问题 解答题
已知A(-4,n),B(2,4)是一次函数y=kx+b的图象和反比例函数y=
m
x
的图象的两个交点.
(Ⅰ)求反比例函数和一次函数的解析式;
(Ⅱ)求直线AB与x轴的交点C的坐标;
(Ⅲ)求△AOB的面积(直接写出答案);
(Ⅳ)求不等式kx+b-
m
x
<0的解集(直接写出答案).
答案

(Ⅰ)将B(2,4)代入反比例函数得:4=

m
2
,即m=8,

∴反比例解析式为y=

8
x

将A(-4,n)代入反比例解析式得:n=-2,即A(-4,-2),

将A与B坐标代入一次函数解析式得:

-4k+b=-2
2k+b=4

解得:k=1,b=2,

则一次函数的解析式为y=x+2;

(Ⅱ)对于直线AB解析式y=x+2,令y=0,得到x=-2,即直线AB与x轴的交点C的坐标为(-2,0);

(Ⅲ)根据题意得:S△AOB=S△AOC+S△BOC=

1
2
×2×2+
1
2
×2×4=6;

(Ⅳ)根据题意得:不等式kx+b-

m
x
<0的解集为x<-4或0<x<2.

阅读理解

阅读理解

     On my first day of teaching,I found that I spent 85 per cent of my energy disciplining and 15 per cent

teaching knowledge.Of course I had some wonderful,serious students who would do well wherever they

were in life,but others worked hard to push themselves to the limit (限度).At night I went home

exhausted,often near tears.What gave me the idea I wanted to teach?

      And then there was Matthew.

     After school Matthew would come into my classroom to dust erasers or empty the wastepaper basket.

     "Why do you come in to visit me?" I asked him one night.

     "Because at home no one listens to me," was his reply.Later I found out that there were eleven children in his family,with Matthew near the middle.

     One time when he came to see me,he said,"Miss Ausmus,the kids are saying that you and Mr D.like each other."

     "Matthew,Mr D.is a nice man and we both teach some of the same students.He is not my boyfriend,

and it's not something the children should be talking about anyway."

     Another time,he said,"Will you wait for me so I can marry you when I grow up?"

     "Sorry,Matthew,but that won't work," I answered in a gentle way.

     When my birthday arrived,his mother made me a cake.She delivered (递送) it after school,and as

Matthew was carrying it up the school steps,he tripped (绊倒),dropping the cake.I found him in tears.I

told him that bringing me a cake was very,very special,whether I was able to eat it or not.

     After my second year of teaching,I said "goodbye" to Matthew and his family.

     Years passed and in 1992,I went back to the little town to visit.Matthew's parents still lived in the same house.His mother greeted me warmly."Janet,"she said,"Thanks for all the time you spent encouraging

Matthew.You taught him to believe in himself.You are the reason he went to college."

     I had made a difference in the life of a young boy.But I wonder...did Matthew ever know the difference he made in mine?

1. How did the author feel at the beginning of her teaching?

A. Embarrassed.  

B. Excited.

C. Frustrated.  

D. Amused.

2. By saying "others worked hard to push themselves to the limit",the author meant other students

________.

A. were forced to challenge themselves

B. made efforts to challenge their classmates

C. needed to be encouraged to learn

D. did everything they could to do well

3. Why did Matthew visit the author after school?

A. Because he had less communication at home.

B. Because he wondered if she liked Mr D.

C. Because he decided to marry her when he grew up.

D. Because he was going to celebrate her birthday.

4. Under the influence of the author,Matthew became________.

A. honest  

B. sincere

C. confident  

D. hardworking

5. What difference did Matthew make to the author?

A. He encouraged her to win Mr D.'s love.

B. He made her become enthusiastic about disciplining.

C. He gave her the courage to continue teaching.

D. He got her to understand what was true love.

选择题