1977年北京英语数学高考试题
一、写出下列单词的变化形式(每空1分)
1.hero (名词复数)
2.enemy (名词复数)
3.railway (名词复数)
4.life (名词复数)
5.sheep (名词复数)
6.woman (名词复数)
7.stop (过去式) (过去分词) (现在分词)
8.die (过去式) (过去分词) (现在分词)
9.hurry (过去式) (过去分词) (现在分词)
10.rise (过去式) (过去分词) (现在分词)
11.win (过去式) (过去分词) (现在分词)
12.catch (过去式) (过去分词) (现在分词)
二、用英语回答下列问题(每题2分)
1.Are you a student?
2.How many people are there in your family?
3.Where were you born?
4.How old were you when you started to go to school?
5.How long have you been studying English?
6.You like to study English,don't you?
7.What subjects did you study at middle school?
8.What did you do after you finished middle school?
三、用所给动词的适当形式填空(每空1分)
1.As soon as our Party secretary (come) back from Tachai next week,we (begin)to build a reservoir.
2.When the teacher (come)into the classroom,the pupils (leave). Only Li Ping still there. He (repair) a broken chair. He (tell) the teacher that he (be) through in a few minutes.
3.What (be) you (do) here?
I (write) a letter to nay brother.
I (not hear) from him for a long time.
4.My father (not work) in Peking. He is in Taching. He (be) there for ten years. He often (write) to us and (tell) us about his work and life there.
四、按句子所给的汉语内容,用英语完成下列各句(每题4分)
1.The magnificent building (矗立在天安门广场上) is the Memorial Hall of Chairman Mao.
2.Great changes have taken place in our country (自从我们在党和华主席领导下粉碎“四人帮”以来).
3.The people of Hsingtai will always remember (我们敬爱的周总理来看望他们的那一天).
4.(如果明天不下雨),we will have a basketball match with PLA men.
5.Is this the subject (你最感兴趣的)?
6.The old peasant asked me (是否到过延安).
五、将下列短文译成英语(满分20分)
我是红星公社的一个新社员。两年前离开城市到农村去插队落户。在贫下中农的帮助下,我提高了政治觉悟,学会了各种农活。今年一月,党支部叫我去当小学教师。从那以后,我一直教语文。我多么热爱我的工作和我的学生啊!
为了达到四个现代化的伟大目标,党号召我们青年人学习科学技术。现在我正在参加大学入学考试。我希望能考上大学。我一定为革命努力学习,争取做到又红又专。如果考不上,就回到农村去,在三大革命运动中更加努力工作。我将为把我们的祖国建设成为一个伟大的、现代化的社会主义强国作出贡献。
一、解答题(共12小题,满分120分)
1.(10分)(1977北京)解方程 .
2.(10分)(1977北京)计算: .
3.(10分)(1977北京)已知lg2=0.3010,lg3=0.4771,求lg .
4.(10分)(1977北京)证明: .
5.(10分)(1977北京)求过两直线x+y﹣7=0和3x﹣y﹣1=0的交点且过(1,1)点的直线方程.
6.(10分)(1977北京)某工厂今年七月份的产值为100万元,以后每月产值比上月增加20%,问今年七月份到十月份总产值是多少?
7.(10分)(1977北京)已知二次函数y=x2﹣6x+5.
(1)求出它的图象的顶点坐标和对称轴方程;
(2)画出它的图象;
(3)分别求出它的图象和x轴、y轴的交点坐标.
8.(10分)(1977北京)一只船以20海里/小时的速度向正东航行,起初船在A处看见一灯塔B在船的北45°东方向,一小时后船在C处看见这个灯塔在船的北15°东方向,求这时船和灯塔的距离CB.
9.(10分)(1977北京)有一个圆内接三角形ABC,∠A的平分线交BC于D,交外接圆于E,求证:AD?AE=AC?AB.
10.(10分)(1977北京)当m取哪些值时,直线y=x+m与椭圆 有一个交点?有两个交点?没有交点?当它们有一个交点时,画出它的图象.
11.(1977北京)求函数f(x)= 的导数.
12.(1977北京)(1)试用ε﹣δ语言叙述“函数f(x)在点x=x0处连续的定义;
(2)试证明:若f(x)在点x=x0处连续,且f(x0)>0,则存在一个x0的(x0﹣δ,x0+δ),在这个邻域内,处处有f(x)>0.