Mathematics (9820)

6 个单元 · 44 个章节

免费 Mathematics (9820) 学习笔记，适合 GCE A-Level - Higher 3 (H3) 学生。每个章节都覆盖一个重点主题，并附例题与可延伸到 thinka app 的练习提示。

Mathematical Statements

Mathematical Proofs and Reasoning Principles

Assumed Knowledge from H2 Mathematics and Additional Content

Problem Solving Heuristics

  • Working backwards

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  • Uncovering pattern and structure

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  • Solving a simpler or similar problem

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  • Considering cases

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  • Restating the problem (e.g. contrapositive)

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Assumed Knowledge from H2 Mathematics — Additional Content

  • Summation of series by the method of differences

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  • Reduction formulae and improper integrals

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  • Bijection and inclusion-exclusion principles

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  • Classical inequalities: AM-GM, Cauchy-Schwarz, triangle

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  • Limits and growth-rate comparisons

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  • Congruence and modular arithmetic

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Mathematical Investigation and Reading Mathematical Texts

  • Formulating a conjecture

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  • Extension, generalisation and special cases

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  • Complete or critique a solution

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  • Applying results and definitions beyond the defined content areas

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