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Mathematics (9820)

5个单元

Mathematical Statements

Definition, Proposition and Theorem

Logical connectives

Mathematical Proofs and Reasoning Principles

Disproof by counterexample

Proof by contradiction

Proof of existence

Proof of uniqueness

Proof by construction

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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