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Appendix 1: Proofs in Mathematics

CBSE · Class 12 · Mathematics

Quick revision notes for Appendix 1: Proofs in Mathematics — CBSE Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

76 questions48 flashcards5 concepts

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Key Topics to Revise

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1. Meaning of Proof and Main Types

  • A proof is a chain of deductive arguments each with its own premises and conclusions.
  • Every statement in a proof must be justified by a definition, an axiom, or a previously established proposition.
  • There are two overarching ways of proving a proposition: directly and indirectly.
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2. Direct Proof Methods

  • Straightforward approach means moving directly from the given statement to the required conclusion.
  • Mathematical induction is a direct proof method used for statements involving natural numbers.
  • Proof by cases is used when the hypothesis can be split into a few separate cases.
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3. Indirect Proof Methods

  • Proof by contradiction starts by assuming the statement is false and reaching a contradiction.
  • Proof by contrapositive proves the equivalent statement ~q ⇒ ~p instead of p ⇒ q.
  • Proof by counter example disproves a general statement by giving one example that fails.
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4. Important Worked Examples to Revise

  • Example 1 uses factorisation to show x^2 - 5x + 6 = 0 implies x = 3 or x = 2.
  • Example 2 shows that f(x) = 2x + 5 is one-one by direct proof.
  • Example 3 uses mathematical induction to prove the formula for powers of the matrix A.

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Full Notes

Key Concepts

A proof is a sequenceA direct proof starts from whatThis is a direct chainIf a statement is trueA statement is split into

Frequently Asked Questions

What are the important topics in Appendix 1: Proofs in Mathematics for CBSE Class 12 Mathematics?
Appendix 1: Proofs in Mathematics covers several key topics that are frequently asked in CBSE Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Appendix 1: Proofs in Mathematics — CBSE Class 12 Mathematics?
Understand the core concepts first, then work through the 76 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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