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Concept Maps

Real Numbers — Concept Maps

Gujarat Board · Class 10 · Mathematics

3 concept maps of Real Numbers for Gujarat Board Class 10 Mathematics, each also written out as a text outline.

45 questions24 flashcards7 formulas & key relations5 concepts

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A nested Venn diagram illustrating the relationships between natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R) as subsets of each other.
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3 Concept Maps

Real Numbers – Chapter Overview Mind Map

Real Numbers – Chapter Overview Mind Map

The map in words

  • root((Real Numbers
  • Class 10))
    • Fundamental Theorem
      • Every Composite
        • Product of Primes
        • Unique Factorisation
      • Factor Tree Method
        • Divide by Primes
        • Ascending Order
      • Applications
        • Find HCF
        • Find LCM
        • Digit Problems
    • HCF and LCM
      • HCF
        • Lowest Power
        • Common Factors
        • Largest Divisor
      • LCM
        • Highest Power
        • All Factors
        • Smallest Multiple
      • Key Formula
        • HCF x LCM = a x b
        • Only for Two Numbers
    • Irrational Numbers
      • Definition
        • Cannot write as p over q
        • q not equal to 0
      • Examples
        • Root 2
        • Root 3
        • Root 5
        • Pi
      • Proof Method
        • Proof by Contradiction
        • Assume Rational
        • Reach Contradiction
      • Key Theorem
        • If p divides a squared
        • Then p divides a
    • Proof Technique
      • Assume Opposite
      • Logical Deduction
      • Find Contradiction
      • Conclude Original

Flowchart showing how the Fundamental Theorem of Arithmetic guarantees unique prime factorization

Flowchart showing how the Fundamental Theorem of Arithmetic guarantees unique prime factorization

The map in words

  • Composite Number
    • Factorize into Prime Factors
      • Product of Prime Powers
        • Try another factorization?
          • Different order: Same prime factors Same powers
            • Factorization is UNIQUE
          • Different primes: Impossible by FTA

Step-by-step flowchart for finding prime factorization of any composite number

Step-by-step flowchart for finding prime factorization of any composite number

The map in words

  • Start with Composite Number N
    • Divide by smallest prime p that divides N
      • Get quotient Q
        • Is Q prime?
          • Yes: Write all prime factors and powers
            • Arrange in ascending order
              • Prime Factorization Complete

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Frequently Asked Questions

What are the important topics in Real Numbers for Gujarat Board Class 10 Mathematics?
Key topics in Real Numbers include The Fundamental Theorem of Arithmetic, Revisiting Irrational Numbers and Proofs, Step-by-Step: Proof that √2 is Irrational. Study these first, then practise questions on each for the Gujarat Board Class 10 board exam.
What do the concept maps for Real Numbers show?
The 3 maps show how the ideas in Real Numbers connect: Real Numbers – Chapter Overview Mind Map; Flowchart showing how the Fundamental Theorem of Arithmetic guarantees unique prime factorization. Each map is also written out as an outline on this page.
How should I revise Real Numbers for the Gujarat Board Class 10 board exam?
Learn the core ideas first, then work through the 45 practice questions on Real Numbers. Revise 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.

More resources for Real Numbers

All Gujarat Board Class 10 Mathematics Concept Maps

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