DSE Further Mathematics Curriculum Proposal Part 3

Foundation Area 第三個 Topic 就係 The bionmial theorem。

Learning Unit 3 – The binomial theorem

Teaching time: 6 hours

Learning objective	Remarks
3.1  Expand binomials and trinomials with positive integral indices using the Binomial Theorem	Proving the Binomial Theorem is required. The use of the summation notation should be introduced. The expansion of trinomials and the properties of binomial coefficients are required are required. Applications to numerical approximation, the greatest coefficient and the greatest term are not required.

呢個 Topic 既要求同舊制 Additional Mathematics 類似，但加入左 Deduction of properties of binomial coefficients，令學生可以更熟習 Summation、Differentiation 及 Integration 既用法，當然，涉及 Calculus 既部分會係之後教到既時候先會 subsume 入去相應既 topics 去教。

另外，加入 trinomial expansion 係因為想令學生唔會見到 (a + b + c)^n 就停左係道唔識 expand，而係可以用番學左既 binomial theorem 去解決，所以，引入呢一個部分係無可厚非既。


至於下一個 Topic 就係 More about rational functions。

Learning Unit 4 – More about rational functions

Teaching time: 4 hours

Learning objective	Remarks
4.1  Decompose rational functions into partial fractions	The maximum degree of the denominator is 4. Application to infinite summation of rational functions is not required. This learning unit can be taught in Learning Unit 11 – Indefinite integrals.

呢個 Topic 就係以前會考都冇既 Topic 黎，而因應 Integration 既要求，為使整個課程完整（只教不需經過 partial fractions 既 integration by substitution 同埋 integration by parts 既題目實在令本身 M2 既課程十分割裂！），以及增加學生在 Mathematics Compulsory Part 對 Rational functions 既認識（只需要認識 operations），此課程特意增加了此課題，以銜接 Mathematics Compulsory Part 與 Further Mathematics。

另外，由於為免冗長計算，此部分的分母的 degree 不會超過 4，而 factors 既種類只會係 linear factors 以及 quadratic factors，另亦可以有 repeating factors。


下次講 proposal 既時候就到 Trigonometry 喇！大家記住要密切留意啊！