杭州市余杭第二高级中学自选模块试题（理科）
注：请在答题时注明题号，每张答卷上注明班级、姓名、学号。
题号：03 科目：数学
“数学史与不等式选讲”模块 (10分)
（Ⅰ）解关于x的不等式
?2x?3?x?2?6；
222（Ⅱ）已知a,b,c?R，且a?b?c?3.求证：
1111???
1?5ab1?5bc1?5ca2
题号：04 科目：数学
“矩阵与变换和坐标系与参数方程”模块 (10分)
如图，已知直线l垂直于极轴Ox，垂足为Q，OQ?3，在l上取一点A，以OA为边作正三角形OAB（其中O,A,B为逆时针方向）.
（Ⅰ）求三角形OAB重心G的轨迹C的极坐标方程； （Ⅱ）记轨迹C将圆O：??2(???0,2??)分成两部分
B S的面积为S1,S2(S1?S2)，求1的值.
S2
G A O Q x 题号：05 科目：英语
阅读理解（分两节， 共5小题；每小题2分， 共10分）
阅读下面短文，并根据短文后的要求答题。
Teenage years can be confusing for both teenagers and parents. ____①______ They start thinking about how they feel about themselves and figuring out how this matches or mismatches what others think of them. Most teens work through this phase by the age of 16 or 17.
Often teenagers are treated like slightly bigger children, but young adults will never become
independent and responsible if they are not allowed to make some decisions for themselves. The role of a parent must change from that of protector and keeper to that of friend and guide.
Even the most caring parents misunderstand their children sometimes, and some think of teenagers as insecure, stubborn and disrespectful. ____②_____ Teens often complain that their parents repeat the
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same things over and over again. Parents must understand that teens need to be allowed to present their side of any problem and express their point of view.
If parents forbid their child from doing something, chances are that they will do it behind their backs anyway. Teens who deal best with their problems usually have parents who take time to listen and
discuss, parents who respect them and who are respected in return. If parents remain calm, teens will do the same. ____③_____
Praise is a good thing too; teens are not always the best at accepting compliments, but that doesn’t mean they don’t need them. Parents need to make sure that praise is meaningful.
It is especially important that parents watch for signs of depression, such as noticeable changes in grades, eating and sleeping habits. These could be symptoms of stress and even alcohol or drug use. Every parent should try to schedule time to be alone with their child, whether going shopping or to the movies, or taking a walk in the park or a short trip. This time allows parents to talk and listen without interruption from work or other family members. It might also be good to encourage teens to discuss important issues at dinner. Discussion time shows teens that parents are interested in them and their lives.
Finally, parents must accept that teens may not want to talk about everything. Their need for privacy should be respected and they must feel and see that their parents are there for them.
___④___They start to learn to justify and defend them. Handling and improving communication with teenagers is not easy, but success will be rewarding for parents and teens alike. A. A person’s teenage years are a time for them to identify their own values. B. This will encourage more open, level-headed communication. C. As a result, teenagers can distance themselves from their parents.
D. It is high time that parents should spare more time to stay with their kids. E. At about 15, many teens become introspective and moody.
第二节：根据短文所给的信息，用一个完整的句子回答下面的问题， 并将序号及相应答案写在答题纸上。
⑤ What is the main idea of the article?
__________________________________________________________
题号：06 科目：英语
填空（共10小题；每小题1分，共10分）
阅读下面的短文，在标有序号的空白处填入一个适当的词，或填入括号中所给单词的正确形式，并将序号及相应的答案写在答题纸上。
Language follows power. In an increasingly globalized world, some languages become the kings in terms 1.______ trade and communication. They jump geographic boundaries, pushing smaller languages toward extinction.
According to National Geographic magazine, one language dies every 14 days. By the next century nearly half of the roughly 7,000 languages spoken on Earth are 2.______ to disappear as communities abandon native tongues in favor of English, Mandarin or Spanish.
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This is 3._______ Google.org is launching a new undertaking called the Endangered Languages Project. It aims to digitally record the world’s little-known tongues and the heritages to which they are central.
What kind of languages are disappearing? Languages like Arogonese, which can be found in northern Spain, for example. Spoken by 4._______ than 10,000 people, this language appears to 5._______ (disappear) within a few generations. Navajo and Ojibwa, both native to the Americas, are also close to extinction. Koro is the native language of a small population 6.________ in the mountains of northeast India. It’s spoken by about 4,000 people.
The Endangered Languages website will record roughly 3,500 of the world’s little-spoken tongues. “7.______ every language that dies, humanity is in danger of losing an enormous cultural heritage”, writes Loek Essers on the website Computerworld.com.
“As each one vanishes, an understanding of how humans relate to the world around them, as well as scientific, medical, and botanical knowledge, are all lost, as is the expression of a community’s humor, love, and life.”
Users of the website can find 8._______ which can be identified by their location on a map, or reached via a list that has been broken down into four categories: at risk, endangered, severely endangered, or unknown. 9._______ can upload video or audio samples as well as share their knowledge of a language.
“Languages are entities that are alive and in constant flux, and their extinction is not new,” write the site’s creators. “10._______ today we have the tools and technology that could become a game changer.”
题号：13 科目：物理 “物理3—3”模块（10分）
（1）下列说法正确的是（ ）
A．布朗微粒做无规则运动的原因是由于它受到水分子有时吸引、有时排斥的结果 B．一定量0℃的水结成0℃的冰，内能一定减少
C．能量耗散是从能量转化的角度反映出自然界中的宏观过程具有方向性
D．气体能充满任何容器是因为分子间的排斥力大于吸引力
（2）如图所示，有一圆筒形导热气缸，质量为M，缸内横截面积S。气缸内用一质量为m的活塞封闭着一定质量的理想气体，一轻弹簧下端与活塞相连，上端固定，系统悬挂在空中，活塞离气缸底部的距离是h0，气体温度是T0。若逐渐降低气体的温度，当温度降到T0/2时保持温度不变。设大气压强P0，弹簧的劲度系数为k，不计活塞与气缸壁间的摩擦，取g=10m/s2。试求：
Ⅰ、在降温过程中气缸相对地面上升了多少距离？ Ⅱ、若降温过程中气体内能减少量为E0，则气体是吸热还是放热？吸热或放热的数量为多大？
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题号：14 科目：物理 “物理3-5”模块（10分）
（1）爱因斯坦因提出了光量子概念并成功地解释光电效应的规律而获得1921年诺贝尔物理学奖。如图所示在用光电管研究光电效应的实验中，用某种频率的单色光照射光电管阴极K，电流计G的指针不发生偏转，要使G表指针偏转可采取的措施是（ ） A．延长此单色光的照射时间 B．改用强度更大的单色光照射 C．改用频率更大的单色光照射
D．调节滑动变阻器P触点向右移动
235（2）核裂变反应是目前核能利用中常用的反应。以原子核92U为燃料的反应堆中，当俘获一个
慢中子后发生的裂变反应可以有多种方式，其中一种可表示为
235921941 U?0n?13954Xe?38Sr?X0n13923594 已知92U的质量为Mu，10n的质量为Mn，54Xe的质量为Mxe，38Sr的质量为MSr，光在
真空的传播速度为c，则（ ）
A．核反应方程中的X表示为2
B．核反应方程中的X表示为3
来源学科网 C．该核反应过程中放出的核能为（MU—MXe—MSr）c2[:##] D．该核反应过程中放出的核能为（MU—MXe—MSr—2Mn）c2
（3）质量为m的两个氢原子都处于基态，其中A氢原子处于静止状态，B以某一初速度向A运动，发生对心碰撞，碰撞后两氢原子一起运动，其中A氢原子跃迁到高能级，B氢原子还是处于基态。然后A氢原子向低能级跃迁，产生3种光子。已知氢原子能级公式为En?为氢原子基态能量，n=1,2,3……。试求：碰撞前B氢原子速度v0。
E1，其中E1n2题号：15 科目：化学 “物质结构与性质”模块（10分）
请回答下列问题:
(1)下列化合物中熔点最高的是 ① 。 A．NaCl B．KBr C．NaF D．KI
(2)基态铬(Cr)原子的外围电子排布式是 ② ,这样排布使整个体系能量最低,原因是 ③ 。
(3)氨水中存在多种形式的氢键，其中与“氨极易溶于水”这种性质相关的氢键可表示为： ④ 。下列各项中与氢键有关的是 ⑤ 。 a．甘油与水互溶b．在HBr的沸点高于HCl c．邻羟基苯甲醛的熔点低于对羟基苯甲醛d．水分子比硫化氢分子稳定 e．碘在乙醇中的溶解度较大，但不能用乙醇从碘水中萃取碘
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(4)下列物质的晶体中含有阳离子的是 ⑥ ，分子中存在π键的是 ⑦ ,既含极性键又含非极性键的是 ⑧ 。
A．K B．H2O2 C．CH3NH2 D．HCOONa E．F2C=CF2 F．CO2 G．C2HCl2Br (5)下列各项的比较中正确的是 ⑨ 。
A．第一电离能：Mg>Al B．电负性:P>Ge C．稳定性:AsH3>H2S D．金属性:20X<30Y
题号：16 科目：化学
“化学与技术”模块（10分）
下图是两座工厂的主要生产流程以及它们之间的生产关系 湖 水设备A 设备B 设备C 装有粗砂 设备D 装有细砂 溶液B 聚氯化铝 废铝屑 气体A 三种试剂溶液A A 粗食设备G 设备F 盐气体B 水 设备E 用户 滤渣 回答下列问题：
（1）与上图中“设备A”的作用相当的实验装置是 ① 。
a b c d
（2）“溶液B”也可以用下列物质中的什么物质代替？ ② 。
a．KAl(SO4)2·12H2O b.ClO2 c.大量O3 d.K2Cr2O7 e.活性炭
（3）聚氯化铝在生产过程中作 ③ 剂，其作用是 ④ ，可用离
子方程式表示其化学原理如下（用Al3+代表聚氯化铝）： ⑤ 。
（4）上图中下方的工厂主要生产两种气体和一种常见强碱，通常称为 ⑥
工业。
（5）加入“三种试剂”主要是为了除去粗食盐水中的Ca2+、Mg2+、SO42-等杂质，按加入的先后
次序写出化学式 ⑦ 。
（6）制取“溶液B”的方法现在已作了改进，其原理图见右边，用离子方程
式表示该装置中发生的反应： ⑧ 。
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