问题 选择题
我们知道,在平面直角坐标系中,方程
x
a
+
y
b
=1
表示的图形是一条直线,具有特定性质:“在x轴,y轴上的截距分别为a,b”;类比到空间直角坐标系中,方程
x
λ
+
y
3
+z=1
表示的点集对应的图形也具有某特定性质,设此图形为m,若m与zoy平面所成角正弦值为
2
5
5
,则正数λ的值是(  )
A.
5
2
B.
2
15
15
C.2
3
D.
3
答案

由题意,方程

x
λ
+
y
3
+z=1表示平面,且在x轴,y轴,z轴上的截距分别为λ,
3
,1

设平面与x轴,y轴,z轴的交点分别为A,B,C,△ABC中,BC边上的高为h,则

∵m与zoy平面所成角正弦值为

2
5
5

2
5
5
=
λ
h
,∴h=
5
2
λ

∵cosC=

AC2+BC2-AB2
2AC•BC
=
1
2
1+λ2

∴sinC=

1-cos2C
=
3+4λ2
2
1+λ2

∵BC=2

∴由等面积可得

1
2
•2•
5
2
λ=
1
2
•2•
1+λ2
3+4λ2
2
1+λ2

∴λ=

3

故选D.

阅读理解

A few days ago my wife sent me out to buy something. When I came home, I handed(交给) her a paper bag and said, “Here are the apples you wanted.” She looked in the bag, and then she looked at me. “I told you,” she said slowly, “to buy some eggs.”

I felt worried about my absent-mindedness, so I went to see a doctor. He was a very kind man. “I have seen many people like you. It’s nothing to worry about,” he said. “If you know you are absent-minded, you are all right. But if you do not know you’re absent-minded, you may be really in trouble.”

“Many famous people were absent-minded,” the doctor told me. “Thomas Edison(爱迪生)was standing in line(排队) one day to pay his taxes(税). When he arrived at the window, he found that he had forgotten his own name. He had to ask the man who was behind him to tell him who he was.”

I felt much better and got up to leave. “Thank you, doctor,” I said. “How much do I have to pay you?”

“Ten dollars for the check-up(检查),” the doctor said.

“But doctor, I did not have a check-up!”

For a moment the doctor looked puzzled. Then he said, “Oh, yes, it was the patient before you who had a check-up. How absent-minded I am!”

小题1:It can be inferred from Paragraph 1 that when the author’s wife heard what her husband told her, she was ______.

A.excited

B.surprised

C.sad

D.proud小题2:The doctor took Edison’s story for example ______.

A.to show absent-mindedness is common among people

B.because he liked telling stories

C.to make the author laugh

D.to make fun of Edison小题3:The underlined word “absent-mindedness” in the second paragraph probably means ______.

A.a feeling of anger

B.a feeling of sadness

C.an emotion (情绪) of excitement

D.a trouble in which people often forget this or that小题4:According to the passage, who was (were) absent-minded?

A.Only the author.

B.The author’s wife.

C.The author and the doctor.

D.The doctor alone.

单项选择题