高二数学必修五知识点难点

高二数学必修五知识点难点（精选9篇）

高二数学必修五知识点难点篇1

[典例]

1). What were you chatting to him about? 2). I had a long chat with her (about her job).

[重点用法]

chat to/with sb (about sth) = have a chat with sb (about sth) 与某人聊天、闲谈……

2. eastward adv. 向东 adj. 向东的;朝东的

[典例]

1). They were traveling eastward(s) to the city which appeared in their dreams. 他们朝着东边向梦想中的城市进发。

2). The plane flied in an eastward direction. [词语归纳]

eastward(s) adj./adv. 向东的，向东地 westward(s) adj./adv. 向西的，向西地

southward(s) adj./adv. 向南的，向南地

northward(s) adj./adv. 向北的，向北地

southeastward(s) adj./adv. 向东南的，向东南地

northeastward(s) adj./adv. 向东北的，向东北地

southwestward(s) adj./adv. 向西南的，向西南地

northwestward(s) adj./adv. 向东北的，向东北地

3. surround vt.&vi. 包围;围绕 surrounding adj. 周围的 surroundings (常用pl.)环境

[典例]

1). Trees surround the pond.

2). The house was surrounded by high walls.

[重点用法]

surround...with... 用……包围……

be surrounded by/with... 周围都是……

4. measure vi.&vt. 测量;衡量;判定 n.[c,u] 尺寸;量具;计量单位;措施

[典例]

1). Can you measure accurately with this ruler? 用这把尺子能量得准吗?

2). It’ s hard to measure his ability when we haven’ t seen his work. 没有见过他的作品, 很难估计他的能力。

[重点用法]

measure A by B 用B衡量A sth. measures 2 metres by 4 metres 某物长4米宽2米

measure sb. for a suit = make a suit to sb’ s measure 给某人量身做一套衣服

高二数学必修五知识点难点篇2

本节是植物激素调节的重点和难点部分，主要包括生长素的发现过程、植物向光生长的原因、生长素的产生、运输和分布四个方面的内容;其中生长素的发现过程是这节内容的重点和难点。生长素的发现过程中所隐含的科学研究的方法是我们学习的重点问题。主要有四个重要实验，分别是由达尔文、詹森、拜尔和温特完成的。我们需要注意每个重要实验的科学的研究方法和对照思路，达尔文通过实验得出的结论是：单侧光照射使胚芽鞘的尖端产生某种刺激，当这种刺激传递到下部的伸长区时，背光面比向光面生长的快，因而出现向光弯曲;詹森的实验结论是胚芽鞘尖端产生的刺激可以透过琼脂片传递给下部;拜尔的实验结论是：胚芽鞘弯曲生长是因为尖端产生的刺激在其下部分布不均匀造成的;温特的实验结论是：胚芽鞘的尖端确实产生了某种物质，这种物质从尖端运输到下部，并且能够促进胚芽鞘下面某些部分的生长。温特把这种物质命名为生长素，但温特并没有把这种物质提取出来，到1934年科学家才最终确认了这种物质就是吲哚乙酸。

生长素的产生部位：幼嫩的芽、叶和发育中的种子等，均为幼嫩且生长旺盛的部位;根尖和成熟叶片合成生长素极少。在这些部位，通过一系列过程将色氨酸转化成生长素。生长素主要分布在生长旺盛的部位，如胚芽鞘、芽和根尖的分生组织、发育中的种子和果实等处，趋向衰老的组织和器官中含量极少。

生长素的运输也是一个重点和难点问题，在胚芽鞘、芽、幼叶和幼根中，生长素只能从植物的形态学上端向形态学下端运输而不能倒过来运输，即极性运输;在成熟的组织中，生长素可以通过韧皮部进行非极性运输;在芽尖、根尖等不成熟组织的尖端，生长素的运输也会受到外界因素(如地球引力、单侧光、离心力)的作用下发生横向运输，如根的向地性和茎的背地性。

【植物生长素的发现考点分析】

本节是植物激素调节重点考查的部分，在平时测试和高考中都会占有一定的比例。从能力要求上看，往往考查科学的思维方法和科学的实验方法，如生长素的发现过程隐含的科学研究的方法与过程往往搭载实际问题，考查学生解决问题的能力等，选择题和简答题的形式都很常见。

【植物生长素的发现知识点误区】

高二语文必修五知识点梳理精选篇3

首联上句“早岁那知世事艰”是作者现在的概叹。小小年纪，便有满腔的爱国热情。但哪里又会懂得世事的艰辛呢?是啊，正如“少年不知愁滋味”“世事艰”暗指投降派把持朝廷。这是为下文“空自许”作铺垫的。“中原北望气如山”遥望着北方被金人占领的中原地带，心中的愤郁积如山。一个“气”字足以看出诗人的悲愤。小小年纪便有抗金报负，可是朝廷正豺狼当道。看着自己的国土被金兵践踏，老百姓被金兵所害。怎么不会“气如山”呢?可这如山的愤怒又向何处发泄，诗人只能“书愤”。

“楼船夜雪瓜洲渡，铁马秋风大散关”想当年，宋军击退金兵，收复失地的那两次胜仗。诗人仍记忆犹新。诗人用“楼船夜雪”“铁马秋风”形象地概括这气壮山河的两次胜利斗争。可以看出作这是多么地渴望投身到这样的战斗中去。同时也表明宋国人民有力量保卫自己的国土。

前两联作者回忆过去，抒写他的抗金报负。早岁的豪情形成全诗气韵雄厚的基调。

从回忆到现实，回应首句诗意转为悲凉。“塞上长城空自许”“塞上长城”是运用了比喻的手法，即意为守边的战士，能保卫国家安全的人。一个“空”字体现出了诗人对壮志未酬的感慨，南宋有如陆游这种壮志的人甚多，却只能“空自许”可见当时的南宋统治是多么的。这怎能不让诗人“气如山”而“书愤”呢?这里“空自许”与“世事艰”照应正是对投降派的愤怒。“镜中衰鬓已先斑”岁月蹉跎，诗人对镜自照，才发现头发已经发白了。诗人的头发为什么会发白呢?不错，诗人是老了，可更多的是诗人为国担忧啊!南宋有如此要精忠报国的“勇士”却落个壮志未酬，诗人头发怎么不会白呢?

颈联诗人感情沉郁悲凉，但感情基调依然斗志昂扬。

高二数学必修四知识点总结篇4

对于形如cos(α-β)cos(β)-sin(α-β)sin(β)这样的形式，运用逆向思维，化解为：

cos(α-β)cos(β)-sin(α-β)sin(β)=cos[(α-β)+β]=cos(α)

2.正切公式的逆向思维。

比如，由tαn(α+β)=[tαn(α)+tαn(β)] / [1-tαn(α)tαn(β)]

可得：

tαn(α)+tαn(β)=tαn(α+β)[1-tαn(α)tαn(β)]

[1-tαn(α)tαn(β)]=[tαn(α)+tαn(β)]/ tαn(α+β)

tαn(α)tαn(β)tαn(α+β)=tαn(α+β)-tαn(α)-tαn(β)

3.二倍角公式的灵活转化

比如：1+sin2α=sin2(α)+cos2(α)+2sin(α)cos(α)

=[sin(α)+cos(α)]2

cos(2α)=2cos2(α)-1=1-2sin2(α)=cos2(α)-sin2(α)=[cos(α)+sin(α)][cos(α)-sin(α)]

cos2(α)=[1+cos(2α)]/2

sin2(α)=[1-cos(2α)]/2

1+cos(α)=2cos2(α/2)

1-cos(α)=2sin2(α/2)

sin(2α)/2sin(α)=2sin(α)cos(α)/2sin(α)=cos(α)

sin(2α)/2cos(α)=2sin(α)cos(α)/2cos(α)=sin(α)

4.两角和差正弦、余弦公式的相加减、相比。

比如：

sin(α+β)=sin(α)cos(β)+cos(α)sin(β)……1

sin(α-β)=sin(α)cos(β)-cos(α)sin(β)……2

1式+2式，得到

sin(α+β)+sin(α-β)=2sin(α)cos(β)

1式-2式，得到

sin(α+β)-sin(α-β)=2cos(α)sin(β)

1式比2式，得到

sin(α+β)/sin(α-β)=[sin(α)cos(β)+cos(α)sin(β)]/ [sin(α)cos(β)-cos(α)sin(β)]

=[tαn(α)+tαn(β)] / [tαn(α)-tαn(β)]

我们来看两道例题，增加印象。

1.已知cos(α)=1/7,cos(α-β)=13/14,且0<β<α<π/2,求β

本题中，α-β∈(0,π/2)

sin(α)=4√3/7 sin(α-β)=3√3/14

cos(β)=cos[α-(α-β)]=cos(α)cos(α-β)+sin(α)sin(α-β)

=1/2

β=π/3

2.已知3sin2(α)+2sin2(β)=1,3sin(2α)-2sin(2β)=0,且α,β都是锐角。求α+2β

由3sin2(α)+2sin2(β)=1得到：

1-2sin2(β)=cos(2β)=3sin2(α)

由3sin(2α)-2sin(2β)=0得到：

sin(2β)=3sin(2α)/2

cos(α+2β)=cos(α)cos(2β)-sin(α)sin(2β)

=cos(α)3sin2(α)-sin(α)3sin(2α)/2

=3sin2(α)cos(α)-3cos(α)sin2(α)

加之0<α+2β<270o

数学必修五知识点篇5

1.函数的概念：设A、B是非空的数集，如果按照某个确定的对应关系f，使对于集合A中的任意一个数x，在集合B中都有确定的数f(x)和它对应，那么就称f：A→B为从集合A到集合B的一个函数.记作：y=f(x)，x∈A.其中，x叫做自变量，x的取值范围A叫做函数的定义域;与x的值相对应的y值叫做函数值，函数值的集合{f(x)|x∈A}叫做函数的值域.

注意：如果只给出解析式y=f(x)，而没有指明它的定义域，则函数的定义域即是指能使这个式子有意义的实数的集合;函数的定义域、值域要写成集合或区间的形式.

定义域补充

能使函数式有意义的实数x的集合称为函数的定义域，求函数的定义域时列不等式组的主要依据是：

(1)分式的分母不等于零;

(2)偶次方根的被开方数不小于零;

(3)对数式的真数必须大于零;

(4)指数、对数式的底必须大于零且不等于1.

(5)如果函数是由一些基本函数通过四则运算结合而成的.那么，它的定义域是使各部分都有意义的x的值组成的集合.

(6)指数为零底不可以等于零

2.构成函数的三要素：定义域、对应关系和值域

再注意：

(1)构成函数三个要素是定义域、对应关系和值域.由于值域是由定义域和对应关系决定的，所以，如果两个函数的定义域和对应关系完全一致，即称这两个函数相等(或为同一函数)

(2)两个函数相等当且仅当它们的定义域和对应关系完全一致，而与表示自变量和函数值的字母无关。相同函数的判断方法：①表达式相同;②定义域一致(两点必须同时具备)

值域补充

(1)、函数的值域取决于定义域和对应法则，不论采取什么方法求函数的值域都应先考虑其定义域.(2).应熟悉掌握一次函数、二次函数、指数、对数函数及各三角函数的值域，它是求解复杂函数值域的基础.(3).求函数值域的常用方法有：直接法、反函数法、换元法、配方法、均值不等式法、判别式法、单调性法等.

3.函数图象知识归纳

(1)定义：在平面直角坐标系中，以函数y=f(x),(x∈A)中的x为横坐标，函数值y为纵坐标的点P(x，y)的集合C，叫做函数y=f(x),(x∈A)的图象.

C上每一点的坐标(x，y)均满足函数关系y=f(x)，反过来，以满足y=f(x)的每一组有序实数对x、y为坐标的点(x，y)，均在C上.即记为C={P(x,y)|y=f(x),x∈A}

图象C一般的是一条光滑的连续曲线(或直线),也可能是由与任意平行与Y轴的直线最多只有一个交点的若干条曲线或离散点组成.

(2)画法

A、描点法：根据函数解析式和定义域，求出x,y的一些对应值并列表，以(x,y)为坐标在坐标系内描出相应的点P(x,y)，最后用平滑的曲线将这些点连接起来.

B、图象变换法(请参考必修4三角函数)

常用变换方法有三种，即平移变换、伸缩变换和对称变换

(3)作用：

1、直观的看出函数的性质;2、利用数形结合的方法分析解题的思路。提高解题的速度。

发现解题中的错误。

4.快去了解区间的概念

(1)区间的分类：开区间、闭区间、半开半闭区间;(2)无穷区间;(3)区间的数轴表示.

5.什么叫做映射

一般地，设A、B是两个非空的集合，如果按某一个确定的对应法则f，使对于集合A中的任意一个元素x，在集合B中都有确定的元素y与之对应，那么就称对应f：AB为从集合A到集合B的一个映射。记作“f：AB”

给定一个集合A到B的映射，如果a∈A,b∈B.且元素a和元素b对应，那么，我们把元素b叫做元素a的象，元素a叫做元素b的原象

说明：函数是一种特殊的映射，映射是一种特殊的对应，①集合A、B及对应法则f是确定的;②对应法则有“方向性”，即强调从集合A到集合B的对应，它与从B到A的对应关系一般是不同的;③对于映射f：A→B来说，则应满足：(Ⅰ)集合A中的每一个元素，在集合B中都有象，并且象是的;(Ⅱ)集合A中不同的元素，在集合B中对应的象可以是同一个;(Ⅲ)不要求集合B中的每一个元素在集合A中都有原象。

常用的函数表示法及各自的优点：

函数图象既可以是连续的曲线，也可以是直线、折线、离散的点等等，注意判断一个图形是否是函数图象的依据;解析法：必须注明函数的定义域;图象法：描点法作图要注意：确定函数的定义域;化简函数的解析式;观察函数的特征;列表法：选取的自变量要有代表性，应能反映定义域的特征.

注意啊：解析法：便于算出函数值。列表法：便于查出函数值。图象法：便于量出函数值

补充一：分段函数(参见课本P24-25)

在定义域的不同部分上有不同的解析表达式的函数。在不同的范围里求函数值时必须把自变量代入相应的表达式。分段函数的解析式不能写成几个不同的方程，而就写函数值几种不同的表达式并用一个左大括号括起来，并分别注明各部分的自变量的取值情况.(1)分段函数是一个函数，不要把它误认为是几个函数;(2)分段函数的定义域是各段定义域的并集，值域是各段值域的并集.

数学集合间的基本关系知识点

1.“包含”关系—子集

注意：A?B有两种可能(1)A是B的一部分;(2)A与B是同一集合。

反之:集合A不包含于集合B,或集合B不包含集合A,记作A?/B或B?/A

2.“相等”关系：A=B(5≥5，且5≤5，则5=5)

实例：设A={x|x2

-1=0}B={-1,1}“元素相同则两集合相等”即：①任何一个集合是它本身的子集。A?A

②真子集:如果A?B,且A≠B那就说集合A是集合B的真子集，记作AB(或BA)

③如果A?B,B?C,那么A?C

④如果A?B同时B?A那么A=B

3.不含任何元素的集合叫做空集，记为Φ

规定:空集是任何集合的子集，空集是任何非空集合的真子集。

有n个元素的集合，含有2n个子集，2n-1个真子集

二·一般我们把不含任何元素的集合叫做空集。

高中数学快速解题法 7大数学万能解题方法

方法1、在解题的过程中，是一个思维的过程。一些基本的、常见的问题，前人已经总结出了一些基本的解题思路和常用的解题程序，只要顺着这些解题的思路，就可以很容易的找到习题的答案。

方法2、做一道题目时，最重要的就是审题。审题的第一步就是读题。读题时要慢，一边读、一边思考，要特别注意每一句话的内在含义，并从中找出隐含条件。很多人并没有养成这种习惯，结果常常会在做题的时候漏掉一些信息，所以在解题的时候要特别注意审题。

方法3、在做了一定数量的习题后，就会对所涉及到的知识、解题方法有比较清晰的了解。这个时候就需要将这些知识进行归纳总结，以便以后的解题思路更加清晰，达到举一反三的效果，这样做数学题的速度就会大大提升了。

方法4、做题只是学习过程中的一部分，所以不能为了解题而解题。解题时，脑海中的概念越清晰、对公式、定理越熟悉，解题的速度就越快。所以在解题时，应该先回归课本，熟悉基本内容，理解其正确的含义，接着再做后面的练习。

方法5、有些题目，尤其是几何体，一定要学会画图。画图是一个把抽象思维变成形象思维的过程，会大大降低解题的难度。很多题目，只要分析图画出来之后，其中的关系就会变得一目了然。所以学会画图，对于提高解题速度非常重要。

方法6、人对事物的认知总是会有一个从易到难的过程，简单的问题做多了，概念清晰了，对解题的步骤熟悉了，解题时就会形成跳跃思维，解题的速度也会大大的提高。所以在学习时，要根据自己的能力，去解那些看似简单，却比较重要的习题，来不断提高解题速度和解题能力。随着速度和能力的提高，在逐渐的去增加难度，就会事半功倍了。

必修五第一章数学知识点篇6

2.(1)映射是“‘全部射出’加‘一箭一雕’”;映射中第一个集合中的元素必有像，但第二个集合中的元素不一定有原像( 中元素的像有且仅有下一个，但中元素的原像可能没有，也可任意个);函数是“非空数集上的映射”，其中“值域是映射中像集的子集”.

(2)函数图像与轴垂线至多一个公共点，但与轴垂线的公共点可能没有，也可任意个.

(3)函数图像一定是坐标系中的曲线，但坐标系中的曲线不一定能成为函数图像.

3.单调性和奇偶性

(1)奇函数在关于原点对称的区间上若有单调性，则其单调性完全相同.

偶函数在关于原点对称的区间上若有单调性，则其单调性恰恰相反.

(2)复合函数的单调性特点是：“同性得增，增必同性;异性得减，减必异性”.

复合函数的奇偶性特点是：“内偶则偶，内奇同外”.复合函数要考虑定义域的变化。(即复合有意义)

4.对称性与周期性(以下结论要消化吸收，不可强记)

(1)函数与函数的图像关于直线(轴)对称.

推广一：如果函数对于一切，都有成立，那么的图像关于直线 (由“ 和的一半确定”)对称.

推广二：函数，的图像关于直线对称.

(2)函数与函数的图像关于直线(轴)对称.

高一英语必修1知识点难点总结篇7

1、重点单词讲解。

(1)add

① add …to… 把…添加…/把…加起来

② add up to 共计，总共

③ add to 增添

(2)upset

过去式：upset 过去分词：upset 现在分词：upsetting

adj.心烦意乱的，不安的，不适的

be upset about/over 为某事心烦、不安

be upset that 心烦

vt.使不安，使心烦

It upsets sb that 让某人心烦的是

It upsets sb to do sth 做某事使某人不安

(3)concern

vt. 使担心，顾虑，涉及，关系到

n. 担心，关注，利害关系

①as far as sb/sth + be concerned 就某人而言，对于某人来说

as far as I am concerned 就我而言，对于我来说

as far as he is concerned 对他来说

as far as English is concerned 关于英语，对于英语

②be concerned about/for 关心，挂念

have no concerned about/for

③be concerned in/with 涉及到，与…有关

have no concerned in/with

(4)go through

①经历，遭受，忍受 go through one difficulty after another.经历一个又一个困难。

②仔细检查，审查 go through your paper 检查你的试卷。

③浏览，翻阅 go through all the related reference.浏览相关资料。

④通过，穿过=pass through go through a great forest.穿过一片大森林。

⑤完成 go through the task.完成任务。

(5)suffer

①suffer 作“遭受”时，后面直接接pain, loss, injury, harm或 punishment.

②suffer 作“受…苦”时，常常搭配：suffer from

(6)get/be tired of 厌烦…

get/be/feel tired of sb / sth / doing sth 厌烦

be tired from 由于…而疲劳(体力上的疲劳)，侧重原因

be tired out 精疲力竭的

(7)join in 参加，加入

区别join ,join in ,attend 与 take part in：

join：多指加入组织，团体，党派等，有作为其中一员的意思。例：join the army 参军

join in：参加某项游戏，活动，讨论等。常用结构：join sb in

例：Will you join us in a walk?

attend：参加会议，婚礼，葬礼，上课，讲座，听报告等。

例：attend a lecture 参加一个讲座。

take part in：多指参加群众性的活动，运动，战争等。

高二英语必修五教案篇8

1. Target language 目标语言

重点词汇与短语

suggest, persuade, observation, contributions, achieve, devote ... to

2. Ability goals 能力目标

Enable the students to learn the way of persuasive writing and descriptive writing.

3. Learning ability goals 学能目标

Learn how to write a persuasive writing and a descriptive writing.

Teaching important points教学重点

Help the students to learn to write a persuasive writing and a report.

Teaching difficult points教学难点

How to write a report about a scientist and his / her job.

Teaching methods 教学方法

Task-based activities.

Teaching aids 教具准备

A computer and a projector.

Teaching procedures & ways 教学过程与方式

Step Ⅰ Presentation

Task 1: Summarize the way of writing a report.

T: Now class, if we want to write a report about a scientist, what contents should we include?

S1: The life of the scientist, such as his birth and death dates, his family, his education, his personality, his achievements and contributions, his key factors to his success.

T: Yes. You are right. And how do we make an outline about it?

S2: We should put the collected information under three headlines: life, achievements and key to success.

Task 2: Remind the students of the writing techniques and writing features of a report.

Show the following to the students.

Report

Formal language with few adjectives

No speech except quotations

Not emotional

Only one main character

Factual structured according to experimental method

Past tense and passive voice

Task 3: Summarize the way of persuasive writing.

T: You know if we want to persuade sb, we always want to reason with him or her. We must develop our own ideas and provide some evidence to support our ideas so there are always three steps to persuade somebody else to change his or her point of view. Can you point out what the three steps are?

S1: I think the first is to give your opinion and idea.

S2: The second is to give the reasons and evidence to support your idea.

S3: The third is to make a conclusion.

Show the following to the students.

A persuasive writing

Formal or informal, vivid use of language

Speech to show feelings, reactions, etc

Emotional or not emotional to describe feelings and facts

Only two main characters

Factual or imaginative based on fact

Reason and persuade step by step

Present tense

Then ask the students to write a short letter as required in Exercise 3.

A sample version:

Dear Nicolaus Copernicus,

I am a student studying history and I would very much like to read your new theory about the solar system. I hope you will publish it for several reasons. I understand the problems with the present theory. The way the planets move is not what you would expect if the earth was the centre of the universe. It is also odd that the brightness of some stars seems to change. So I agree with you that we need new theory.

I know your observations have been very carefully carried out over many years. Now you must have the courage to publish them. Science can never advance unless people have the courage of their beliefs. I know you worry about what will happen if you publish your new theory. No matter how people oppose it, time will show if your ideas are right or wrong.

So I hope you can publish your new theory.

Step Ⅱ Writing

Ask the students to write a report about a scientist.

Sample versions (见附件3, 4, 5)

Step Ⅲ Homework

Ask the students to do the Project on page 47.

附件

1. How to do a science research

A science project is an investigation using the scientific method to discover the answer to a scientific problem. Before starting your project, you need to un derstand the scientific method. This section uses examples to illustrate and explain the basic steps of the scientific method. The scientific method is the “tool” that scientists use to find the answers to questions. It is the process of thinking through the possible solutions to a problem and testing each possibility to find the best solution. The scientific method involves the following steps: doing research, identifying the problem, stating a hypothesis, con-ducting project experimentation, and reaching a conclusion.

Research

Research is the process of collecting information from your own experiences, knowledgeable sources, and data from exploratory experiments. Your first research is used to select a project topic. This is called topic research. For example, you observe a black growth on bread slices and wonder how it got there. Because of this experience, you decide to learn more about mold growth. Your topic will be about fungal reproduction. (Fungal refers to plant-like organisms called fungi, which cannot make their own food, and reproduction is the making of a new offspring.) CAUTION: If you are allergic to mold, this is not a topic you would investigate. Choose a topic that is safe for you to do.

After you have selected a topic, you begin what is called project research. This research is to help you understand the topic, express a problem, propose a hypothesis, and design one or more project experiments — experiments designed to test the hypothesis. An example of project research would be to place a fresh loaf of white bread in a bread box and observe the bread over a period of time as an exploratory experiment. The result of this experiment and other research give you the needed information for the next step — identifying the problem.

Problem

The problem is the scientific question to be solved. It is best expressed as an “open-ended” question, which is a question that is answered with a statement, not just a yes or a no.

Hypothesis

A hypothesis is an idea about the solution to a problem, based on knowledge and research. While the hypothesis is a single statement, it is the key to a successful project.

All of your project research is done with the goal of expressing a problem, proposing an answer to it (the hypothesis), and designing project experimentation. Then all of your project experimenting will be performed to test the hypothesis.

Do state facts from past experiences or observations on which you base your hypothesis.

Do write down your hypothesis before beginning the project experimentation.

Don’t change your hypothesis even if experimentation does not support it. If time permits, repeat or redesign the experiment to confirm your results.

Project Experimentation

Project experimentation is the process of testing a hypothesis. The things that have an effect on the experiment are called variables. There are three kinds of variables that you need to identify in your experiments: independent, dependent, and controlled variables.

The independent variable is the variable you purposely manipulate (change). The dependent variable is the variable that is being observed, which changes in response to the independent variable. The variables that are not changed are called controlled variables.

Do have only one independent variable during an experiment.

Do repeat the experiment more than once to verify your results.

Do have a control.

Do have more than one control, with each being identical.

Do organize data.

Project Conclusion

The project conclusion is a summary of the results of the project experimentation and a statement of how the results relate to the hypothesis.

If your results do not support your hypothesis:

DON’T change your hypothesis.

DON’T leave out experimental results that do not support your hypothesis.

DO give possible reasons for the difference between your hypothesis and the experimental results.

DO give ways that you can experiment further to find a solution.

If your results support your hypothesis:

You might say, for example, “As stated in my hypothesis, I believe that light is not necessary during the germination of bean seeds. My experimentation supports the idea that bean seeds will germinate without light. After seven days, the seeds tested were seen growing in full light and in no light. It is possible that some light reached the ‘no light’ containers that were placed in a dark closet. If I were to improve on this experiment, I would place the ‘no light’ containers in a light-proof box and / or wrap them in light-proof material, such as aluminum foil.”

2. On women scientists : A speech in the International Women’s Day

Women thou hast encircled the world’s heart with the depth of thy tears as the sea has the earth.

Women in your laughter you have the music of the fountain of life.

The message is clear; it is inspiring and presents a deep philosophy. Women would be the change agent in this fast moving world’s socio-economic scenario.

We have assembled here today to celebrate the International Women’s Day and also the Year of Empowerment of Women.

...

Madam Curie who got the Nobel Prize just after two years of establishment of the Nobel Foundation — first in 1903 in Physics when she shared it and then the second one in 1911 in Chemistry, created a history by winning two Nobel Prizes in a span of 8 years. I am sure, the group here is aware of the difficult conditions and laboratory arrangements under which she worked and yet, she excelled.

Biotechnologists can never forget the work of Dorothy Crowfoot Hodgkin on Crystallography leading to the structure of the important biological crystals. She won the Nobel Prize in Chemistry in 1964. The work of Barbara McClintock, a geneticist won her the Nobel Prize in 1983.

Just as someone said: “Developing countries that have made remarkable social progress, have done so primarily through the empowerment of women, which has had enormous impact in terms of literacy, health and economic well being of families.” What we need to do is to ensure the valuable contribution from 50% of our human resource.

...

It is a matter of great pleasure for all of us to see that the women are not only confined to biology, a subject in which they have been contributing significantly, they are also joining the areas of physical sciences and engineering and performing equally well.

Somehow, in many parts of the world today, science and technology interventions have treated women primarily as recipient of knowledge and have under estimated their importance as generators of innovations and as a dynamic agent of economic and social change. In empowering the women with scientific and technological skills, women scientists and technologists have a major role. Biotechnology and biosciences including medical, agriculture and basic research have opened up new opportunities. The involvement of women scientists and technologists in physical sciences, especially in the National Aeronautics and Space Administration (NASA) dates back to 1903, they worked as explorers, pioneers and innovators. By the end of the 20th century, at least 25% of the astronauts at NASA were women, 16% scientists and engineers.

Of course, it is extremely important that women scientists and technologists are appreciated for their dual role in the society while pursuing scientific research as a career. They should also nurture and cherish their qualities of culture, compassion, courage and creativity. And above all, the cooperative spirit. The five ‘Cs’ are personified in women’s personality.

3. Charles Drawin Origin of Species

The English scientist, Charles Darwin was born on February 12, 1809, the same day that Abraham Lincoln was born. Darwin caused a change in thinking about evolution, whereas Lincoln caused a change in the role of the black slave, allowing the black man to be a free man in American society.

Darwin’s father tried to influence his son to become a worthy student in school. However, Charles did not like to study Latin or Greek, which was required for a classical education. Instead, he made a secret laboratory in his father’s garden where he could experiment in chemistry and physics.

His headmaster had a very low opinion of his scholarly abilities. So his father decided to send him to Edinburgh, Scotland, to medical school. However, Charles couldn’t bear the sight of surgical demonstrations. One time, a child was being operated on without any painkiller or anesthesia. The child began to scream in agony and Charles ran from the room. Those screams haunted his mind for many years.

Since he failed at medical school, his father sent him to study theology at Christ’s Church at Cambridge University. However, in his own words, he said his time was sadly wasted “in playing, drinking, singing, flirting and card playing.” But he found a science professor there who recommended he sail as a naturalist on the ship called hte Beagle. This ship would travel for 5 years exploring South America and the Galapagos Islands off the coast of Ecuador in the Pacific Ocean.

On these islands, he observed the world’s largest turtles, the iguana lizards, and finches, a type of bird. These birds were on different islands and varied from each other, especially in their beaks.

Darwin took many notes on this long adventure. When he returned to England, his body was broken and he was essentially ill for the rest of his life. However, he came to the interesting conclusion that certain finches adapted better to their environment in a process called natural selection. Those species more fitted to their environment would be the ones most likely to breed and succeed in producing the next generation.

In 1859, he wrote On the Origin of Species, which became the most significant book ever written on the theory of evolution. His ideas have had more influence than anyone concerning how living species developed over time.