23. Yiwu is short of water now
Yes I think it,s very important for us to _______.
A waste water B save and protect water
C make the water dirty D throw the rubbish into the river
17. .-Would you like to see Beijing Opera with tonight?
-I,d like to ,but I,m afriend I_______,I have to write to my pen friend
A. need B.needn,t C can .D can,t
18 Don,t forget to wash your hands_______you have meals
A until B.before C when .D while
19 I,ve just borrowed a CD player, but I don,d know_______.
You can read the instructions
A how to use B.where to buy it C when to return it .D where to put it
20 ______do you spend on your homework every day?
A.How often B.How long C How many .D How much
21 Yaoming is one of the best players in NBA We are all__________him
A.angry with Bstrict with C worried about .Dproud of
22 The programme“Xiuhu Stories”________on Yiwu TV twice a week
A.is shown Bshowed C will show . D is showing
请从A.B.C.D四个选项中选出可以填入空白处的最佳选项
16.- Do you know the story of Goldilocks and the Three Bears?
- Yes Ido It,s______interesting story
A. a B. an C the .D 不填
第三节:听独白,请从A.B.C三个选项中选择正确的选项,完成信息记录表。
11. A. Car B. Bus C. Bike
12. A .4:00 B.5:00 C. .6:00
13. A.opposite B. behind C. inside
14. A. truck B. driver C. wall
15. A. left foot B.left arm C. right arm
第二节:听长对话,请从A.B.C三个选项中选择正确的选项。
听下面一段较长的对话,回答第6~7两小题。
6.Who is the letter from ?
A. John B. Betty C. Alice
7.Where does the girl come from ?
A. London B. Beijing C.New York
听下面一段较长的对话,回答第8~10三小题。
8.Which club does the man want to jonh ?
A.The English club B. The Japanese club C. The French club
9.What,s the man,s job ?
A. A doctor B.A taxi driver C.A businessman
10.Why does the man want to go john the club ?
A. Because he wants to go abroad
B. Because he wants to pass an English exam
C Because he wants to make more foreign friends
第一节:听小对话,请从A.B.C三个选项中选择符合对话内容的图片。
1.What are they doing now ?
2.Which animal does Kate like best ?
3.Where would Bruce like to go this weekend ?
4.What did Tom have for lunch yesterday ?
5.How does Tina feel ?
22.解法一:(1)取BC的中点H,连EH,易得EH是EF在平面AC上的射影,
∵BD⊥EH,∴由三垂线定理,得 EF⊥BD;
又∵EF在平面AB1上的射影是B1E,由△BB1E∽△ABG,得B1E⊥BG,∴由三垂线定理,得 EF⊥BG,
∵BG∩BD=B,∵EF⊥平面GBD.
(2)取C1D1的中点M,连EM,易得EM∥AD1,所以∠EFM就是异面直线AD1与EF所成的角,
∵MF∥BD,∴EF⊥MF .在Rt△EFM中,由EM=,(a为正方体的棱长),EF=,得
∠EFM=30º.即异面直线AD1与EF所成的角为30º.
解法二:(向量法)(1) 以AD为x轴,DC为y轴,DD1为z轴建立空间坐标系,不妨设正方体的棱长为2,
则D(0,0,0),A(2,0,0),B(2,2,0),E(2,1,0),F(1,2,2),G(2,,0,1) ,D1(0,0,2 )
∵(2,2,0)·(1,-1,-2)=0,(0,-2,1)·(1,-1,-2)=0
∴,,又∵BG∩BD=B,∵EF⊥平面GBD.
(2)=(-2,0,2),=(1,-1,-2) . =,
即异面直线AD1与EF所成的角为30º.
21.解:(I)
正面向上次数m |
3 |
2 |
1 |
0 |
概率P(m) |
|
|
|
|
正面向上次数n |
2 |
1 |
0 |
概率P(n) |
|
|
|
(II)甲获胜,则m>n,当m=3时,n=2,1,0,其概率为
当m=2时,n=1,0. 其概率为
当m=1时,n=0 其概率为
所以,甲获胜的概率为
20.解:(I)∵ △为以点M为直角顶点的
等腰直角三角形,
∴ 且.
∵ 正三棱柱,
∴ 底面ABC.
∴ 在底面内的射影为CM,AM⊥CM.
∵ 底面ABC为边长为a的正三角形,
∴ 点M为BC边的中点.
(II)由(1)知AM⊥且AM⊥CM,∴ AM⊥平面,
过点C作CH⊥于H, ∵ CH在平面内, ∴ CH⊥AM,
又,有CH⊥平面,
即CH为点C到平面AMC1的距离
由(1)知,, 且 .
∴ ∴
∴ 点C到平面的距离为底面边长为.
(III)过点C作CI⊥于I,连HI, ∵ CH⊥平面,
∴ HI为CI在平面内的射影,
∴ HI⊥,故∠CIH是二面角的平面角.
在直角三角形中,
,
∴ ∠CIH=45°, ∴ 二面角的大小为45°
19.解:(1)令红色球为x个,则依题意得, 所以得x=15或x=21,又红色球多于白色球,所以x=21.所以红色球为21个,白色球为15个.
(2)设从袋中任取3个小球,至少有一个红色球的事件为A,均为白色球的事件为B,
则P(B)=1-P(A)= =
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