STPM数学教学 [第2页加入paper 2计算机使用法，更新至regression

peaceboy

其实已经发过了，从新开帖纯粹为了方便整理
http://www.khanacademy.org/#

点击你要的题目进入 (right click , open in new tab/window)
===============================================

Paper 1

Chapter 1 : Number and set

1.1 Absolute value :
concept
how to solve more than or less than question

1.2 Logarithms
concept
law of logarithm 1
law of logarithm 2

1.3 Complex number

introduction to i[imaginary number]
complex number 1
complex number 2
Rationalize a Denominator

xxxxx Argand diagram

1.4 Sets

xxxxx


===============================================


Chapter 2 Polynomials

long division

polynomials divison

completing the square
discrimination of quadratic equation, b^2 -4ac

quadratic inequalities-basic

xxx (cubic inequalities)

partial fraction 1
partial fraction 2
partial fraction 3

===============================================



Chapter 3 Sequence and Series


intro to sum , AP Formula GP formula prove
intro to sum , AP Formula GP formula prove 2


binomial Expansion- (ax+b)^n
binomial Expansion- (ax+b)^n 2
binomial Expansion- (ax+b)^n 3 (u can ignore this)
  if n is not a positive integer , got other way....

================================================
Chapter 4 Matrix

introduction

multiplication matrix 1
multiplication matrix 2

inverse matrix 1
inverse matrix 2
inverse matrix 3 Gauss-Jordan elimination  not in our syllabus

Use Matrices to solve equations

===============================================

Chapter 5 Coordinate Geometry

distance formula  
Midpoint Formula
xxxxx--ratio formula

Intro to Circles
Intro to Ellipses
foci of ellipses
Intro to Hyperbolas  

asymptote

Hyperbolas 2
Hyperbolas 3
foci of hyperbolas



identifying conic (draw the graph from the formula)
identifying conic 2
identifying conic 3

parametric equation 1
parametric equation 2
parametric equation 3
parametric equation 4


Parabola Focus and Directrix 1
Parabola Focus and Directrix 2
===============================================

Chapter 6 Function

introduction
function 2
function 3
function 4

domain of function

inverse function
inverse function example
inverse funtion example 2
inverse function example 3

--limit--
intro
limit 2
limit 3
limit 4

Squeeze Theorem

===============================================

Chapter 7 Differentiation

understanding
1st principle
basic
basic
chain rule--important knowledge
example of chain rule
Even more examples using the chain rule.
product rule-basic
quotient rule ,differentiation of e^x, ln x, sin x, cos x, and tan x
more example

Implicit Differentiation 1
Implicit Differentiation 2

newton raphson method

Maxima Minima Slope
Inflection Points and Concavity Intuition
asymptote

Introduction to rate-of-change
Rates-of-change (part 2)


===================================================

Chapter 8 Integration

intro
example
formula   formula rewrite  : integrate ([f(x)]^n)f'(x) = {[f(x)]^(n+1)}/(n+1) + c

integration by substitution
intro of integration by part
example of integration by part
Another example using integration by parts.

Why Definite Integrals = Area Under Curve 1
Why Definite Integrals = Area Under Curve 2
Why Definite Integrals = Area Under Curve 3

Trigonometry substitution integration 1 not in our syllabus
Trigonometry substitution integration 2 not in our syllabus
Trigonometry substitution integration 3 not in our syllabus


Use of definite integrals to find the area under a curve 1
Use of definite integrals to find the area under a curve 2

Volume 1
Volume 2
Volume 3
Volume 4

Volume 5 not in our syllabus
Volume 6 not in our syllabus
Volume 7 not in our syllabus
Volume 8 not in our syllabus

peaceboy

PAPER 2 MATH S

Linear Programming

xxx

Network Planning

xxx

Data Description

Average or Central Tendency: Arithmetic Mean, Median, and Mode not included group data
Range, Variance and Standard Deviation as Measures of Dispersion not included group data
Stem and Leaf Plots
Bloxspot   not included outliner ..

Probability
permutations
Combination


Probability intro
Probability 2
Probability 3
Probability 4
Probability 5
Probability 6 -- conditional probability
Probability 7-- conditional probability
Probability 8-- conditional probability

Probability Using Combination
Probability and combination2
Conditional Probability and Combinations Much more harder than what STPM got , i think ...

Probability Distributions
Introduction to Random Variables
Probability Density Functions math T

Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Z-score

Expected Value: E(X) including prove
Expected Value of Binomial Distribution including prove
Poisson Process 1 math T
Poisson Process 2  math T


Sampling and Estimation
The Average
Sample vs. Population Mean
Population Variance
Sample Variance * note that unbiased estimation is used to find variance of population from a sample variance difference formula is used to find variance of sample from population variance , refer Standard Error of the Mean down here
Alternate Variance Formulas
Standard Deviation

Law of large number concept thing
Central limit theorem concept thing

Sampling distribution of sample mean concept thing
Sampling distribution of sample mean 2 concept thing
Standard Error of the Mean concept thing

Correlation and Regression
xxx

Time Series and Index Number
xxx

peaceboy

PAPER　２　MATH T

Differential Equations  credit to Allmaths
Introduction to differential equations
Separable Differential Equations
Separable differential equations 2
First order homegenous equations
First order homogenous equations 2


Trigonometry
xxx

Deductive Geometry
xxx

Vectors credit to Allmaths

Position Vector Valued Functions
Derivative of a position vector valued function
Unit Vectors
Matrix Vector Products
Proving Vector Dot Product Properties
Matrices to solve a vector combination problem
Unit Vector Notation
Unit Vector Notation (part 2)


Data Description

Average or Central Tendency: Arithmetic Mean, Median, and Mode not included group data
Range, Variance and Standard Deviation as Measures of Dispersion not included group data
Stem and Leaf Plots
Bloxspot   not included outliner ..


Probability
permutations
Combination


Probability intro
Probability 2
Probability 3
Probability 4
Probability 5
Probability 6 -- conditional probability
Probability 7-- conditional probability
Probability 8-- conditional probability

Probability Using Combination
Probability and combination2
Conditional Probability and Combinations Much more harder than what STPM got , i think ...

Probability Distributions
Introduction to Random Variables

Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Z-score

Expected Value: E(X) including prove
Expected Value of Binomial Distribution including prove
Poisson Process 1
Poisson Process 2


Continuous Probability Distributions
Probability Density Functions

===================================================================

Allmaths

其实已经发过了，从新开帖纯粹为了方便整理


Chapter 6 Function

introduction
function 2
function 3
function 4

domain of function

inverse function
inverse function example
inverse funtion example 2
inverse function example 3

--limit--
intro
limit 2
limit 3
limit 4

Squeeze Theorem
peaceboy 发表于 12-10-2010 11:40 PM

    squeeze theorem 都跑出来了。。。

Jacss

哈哈..连squeeze theorem都学了.. 厉害.

Lov瑜瑜4ever

不错哦。。。
这样就很方便找了。。。
哈哈。。。
多谢。。。

peaceboy

我就来分享下计算机的功能，让那些自修的学下
Calculator： Casio 570MS
[ ]<<<每一个这个代表一个按键
[X] <<<按[ALPHA] [ ) ]

Polynomial
exp ques p(x)=6x^5+3x+9
find P(2)
Using Calculator
先输入equation,
[6] [X] [^] [5] [+] [3] [X] [+] [9]
然后按[CALC]
荧幕出现 X?
按[2]
按[=]
就有答案了
很常用的一个技巧

同一个equation, p(x)=6x^5+3x+9
find zero of p(x)
一样先输入 [6] [X] [^] [5] [+] [3] [X] [+] [9]
然后按[shift] [CALC]
出现 X?
再按多一次 [shift] [CALC]
出现 X=-1
就是其中一个答案（这个方法这能找到一个答案 ）

Solving equation with power x^2 and x^3
先按[mode] 3次
看到 EQN MAT VCT
按 [1]
出现Unknowns ?
按去右边 [->]
出现degree (power的意思)
然后下列我分成两种状况
1）问题是2x^2 + 4x - 3 = 0
注意最高的power是2 ， 所以按[2]
根据ax^2 + bx + c ,我们知道
a=2 , b=4 ,c=-3
所以出现a=? , 输入 [2] [=]
出现b= ? ,  输入 [4] [=]
出现c= ? , 输入 [-] [3] [=]
就有答案了
2）问题是3x^3+x+3 =0
最高的power是3 ， 所以按[3]
根据ax^3 + bx^2 + cx + d ,我们知道
a=3 , b=0 ,c=1, d= 3
所以出现a=? , 输入 [3] [=]
出现b= ? ,  输入 [0] [=]
出现c= ? , 输入[1] [=]
出现d= ? , 输入[3] [=]
就有答案了

Solving simultaneous equation
同样按[mode] 3次
出现EQN MAT VCT
按[1]
出现Unknowns , 2就代表有两个unkown(或者说是两个equation) ,3就是三个
假设问题是
x+2y=3
4x+5y=6
两个unknow,选2
就代表着a1x +b1y =c1
和a2x+b2y =c2
a1=1 , b1=2 , c1=3
a2=4 , b2=5 , c2=6
所以就输入 [1] [=] [2] [=] [3] [=] [4] [=] [5] [=] [6] [=]
就有答案了

同样的如果问题是
x+2y+3z=10
2x+5y+6z=22
x+8y+9z = 28
就在输入[mode]过后
出现unknowns的时候选3
一样输入
a1=1 , b1=2 , c1=3 ,d1=10
a2=2 , b2=5 , c2=6 , d2=22
a3=1 , b3=8 , c3=9 , d3=28
（我当作你已经懂怎么按了）
就会出现答案了

如果要回到一般模式请按[mode] [1]
要回到最原始模式请按 [shift] [mode] [3] [=]

special case :
我们知道在solve quadratic equation的时候，b^2-4ac<0的时候，会有imaginary number
那么计算机(casio 570)怎么没有出现呢？
其实是有的
假设问题是x^2+x+1 =0
你用计算机按[mode] [mode] [mode] [->] [2]
输入[1][=][1][=][1][=]
出现答案
你发现荧幕右上角有一个 R<=>i 的字眼，那就是告诉你有imaginary number
假设答案是a+bi
你现在看到的就是a的数字
你按 [shift][=]
出现的就是 b的数字

当我们要输入的equation有modulas 还是imaginary number的时候怎么办么？
这时候请换去complex mode， 按[mode] [2]
然后你输入 [(] [2] [+] [3] [shift] [ENG] [)] [x^3] [=]
你会惊奇的发现竟然有答案~
一样要看img num请按[shift] [=]

modulas也一样，要换去complex mode
假设问题是 f(x) = l3x^2 - 6xl - l 2x-7 l
我们要知道f(2)是多少
那么要怎么输入 l  l <<<这个东西呢？
首先请按[shift] [)]
出现了Abs (absolute value的意思)
在按 [(] [3] [ALPHA] [(-)] [^] [2] [-] [6] [ALPHA] [(-)] [)] [-] [shift] [)] [(] [2] [ALPHA] [(-)] [-] [7] [)]
出现了 Abs(3A^2-6A)- Abs (2A-7)
按[CALC] [2]
就有答案了
注意在complex mode 是不能用 X做unknown的，所以我们用A做unknown

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eassaic

kut lat de ginna~ xD

kelfaru

小弟要MATHS S的~

eassaic

小弟要MATHS S的~
kelfaru 发表于 13-10-2010 07:02 PM

    这个就是Math S的~

kelfaru

ALLMATHS要FMT的~

Log

..
不错。。

ELFofWAR

...
楼主得空么
顺边整理化学的

peaceboy

回复 13# ELFofWAR


    很抱歉我是商科的，没读过化学

kelfaru

我也来整理一下~
2010 STPM TRIAL

Kelantan和Kedah
-http://papercollection.batukawa.info/

Selangor,Perak,Pahang,Johor,Ngri Sembilan
-http://cid-8104a436014490a6.office.live.com/browse.aspx/.Documents?sa=721889743

STPM pass year 2002-2009
http://www.scribd.com/doc/37361027/STPM-Past-Year-Question

Exercises by chapter
http://www.scribd.com/doc/35279357/STPM-Maths-Until-2009-New-Edition

College Level Exercise
http://www.scribd.com/doc/23414166/math-model-qs-by-NRB

Allmaths

我也来整理一下~
College Level Exercise
http://www.scribd.com/doc/23414166/math-model-qs-by-NRB
kelfaru 发表于 15-10-2010 10:16 PM

你所提供的college exercises 也有FMT的。。。

kelfaru

你所提供的college exercises 也有FMT的。。。
Allmaths 发表于 15-10-2010 11:38 PM

多数是FMT~

Allmaths

多数是FMT~
kelfaru 发表于 15-10-2010 11:46 PM

谁要做？

xiang911

谁要做？
Allmaths 发表于 16-10-2010 12:03 AM

    你咯

Allmaths

你咯
xiang911 发表于 16-10-2010 11:46 AM

   我不会做的说...