Introduction of HKCEE Subject Additional Mathematics 附加數學

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1 Introduction of HKCEE Subject Additional Mathematics 附加數學

2 Content 內容 Nearly all topics are brand-new to S3 students. They include: 1. Mathematical Induction (數學歸納法) 2. Binomial Theorem for Positive Integral Indices (二項式定理) 3. Quadratic Equations and Quadratic Functions (二次方程、二次函數) 4. Trigonometry (三角學) 5. Limits and Differentiation (極限、微分法)

3 Content 內容(Cont’d) 6. Integration (積分法) 7. Inequalities (不等式)
8. Coordinate Geometry (解析幾何) 9. Vectors in Two-dimensional Space (向量)

4 Actually, what will you learn
Actually, what will you learn? Let’s have a look of the tip of the iceberg ! Mathematical Induction (數學歸納法) Do you know how to simplify 簡化 If we know that How do you PROVE (證明) that it is true for all positive integers?

5 Binomial Theorem (二項式定理) for Positive Integral Indices
Could you find the term (項) of x65 in the expansion(展開式) of We can find the term without expanding it !

6 Differentiation (微分法)
Do you know how to sketch the graph (圖像)of y=(x-1)2(x+1) without the aid of graphing software(繪圖軟件)?

7 Integration (積分法) Find the area (面積) under a curve. y=sinx

8 Find the volume (體積) of solid of revolution (旋轉體)

9 我是否適合讀附加數?! 讀附加數所需條件及注意事項: 對數學有濃厚的興趣，喜歡邏輯推理、思考 初中數學(中一至三)已達高的水平
勇於接受新事物，因大部份課程內容都從未見過 勇於及樂於挑戰、面對數學難題，有恆心及毅力克服困難，不輕易放棄 不怕面對及運算一大堆複雜的數學符號或表達式 要記許多數學公式，別以為讀附加數不用記公式，但明白公式背後原理之後才記，會較容易記到 須理解長的英文題目 所以，讀附加數更須明白數學概念，做更多練習，以致更熟習及靈活地運用公式

10 選修附加數跟升中六七有關係嗎??? 中四五 選讀附加數 沒有選讀附加數 中六七 選讀純數學 選讀數學與統計
大學內許多有關工程、電腦、理科的學系都要求學生修讀純數學 小半課程跟附加數重疊，而大學內一些工商科、社會科的學系都希望學生修讀數學與統計

11 我應否選修附加數????? 切勿羊群心理，朋友選，自己又選，自己的前途應該掌握在自己手裡的！ 根據以上提供的資料，然後再衡量個人的能力、
興趣、將來前途的取向等，然後再決定 如有疑問，可請教數學科科任老師 切勿羊群心理，朋友選，自己又選，自己的前途應該掌握在自己手裡的！

12 ~THE END~

13 從未見過的課程內容 Integration (積分法) Vectors (向量) M.I. (數學歸納法)
Binomial Theorem (二項式定理) Differentiation (微分法) Vectors (向量)

14 Let S(n) be the statement.
S(1) is true. If S(k) is true, then S(k+1) is true

15 一大堆複雜的數學符號或表達式 e.g. Let the line L1 be y = mx+2 Since A, B are on L1,
Let A, B be (, m  +2), ( ,m+2)

16 要記許多數學公式

17 須理解長的英文題目 (HKCEE 1996) Fig (a) shows a vessel with a capacity of 24 cubic unit. The length of the vessel is l and its vertical cross-section is an equilateral triangle of side x. The vessel is made of thin metal plates and has no lid. Let S be the total area of metal plates used to make the vessel. Show that Find the values of x and l such that the area of metal plates used to make the vessel is minimum. At time t = 0, the vessel described in part (b) is completely filled with water. Suppose the water evaporates at a rate proportional to the area to water surface at that instant such that where V and A are respectively the volume of water and the area of water surface at time t. (i)Let h be the depth of water in the vessel at time t. Show that A = 4h and V=2h2 Hence, or otherwise, find (ii)Find the time required for the water in the vessel to evaporate completely.