中五 · 复习
概率分布，复习笔记
概率分布的精要复习笔记，每一项内容标准、考试公式，以及如何复习才能得分。
需要复习什么
本笔记涵盖概率分布，中五SPM高级数学第5章。本章由3项内容标准构成，下表列出每一项要求你掌握的能力。
逐项复习：理解概念、掌握方法、反复练习直到解题成为本能。由于SPM评分是分析式的，清晰有序的步骤能在最终答案出错时仍保住分数，因此把整洁的排版当作复习的一部分。
内容标准
| 代码 | 内容标准 | 你必须掌握的 |
|---|---|---|
| 5.1 | 随机变量 | Describe the meaning of random variable.; Compare and contrast discrete random variable and continuous random variable. Set builder notations for discrete random variable and continuous random variable need to be involved. Example of representation for discrete random variable: X = {x: x = 0, 1, 2, 3} Example of representation for continuous random variable: X = {x: x is the height of pupils in cm, a1 < x < a2 } Tree diagram and probability formula need to be used to introduce the concept of probability distribution for discrete random variable.; Describe the meaning of probability distribution for discrete random variables. Probability Distribution is a table or a graph that displays the possible values of a random variable, along with respective probabilities.; Construct table and draw graph of probability distribution for discrete random variable. |
| 5.2 | 二项分布 | Describe the meaning of binomial distribution.; Determine the probability of an event for binomial distribution. Tree diagram needs to be used to study the values of probability for the binomial distribution. Formula r n r r n q p C r X P need not be derived. n i X P ) ( .; Interpret information, construct table and draw graph of binomial distribution.; Determine and describe the value of mean, variance and standard deviation for a binomial distribution. Mean as an expected average value when an event happens repeatedly needs to be emphasised.; Solve problems involving binomial distributions. Interpretation of solutions needs to be involved. |
| 5.3 | 正态分布 | Describe the meaning of standard normal distribution. The importance of converting normal distribution to standard normal distribution needs to be emphasised. The relation between normal distribution graph and standard normal distribution graph need to be discussed.; Determine and interprete standard score, Z.; Determine the probability of an event for normal distribution. The use of the Standard Normal Distribution Table needs to be emphasised. The use of calculator, mobile application or website can be involved. Skill to determine the standard score, Z when given the probability value needs to be involved.; Solve problems involving normal distributions. PERFORMANCE STANDARDS PERFORMANCE LEVEL DESCRIPTOR 1 Demonstrate the basic knowledge of random variables. 2 Demonstrate the understanding of probability distribution. 3 Apply the understanding of probability distribution to perform simple tasks. Apply appropriate knowledge and skills of probability distribution in the context of simple routine problem- solving. Apply appropriate knowledge and skills of probability distribution in the context of complex routine problem-solving. Apply appropriate knowledge and skills of probability distribution in the context of non-routine problem- solving in a creative manner. LEARNING AREA TRIGONOMETRY TOPIC |
本章公式
以下公式在考试中提供（列于SPM公式表）。你仍需知道何时与如何使用：
如何为分数而复习
本章的位置，以及顺序为何重要
概率分布是中五课程的第5章，而高级数学更青睐按课程顺序复习、而非跳到看起来最难部分的学生。几乎每一章都倚赖中四的代数，移项、处理函数、干净地运算指数与根式，因此若其中任何一项不稳，花一小时把它夯实，会在概率分布以及之后的一切中都得到回报。
复习本章时，随手记下任何你不得不回查的旧技能：这份笔记就是值得修补的基础地图。稳健的复习计划不是一口气冲完全部3项标准，而是短而规律的多次学习：复习一项标准，几天后自测，只有当你能不看笔记复现方法时才继续下一项。
老师如何帮助概率分布
笔记与练习能让学生走很远，但概率分布正是那种"第二双眼睛"能把"大致会"变成"稳定会"的章节。一对一时，老师边做边看你的解题，捕捉出错的确切一步，某处漏了符号、某处忘了条件、公式用对了地方却用错了方法。
这是书本上的标准答案永远做不到的，因为错误发生在动手时，而非阅读时。由于概率分布建立在前面的章节之上，老师还能发现真正的缺口其实不在概率分布，而在它默认掌握的某项中四技能，从而先重建它，让新内容终于扎根。
每一堂课的重点都相同：理解概念、展示方法，并把步骤写得足够清晰，即便某天最终答案出错也能得分。课程为一对一在线、以英文进行，老师会围绕孩子在概率分布上的确切水平来安排每一节，从重建薄弱基础到冲刺A+。
由于老师面对的是一名学生而非三十名，节奏由理解而非教学进度表决定：五分钟就领会的概念不会被拖沓，一时未领会的则会给足所需时间，而不是为了让全班往前赶而被撇下。
这一切都不取代本站的笔记、例题与练习，而是让它们发挥更大的作用。读过概率分布笔记、做过练习的学生，会带着真实的疑问而非一张白纸走进课堂，而针对这些疑问的一小时教学，远胜于用一小时讲解课本已经写明的内容。
这正是我们希望学生把两者结合使用的方式：在这里学习材料，留意它在何处开始讲不通，然后把那一点带给能够彻底弥合缺口的老师。
获取一对一辅导。
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