增城中学2011届高三级第三次阶段综合测试
高三级数学理科试卷
一、选择题:本大题共8小题,每小题5分,满分40分.在每小题给出的四个选项中,只有一项是符合题目要求的. 1.复数i
i
+?11的虚部为 ( )
A.0
B.2
C.1
D.-1
2.已知向量()13,a =r ,()3,b x =r ,若//a b r r
,则实数x 等于( )
A.6 B. 9 C. 1 D. –1 3. 在等比数列{}n a 中,11a =,公比1q ≠.若12345m a a a a a a =,则m = A.9 B.10 C.11 D.12
4. 若实数
,x y
满足12,1,3,2?+=??
?
??≥+≤≤y x S y x y x 则的最大值为( )
A.6 B.4 C.3 D.2
5. 下列函数中,最小正周期为π的偶函数是( )
A.sin 2y x = B.tan y x = C.22cos 1y x =? D.cos 2
x
y =
6.方程1202x
x ????=????
的根所在的区间为 ( )
A. (1,2) B.(0,1) C. (1,0)? D.(2,3)
7. 某器物的三视图如右图所示,根据图中数据可知该器物 的表面积为( ) A.4π B.5π
C.8π
D.9π
8. 已知函数()|2||3|f x x x =?++,命题p :,x R ?∈使()f x a < .则“命题p 是假命题”
,是“5a <”的( )
A. 充要条件
B. 既不充分也不必要条件
C. 充分不必要条件
D. 必要不充分条件
二、填空题: 本大题共7小题,考生作答6小题,每小题5分,满分30分. (一)必做题(9~13题)
9.为了调查某厂工人生产某种产品的能力,随机抽查了20位工人某天生产该产品的数量.产品数量的分组区间为[)45,55,[)[)55,65,65,75,[)75,85,[)85,95由此得到频率分布直方图如图,则由此估计该厂工人一天生产该产品数量在[)55,75的人数约占该厂工人总数的百分率是 .
10.二项式41
()x x
?的展开式的常数项是 。
(用数字作答) 11.若双曲线22
14
x y m ?=的右焦点与抛物线212y x =的焦点重合,则=m 。
12.如右图是一个算法的程序框图,当输出值y 的 范围大于1时,则输入值x 的取值范围是 .
13.设()123,,=A a a a ,123????
=??????
b B b b ,
记{}112233max , , ?=A B a b a b a b , 若()1,1,1=?+A x x , 121????
=????????
B x x ,且
1?=?A B x ,
则实数x 的取值范围是
(二) 选做题(14~15题,考生只能从中选做一题) 14.(几何证明选讲选做题)
如图,四边形ABCD 是圆O 的内接四边形,延长AB 和DC 相交于点P。若PB=1,PD=3,则
BC AD
的值为
15.(坐标系与参数方程选讲选做题)
在平面直角坐标系xOy 中,
已知直线l 的参数方程为????=?=.
24,
12t y t x (参数R ∈t ),以直角坐标原点为极点,
x 轴的正半轴为极轴建立相应的极坐标系.在此极坐标系中,若圆C 的极坐标方程为2cos ρθ=,则圆
心C 到直线l 的距离为
三、解答题:本大题共6小题,满分80分.解答须写出文字说明,证明过程或演算步骤. 16. (本小题满分12
分)
已知向量()2cos ,sin =r a x x
,()
=r b x ,设(
)=?r r
f x a b ,()∈x R
(Ⅰ)求()f x 的单调递增区间;
(Ⅱ)当,44??
∈?????
x ππ时,求函数
()f x 的最小值。
17.(本小题满分12分)
第16届亚运会将于2010年11月12日在广州举办,运动会期间来自广州大学和中山大学的共计6名大学生志愿者将被随机平均分配到跳水、篮球、体操这三个比赛场馆服务,且跳水场馆至少有一名广州大学志愿者的概率是
35
。 (1)求6名志愿者中来自广州大学、中山大学的各有几人?
(2)设随机变量X 为在体操比赛场馆服务的广州大学志愿者的个数, 求X 的分布列及期望。
18.(本小题满分14分)
如图,四棱锥
倍,P 为侧棱SD 上的点。 (Ⅰ)求证:AC⊥SD;
(Ⅱ)若SD⊥平面PAC,求二面角P-AC-D 的大小
(Ⅲ)在(Ⅱ)的条件下,侧棱SC 上是否存在一点E,使得BE∥平面PAC。 若存在,求SE:EC 的值;若不存在,试说明理由。
19.(本小题满分14分)
设函数2
()ln()2f x x a x =++。
(Ⅰ)若当1x =?时,()f x 取得极值,求a 的值;
(Ⅱ)在(I)的条件下,方程2
ln()20x a x m ++?=恰好有三个零点, 求m 的取值范围;
(Ⅲ)当01a <<时,解不等式(21)ln f x a ?<。 20.(本小题满分14分)
已知抛物线G 的顶点在原点,焦点在y 轴正半轴上,点P(m,4)到其准线 的距离等于5。
(I) 求抛物线G 的方程;
(II) 如图,过抛物线G 的焦点的直线依次与抛物线G 及圆1)1(22=?+y x 交 于A、C、D、B 四点,试证明||||BD AC ?为定值;
(III)过A、B 分别作抛物G 的切线2121,,,l l l l 且交于点M,试求BDM ACM ΔΔ与 面积之和的最小值。
21.(本小题满分14分)
已知函数()1f x x =,数列{}n a 的前n 项和为n S ,对任意n N ?∈,点221,4n n n P a a ???????
都在函数
()f x 图像上,且1 1 , 0n a a =>;
(Ⅰ)求数列{}n a 的通项公式; (Ⅱ)求证:对任意n N ?∈
,)
112
n S >?
17. 解:(1)记至少一名广州大学志愿者被分到跳水比赛场馆为事件A , 则A 的对立事件为“没有广州大学志愿者被分到跳水比赛场馆”, 设有广州大学大学生志愿者x 人(16x ≤<),
则226422643()15x C C P A C C ?=?=,即211180x x ?+=, 解得2x =,9x =(舍去)
, 即来自广州大学的志愿者有2人,来自中山大学的志愿者有4人. ………6分 (2)X 的所有可能取值为0,1,2
22442264
2(0)5
C C P X C C ===,1122442264
8(1)15
C C C P X C C ===, 2
422
64
1
(2)15C P X C C ===……9分
故X 的分布列为
………10分
从而2812
()012515153
E X =×+×+×=(人). (12)
分
解法二:
(Ⅰ);连BD ,设AC 交于BD 于O ,由题意知SO ABCD ⊥平面.
以O 为坐标原点,OB OC OS ,
,分别为x 轴、y 轴、z 轴正方向, 建立坐标系O xyz ?如图。……1分
设底面边长为a ,则高2
SO a =
。
于是 ),(,0,0)2S D a , ,0)2
C a
,0)OC =, (,0,)2SD a = 0OC SD ?= 故 OC SD ⊥,从而 AC SD ⊥………3分
19.解: (1)()/1
4f x x x a
=
++ …………………………………..…….2分 Q 当1x =?时,()f x 取得极值, ()15
140,14f a a
∴?=
?==?+….…..4分
(2) 由25ln 204x x m ??++?=????得25ln 24x x m ?
?++=????,
令()()25ln 2,4f x x x g x m ?
?=++=???
?
则由已知条件转化为()f x 与()g x 的图像有3个交点………..….…….5分
Q ()()()
/4411154,()45
4
4
x x f x x x x x ++=
+=
>?++
∴由()/510144f x x x >??<>?或;()/1
014
f x x ?<……….6分
故函数()f x 在5,14????????单调递增,在11,4????????单调递减, 1,4??
?+∞????单调递增…..7分
()122ln 2f ?=?为极大值; 11
48f ???=????为极小值……………………………..……8分
如图,当()114f m f ??
?<????时, ()f x 与()g x 的图像恰有3个交点
1
22ln 28
m ∴< (9)
分
20. 解:(1)由题知,抛物线的准线方程为12
,01==+p
y …………2分
所以抛物线C 的方程为,42y x =
…………3分
(2) 设直线AB 方程:1+=kx y ,且AB 交抛物线C 于点),(),,(2211y x B y x A 由抛物线定义知1||,1||21+=+=y BF y AF …………4分 所以21||,||y BD y AC ==
…………5分
由??
?+==142kx y y
x 得0442=??kx x …………6分 显然4,4,02121?=?=+>Δx x k x x 则
…………7分
所以||||,116
2
2
2121BD AC x x y y ?=?=
?所以为定值1 (8)
分
21.解
初三月考联考测试卷 英 语 学 科 本份试卷分第一部分和第二部分两部分;第一部分1至10页,第二部分11至12页,共12页,满分135分。考试时间120分钟。 第一部分(共100分) 注意事项: 1、答卷前,考生务必在答题卡上用黑色字迹的钢笔或签字笔填写自 己的考生号、姓名;填写考场试室号、座位号,再用2B铅笔把对应的这两个号码的标号涂黑。 2、选择题每小题选出答案后,用HB铅笔把答题卡上对应题目的答 案标号涂黑。如需要改动,用橡皮擦干净,再选涂其他答案。不 能答在试卷上。 3、非选择题必须用黑色字迹的钢笔或签字笔作答,答案必须写在答 题卡各题目指定区域的相应位置上;如需要改动,先划掉原来的 答案,然后再写上新的答案,改动的答案也不能超出指定的区 域;不准使用铅笔、圆珠笔和涂改液。不按以上要求作答的答案 无效。 4、考生必须保持答题卡的整洁,考试结束,将本试卷和答题卡一并 交回。 5、本卷共四大题,70小题,听力部分的第一大题“听取信息”的题号 用A~E表示。请考生检查题数。 1、听力测试(共20小题,30分) 1、听取信息(共5小题,5分;每小题1分) 听下面一段对话,从所给的内容中获取必要的信息,填入Ⅱ答题卷的题号为A~E的空格中。听对话前,你将有10秒钟的时间阅读题目。录音读两遍。你有100秒钟的做答时间。 Place Day People The students in __________ Departure(离开) Time At ___________ o’clock Transport(交通工具)On ___________ big buses
2、对话理解(共10小题,15分;每小题1.5分) 听下面五段对话,每段对话后有几个小题,从题中所给的三个选项中选出最佳选项,并涂在答题卷的相应位置上。听每段对话前,你将有时间阅读各小题,每小题5秒钟;听完后,各小题将给出5秒种的作答时间。每段对话读两遍。 听第一段对话,回答第1小题。 1. Where is the cinema? A. B. C. Start start start 听第二段对话,回答第2~3小题。 2. What’s Johnson’s favourite hobby? A. Watching TV. B. Listening to pop songs. C. Reading the stories of famous people. 3. What kinds of programmes does Sally often watch? A. Stories of famous people. B. CCTV news. C. Both A and B. 听第三段对话,回答第4~5小题。 4. How many cities did the Blacks visit? A. 5 B. 6 C. 7 5. Which city did they like best? A. New York. B. Sydney. C. Paris. 听第四段对话,回答第6~7题。 6. What does the man want to buy? A. A pair of brown shoes. B. A pair of black shoes. C. A pair of blue shoes. 7. The man will buy the shoes, won’t he? A. Yes, he will though they are a bit expensive. B. No, he won’t because they haven’t got the size he wants. C. Yes, he will because he likes the colour. 听第五段对话,回答第8~10小题。 8. What is the woman doing? A. She is cooking. B. She is reading a book. C. She is writing a letter. 9. Where did the man ask the woman to see him? A. Near the flower garden. B. In the flower garden. C. Outside the flower garden. 10. How long did the woman ask the man to wait for her? A. About 12 minutes. B. About 15 minutes. C. About 20 minutes. 3、讲话理解(共5小题,10分;每小题2分)
2015年上海市杨浦区控江中学高三月考考试卷 II. Grammar and Vocabulary (26’) Section A Directions: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that fits each blank. (16’) (A) It is a particularly useful time for America to reflect on those who 25_____ (sacrifice) so much for our freedom. When I first 26____ (speak) at West Point in 2009, we still had more than 100,000 troops in Iraq. We ____27___(prepare)to surge in Afghanistan. Our counterterrorism efforts 28____ (focus) on al-Qaida’s core leadership -- those who had carried out the 9/11 attacks. And our nation was just beginning a long climb out of the worst economic crisis. Four and a half years later, as you graduate, the landscape has changed. We 29____(remove)our troops from Iraq. We are winding down our war in Afghanistan. Al-Qaida’s leadership on the border region between Pakistan and Afghanistan has been decimated, and Osama bin Laden is no more. Meanwhile, our economy30_____( remain) the most dynamic on Earth, our businesses the most innovative. Each year, we grow more energy independent. But the world 31____(change)with accelerating speed. This presents opportunity, but also new dangers. It will be your generation’s task to respond to this new world. The question we face, the question each of you will face, is not whether America__32___ (lead) but how we will lead, not just to secure our peace and prosperity but also extend peace and prosperity around the globe. (B) Many kinds of music can stir the imagination and produce strong feeling. For some people, romantic composers such as Chopin and Tchaikovsky enhance feelings of love and sympathy. Religious and spiritual music ___33___ help some people feel peace or lessen their pain. But one musician seems to have a unique ability of healing(治愈) the human body – Wolfgang Amadeus Mozart. Scientists have found Mozart’s music to be remarkable in its ability 34____ (calm) its listeners. It can also increase their perceptions, and help them express themselves more clearly. Many amazing cases have been documented using Mozart 35____ a healing aid. For example, a tiny premature baby 36______ (name) Kissy, who weighed just 1.5 pounds at birth, was on total life support. Doctors thought she had little chance of survival. Her mother insisted on playing Mozart for Krissy, and thought 37_____ saved her daughter’s life. Krissy lived, __38___ she was very small for her age and slower than the average child. At the age of four, she showed an interest in music and her parents gave her violin lessons. 39_____ their astonishment, Krissy was able to play musical pieces from memory that were far beyond the ability of an average four-year-old. __40___ (play) music helped her improve in all areas of her life. Section B
初三月考英语试题 (时间90分钟,满分120分) 一.单项选择(20分) ( ) 1. ----Have you decided _____for Shanghai? ----Not yet. Maybe next week. A. how to leave B. when to leave C. where to leave D. why to leave ( ) 2. The best way to learn new words is by____English magazines. A.Read B. reading C. to read D. have read ( ) 3. If you keep _____every day, you will be a good player. A. practice to run B. practicing running C. to practice to run D. to practice running ( ) 4. Marie _____shy, but now she is quite outgoing. A.was used to be B. is used to be C. used to be D. used to ( )5. I think teenagers should _____to choose their own clothes. A. be allowed B. allow C. be allow D. to allow ( ) 6. What would you do if you won____dollars? A.two millions B. million of C. two million D. two million of ( )7. The notebook must ____Li Hua’s, it has his name on it. A.Belong B. be C. belong to D. be to ( )8. He can’t go to school today_____his illness. A.because B. as for C. instead of D. because of ( ) 9. Anna is very quiet, she is afraid _____in public. A. of speak B. speaking C. spoke D. to speak ( )10. If you don’t know how to read English words,you can ____them____in the dictionary. A. look; for B. look; into C. look; at D. look; up ( )11. I’m really shy and I just enjoy being alone.____I don’t know anyone else there? A. How if B. What if C. What’s up D. Why ( )12. -----Look at the man, is it Mr White? -----No. It ____Mr White. He has gone to Beijing. A.can B. can be C. can’t D.can’t be ( )13 This music____me of my hometown. A.talks B .tells C. reminds D. asks ( )14. This is the boy____broke my windows.
一、填空题(15*2分=30分) 1、在Flash中按Ctrl+F8 键可新建一个元件;用线条工具绘制直线时,按住Shift 键则可绘出水平、垂直或倾斜45度的直线;绘制椭圆时,若按住Shift 可绘制正圆 2、用于绘制矢量直线的工具是线条工具;用于绘制精确的路径平滑流畅的线条是钢笔工具;用来输入文本或设置不同的文本样式是文本工具;用来绘制矩形或多边形和星形的是矩形工具;用来更改线条或形状轮廓的笔触颜色、宽度和样式的是墨水瓶工具;用来在封闭的图形内填充选定的颜色是颜料桶工具;用来对矢量的线条或色快进行擦除是橡皮擦工具。 3、插入普通帧的快捷键是 F5 插入关键帧的快捷键是 F6 插入空白关键帧的快捷键是 F7 。 4、按住 Ctrl+G键可以将形状组合;按住 Ctrl+Shift+G键可以取消组合 二、判断题(10题*2分=20分) 1、文字动画是Flash中最常用、表现方式最灵活的一种动画形式。 (×) 2、使用导入的声音或视频素材,制作文字效果,可以加强文字效果的表现 力。(√) 3、按“Ctrl+B”组合键可以将打散的文字组合。(×) 4、文本工具是用输入文字的。(√) 5、滴管工具不能提取位图的颜色。(×) 6、用来绘制矩形或多边形和星形的是椭圆工具。(×) 7、元件的注册点是元件的中心点。(×) 8、使用任意变形工具可直接将元件翻转。(√) 9、形状补见动画的对象既可以是形状也可以是组合或元件。(×) 10、两个关键帧之间是虚线表示两个关键帧之间创建的补间动画失败。 (√) 三、简答题(50分) 1、Flash有哪些特点?(15分) 答:1、使用矢量图形和流失播放技术 2、体积小 3、兼容性强 4、功能强大 5、动画效果丰富 2、如何删除库中元件,写出三种方法?(15分) 答:1、选中库中的元件后,按Delete键 2、在库中直接单击鼠标右键要删除的元件,在弹出的列表中选择 删除 3、将元件直接拖动到删除按钮上或选中要删除的元件后单击删除 按钮。 3、Flash动画有那几种类型,都有什么特点?(20分) 答:有逐帧动画、形状补见动画、动画补间、引导动画、遮罩动画、 Action Script动画六种类型。 特点: 逐帧动画的特点是指依次在每一个关键帧上安排图形或元件 而形成的动画类型;形状补间动画是指Flash中的矢量图形或线条之 间互相转化而形成的动画;动画补间是根据对象在两个关键帧中的位 置、大小、旋转、透明度等属性的差别计算生成的;引导动画是指Flash 里的运动引导层控制元件的运动而形成的;遮罩动画是指使用Flash 中遮罩层的作用而形成的一种动画效果;Action Sction动画是指使 用Flash的编程语言来控制或制作的动画类型。 第 1 页共2 页