篇一：2015唐山二模理科数学试题及答案
唐山市2014—2015学年度高三年级第二次模拟考试
理科数学参考答案
一、选择题：
A卷：CBDAD CBADA BC B卷：BCDAD CBAAD CB 二、填空题：
20 1
（13）150°； （14）； （15）20π； （16）．
276
三、解答题： （17）解：
（Ⅰ）因为2accosB＝a2＋c2－b2，所以2(a2－b2)＝a2＋c2－b2＋bc． ?2分
1 2π
整理得a2＝b2＋c2＋bc，所以cosA，即A＝
23
?4分 ?6分
π π
（Ⅱ）因为∠DAB＝AD＝BD·sinB，∠DAC＝．
26
在△ACD中，有
ADCDBD＝3CD， sinCsin∠DAC
π3333
所以3sinB＝2sinC， 由B＝－C得cosC－sinC＝2sinC，整理得tanC＝
3227（18）解：
（Ⅰ）证明：
取PD中点E，连AE，EM， 则EM∥AN，且EM＝AN，
四边形ANME是平行四边形，MN∥AE． ?2分 因为MN⊥CD，所以AE⊥CD．
取AD中点O，连PO，则PO⊥AD．又因为平面PAD⊥平面ABCD，
所以PO⊥平面ABCD，PO⊥CD． ?4分 故CD⊥平面PAD，AD⊥CD．?5分
（Ⅱ）由AB＝AD，AD⊥CD，得□ABCD是正方形， 建立如图所示空间直角坐标系，设AB＝2，则
13
A(1，0，0)，B(1，2，0)，D(－1，0，0)，P(0，03)，E，0，．
22
(
)
→DB＝(2，2，0)，→DP＝(1，0，3)，
设平面PBD的法向量m＝(x，y，z)，则
?2×x＋2×y＋0×z＝0，33? 取m＝3，－3，－1)． →MN＝→EA＝0，
22x＋0×y＋3×z＝0，?1×
(
)
→|MN·m|2→设直线MN与平面PBD所成的角为θ，则sinθ＝| cos?MN，m?|＝．
7→|MN||m|
（19）解：
560(80×200－40×240)2
（Ⅰ）K＝5.657，因为5.657＞5.024，
120×440×320×240
所以能在犯错概率不超过0.025的前提下认为“是否支持节能降耗技术改造”与“企业规模”有关． ?4分
（Ⅱ）由（Ⅰ）可知“支持”的企业中，中小企业家数之比为1:3， 按分层抽样得到的12家中，中小企业分别为3家和9家．
设9家获得奖励的企业中，中小企业分别为m家和n家，则（m，n）可能为 （0，9），（1，8），（2，7），（3，6）．与之对应，X的可能取值为90，130，170，210．
0918CC1CC27
P(X＝90)＝，P(X＝130)＝，
C12220C12220
2
篇二：河北省唐山市2015年高三英语二模 答案
唐山市2014-2015学年度高三年级第二次模拟考试
英语试题参考答案
卷A
1. A 10. A19. C28. D37. D46. B55. C
2. C11. B20. B29. C38. A47. D56. D
3. B12. C21. B30. A 39. F48. C57. A
4. A 13. B 22. D31. B40. C49. A58. B
5. B14. A23. A32. B41. D50. C 59. D
6. A 15. C24. C33. C42. B51. C 60. B
7. C16. C25. A34. D43. A52. B
8. C17. A 26. B35. A44. C53. D
9. B 18. C27. A36. G 45. A54. A
卷B
1. C 10. B19. B28. C37. D46. A55. C
语法填空： 61. wonderful
62. were greeted
63. whether
64. he 69. best
65. hoping 70. on
66. caught 67. a
68. which
2. A11. A20. C29. D38. A47. D56. D
3. C12. A21. A30. A 39. F48. C57. C
4. B 13. C 22. A31. D40. C49. B58. B
5. B14. A23. D32. B41. D50. A 59. C
6. A 15. A24. B33. A42. A51. D 60. D
7. B16. B25. C34. C43. B52. B
8. C17. C 26. C35. B44. A53. B
9. B 18. C27. B36. G 45. C54. A
短文改错
If you monitor the wasting of energy at home, you’amazed
and you watch∧the rooms
alone
withleave
Aren’
Let’s be more concerned about the future, because that’s where we ！ If makes
One possible version
’m concerned, all your symptoms come from test anxiety. It is common for a student to feel nervous in face of the exam. So just face it and take it easy.
I advise you to focus on the problems rather than the exam results. For example, you can go through your exam papers, find out what your problems are and make improvements. And by opening yourself up to your parents, teachers and classmates, you may get valuable advice. Besides, you can consult a doctor if all these efforts do not seem to work. Above all, believe in yourself, and everything is going to be OK.
听力原文
第一节 Text 1
W: Good morning, this is United Airlines. What can I do for you? M: Yes, I’d like two seats on today’s Flight 7 to Chicago, please. Text 2
M: Hello, Miss. What can I do for you? W: I need a haircut. But you seem so busy today.
M: Yes, it is busy today. Would you like to take a seat and wait for a while, please? Text 3
W: Excuse me. Is this where I catch the bus for the zoo?
M: Well, you can take the No. 20 bus, and it’s a 10 minute ride. But, then you have to walk about 15 minutes. Text 4
W: Happy birthday! This is for you, Frank.
M: Oh, thanks, Carol. I am so happy you remembered. Please come in and enjoy the party. But before that, I’d like you to meet my little sister Angelina. I am sure you two will get along well. Text 5
M: Paris is really a good place to visit. W: How long have you been here?
M: Since September. I had a great tour of Paris and attended the 2014 Paris Fashion Week. It’s been wonderful. 第二节
W: Hello, Lost and Found Office.
M: Hello. I’m calling about a wallet. I did a little shopping at your department store on Monday afternoon and took a rest on the bench. W: A wallet? What’s it like?
M: Yes. It’s a black leather wallet. My passport is in it. My name is David Smith.
W: We have it here. A cashier found it at the counter on Tuesday morning and turned it in immediately.
M: Oh, good. How and when can I get it back?
W: Well, you have to come here and fill out a form this Friday and we will give it to you. M: Thank you. Text 7
W: Home at last. Tonight we have a lot of math homework, Eason.
M: Are you saying we don’t have time to watch our favorite show tonight? Jane, you know I really don’t like our math teacher. He’s kind of boring and not very active. W: To tell the truth, I don’t like him either. He gives far too much homework. M: Yes, and he also…
W: Do you think we should be talking about him like this behind his back?
M: Probably not. After all, he is our teacher. We should try to find something nice to say. W: I absolutely agree. It’s getting dark. We should finish our homework now. M: All right. I want to take a shower first. I am so tired. Text 8
M: What are you reading, Linda?
W: I am reading a novel The Mill on the Floss, written by the famous novelist, George Eliot. M: What’s it about?
W: It is mainly about the relationship between a brother and sister, who live in a mill on River Floss. It describes their childhood and an argument that causes them to separate. The book ends with them happily together again, but they are unfortunately both killed in a flood. M: Is it difficult to understand? W: Not really, I would consider it easy.
M: Besides novels, are there any other types of literary works that interest you? W: I am really fond of short stories. But not science fiction or detective stories. M: Have you read anything besides literature?
W: Certainly I have. I like to read books on various subjects and I read everything I can get my hands on in my spare time. I don’t want to hang around and waste my time. M: I agree. Books are like food for the mind.
M: Here’s your key card. Before you go to your room, let me tell you about the hotel’s wide range of services. We have a 24-hour laundry service, the price list can be found in your room. Are you here for business?W: Yes, I am.
M: There’s a business centre just down the hall. You can send faxes, photocopy and email from there. If you have a laptop we also have free wireless internet access.W: Great.
M: Facing the business centre there is a coffee shop and a hairdresser’s. In the evening you can relax in our excellent restaurant and enjoy a beer at the bar. We also have a swimming pool, and a gym.
W: Is your room service 24-hour?
M: Yes, it is, just in case you get hungry in the night. W: Do you know where I can hire a car?
M: The hotel has excellent car service. We can provide you with a car and a driver and have it charged to your bill.
W: OK, I might need to do that. Thank you so much for your consideration and I am really glad I’ve chosen your hotel. Text 10
I’m Alexandra Grace, Educator at New Zealand Embassy Beijing. Today I will give you a brief introduction of New Zealand’s higher education. Small as it may be, New Zealand offers quality higher education opportunities, with two thirds of its higher education institutes within the top 10 of QS World University Rankings 2014. What makes New Zealand’s universities stand out is their abilities to provide high-end education.
Though Chinese students form the largest international student group in New Zealand, the country only ranks the 7th on Chinese students’ most desirable overseas destination list. The size of the country prevents it becoming a hot study destination. But it draws students with its safe and multi-cultural environment.
While it attracts mainly wealthy students, higher education in New Zealand is also affordable for many common Chinese families. Chinese students can get a British-based education with the school fee being some of the lowest in the world. On average, the school fee was about 25,000 dollars per year, and the living costs were about 20,000 dollars a year. Besides, students can do some part-time jobs. The money earned in those jobs is enough for them to travel around the country and enjoy its breath-taking scenery.
篇三：河北省唐山市2015年高考数学二模试卷(理科)【解析】
2015年河北省唐山市高考数学二模试卷（理科）
一、选择题（本大题共12小题，每小题5分，共60分，在每小题给出的四个选项中，有且只有一项是符合题目要求）
1．设集合A={﹣1，0，1，2，3}，B={x|x﹣2x＞0}，则A∩B=（ ） A．{3} B．{2，3} C．{﹣1，3} D．{0，1，2}
2．在复平面内，复数z与A．2+i B．2﹣i C．﹣2+i
的对应点关于虚轴对称，则z=（ ） D．﹣2﹣i
2
3．在等差数列{an}中，a7=8，前7项和S7=42，则其公差是（ ） A．﹣ B．
C．﹣ D．
4．执行如图的程序框图，若输入的a=209，b=76，则输出的a是（ ）
A．19 B．3
C．57 D．76
5．设a=log3π，b=logπ3，c=cos3，则（ ） A．b＞a＞c B．c＞b＞a C．a＞c＞b D．a＞b＞c
6．函数y=4sin（ωx+φ）（ω＞0，|φ|＜π）部分图象如图，其中点A（
，0），B（
，
0），则（ ）
A．ω=，φ=﹣
B．ω=1，φ=﹣ C．ω=，φ=﹣ D．ω=1，φ=﹣
7．设实数x，y满足约束条件，则z=的取值范围是（ ）
A．[，1] B．[，] C．[，] D．[，]
8．某几何体的三视图如图所示，则该几何体的体积为（ ）
A．
B．
C．
D．
9．一种团体竞技比赛的积分规则是：每队胜、平、负分别得2分、1分、0分，已知甲球队已赛4场，积4分，在这4场比赛中，甲球队胜、平、负（包括顺序）的情况共有（ ） A．7种 B．13种 C．18种 D．19种
10．在△ABC中，AB=2BC，以A，B为焦点，经过C的椭圆和双曲线的离心率分别为e1，e2，则（ ） A．
﹣
=1
B．
﹣
=2
C．
﹣=1 D．﹣=2
11．已知函数f（x）=﹣，g（x）=xcosx﹣sinx，当x∈[﹣3π，3π]时，方程f（x）=g
（x）根的个数是（ ）
A．8 B．6 C．4 D．2
12．已知圆C：x+y=1，点M（t，2），若C上存在两点A，B满足是（ ）
A．[﹣2，2] B．[﹣3，3] C．[﹣
2
2
=，则t的取值范围
，] D．[﹣5，5]
二、填空题（本大题共4小题，每小题5分，共20分） 13．已知||=
14．设Sn是数列{an}的前n项和，an=4Sn﹣3，则S4=．
15．在三棱锥P﹣ABC中，△ABC与△PBC都是等边三角形，侧面PBC⊥底面ABC，AB=2则该三棱锥的外接球的表面积为．16．曲线
+
=1与两坐标轴所围成图形的面积是．
，||=2，若（+）⊥，则与的夹角是．
，
三、解答题（本大题共70分，其中17-21题为必考题，22-24题为选考题，解答应写出文字说明、证明过程或演算步骤）
17．在△ABC中，角A，B，C所对的边分别为a，b，c，2（a﹣b）=2accosB+bc． （Ⅰ）求A；
（Ⅱ）D为边BC上一点，BD=3DC，∠DAB=
，求tanC．
2
2
18．如图，四棱锥P﹣ABCD的底面ABCD是平行四边形，侧面PAD是等边三角形，平面PAD⊥平面ABCD，M，N分别是棱PC，AB的中点，且MN⊥CD． （Ⅰ）求证：AD⊥CD；
（Ⅱ）若AB=AD，求直线MN与平面PBD所成角的正弦值．
19．某市工业部门计划对所辖中小型工业企业推行节能降耗技术改造，对所辖企业是否支持改造进行问卷调查，结果如下表：
（Ⅰ）能否在犯错误的概率不超过0.025的前提下认为“是否支持节能降耗技术改造”与“企业规模”有关？
（Ⅱ）从上述320家支持节能降耗改造的中小企业中按分层抽样的方法抽出12家，然后从这12家中选出9家进行奖励，分别奖励中、小企业每家50万元、10万元，记9家企业所获奖金总数为X万元，求X的分布列和期望． 附： K=
2
2
20．已知抛物线E：x=4y，m、n是过点A（a，﹣1）且倾斜角互补的两条直线，其中m与E有唯一公共点B，n与E相交于不同的两点C，D． （Ⅰ）求m的斜率k的取值范围；
（Ⅱ）是否存在常数λ，使得|AC|?|AD|=λ|AB|？若存在，求λ的值；若不存在，说明理由．
21．设函数f（x）=x++alnx，g（x）=x++（﹣x）lnx，其中a∈R． （Ⅰ）证明：g（x）=g（），并求g（x）的最大值；
（Ⅱ）记f（x
）的最小值为h（a），证明：函数y=h（a）有两个互为相反数的零点．
请考生在第22、23、24题中任选一题作答，如果多做，则按所做的第一题记分【选修4-1：几何证明选讲】
22．如图，AB为圆O的直径，PB，PC分别与圆O相切于B，C两点，延长BA，PC相交于点D．
（Ⅰ）证明：AC∥OP；
（Ⅱ）若CD=2，PB=3，求AB．
2
【选修4-4：极坐标与参数方程】
23．在极坐标系中，曲线C：ρ=2acosθ（a＞0），l：ρcos（θ﹣有一个公共点．
）=，C与l有且仅
（Ⅰ）求a；
（Ⅱ）O为极点，A，B为C上的两点，且∠AOB=
【选修4-5：不等式选讲】
24．设f（x）=|x﹣1|﹣2|x+1|的最大值为m． （Ⅰ）求m；
（Ⅱ）若a，b，c∈（0，+∞），a+2b+c=m，求ab+bc的最大值． 2
2
2
，求|OA|+|OB|的最大值．
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