【DSE M1 M2】考試必温概念中英對照Formula公式表

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M1必温概念 💡

1. Binomial Theorem

注意⚠️

搵第R項 (Rth Term) 係代R-1而唔係代R
搵Constant Term就即係冇x既Term

2. Limit Theorem

注意⚠️

記得溫Limit when n→∞點處理：全式除最大次方既n (多數字面會提示very long time)

3. Calculus Section

注意⚠️

記得要用Chain Rule (可能唔只用一次)
可以用Product Rule去避開用Quotient Rule嘅麻煩 (將次方變負搬上去)
Implicit Differentiation記得要係後面用Chain Rule補番個 dy/dx (Rate of Change題目多數係d?/dt)
記得點Describe Rate of Change of N and dN/dt (2015 & 2016 Last Q)
Integrate x^(-1) 記得要加Absolute Value (除非題目講到明x>0)
Indefinite Integral 記得要加C
Integration by Substitution之前有機會要用Partial Fraction (2014 Q4b)
要記得Area Bounded by Curve嘅Assumption: Area is assumed to be positive if the curve is above x-axis, f(x)>0.
Area Bounded by Curve唔一定係得一個Sector of Area！有可能要拆開個definite Integral
Trapezoidal Rule要同Second Derivative一齊溫，要搵Error或者Absolute Difference嘅話建議加個Absolute Sign

4. Probability/ Statistic Section

記熟 P(A∪B) = P(A) + P(B) – P(A⋂B)
諗唔到就畫個Venn Diagram睇
Mutually Exclusive Condition: P(A⋂B) = 0
Independent Condition: P(A⋂B) = P(A)P(B)，唔等於就係Dependent
問Bayes Theorem最好畫個Tree Diagram
記熟四個Common Distribution
Binomial常見題型：第N個Event A係會喺第M次嘅Event B (2013 Q13(b), 2014 Q13(cii), 2015 Q10(b),…, 2019 Q10(bii))
Normal Distribution個圖由中間開始，記得適當加減0.5
要小心睇計緊Population定Sample，Variance條式係唔同
要識得喺表度睇Confidence Interval嘅Z，因為唔一定出90%、95%、99%

回到目錄

M1公式表 📖

1. Binomial Expansion 二項展式

2. Exponential Function 指數函數

3. Logarithmic Function 對數函數

4. Compound Interest 複利

A = Pert

5. Exponential Growth 指數增長

P = P0ekt

6. Exponential Decay 指數衰變

Q = Q0e − λt

7. Logarithmic Transformation 對數轉換

y = kxn → logy = nlogx + logk
y = kax → logy = logax + logk

8. Limits 極限

8. Differentiation 微分

9. Indefinite Integration 不定積分

10. Definite Integration 定積分

11. Probability 概率

12. Random Variable 隨機變數

回到目錄

M2必温概念 💡

1. Binomial Theorem

注意⚠️

搵第R項 (Rth Term) 係代R-1而唔係代R
搵Constant Term就即係冇x既Term

2. Mathematical Induction (M.I.)

注意⚠️要背熟：

Define statement p(n)
Check n=1 case
Assume n=k is true
Check n=k+1 case
Conclusion by M.I.

3. Limit Section

注意⚠️

limit when n->∞點處理：全式除最大次方既n (多數字面會提示very long time)
點搵Horizontal and Vertical Asymptotes
溫Oblique Asymptotes

4. Calculus Section (Differentiation)

注意⚠️

要明白First Principle既Concept，唔好淨係背式！
記得要用Chain Rule (有時可能唔只要用一次)
可以用product rule去避開用Quotient Rule嘅麻煩 (將次方變負搬上去)
Implicit Differentiation記得要係後面用Chain Rule補番個dy/dx (Rate of change題目多數係d?/dt)
Describe rate of change of N and dN/dt
Relative同Absolute maximum/minimum嘅分別
f’(x) = 0唔一定等於有Maximum/Minimum Point (可以係Inflection Point)
Curve Sketching

5. Calculus Section (Integration)

注意⚠️

Integrate x^(-1)記得要加Absolute Value (除非題目講到明x>0)
Indefinite Integral記得要加C
Integration by Substitution之前有機會要用Partial Fraction
Area Bounded by Curve Assumption: Area is assumed to be positive if the curve is above x-axis, f(x)>0.
Area Bounded by Curve唔一定得一個Sector of Area有可能要拆開個Definite Integral
Trigo Substitution：小心邊個數要開方/二次，可能要Complete Square先再代U
By Part代數既先後次序 (e^x, sinx/cosx, x^n…)
Recursive By part
Reduction Formula
Disk Method

6. Matrices ＋System of Equations

注意⚠️