试题与答案

(1)化简(aa+b-a2a2+2ab+b2)÷(aa+b-a2a2-b2);(

题型:解答题

题目:

(1)化简(
a
a+b
-
a2
a2+2ab+b2
)÷(
a
a+b
-
a2
a2-b2
)

(2)计算
1
2
lg25+lg2-lg
0.1
-log29×log32

(3)
-1
=i
,验算i是否方程2x4+3x3-3x2+3x-5=0的解;
(4)求证:
sin(
π
4
+θ)
sin(
π
4
-θ)
+
cos(
π
4
+θ)
cos(
π
4
-θ)
=
2
cos2θ

答案:

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题型:阅读理解

An old woman had two large pots (罐), one on each end of a pole (扁担). She carried the pole with the pots across her neck.

One of the pots had a crack (裂缝) in it while the other pot was perfect and always delivered (递送) a full pot of water. At the end of the long walk from the well to the house, the cracked pot arrived only half-full.

For two years this happened daily, with the woman bringing home only one and a half pots of water. Of course, the perfect pot was proud. But the poor cracked pot was ashamed of its own imperfection.

One day, the cracked pot spoke to the woman by the well: “I am ashamed of myself because this crack in my side causes water to leak out all the way back to your house.”

The old woman smiled: “Did you notice that there are flowers on your side of the path, but not on the other pot’s side? That’s because I have always known about your crack, so I planted flower seeds on your side of the path. And every day while we walk back, you water them.”

“For two years I have been able to pick these beautiful flowers to decorate (装饰) the table. Without you being just the way you are, I would not have this beauty.”

Each of us has our own cracks. But it’s these cracks that make our lives together so interesting and meaningful.

小题1:How did the cracked pot feel about itself at first?

A.Proud.

B.Happy.

C.Excited.

D.Ashamed.小题2:Where were the flowers growing?

A.On both sides of the path.

B.In the woman’s house.

C.On the perfect pot’s side.

D.On the cracked pot’s side.小题3:Which is the correct order of the following events?

① The woman picked the flowers and decorated the table.

② The woman told the truth to the cracked pot.

③ The cracked pot talked to the woman about its crack.

④ The woman found a crack on one pot.

⑤ The woman planted some flower seeds.

A.④⑤①③②

B.⑤④③②①

C.④③①②⑤

D.④⑤③①②小题4:What does the passage mainly want to tell us?

A.Never laugh at old women.

B.Imperfection makes life meaningful.

C.Try your best to be perfect in life.

D.Don’t use a cracked pot to carry water.

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