椭圆94
坐标的取值范围是22
(15)设{an}是首项为1的正项数列，且(n+1)an?1—nan+ an+1an=0(n=1，2，3…)，则它的通
项公式是an
(16)如图，E、F分别为正方体的面ADD1A1、面BCC1B1的中心，则四边形BFD1E在该正方体的面上的射影可能是(要求：把可能的图的序号都填上
) ．
三、解答题：本大题共6小题；共74分，解答应写出文字说明、证明过程或 演算步骤。
(17)(本小题满分12分)
已知函数y=sinx+cosx，x∈R．
(Ⅰ)当函数y取得最大值时，求自变量x的集合；
(Ⅱ)该函数的图像可由y= sinx (x∈R)的图像经过怎样的平移和伸缩变换得到？
(18)(本小题满分12分)
设{an}为等差数列，Sn为数列{an}的前n项和，已知S7=7，S15=75，Tn为数列?前n项和，求Tn．
(19)(本小题满分12分)
如图，已知平行六面体ABCD－A1B1C1D1的底面ABCD是菱形，且∠C1CB=∠C1CD=∠BCD． (Ⅰ)证明：C1C⊥BD； (Ⅱ)当
?Sn?
?的n??
CD
的值为多少时，能使A1C⊥平面C1BD？请给出证明． CC1
(20)(本小题满分12分)
设函数f(x)=x2?1－ax，其中a>0． (Ⅰ)解不等式f(x)≤1；
(Ⅱ)证明：当a≥1时，函数f(x)在区间?0，???上是单调函数．
(21)(本小题满分12分)
某蔬菜基地种植西红柿，由历年市场行情得知，从二月一日起的300天内，西红柿市场售价与上市时间的关系用图一的一条折线表示；西红柿的种植成本与上市时间的关系用图二的抛物线段表示．
(Ⅰ)写出图一表示的市场售价与时间的函数关系式p=f(t)； 写出图二表示的种植成本与时间的函数关系式Q=g(t)；
(Ⅱ)认定市场售价减去种植成本为纯收益，问何时上市的西红柿纯收益最大？
(注：市场售价和种植成本的单位：元/102kg，时间单位：天)
(22)(本小题满分14分)
如图，已知梯形ABCD中|AB|=2|CD|，点E分有向线段AC所成的比为
8
，双曲线过C、D、E三点，且以A、B为焦点．求11
双曲线的离心率．
篇二：2000年高考英语试题(全国卷)
2000年普通高等学校招生全国统一考试
英 语（全国卷）
第一卷 （三大题，共95分）
Ⅰ.单项填空（共25小题，每小题1分；满分25分）
A）从A、B、C、D中找出其划线部分与所给单词的划线部分读音相同的选项。 例：have
A.gave B.saveC.hatD.made
答案是C. A.dull B.butcherC.sugarD.push
B）从A、B、C、D四个选项中，选出可以填入空白处的最佳答案。
例：We last night,but we went to the concert instead.
A.must have studied B.might study
C.should have studied D.would study
答案是C.
6.—What
—
A.Good idea.B.Help yourself.
C.Go ahead，please. D.Me，too.
7.I don’t think I’ll need any money but I’.
A.at last B.in case
C.once againD.in time
A.Brave enough students B.Enough brave students
C.Students brave enough D.Students enough brave
9.—Waiter!
— —I can’t eat this.It’s too salty.
A.Yes，sir？ B.What？
C.All right？ C.Pardon？
10.Most animals have little connection with animals of them for food.
A.the；a B.不填；a
C.the；the D.不填；the
11.It’s always difficult being in a foreign country, if you don’t speak the language.
A.extremely B.naturally
C.basically D.especially
12.Let Harry play with your toys as well，Clare-you must learn toA.support B.care
C.spare D.share
13.—you’ve left the light on.
—Oh，so I have. and turn it off.
A.I’ll go B.I’ve gone
C.I go D.I’m going
14.Someone called me up in the middle of the night，but they hung up phone.
A.as B.since
C.until D.before
15.—Are you coming to Jeff’s party？
—I’m not sure.I go to the concert instead.
A.must B.would
C.should D.might
16.If you want to change for a double room you’ll have to pay ＄15.
A.another B.other
C.more D.each
17.Dorothy was always speaking highly of her role in the , of course,made the others unhappy.
A.who B.which
C.this D.what
production up by 60%,the company has had another excellent year.
A.As B.For
C.With D.Through
19.I’ve worked with children before,so I know what in my new job.
A.expected B.to expect
C.to be expecting D.expects
20.—How are you today？
—Oh,I as ill as I do now for a very long time.
A.didn’t feelB.wasn’t feeling
C.don’t feel D.haven’t felt
21.The WTO cannot live up to its name it does not include a country that is home to one fifth of mankind.
A.as long as B.while
C.if D.even though
22.The managers discussed the plan that they would like to see the next year.
A.carry out B.carrying out
C.carried outD.to carry out
23.—Why don’t we take a little break？
—Didn’t we just have ？
A.it B.that
C.one D.this
24.It is the ability to do the job matters not where you come from or what you are.
A.one B.that
C.what D.it
25.The reporter said that the UFO east to west when he saw it.
A.was travellingB.travelled
C.had been travelling D.was to travel
Ⅱ.完形填空（共25小题，每小题1分；满分25分）
阅读下面短文，掌握其大意，然后从26~50各题所给的四个选项中，选出一个最佳答案。
I climbed the stairs slowly,carrying a big suitcase,my father following with two more.By the time I got to the third floor,I was and at the same time feeling lonely.Worse still,Dada step and fell,sending my new suitcases
down the stairs.“Damn!”he screamed,his face turning red.I knew
was ahead.Whenever Dad’How could I ever him to finish unloading the car screaming at me and making a scene in front of the other girls,I would have to spend the
of the year with？Doors were opening and faces peering out（探出），as Dad walkedclose behind.I felt it in my bones that my college life was getting off to a（n）“ 36 the room quickly,.”I thought.“Get him into a chair and calmed down.”But？Or would it be a（n）
room？
I turned the key in the lock and the door open,with Dad
complaining（抱怨）about a hurting knee or something.I put my head in,expecting the empty at all!It had furniture，curtains，a TV，and even paintings on the walls.
And there on a well-made bed sat Amy,my new ，dressed neatly，Greeting me with a nod，she said in a soft voice，“Hi，you must be Cori.”Then，she the music and looked over at “And of course，you’re Mr. Faber.”she said，“Would you like a glass of iced tea？”Dad’s face turned decidedly “yes”.
I knew Amy and I would be and my first year of college would be a success.
26.A.helplessB.lazyC.anxious D.tired
27.A.tookB.mindedC.missedD.picked
28.A.rollingB.passingC.dropping D.turning
29.A.sufferingB.difficulty C.troubleD.danger
30.A.go aheadB.look out C.hold onD.give up
31.A.lead B.helpC.encourage D.get
32.A.afterB.withoutC.whileD.besides
33.A.best B.beginning C.endD.rest
34.A.with difficulty B.in a hurry C.with firm steps D.in wonder
35.A.freshB.lateC.badD.unfair
36.A.SearchB.FindC.EnterD.Book
37.A.in factB.by chance C.once more D.then again
38.A.smallB.emptyC.newD.neat
39.A.FinallyB.Meanwhile C.Sooner or later D.At the moment
40.A.knockedB.forcedC.pushedD.tried
41.A.yet B.onlyC.evenD.still
42.A.worst B.chairC.bestD.tea
43.A.regretB.disappointment C.surpriseD.knowledge
44.A.roommateB.classmate C.neighbour D.companion
45.A.turned onB.turned down C.playedD.enjoyed
46.A.Dad B.me C.the doorD.the floor
47.A.questioning B.wondering C.smilingD.guessing
48.A.red B.less paleC.less redD.pale
49.A.soon B.thereC.laterD.then
50.A.sistersB.friendsC.studentsD.fellows
Ⅲ.阅读理解（共25小题。A节每小题2分，B节每小题1分；满分45分）
A）阅读下列短文，从每题所给的四个选项中，选出一个最佳答案。
A
New York,10 November-5：27 pm,yesterday.Biggest power failure in the city’s history.
*Thousands of people got stuck in lifts.Martin Saltzman spent three hours between the 21st and 22nd floors of the Empire State Building.“There were twelve of us.But no one panicked.We passed the time telling stories and playing word games.One man wanted to smoke but we didn’t let him.Firemen finally got us out.”
*“It was the best night we’ve ever had.”said Angela Carraro.who runs an Italian restaurant on 42nd Street.“We had lots of candles on the tables and the waiters were carrying candles on their trays.The place was full-and all night，in fact，for after we had closed，we let the people stay on and spend the night here.”
*The zoos had their problems like everyone else.Keepers worked through the night.They used blankets to keep flying squirrels and small monkeys warm.While zoos had problems keeping warm，supermarkets had problems keeping cool.“All of our ice cream and frozen foods melted.”said the manager of a store in downtown Manhattan.“They were worth ＄50，000.”
*The big electric clock in the lobby（大厅）of the Waldorf-Astoria Hotel in downtown Manhattan started ticking（滴答）again at 5：25 this morning.It was almost on time.
51.Throughout the period of darkness，Martin Saltzman and the eleven others wereA.nervousB.excitedC.calmD.frightened
52.In what way was the night of November 9 the best night for Angela Carraro？
A.She had a taste of adventure.
B.Burning candles brightened the place.
C.Business was better than usual.
D.Many people stayed the night in her restaurant.
53.How long did the power failure last？
A.Nearly 12 hours.B.More than 12 hours.
C.Nearly 24 hours.D.More than 24 hours.
B
The easy way out isn’t always easiest.I learned that lesson when I decided to treat Doug，my husband of one month，to a special meal.I glanced through my cookbook and chose a menu which included homemade bread.Knowing the bread would take time.I started on it as soon as Doug left
for work.As I was not experienced in cooking，I thought if a dozen was good，two dozen would be better，so I doubled everything.As Doug loved oranges，I also opened a can of orange and poured it all into the bowl.Soon there was a sticky dough（面团）covered with ugly yellowish marks.Realizing I had been defeated，I put the dough in the rubbish bin outside so I wouldn’t have to face Doug laughing at my work.I went on preparing the rest of the meal，and，when Doug got home，we sat down to Cornish chicken with rice.He tried to enjoy the meal but seemed disturbed.Twice he got up and went outside，saying he thought he heard a noise.The third time he left，I went to the window to see what he was doing. Looking out,I saw Doug standing about three feet from the rubbish bin，holding the lid up with a stick and looking into the container.When I came out of the house，he dropped the stick and explained that there was something alive in our rubbish bin.Picking up the stick again，he held the lid up enough for me to see.I felt cold.But I stepped closer and looked harder.Without doubt it was my work.The hot sun had caused the dough to double in size and the fermenting yeast（酵母）made the surface shake and sigh as though it were breathing.It looked like some unknown being from outer space.I could see why Doug was so shaken.I had to admit what the“living thing”was and why it was there.I don’t know who was more embarrassed（尴尬）by the whole thing-Doug or me.
54.The writer’s purpose in writing this story isA.to tell an interesting experience
B.to show the easiest way out of a difficulty
C.to describe the trouble facing a newly married woman
D.to explain the difficulty of learning to cook from books
55.Why did the woman’s attempt at making the bread turn out to be unsuccessful？
A.The canned orange had gone bad.
B.She didn’t use the right kind of flour.
C.The cookbook was hard to understand.
D.She did not follow the directions closely.
56.Why did the woman put the dough in the rubbish bin？
A.She didn’t see the use of keeping it.
B.She meant to joke with her husband.
C.She didn’t want her husband to see it.
D.She hoped it would soon dry in the sun.
57.What made the dough in the bin look frightening？
A.The rising and falling movement.
B.The strange-looking marks.
C.Its shape.
D.Its size.
58.When Doug went out the third time，the woman looked out of the window because she was .
A.surprised at his being interested in the bin
B.afraid that he would discover her secret
C.unhappy that he didn’t enjoy the meal
D.curious to know what disturbed him
C
Decision-thinking is not unlike poker-it often matters not only what you think，but also what
篇三：2000高考数学全国卷及答案理
2000年普通高等学校招生全国统一考试
数学(理工农医类)
本试卷分第I卷(选择题)和第II卷(非选择题)两部分．第I卷1至2页．第II卷3至9页．共150分．考试时间120分钟．
第Ⅰ卷(选择题共60分)
一、选择题：本大题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只(1) 设集合A和B都是自然数集合N，映射f:A?B把集合A中的元素n映射到集合B中的元素2n?n，则在映射f下，象20的原象是
(A) 2
(B) 3
(C) 4
(D) 5
( )
(2) 在复平面内，把复数3?i对应的向量按顺时针方向旋转数是
(A) 23
(B) ?23i
(C)
?
3
，所得向量对应的复
( )
?3i (D) 3?i
(3) 一个长方体共一顶点的三个面的面积分别是2，，6，这个长方体对角线的长是
(A) 23
(B) 32
(C) 6
(D)
( )
6
( )
(4) 已知sin??sin?，那么下列命题成立的是 (A) 若?、?是第一象限角，则cos??cos? (B) 若?、?是第二象限角，则tg??tg? (C) 若?、?是第三象限角，则cos??cos? (D) 若?、?是第四象限角，则tg??tg?
(5) 函数y??xcosx的部分图像是
( )
(6)《中华人民共和国个人所得税法》规定，公民全月工资、薪金所得不超过800元的部分不必纳税，超过800元的部分为全月应纳税所得额．此项税款按下表分段累进计算：
( )
某人一月份应交纳此项税款26.78元，则他的当月工资、薪金所得介于 (A) 800~900元
(B) 900~1200元
(C) 1200~1500元
(D) 1500~2800元
( )
(7) 若a?b?1，P=lga?lgb，Q=(A) R?P?Q
(B) P?Q ?R
a?b?1
?lga?lgb?，R=lg???，则 2?2?
(C) Q ?P?R
(D) P ?R?Q
( )
(8) 以极坐标系中的点?1 , 1?为圆心，1为半径的圆的方程是
???
(A) ??2cos????
4??
(C) ??2cos???1?
???
(B) ??2sin????
4??
(D) ??2sin???1?
(9) 一个圆柱的侧面展开图是一个正方形，这个圆柱的全面积与侧面积的比是 ( ) (A)
1?2?
2?
(B)
1?4?
4?
(C)
1?2?
?
(D)
1?4?
2?
(10) 过原点的直线与圆x2?y2?4x?3?0相切，若切点在第三象限，则该直线的方程
是
(A) y?x
(11) 过抛物线y?ax2?a?0?的焦点F作一直线交抛物线于P、Q两点，若线段PF与
(B) y??3x
(C) y?
( )
x 3
(D) y??
x 3
FQ的长分别是p、q，则
(A) 2a
11
?等于 pq
(B)
( )
(C) 4a
(D)
1 2a4 a
(12) 如图，OA是圆锥底面中心O到母线的垂线，OA绕轴旋转一周所得曲面将圆锥分成体积相等的两部分，则母线与轴的夹角为
(A) arccos
( )
1
2
(B) arccos(D) arccos
1 21
(C) arccos
1 2
2
第II卷(非选择题共90分)
二、填空题：本大题共4小题，每小题4分，共16分．把答案填在题中横线．
(13) 乒乓球队的10名队员中有3名主力队员，派5名参加比赛．3名主力队员要安排在第一、三、五位置，其余7名队员选2名安排在第二、四位置，那么不同的出场安排共有_____种(用数字作答) x2y2
??1的焦点为F1、F2，点P为其上的动点，当?F1PF2为钝角时，点(14) 椭圆94
P横坐标的取值范围是22
(15) 设?an?是首项为1的正项数列，且?n?1?an2，3，…)，?1?nan?an?1an?0(n=1，
则它的通项公式是an(16) 如图，E、F分别为正方体的面ADD1A1、面
BCC则四边形BFD1E在该正方体的面上的射1B1的中心，
影可能是_______．(要求：把可能的图的序号都填上) ．
三、解答题：本大题共6小题，共74分，解答应写出文字说明、证明过程或演算步骤．
(17) (本小题满分12分) 已知函数y?
13cos2x?sinxcosx?1，x?R． 22
(I) 当函数y取得最大值时，求自变量x的集合；
(II) 该函数的图像可由y?sinx?x?R?的图像经过怎样的平移和伸缩变换得到？ (18) (本小题满分12分)
如图，已知平行六面体ABCD-A1B1C1D1的底面ABCD是
C1
B1
D1
A1
菱形，且?C1CB=?C1CD=?BCD=60?．
(I) 证明：C1C⊥BD； (II) 假定CD=2，CC1=
3
，记面C1BD为?，面CBD为2
C
D
A
?，求二面角 ??BD??的平面角的余弦值；
(III) 当
CD
的值为多少时，能使A1C?平面C1BD？请给出证明． CC1
(19) (本小题满分12分)
设函数f?x??x2?1?ax，其中a?0． (I) 解不等式f?x??1；
(II) 求a的取值范围，使函数f?x?在区间?0,???上是单调函数． (20) (本小题满分12分)
(I) 已知数列?cn?，其中cn?2n?3n，且数列?cn?1?pcn?为等比数列，求常数p； (II) 设?an?、?bn?是公比不相等的两个等比数列，cn?an?bn，证明数列?cn?不是等比数列．
(21) (本小题满分12分)
某蔬菜基地种植西红柿，由历年市场行情得知，从二月一日起的300天内，西红柿市场售价与上市时间的关系用图一的一条折线表示；西红柿的种植成本与上市时间的关系用图二的抛物线段表示．
(Ⅰ) 写出图一表示的市场售价与时间的函数关系式P=f?t?； 写出图二表示的种植成本与时间的函数关系式Q=g?t?；
(Ⅱ) 认定市场售价减去种植成本为纯收益，问何时上市的西红柿收益最大？ (注：市场售价和种植成本的单位：元/102kg，时间单位：天) (22) (本小题满分14分)
如图，已知梯形ABCD中AB?2CD，点E分有向线段AC所成的比为?，双曲线过C、D、E三点，且以A、B为焦点．当时，求双曲线离心率e的取值范围．
23???34
2000年普通高等学校招生全国统一考试
数学试题（理工农医类）参考解答及评分标准
一．选择题：本题考查基本知识和基本运算，每小题5分，满分60分．
(1)C (2)B (3)D (4)D (5)D (6)C (7)B (8)C (9)A (10)C (11)C (12)D
二．填空题：本题考查基本知识和基本运算，每小题4分，满分16分．