Question

谁能给几道经典高中英语或数学题，有答案和解释，谢谢

麻烦给几道经典高中英语或数学题，有答案和解释，谢谢

Answer 1

5 在长方体ABCD—A1B1C1D1中，AB=4，BC=3，CC1=2，如图

(1)求证 平面A1BC1∥平面ACD1；
(2)求(1)中两个平行平面间的距离；
(3)求点B1到平面A1BC1的距离
6 已知正四棱柱ABCD—A1B1C1D1，点E在棱D1D上，截面EAC∥D1B且面EAC与底面ABCD所成的角为45°,AB=a,求

(1)截面EAC的面积；
(2)异面直线A1B1与AC之间的距离；
(3)三棱锥B1—EAC的体积
7 如图，已知三棱柱A1B1C1—ABC的底面是边长为2的正三角形，侧棱A1A与AB、AC均成45°角，且A1E⊥B1B于E，A1F⊥CC1于F

(1)求点A到平面B1BCC1的距离；
(2)当AA1多长时，点A1到平面ABC与平面B1BCC1的距离相等
8 如图，在梯形ABCD中，AD∥BC，∠ABC= ,AB= AD=a,

∠ADC=arccos ,PA⊥面ABCD且PA=a
(1)求异面直线AD与PC间的距离；
(2)在线段AD上是否存在一点F，使点A到平面PCF的距离为
参考答案
5 (1)证明 由于BC1∥AD1，则BC1∥平面ACD1
同理，A1B∥平面ACD1，则平面A1BC1∥平面ACD1
(2)解 设两平行平面A1BC1与ACD1间的距离为d，则d等于D1到平面A1BC1的距离 易求A1C1=5，A1B=2 ，BC1= ，则cosA1BC1= ,则sinA1BC1= ,则S = ,由于 ，则 S ·d= ·BB1,代入求得d= ,即两平行平面间的距离为
(3)解 由于线段B1D1被平面A1BC1所平分，则B1、D1到平面A1BC1的距离相等，则由(2)知点B1到平面A1BC1的距离等于
6 解 (1)连结DB交AC于O，连结EO，
∵底面ABCD是正方形
∴DO⊥AC，又ED⊥面ABCD
∴EO⊥AC，即∠EOD=45°
又DO= a，AC= a，EO= =a，∴S△EAC= a
(2)∵A1A⊥底面ABCD，∴A1A⊥AC，又A1A⊥A1B1
∴A1A是异面直线A1B1与AC间的公垂线
又EO∥BD1，O为BD中点，∴D1B=2EO=2a
∴D1D= a，∴A1B1与AC距离为 a
(3)连结B1D交D1B于P，交EO于Q，推证出B1D⊥面EAC
∴B1Q是三棱锥B1—EAC的高，得B1Q= a

7 解 (1)∵BB1⊥A1E，CC1⊥A1F，BB1∥CC1
∴BB1⊥平面A1EF
即面A1EF⊥面BB1C1C
在Rt△A1EB1中，
∵∠A1B1E=45°，A1B1=a
∴A1E= a,同理A1F= a,又EF=a，∴A1E= a
同理A1F= a,又EF=a
∴△EA1F为等腰直角三角形，∠EA1F=90°
过A1作A1N⊥EF，则N为EF中点，且A1N⊥平面BCC1B1
即A1N为点A1到平面BCC1B1的距离
∴A1N=
又∵AA1∥面BCC1B，A到平面BCC1B1的距离为
∴a=2，∴所求距离为2
(2)设BC、B1C1的中点分别为D、D1，连结AD、DD1和A1D1，则DD1必过点N，易证ADD1A1为平行四边形
∵B1C1⊥D1D,B1C1⊥A1N
∴B1C1⊥平面ADD1A1
∴BC⊥平面ADD1A1
得平面ABC⊥平面ADD1A1，过A1作A1M⊥平面ABC，交AD于M，
若A1M=A1N，又∠A1AM=∠A1D1N，∠AMA1=∠A1ND1=90°
∴△AMA1≌△A1ND1,∴AA1=A1D1= ,即当AA1= 时满足条件
8 解 (1)∵BC∥AD,BC 面PBC,∴AD∥面PBC
从而AD与PC间的距离就是直线AD与平面PBC间的距离
过A作AE⊥PB，又AE⊥BC
∴AE⊥平面PBC，AE为所求
在等腰直角三角形PAB中，PA=AB=a
∴AE= a
(2)作CM∥AB，由已知cosADC=
∴tanADC= ,即CM= DM
∴ABCM为正方形，AC= a,PC= a
过A作AH⊥PC,在Rt△PAC中，得AH=
下面在AD上找一点F，使PC⊥CF
取MD中点F，△ACM、△FCM均为等腰直角三角形
∴∠ACM+∠FCM=45°+45°=90°
∴FC⊥AC,即FC⊥PC∴在AD上存在满足条件的点F

Answer 2

英语：
1. The slave____from morning till night.
A.made to work B.was made working C.was made worked
D.was made to work
选c3.The wine____ ,but it was still rather cold.
A.no longer blew B.would no longer blow
c.was no longer blowing D.had no longer blown 选a
2.Your proposal____by the committee soon.
A.Is discussed B.has been discussed C. is going to be discussed
D.will have been discussed
选c

Answer 3

（b)1.There were many people present and he appeared only for a few seconds, so I only caught a _____ of him.A. glance B. glimpse C. look D. sight
(a)3.He looks sad. Could you please tell me ____ that prevents her from being as happy as before?
A. what it is B. it is what C. how it is D. it is how
(d)4.So involved with their computers _____ that leaders at summer computer camps often have to force them to break for sports and games.A. became the children B. become the children C. had the children become D. do the children become
(C)5.This book <javascript> will show the readers ___ can be used in other contexts.A. how that they have observed B. that how they have observed C. how what they have observed D. that they have observed
(B)6._______ , the mountain climbers conquered Mount Qomolangma in the end.
A．As the difficulty was great B．Great as the difficulty was
C．Great difficulty as it was D．The difficulty was great
(d)7.-----What about ______lesson this morning?
-----A piece of cake; it was too easy________ lesson for me.
A. the; the B. a; a C. a; the D. the; a
(a)8.Jack, to his _____, risked her life to save her classmate from the earthquake.
A. credit B. anxiey C. relief D. benefit
(b)9. The kind of office equipment will certainly makes a(n)____ to the way I do my job.
A. sense B. difference C. effect D. Meaning
(d)10. --Is the film Finding Nemo_____for small children?
--- Certainly. It is about a ugly fish. w.w.w.k.s.5.u.c.o.m
A. available B. approachable C. automatic D. appropriate
(b)11. The report was not concrete and in a way lacks persuasion. But______, I felt it is fair.
A. above all B. in a word C. on the whole D. in other word