2016年课改实验班招生考试试题及答案.doc

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2016年初中升高中
课改实验班招生考试试卷

温馨提示：
1、本试卷分三个部分，数学部分、英语部分和物理部分。数学部分满分80分，英语部分满分40分，物理部分满分30分，总计满分150分。
2、考试时间总计120分钟。
3、请各位考生将乡镇场、在读学校、考号、姓名填写清楚。
数学部分（满分80分）
一、填空（每小题3分，共计24分）
第3题图
1、分解因式=
2、△ABC中，AB=5，AC=3，则BC边上的中线AD的长的取值范围是 。
3、如图在△ABC中，AB=AC，DE为AB的中垂线，且△BEC的周长为14，BC=5，那
么AB= 。
4、已知，样本的方差是2，则样本的方差
是 。
5、已知，a、b、c为△ABC的三边，且满足，则△ABC的形状是 。
6、计算： = 。
7、关于x的方程mx2－2(3m－1) x + 9m－1= 0有两个实数根，那么m的取值范围是 。
8、在直角坐标系中，有四点A（﹣8，3），B（﹣4，5），C（0，n），D（m，0），当四边形ABCD周长最短时，= 。
二、解答题
9、（本题6分）先简化，再求值。 其中

10、（本题6分）解方程组

第11题图
11、（本题6分）△ABC中，AD是∠BAC的外角平分线，P是AD上异于A的任意一点，试比较PB+PC与AB+AC的大小，并说明理由。

12、（本题8分）已知，反比例函数和一次函数 y= k x—5的图像都经过点P（m，3）
第12题图
(1)求k值。
(2)作直线平行于y轴，并交一次函数的图像于A，交反比例函数图像于B，设A、B的横坐标为a，求a为何值时有PA=PB?

13、（本题8分）如图， 已知正方形ABEF和ACGH在△ABC的外侧，M是BC边上的中点，求证：FH=2AM。
第13题图

14、（本题10分）黄石某楼盘准备以每平米7000元的均价对外销售，由于国务院有关房地产的新政策出台后，购房者持币观望，房地产开发商为了加快资金周转，对价格经过两次下调后，决定以每平米5670元的均价开盘销售。
（1）求平均每次下调的百分率。
（2）某人准备以开盘价均价购买一套120平米的住房，开发商给予以下两种优惠方案选择：①打9.8折销售；②不打折，一次性送装修费每平米100元，试问哪种方案更优惠？

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15、（本题12分）如图，在平面直角坐标系中，矩形AOCD的顶点A的坐标是（0，4），现有两动点P，Q，点P从点O点出发沿线段OC（不包括端点O，C）以每秒2个单位长度的速度匀速向点C运动，点Q从点C出发沿线段CD（不包括端点C、D）以每秒1个单位长度的速度匀速向点D运动，点P，Q同时出发，同时停止。设运动的时间为t（秒），当t=2（秒）时，PQ=2。
（1）求点D的坐标，并直接写出t的取值范围：
（2）连接AQ并延长交x 轴于点E，把AE沿AD翻折交CD延长于点F，连接EF，则△AEF的面积S是否随t的变化而变化？若变化，求出S与t的函数关系式；若不变化，求出S的值；
第15题图
（3）在（2）的条件下，t为何值时，四边形APQF是梯形？

英语部分（满分40分）
一、阅读理解
（1—10每小题2分，11—20题每题1分，共30分）
A
When I was in primary school, sometimes I would meet a girl of the same age as me. Lisa was never active, but she was always very sweet and nice. In the 5th grade she came to my class.
She was absent（缺席） a lot, and one day I had the courage to ask why. She told me she was sick, and she explained she wore a wig（假发） because her medicine made her lose her hair. We left it at that. Anytime Lisa came to class—seldom---I would hang with her on the playground.
I received much ridicule（嘲弄） from my friends for this because they thought I was ignoring(忽视)them for Lisa. My family education taught me to be nice, and I felt Lisa’s needs were much more important than others I knew.
It had been months since Lisa was in our class, and one day our teacher was crying. She explained Lisa died the day before and would no longer be our classmates. She told us Lisa had fought a battle（斗争） with cancer for years.
I was shocked. Lisa never spoke of her illness as if it could kill her. Well, all these years I have kept Lisa in my mind and heart. When I go through the important events in my life, I think of Lisa. I’ve had a strong wish recently to find her parents. I’d like to tell them that though they never met me, their daughter had a sweet effect （影响）on my life. I have no idea what her parents’ first names are. I write to your column（栏目） and hope you can point me in the right direction.
Lisa was such a lovely girl. Maybe her parents would be comforted by the fact that after all these years they are not the only ones who remember her.
（ ）1. The underlined sentence “ We left it at that” probably means____________.
A. we just stopped talking about her illness. B. we discussed the topic and left together.
C. we kept on talking about her illness later D. we went away after talking about her illness.
（ ）2. Why was the writer being laughed at?
A. Because she wore a wig to school. B. Because she always played with Lisa.
C. Because she cried in the classroom. D. Because she lost her friends because of Lisa.
（ ）3. What can we know about the writer from the passage?
A. She had known Lisa since they were born. B. She has been to Lisa’s house.
C. She had a good family education. D. She was the first one to know about Lisa’s death.
（ ）4. What did the writer learn from Lisa?
A. To keep your illness a secret. B. To be nice to everyone everywhere.
C. To put others’ needs above yours.. D. To face challenges in life bravely.
（ ）5. The writer wrote this passage mainly to ______ .
A. remember a true friend B. ask for help to find a friend’s parents
C. show her concern for a friend D. tell her experience of fighting cancer.
B
There are many things we need to know but we do not learn at school. For example, if we want to use our allowance(津贴) wisely, we need to shop carefully. We need to know how to compare the prices of things in different shops. We need to be able to compare the quality of different brands（品牌）. We need to know how to make sensible（明智的） choices when we shop. Knowing how to make such choices is a “life skill”, and we need these skills if we are to lead a useful and happy life.
Some of these choices（决定） are small. For example, will I take an apple for lunch or a pear? Will I take a bus to school today or will I walk? Will I wear the red T-shirt or the blue one to the movies? Other choices are more important. For example, will I eat healthy food for lunch or will I eat junk food because it is tastier? Will I work hard at all my lessons or will I only work hard at the lessons which I enjoy? We make decisions like these every day.
Making wrong choices can result in unhappiness. We have to realize that the choices we make can affect（影响） the rest of our life. Just as importantly, our choices can also affect other people. Next time you decide to waste time in class, play a joke on someone or talk loudly at the movies, consider this: who else does my choice affect?
（ ）6. What helps us use our allowance more wisely?
A. Comparing the prices and the quality. B. Buying things in different shops.
C. Choosing different brands. D. Choosing famous brands.
（ ）7. Why do we need “life skills”?
A. To know how to shop sensibly. B. To lead a useful and happy life.
C. To compare brands and prices. D. To learn things at school.
（ ）8. Which of these choices is the most important?
A. Which fruit to take for lunch. B. How to get to school.
C. Which T-shirt to wear to the movies. D. Which subject to work hard at.
（ ）9. Why is it important to make right choices?
A. Because they can affect the rest of our life. B. Because they can make us waste time.
C. Because they keep us from being happy. D. Because we make choices every day.
（ ）10. Who do our choices may affect?
A. Ourselves and our parents. B. Only ourselves.
C. Ourselves and other people. D. Everybody except us.
C
阅读下面短文，并根据所读内容，在文章后第11--20小题的空格里填入一个最恰当的单词。注意：每空只填1个单词。
The Chinese are very generous when it comes to educating their children. Some parents send their children to the best schools or even foreign countries, for example, England, the US or Australia although it costs much. Many also want their children to take after-school activities. Their children either learn a musical instrument or ballet, or other classes that will give them a head start in life. The Chinese believe that the more expensive an education is , the better it is, so parents often spend a big amount of money on education. Even poor couples(夫妇) buy a computer for their son or daughter.
However, what most parents fail to see is that the best education they can give their children is usually very cheap. Parents should know their children’s various skills. Children will usually be good in some areas while poor in others. What most parents fail to realize is that today’s children lack(缺乏)confidence.
The problem is that parents only care about their children on how to achieve high marks in exams. They are not teaching children the most important skills that can be helpful to their growth. These skills also can build their confidence.
Parents can help achieve this by teaching their children practical skills like cooking, cleaning and other housework.
Teaching a child to cook will improve many of the skills that he will need later in life. Cooking requires patience and time. It is a pleasant but difficult experience. A good cook always tries to improve his cooking, so he will learn to work hard and successfully finish his job step by step. The result, a well-cooked dinner, will give a child a lot of satisfaction and confidence.
An old machine such as a broken radio or TV set that you give your child as a toy may make him curious. If he spends hours looking at it and trying to repair it, your child might become an engineer when he grows up. It’s better to do such activities than teach a child to read a book. These activities can teach them to think, and to use their minds.
Title
How Chinese parents should 11 their children

Common practice
l Being 12 with money when it comes to education.
l Sending them to the best schools at home or even 13 .
l Making children take after-school activities in order to 14 them a head start in life.
l Spending more 15 than they can afford on education.
16 results
l Children are not confident.

Suggested ideas
l Teaching their children practical skills, which are of the greatest importance.
l 17 .
l Cleaning.
l Other housework.
l 18 a broken radio or TV.
Good results
l 19 the children curious and creative.
l Teaching the children to think and use their 20 .
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二、书面表达（10分)
假定你是李明，美国的笔友Lisa想了解中国学生现在的假期生活。请写封回信。要点如下：如今，中学生的假期生活发生了很大变化；学习和休闲仍然重要; 帮忙做家务；参加社会活动，做志愿者工作，帮助他人。
注意：　1.词数80一100;
　　 2.请结合实际增加细节，适当发挥;
　　 3.信的开头和结尾已为你写好，不计入总词数。
Dear Lisa,
I'm glad to have received your letter. Our holiday life has…

Best wishes !
Li Ming

物理部分（满分30分）
第1题图
1、（本题4分）向一个质量可以忽略不计的塑料瓶中装入某液体后密闭，把它分别放在盛有密度为ρ甲、ρ乙两种液体的容器中，所受浮力分别为F甲、F乙，如下图所示，则ρ甲 ρ乙，F甲 F乙（填“>”、“=”或“<”）
2、（本题2分）甲、乙两溢水杯放在实验桌上，分别装满水和酒精，酒精的密度为0.8×103kg/m3。将密度为0.9×103kg/m3的小球M轻轻放入甲溢水杯的水中，小球M静止时从甲溢水杯中溢出9g的水，将小球M轻轻放入乙溢水杯的酒精中，小球M静止时从乙溢水杯中溢出 8
g的酒精。
3、（本题2分）猎豹的心脏每跳动一次输送的血液为△V，其血压的平均值为P，心跳频率为f（即每秒心跳次数），于是他利用上述数据求出了猎豹心脏的平均功率为 。
第5题图
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4、（本题2分）黄石地区今年受到北方沙尘暴天气的影响。沙尘暴可简化为如下情景：快速向上刮起的大风将大量沙尘颗粒扬起后悬浮在空中，这时风对沙尘的作用力与沙尘的重力平衡，其作用力大小可近似表达为，其中沙尘粒近似看成球体，体积V沙=,ρ为空气密度，r为沙尘粒半径，v为风速。如果沙粒密度ρ沙为3×103kg／m3，沙粒半径r为2.5×10－4m，地面空气密度ρ为1.25kg/m3，那么要形成沙尘暴现象，地面的风速至少为 m/s 。
5、（本题2分）右图为蹦极运动的示意图。弹性绳的一端固定在点，另一端和运动员相连。运动员从点自由下落，至点弹性绳自然伸直，经过合力为零的点到达最低点，然后弹起。整个过程中忽略空气阻力。运动员从点到点，速度 （填速度变化情况）。
6、如图所示，正方体合金块A的边长为0.2m，把它挂在以O为支点的轻质杠杆的M点处，在A的下方放置一个同种材料制成的边长为0.1m的立方体B，物体B放置在水平地面上；OM：ON=1：3。一个重为640N的人在杠杆的N点通过定滑轮用力F1使杠杆在水平位置平衡，此时A对B的压强为1.4×104Pa，人对水平地面的压强为1.45×104Pa；若人用力F2=80N仍使杠杆在水平位置平衡，此时物体B对地面的压强为p。已知人单独站在水平地面上，对地面的压强为1.6×104 Pa．（g取10N/kg）（共18分）
第6题图
求：(1)力F1的大小；(2)合金块的密度；(3)压强p的大小。

课改实验班招生考试答案
数学部分答案

一、 填空题
1、（x+2）(x－4) 2、1＜AD＜4 3、9 4、18.
5、等腰三角形或直角三角形 6、 7、且m≠0 8、.
二、解答题
9、 10、
11、 解：在BA的延长线上取一点D，使AD=AC.则△ACP≌△ADP ∴PC=PD. 于是在△BPD中，PD+PB＞BD=AB+AD, ∴PB+PC＞AB+AC
12、解：（1）k=4 （2）作PE⊥PB，只需BE=EA. ∵A、B横坐标为a，∴A（）B（）E（），由BE=EA ∴—3=3—（4a—5）∴（a－2）(4a－3)=0 ∴,
又直线y=4x—5与反比例函数的图像另一点Q（—，—8）也满足条件所以= —，
故a=2或=±
13、简证：延长AM至N，使AM=MN，∴△ABM≌△NCM，∴NC=AB=AF，∠N=∠BAM，
∠CAN=180°—∠N—∠CAM=180°—∠BAC，∠FAH=360°—90°—90°—∠BAC
∴∠CAN＝∠FAH ∴△FAH≌△NCA ∴FH=2AM

14、解：（1）设平均每次下调百分率x，则7000（1— x）2=5670
解得x1=0.1 x2=1.9（舍）故平均每次下调10%
（2）方案①可优惠5670×120（1—0.98）=13608元 。 方案②可优惠120×100=12000元
故方案①更优惠。
15、解：（1）设OC= x ，当t = 2时，OP=4，PC= x—4，CQ=2. 在Rt△PQC中，PQ2=PC2+CQ2,，
即（2）2=（x—4）2+22，解得x1=0（不合题意，舍去），x2=8，∴点D的坐标为（8，4），0＜t＜4；
（2）由翻折可知，点Q和点F关于直线AD的对称，∴QD=DF=4—t ，而AD=8，
∴S△AQF=×8×2（4—t）=32—8t ，设经过A（0，4）、Q（8，t）两点的一次函数解析式为y=kx+b，
故有解得k=∴一次函数的解析式为y=x+4，易知一次函数与x轴的交点的坐标为（，0） ∴EC=— 8 . ∴S△EQF=×2（4 — t）=8t
∴S△AFE=S△AFQ + S△QFE=32－8t + 8t =32 ∴△AEF的面积S不随t的变化而变化，S的值为32；
（3）因AP与QF不平行，要想使四边形APQF是梯形，须有PQ//AF. ∵AF=AQ，∴∠AFQ=∠AQF，
而∠CQE=∠AQF，要想PQ//AF，须有∠AFQ=∠PQC，故只需具备条件∠PQC=∠CQE，又∵QC⊥PE，
∴∠PCQ=∠QEC，QC=QC，∴△CQP≌△CQE，∴PC=CE，即8—2t =—8，
解得t1=6+2（不合题意，舍去），t2=6—2. 故当t =6—2时，四边形APQF是梯形

英语部分答案
1—5 A B C D B 6—10 A B D A C
11. educate 12. generous 13. abroad 14. give 15. money 16. bad 17. cooking 18. repairing 19. Making 20. minds

物理部分答案
1、< = 2、8 3、1∶ 4、△V·P·f 5、先变大后变小
6． (1) ————————————2分
F1=G人—p1S=640N—1.45×104Pa×0.04m2=60N ————————————2分
(2)杠杆在水平位置平衡时，有： OM·FA=ON·F1
FA=3F1=3×60N=180N ————————————2分
×104Pa GA=320N ———————————2分
————————————2分
(3)当F2=80N时，杠杆在水平位置平衡
OM·FA=ON·F2
FA=3F2=3×80N=240N ————————————2分
GA=FA+ NA =240N+ NA =320N NA=80N ————————————2分
A对B的压力 F压=80N
GB=ρgVB=4.0×103×10×(0.1)-3 N =40 N ————————————2分
×104Pa ————————————2分

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