Mathematics (9820)

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GCE A-Level - Higher 3 (H3) の学習者向けの無料Mathematics (9820)学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。

Mathematical Statements

Definition, Proposition and Theorem
Conditionals
Quantifiers
Logical connectives
Converse
Inverse
Contrapositive
Negation

Mathematical Proofs and Reasoning Principles

Direct proof
Disproof by counterexample
Proof by contradiction
Proof of existence
Proof of uniqueness
Proof by construction
Proof by cases
Proof by mathematical inducti
Pigeonhole principle
Symmetry principle
Combinatorial arguments and proofs

Problem Solving Heuristics

Working backwards
Uncovering pattern and structure
Solving a simpler/similar problem
Considering cases
Restating the problem (e.g., contrapositive)

Assumed Knowledge from H2 Mathematics and Additional Content

Functions and Graphs concepts
Sequences and Series concepts
Summation of series by the method of differences
Complex Numbers concepts
Calculus concepts
Reduction formulae
Improper integrals
Probability (including counting) concepts
Bijection principle (include the case of distributing indistinguishable objects into distinguishable boxes)
Inclusion-Exclusion principle
AM-GM inequality
Cauchy-Schwarz inequality
Triangle inequality
Comparing polynomial, exponential, and logarithmic growth rates
Operations involving limits
Concepts of congruence and modular arithmetic

Mathematical Investigation and Reading Mathematical Texts

Formulating a conjecture
Extension, generalisation, special cases
Complete or critique a solution

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