Introduction of HKCEE Subject Additional Mathematics 附加數學

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)

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)

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?

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 !

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)?

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

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

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

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

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！

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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)

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

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)

要記許多數學公式

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.