问题 解答题
设函数f(x)=cos(
3
x+
φ)(0<φ<π),且f(x)+f′(x)为奇函数.
(1)求φ的值;
(2)求f(x)+f′(x)的最值.
答案

(1)f(x)+f'(x)=cos(

3
x+φ)-
3
sin(
3
x+φ)=2sin(
3
x+φ+
6
)

又f(x)+f'(x)是奇函数,

∴f(0)+f'(0)=0,又0<φ<π,

∴φ=

π
6

(2)由(1)得f(x)+f'(x)=2sin(

3
x+π)=-2sin
3
x.

∴f(x)+f'(x)的最大值为2,最小值为-2.

单项选择题 B1型题
完形填空
He lost his arms in an accident that claimed his father’s life who was the main   36 of support for the family. He had to   _37__  the arms of his younger brother,and his younger brother became his ___38 _ ,never leaving him alone for years. Except for writing with his toes,he was completely unable to do   _39_  in his life.
One late night,his younger brother accompanied him into the toilet and went back to  __40__ . But being so   41___,his younger brother fell asleep,leaving him on the toilet for two hours. As the two brothers grew up together,they had their share of problems and they would often  __42__  . His younger brother wanted to live   _43__  from him,living his own life,as many normal people do. So he was   44 __ and didn’t know what to do.
A   _45__  misfortune befell(降临) a girl. One night her mother,who suffered from mental illness ___46_ . So her father went out looking for her mother,leaving her alone at home. She tried to prepare a  __47_  for her parents,only to overturn the stove,  _48 __  in a fire which took her hands away.
Though her elder sister who was studying in another city,showed her   _49__  to take care of her,she was determined to be completely   _50__ . At school,she always studied hard.
One day,the boy and the girl were both invited to appear on a television interview program. They were both asked to write something on a piece of paper with their toes. The boy wrote: My younger brother’s arms are my arms;  51_  the girl wrote: Broken wings,flying heart.
Disasters can    52_ at any time. If you choose only to complain and    53   from the ordeal(苦难的经历),it will always follow you wherever you go. But if you decide to be       ___54   ,the hardship will turn out to be a(n)   55  on which new hopes will arise.
小题1:
A.causeB.strengthC.sourceD.course
小题2:
A.live onB.take onC.turn onD.depend on
小题3:
A.shadowB.volunteerC.bodyguardD.servant
小题4:
A.somethingB.anythingC.nothingD.everything
小题5:
A.playB.workC.waitD.wash
小题6:
A.tiredB.angryC.impatientD.unfair
小题7:
A.supportB.separateC.quarrelD.avoid
小题8:
A.lonelyB.differentC.separatedD.divided
小题9:
A.heartlessB.heart-brokenC.kind-heartedD.heart-warming
小题10:
A.sameB.similarC.simpleD.strange
小题11:
A.diedB.disappearedC.dismissedD.failed
小题12:
A.mealB.medicineC.heatingD.plan
小题13:
A.leadingB.resultingC.takingD.bringing
小题14:
A.willingnessB.anxietyC.contributionD.respect
小题15:
A.independentB.relaxedC.disabledD.energetic
小题16:
A.sinceB.whileC.asD.though
小题17:
A.strikeB.affordC.formD.return
小题18:
A.hideB.remainC.surviveD.escape
小题19:
A.carefulB.strongC.healthyD.polite
小题20:
A.difficultyB.fortuneC.occupationD.attitude